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https://www.global-sci.org/intro/article_detail/getBib?article_id=9226 | [
"@Article{JCM-14-143, author = {}, title = {A Class of Factorized Quasi-Newton Methods for Nonlinear Least Squares Problems}, journal = {Journal of Computational Mathematics}, year = {1996}, volume = {14}, number = {2}, pages = {143--158}, abstract = {\n\nThis paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like updating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.\n\n}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9226.html} }"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8634689,"math_prob":0.93672776,"size":1052,"snap":"2022-05-2022-21","text_gpt3_token_len":235,"char_repetition_ratio":0.116412215,"word_repetition_ratio":0.0,"special_character_ratio":0.24524716,"punctuation_ratio":0.123595506,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98643667,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-22T17:46:22Z\",\"WARC-Record-ID\":\"<urn:uuid:3b301575-3da1-4c4f-a4e7-16a3d8b60cfc>\",\"Content-Length\":\"1390\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d9cccfa3-e7ca-4272-987a-68c3da802312>\",\"WARC-Concurrent-To\":\"<urn:uuid:16ec8f87-ac83-4021-9f95-f95d88138021>\",\"WARC-IP-Address\":\"8.218.69.127\",\"WARC-Target-URI\":\"https://www.global-sci.org/intro/article_detail/getBib?article_id=9226\",\"WARC-Payload-Digest\":\"sha1:XLGRSJXNCA2X4JATIIN5GCV25OJD3OEZ\",\"WARC-Block-Digest\":\"sha1:5SMHM77G6G6YXLFXYXTXKQHK4P7DDVCX\",\"WARC-Identified-Payload-Type\":\"application/x-bibtex-text-file\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662545875.39_warc_CC-MAIN-20220522160113-20220522190113-00523.warc.gz\"}"} |
https://codereview.stackexchange.com/questions/225485/ruby-implementation-for-hacker-rank-connected-cells-in-a-grid/226042 | [
"# Ruby implementation for Hacker Rank connected cells in a grid\n\nhttps://www.hackerrank.com/challenges/connected-cell-in-a-grid/problem\n\nproblem statement:\n\nConsider a matrix where each cell contains either a 1 or a 0. Any cell containing a 1 is called a filled cell. Two cells are said to be connected if they are adjacent to each other horizontally, vertically, or diagonally. In the following grid, all cells marked X are connected to the cell marked Y.\n\nXXX\nXYX\nXXX\nIf one or more filled cells are also connected, they form a region. Note that each cell in a region is connected to zero or more cells in the region but is not necessarily directly connected to all the other cells in the region.\n\nGiven an matrix, find and print the number of cells in the largest region in the matrix. Note that there may be more than one region in the matrix.\n\nFor example, there are two regions in the following matrix. The larger region at the top left contains cells. The smaller one at the bottom right contains .\n\n110\n100\n001\n\nmy solution:\n\n# Complete the connectedCell function below.\ndef connectedCell(matrix)\nhighest_count = 0\nvisited = {}\n\n(0...matrix.length).each do |i|\n(0...matrix.length).each do |j|\nnext if visited[[i,j]]\nif matrix[i][j] == 1\nres = get_area_count([i,j], matrix)\nif res > highest_count\nhighest_count = res\nend\n\nvisited = visited.merge(res)\nend\nend\nend\n\nhighest_count\nend\n\ndef get_area_count(pos, matrix)\nq = [pos]\nvisited = {}\ncount = 0\nwhile q.length > 0\ntile_pos = q.shift\nif !visited[tile_pos]\ncount += 1\nvisited[tile_pos] = true\nq += nbrs(tile_pos, matrix)\nend\nend\n\nreturn [count, visited]\nend\n\ndef nbrs(pos, matrix)\nright = [pos, pos + 1]\nleft = [pos, pos - 1]\ntop = [pos + 1, pos]\nbottom = [pos - 1, pos]\ntop_right = [top, right]\nbottom_right = [bottom, right]\ntop_left = [top, left]\nbottom_left = [bottom, left]\npositions = [right, left, top, bottom, top_right, bottom_right, top_left, bottom_left]\npositions.select{|npos| in_bounds?(npos, matrix.length, matrix.length) && matrix[npos][npos] == 1}\nend\n\ndef in_bounds?(pos, m, n)\npos >= 0 && pos < m && pos >= 0 && pos < n\nend\n\n\nthought process: My thought was to iterate through each cell in the matrix and then if it was a 1 I would do a depth-first traversal to find all other cells that had a 1and were connected to the parent cell. then I would add 1 to the count whenever I visited a cell and add it to the visited hash so that it wouldn't be added to the count. I added helper methods for in_bounds? and nbrsmostly for better readability in the get_area_count method(which is the dfs implementation). The nbrs method is pretty verbose, but I kept it that on purpose because I'm preparing for technical interviews, where accuracy is important, and I thought actually listing out each direction would help in debugging / explaining it to the interviewer.\n\nI really like clear and speaking method names, I quickly tried to refactor the first method but have had not much time, I hope this helps anyway.\n\nI have not understand the other initialization of the visited hash in the area_count method (yet).\n\nThe new neighbors method indeed looks some kind of overloaded with information, no good idea yet how to change it, if needed at all as you described.\n\nrequire 'json'\nrequire 'stringio'\n\ndef connectedCell(matrix, visited = {})\n(0...matrix.length).each do |row|\n(0...matrix.length).each do |col|\nnext if visited[[row, col]]\nif matrix[row][col] == 1\nreturn update_count_stats(row, col, matrix, visited)\nend\nend\nend\nend\n\ndef update_count_stats(row, col, matrix, visited)\nresult = area_count([row, col], matrix)\nvisited.merge(result)\nresult > 0 ? result : 0\nend\n\ndef area_count(pos, matrix)\nq = [pos]\nvisited = {}\ncount = 0\nwhile q.length > 0\ntile_pos = q.shift\nif !visited[tile_pos]\ncount += 1\nvisited[tile_pos] = true\nq += neighbors(tile_pos, matrix)\nend\nend\n\nreturn [count, visited]\nend\n\ndef neighbors(pos, matrix)\nright = [pos, pos + 1]\nleft = [pos, pos - 1]\ntop = [pos + 1, pos]\nbottom = [pos - 1, pos]\n\ntop_right = [top, right]\nbottom_right = [bottom, right]\ntop_left = [top, left]\nbottom_left = [bottom, left]\n\npositions = [right, left, top, bottom, top_right, bottom_right, top_left, bottom_left]\npositions.select{|npos| in_bounds?(npos, matrix.length, matrix.length) && matrix[npos][npos] == 1}\nend\n\ndef in_bounds?(pos, number_of_columns, number_of_rows)\npos >= 0 && pos < number_of_columns && pos >= 0 && pos < number_of_rows\nend\n\nnumber_of_rows = 4 # just for testing, was gets.to_i\nnumber_of_columns = 4 # just for testing, was gets.to_i\nmatrix = Array.new(number_of_rows)\n\n# sample input\n# 1 1 0 0\n# 0 1 1 0\n# 0 0 1 0\n# 1 0 0 0\n\nnumber_of_rows.times do |i|\nmatrix[i] = gets.rstrip.split(' ').map(&:to_i)\nend\nresult = connectedCell matrix\nputs result\n$$$$\n\n\n## Rubocop Report\n\n### connectedCell\n\nAvoid nested code blocks if clean alternative statements are available. For instance, in method connectedCell you have the following block:\n\nif matrix[i][j] == 1\n# .. code omitted\nend\n\n\nReplace the if-statement with next unless matrix[i][j] == 1 and you'll be able to reduce nesting with 1 level.\n\nThe next part has a similar avoidable nesting, only this time we can use an inline if-statement.\n\nif res > highest_count\nhighest_count = res\nend\n\n\nThis could be replaced with highest_count = res if res > highest_count.\n\nAnd prefer to use snake_case for method names: connected_cell.\n\nThe complete method could then be written as:\n\ndef connected_cell(matrix)\nhighest_count = 0\nvisited = {}\n\n(0...matrix.length).each do |i|\n(0...matrix.length).each do |j|\nnext if visited[[i, j]]\n\nnext unless matrix[i][j] == 1\n\nres = get_area_count([i, j], matrix)\nhighest_count = res if res > highest_count\n\nvisited = visited.merge(res)\nend\nend\n\nhighest_count\nend\n\n\n### get_area_count\n\nThe while condition while q.length > 0 should be replaced by until q.empty? because it's considered a negative condition (pseudo: while !empty).\n\nWe have another case of avoidable nesting: replace the if !visited[tile_pos] block with next if visited[tile_pos].\n\nThe method rewritten:\n\ndef get_area_count(pos, matrix)\nq = [pos]\nvisited = {}\ncount = 0\nuntil q.empty?\ntile_pos = q.shift\nnext if visited[tile_pos]\n\ncount += 1\nvisited[tile_pos] = true\nq += nbrs(tile_pos, matrix)\nend\n\n[count, visited]\nend\n`"
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https://discuss.px4.io/t/sih-with-custom-airframe/21666 | [
"# SIH with custom airframe\n\nHi px4 community, I am trying to test out a custom tricopter airframe. I would like to make use of the SIH Module so I’m trying to set it up for the default tricopter as a start.\n\nI am trying to modify the src/lib/modules/sih.cpp file. There is a section which generates the torques and thrusts, and I have confirmed from @Romain_Chiappinelli that this is the section I need to modify.\n\nAlso, I have created a new airframe config for the sih which points to the default tri mixer, rather than the quad_x one. I simply duplicated the config file here PX4-Autopilot/1100_rc_quad_x_sih.hil at master · PX4/PX4-Autopilot · GitHub\n\nNow my question is: for a tricopter, with 3 rotors and 1 servo, looking at the sih.cpp file, I suppose u1,u2,u3 would refer to the motors, and u4 would refer to the tail servo?\n\nThank you\n\nHi Daniel,\n\nYou can set your custom forces in Sih::generate_force_and_torques().\n\nAs for the mixer tri_y_yaw+, yes the motors are u1 u2 u3 and the servo is u4.\n\nBe careful, u4 should be in the range [-1;1], you may want to modify Sih::read_motors() to include something like this.\n\nBest,\n\nRomain\n\nHI @Romain_Chiappinelli , thanks once a gain for your response. Firstly, I’m a total beginner with c++. However, I can program in matlab and a bit in python so I have tried to joggle a few things as follows:\n\n• I added a new parameter SIH_L_ARM in the src/modules/sih/sih_params.c file, this is because the tricopter has three different lengths, one corresponding to the roll, two separate ones which relate to pitch, where I have assumed the one between the two front rotors and CG along x-direction to be L_pitch and then the new length I defined is the one between the tail rotor and the CG along the x-direction, which is the length of each arm in essence.\n• Added new default values for L_ROLL and L_PITCH.\n• Modified the sih_parameters_updated() function to include the newly added parameter.\n• Changed the model to that representing a tricopter\n\nA snap shot of all these is below:\n\nvoid Sih::parameters_updated()\n{\n_T_MAX = _sih_t_max.get();\n_Q_MAX = _sih_q_max.get();\n_L_ROLL = _sih_l_roll.get();\n_L_PITCH = _sih_l_pitch.get();\n_L_ARM = _sih_l_arm.get();\n_KDV = _sih_kdv.get();\n_KDW = _sih_kdw.get();\n_H0 = _sih_h0.get();\n\n{\nactuator_outputs_s actuators_out;\n\n``````if (_actuator_out_sub.update(&actuators_out)) {\nfor (int i = 0; i < NB_MOTORS; i++) { // saturate the motor signals\nif (i < NB_MOTORS) {\n\nfloat u_sp = constrain((actuators_out.output[i] - PWM_DEFAULT_MIN) / (PWM_DEFAULT_MAX - PWM_DEFAULT_MIN), 0.0f, 1.0f);\n\n} else {\n\nfloat u_sp = constrain((actuators_out.output[i] - PWM_DEFAULT_MIN) / ((PWM_DEFAULT_MAX - PWM_DEFAULT_MIN), -1.0f, 1.0f);\n}\n\n_u[i] = _u[i] + _dt / _T_TAU * (u_sp - _u[i]); // first order transfer function with time constant tau\n}\n}\n``````\n\n}\n\nPlease see if the read_motors() one makes sense as per limiting the servo to {-1,1}.\n\nvoid Sih::generate_force_and_torques()\n{\n_T_B = Vector3f(0.0f, 0.0f, -_T_MAX * (+_u + _u + _u * cos(_u)));\n_Mt_B = Vector3f(_L_ROLL * _T_MAX * (-_u + _u),\n_L_PITCH * _T_MAX * (+_u + _u) - (_L_ARM * _T_MAX * (_u * cos(_u))) - (_Q_MAX * (_u * sin(_u))),\n_Q_MAX * (-_u - _u - _u * cos(_u)) + (_L_ARM * _T_MAX * (_u * sin(_u)));\n\nThe corresponding equations are:",
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"",
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"So Ti = kt x omega_i^2, and Qi = kq x omega_i^2, where i = 1,2,3. Note I ignored Fy.\n\nYou can view it better on my fork here: PX4-Autopilot/sih.cpp at sih_tri · DanAbara/PX4-Autopilot · GitHub"
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"https://discuss.px4.io/uploads/default/original/2X/6/6f897531271bcec30af8e46f89a77dc7a67d2188.png",
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https://www.prepanywhere.com/prep/textbooks/10-math-workbook/chapters/chapter-4-quadratic-relations/materials/chapter-4-review | [
"Chapter 4 Review\nTextbook\n10 Math Workbook\nChapter\nChapter 4\nSection\nChapter 4 Review\nSolutions 25 Videos\n\nWhich scatter plot(s) could be modelled using a curve instead of a line of best fit? Explain.",
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"",
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"Coming Soon\nQ1\n\nThe table shows the operating revenue from dry cleaning and laundry services in Canada for the years from 2000 to 2004 in millions of dollars.",
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"a) Make a scatter plot of the data. Draw a curve of best fit.\n\nb) Describe the relationship between the year and the operating revenue.\n\nc) Use your curve of best fit to predict the operating revenue in 2005.\n\nComing Soon\nQ2\n\nUse finite differences to determine whether each relation is linear, quadratic, or neither.",
null,
"Coming Soon\nQ3a\n\nUse finite differences to determine whether each relation is linear, quadratic, or neither.",
null,
"Coming Soon\nQ3b\n\nUse finite differences to determine whether each relation is linear, quadratic, or neither.",
null,
"Coming Soon\nQ3c\n\nThe flight of an aircraft from Toronto to Halifax can be modelled by the relation h = -3.5 t ^{2} + 210t, where t is the time, in minutes, and h is the height in metres.\n\na) Graph the relation.\n\nb) How long does it take to fly from Toronto to Halifax?\n\nc) What is the maximum height of the aircraft? At what time does the aircraft reach this height?\n\nComing Soon\nQ4\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y = 3x^2\n\nComing Soon\nQ5a\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y =\\dfrac{2}{3}x^2\n\nComing Soon\nQ5b\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y = x^2 -5\n\nComing Soon\nQ5c\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y = -\\dfrac{1}{5}x^2\n\nComing Soon\nQ5d\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y = (x+7)^2\n\nComing Soon\nQ5e\n\nSketch the graph of each parabola. Describe the transformation from the graph of y = x^2.\n\n y = -x^2 + 5\n\nComing Soon\nQ5f\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = 2(x+2)^2\n\nComing Soon\nQ6a\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = -(x-5)^2\n\nComing Soon\nQ6b\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = 3x^2 - 4\n\nComing Soon\nQ6c\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = -5x^2 +3\n\nComing Soon\nQ6d\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = 4(x+5)^2 +2\n\nComing Soon\nQ6e\n\nCopy and complete the table for each parabola. Replace the heading for the second column with the equation for the parabola.",
null,
"y = -\\dfrac{1}{2} (x-4)^2 - 5\n\nComing Soon\nQ6f\n\na) Find an equation for the parabola with vertex (3,-1) that passes through the point (1,7).\n\nb) Find an equation for the parabola with vertex (-5,-5) that passes through the point (3,27).\n\nComing Soon\nQ7\n\nSketch a graph of each quadratic. Label the x-intercept and the vertex.\n\n y = 2(x+2)(x-4)\n\nComing Soon\nQ8a\n\nSketch a graph of each quadratic. Label the x-intercept and the vertex.\n\n y = -\\dfrac{1}{2}(x-3)(x+1)\n\nComing Soon\nQ8b\n\nThe path of a soccer ball can be modelled by the equation h = -0.06d(d-50), where h represents the height, in metres, of the soccer ball above the ground and d represents the horizontal distance, in metres, of the soccer ball from the player.\n\na) Sketch a graph of this relation.\n\nb) At what horizontal distance does the soccer ball land?\n\nc) At what horizontal distance does the soccer ball reach its maximum height? What is the maximum height?\n\nComing Soon\nQ9\n\nEvaluate.\n\n 4^{-2}\n\n 3^{-5}\n\n 5 ^{0}\n\nComing Soon\nQ10abc\n\nEvaluate.\n\n (-3)^{-1}\n\n (\\dfrac{3}{4})^{-3}\n\n(-7)^{0}\n\nAndy has \\$10 000 to invest. He decides to invest \\dfrac{1}{2}, or 2^{-1}, of his money in May, then invest half of the remaining amount in June, half again in July, and so on."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8508578,"math_prob":0.9946431,"size":3754,"snap":"2021-31-2021-39","text_gpt3_token_len":1017,"char_repetition_ratio":0.1784,"word_repetition_ratio":0.42026827,"special_character_ratio":0.27650505,"punctuation_ratio":0.1043257,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9981828,"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,2,null,2,null,2,null,2,null,2,null,2,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-25T11:43:53Z\",\"WARC-Record-ID\":\"<urn:uuid:2e1a868b-b3af-4136-898a-70e19ce5ab1a>\",\"Content-Length\":\"37171\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:277451e1-716b-4fee-808f-016c78c953cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:45597e62-c624-4015-b114-150aef4833ef>\",\"WARC-IP-Address\":\"54.83.182.59\",\"WARC-Target-URI\":\"https://www.prepanywhere.com/prep/textbooks/10-math-workbook/chapters/chapter-4-quadratic-relations/materials/chapter-4-review\",\"WARC-Payload-Digest\":\"sha1:ZGXL2ZGCZH7AR4XJ5LJM464UREROAWEN\",\"WARC-Block-Digest\":\"sha1:E27VOUIFTYQMZEJNGOXXHGG7MSRXNSHC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046151672.96_warc_CC-MAIN-20210725111913-20210725141913-00284.warc.gz\"}"} |
https://gmplib.org/list-archives/gmp-discuss/2016-November/006059.html | [
"# mpz_probab_prime_p reproducibility\n\nPierre Chatelier pierre at chachatelier.fr\nFri Nov 11 08:39:48 UTC 2016\n\n```Hello,\n\nI would like to know if two runs of mpz_probab_prime_p(N, 50) for the same number N, on two different machines, trigger the same probabilistic primality tests.\n\nIf this is the case, is there at the current time, a known M value, such that for each integer N < M, the probabilistic answer of mpz_probab_prime_p(N, 50) is exact ?\nIn other words, is there any known integer N for which mpz_probab_prime_p(N, 50) is wrong or unsure ?\n\nRegards,\n\nPierre Chatelier\n\n```\n\nMore information about the gmp-discuss mailing list"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.84978706,"math_prob":0.97250503,"size":620,"snap":"2021-21-2021-25","text_gpt3_token_len":169,"char_repetition_ratio":0.13636364,"word_repetition_ratio":0.0,"special_character_ratio":0.25,"punctuation_ratio":0.14754099,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96504986,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-23T23:54:58Z\",\"WARC-Record-ID\":\"<urn:uuid:f77d6b02-aefb-45b9-a839-d5312b85cd74>\",\"Content-Length\":\"3145\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c1ed3c9-8dfa-4fe2-9b87-e14d77b82927>\",\"WARC-Concurrent-To\":\"<urn:uuid:b56eabdf-eca7-4763-91cd-a1cf8de4ba29>\",\"WARC-IP-Address\":\"130.242.124.102\",\"WARC-Target-URI\":\"https://gmplib.org/list-archives/gmp-discuss/2016-November/006059.html\",\"WARC-Payload-Digest\":\"sha1:27OLXHAL6BGVEEYXQ3QCAJGIKFWI4737\",\"WARC-Block-Digest\":\"sha1:WTIDYNOQONBEVR6AOC537II7OXS74Y3C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488544264.91_warc_CC-MAIN-20210623225535-20210624015535-00025.warc.gz\"}"} |
https://www.int.uni-rostock.de/Projektseminar-Funkkommunikati.220.0.html | [
"Language switch: Deutsch\nYou are here:\n\n### Lecture: Direction of Arrival (DOA) Estimation\n\nThe lecture will teach the theoretical basics required for the study of scientific publications in the field of direction of arrival estimation. Furthermore, some state of the art direction of arrival estimation techniques will be discussed.\n\n#### Introduction\n\n• direction of arrival estimation \n\n#### Linear Algebra\n\n• matrices\n• Hermitian matrices\n• Singular Value Decomposition (SVD)\n\n#### Modelling\n\n• phasor notation\n• antenna arrays\n• random signals \n• normal distribution\n\n#### Subspaces\n\n• correlation matrix\n• measurements\n• correlated sources [3, 4]\n\n#### Parametric Methods\n\n• Maximum Likelihood Estimator (MLE)\n• Deterministic Maximum Likelihood (DML) \n\n#### Conventional Methods\n\n• beamforming network\n• conventional beamformer \n• Capon’s beamformer (Minimum Variance Distortionless Response, MVDR) \n\n#### Subspace Methods\n\n• MUltiple SIgnal Classification (MUSIC) \n• Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) \n\n#### General References for the Lecture\n\nmathematical basics: [10, 11]\n\nestimation theory: \n\nspectral analysis, array signal processing: [13, 14, 15]\n\nRadar signal processing is an important application of direction of arrival estimation. From a mathematical perspective, direction of arrival estimation as well as range estimation and velocity estimation are spectral estimation problems. The lab activities are described in the lab manual. Also have a look at the introduction to FMCW radar [16, 17, 18, 19].\n\n#### General References for the Lab\n\ndigital signal processing: \n\nMatlab: \n\n### Presentations\n\nThe student shall give a talk on a given topic. As a starting point a paper will be recommended. However, the talk shall not be a mere summary of this paper. It shall rather comprise an original presentation of the theory linked to the lecture and own simulation results.\n\n1. Pisarenko Method \n2. Stochastic Maximum Likelihood (SML) \n3. Minimum Norm Method \n4. Unitary ESPRIT \n5. Single Frequency Estimator \n6. Root MUSIC \n7. Alternating Projection Algorithm (APA) \n8. TLS ESPRIT \n9. Unitary Root MUSIC"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.78939736,"math_prob":0.8151304,"size":7289,"snap":"2023-40-2023-50","text_gpt3_token_len":2088,"char_repetition_ratio":0.14550446,"word_repetition_ratio":0.062440872,"special_character_ratio":0.29030046,"punctuation_ratio":0.27811044,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9711717,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-27T15:32:10Z\",\"WARC-Record-ID\":\"<urn:uuid:bc73fc29-ee37-4c5f-be3b-ec263c9a5bbb>\",\"Content-Length\":\"30502\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1ee09d45-7361-4cf9-a308-d073b71550ca>\",\"WARC-Concurrent-To\":\"<urn:uuid:f491a774-21be-4ef3-b5d7-b9b737056f11>\",\"WARC-IP-Address\":\"139.30.208.8\",\"WARC-Target-URI\":\"https://www.int.uni-rostock.de/Projektseminar-Funkkommunikati.220.0.html\",\"WARC-Payload-Digest\":\"sha1:R5WWDJEY4AEK5JS27NDHZ3HP5223ZD6Y\",\"WARC-Block-Digest\":\"sha1:CUNZH3MH6CLGY6GAU66JNF7QOMUOPKT7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510300.41_warc_CC-MAIN-20230927135227-20230927165227-00393.warc.gz\"}"} |
https://au.mathworks.com/help/images/process-big-image-efficiently.html | [
"Main Content\n\n# Process Blocked Images Efficiently Using Partial Images or Lower Resolutions\n\nThis example shows how to process a blocked image quickly using two strategies that enable computations on smaller representative samples of the high-resolution image.\n\nProcessing blocked images can be time consuming, which makes iterative development of algorithms prohibitively expensive. There are two common ways to shorten the feedback cycle: iterate on a lower resolution image or iterate on a partial region of the blocked image. This example demonstrates both of these approaches for creating a segmentation mask for a blocked image.\n\nIf you have Parallel Computing Toolbox™ installed, then you can further accelerate the processing by using multiple workers.\n\nCreate a `blockedImage` object using a modified version of image \"tumor_091.tif\" from the CAMELYON16 data set. The original image is a training image of a lymph node containing tumor tissue. The original image has eight resolution levels, and the finest level has resolution 53760-by-61440. The modified image has only three coarse resolution levels. The spatial referencing of the modified image has been adjusted to enforce a consistent aspect ratio and to register features at each level.\n\n```bim = blockedImage('tumor_091R.tif'); ```\n\nDisplay the blocked image by using the `bigimageshow` function.\n\n```bigimageshow(bim); ```",
null,
"### Accelerate Processing Using Lower Resolution Image\n\nMany blocked images contain multiple resolution levels, including coarse lower resolution versions of the finest high-resolution image. In general, the distribution of individual pixel values should be roughly equal across all the levels. Leveraging this assumption, you can compute global statistics at a coarse level and then use the statistics to process the finer levels.\n\nExtract the image at the coarsest level, then convert the image to grayscale.\n\n```imLowRes = gather(bim); % default is coarsest imLowResGray = rgb2gray(imLowRes); ```\n\nThreshold the image into two classes and display the result.\n\n```thresh = graythresh(imLowResGray); imLowResQuant = imbinarize(imLowResGray,thresh); imshow(imLowResQuant) ```",
null,
"Validate on the largest image. Negate the result to obtain a mask for the stained region.\n\n```bq = apply(bim, ... @(bs)~imbinarize(rgb2gray(bs.Data),thresh)); ```\n\nVisualize the result at the finest level.\n\n```bigimageshow(bq,'CDataMapping','scaled'); ```",
null,
"### Accelerate Processing Using Using Partial Regions of blocked Image\n\nAnother approach while working with large images is to extract a smaller region with features of interest. You can compute statistics from the ROI and then use the statistics to process the entire high-resolution image.\n\n```% Zoom in on a region of interest. bigimageshow(bim); xlim([2400,3300]) ylim([900 1700]) ```",
null,
"Extract the region being shown from the finest level.\n\n```xrange = xlim; yrange = ylim; imRegion = getRegion(bim,[900 2400 1],[1700 3300 3],'Level',1); imshow(imRegion); ```",
null,
"Prototype with this region then display the results.\n\n```imRegionGray = rgb2gray(imRegion); thresh = graythresh(imRegionGray); imLowResQuant = ~imbinarize(imRegionGray,thresh); imshow(imLowResQuant) ```",
null,
"Validate on the full blocked image and display the results.\n\n```bq = apply(bim, ... @(bs)~imbinarize(rgb2gray(bs.Data),thresh)); bigimageshow(bq,'CDataMapping','scaled'); ```",
null,
"### Accelerate Processing Using Parallel Computing Toolbox\n\nIf you have the Parallel Computing Toolbox™ installed, then you can distribute the processing across multiple workers to accelerate the processing. To try processing the image in parallel, set the `runInParallel` variable to `true`.\n\n```runInParallel = false; if runInParallel % Open a pool p = gcp; % Ensure workers are on the same folder as the file to be able to % access it using just the relative path sourceDir = fileparts(which('tumor_091R.tif')); spmd cd(sourceDir) end % Run in parallel bq = apply(bim, ... @(bs)~imbinarize(rgb2gray(bs.Data),thresh),'UseParallel',true); end ```\n\nDownload ebook"
]
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null,
"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_01.png",
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"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_02.png",
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"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_03.png",
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"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_04.png",
null,
"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_05.png",
null,
"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_06.png",
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"https://au.mathworks.com/help/examples/images/win64/ProcessBigImagesEfficientlyExample_07.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7658906,"math_prob":0.92039835,"size":3629,"snap":"2021-21-2021-25","text_gpt3_token_len":807,"char_repetition_ratio":0.12855172,"word_repetition_ratio":0.032128513,"special_character_ratio":0.21631303,"punctuation_ratio":0.14808917,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96232784,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-23T04:33:51Z\",\"WARC-Record-ID\":\"<urn:uuid:ea12a0b6-0179-4642-ab75-fba7c44bc82a>\",\"Content-Length\":\"75017\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7c92dbec-015e-4816-bb77-49c7aa6b94fb>\",\"WARC-Concurrent-To\":\"<urn:uuid:c02a54c6-436c-4dda-8e12-04533c755ec7>\",\"WARC-IP-Address\":\"23.197.108.134\",\"WARC-Target-URI\":\"https://au.mathworks.com/help/images/process-big-image-efficiently.html\",\"WARC-Payload-Digest\":\"sha1:BJH3VP532AXJR7GKB36BLBLDV4HRQU6H\",\"WARC-Block-Digest\":\"sha1:35WEWDJDKTCVEJYH4ORFN5PM3BULHZFU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488534413.81_warc_CC-MAIN-20210623042426-20210623072426-00509.warc.gz\"}"} |
https://ounces-to-grams.appspot.com/pl/9950-uncja-na-gram.html | [
"Ounces To Grams\n\n# 9950 oz to g9950 Ounce to Grams\n\noz\n=\ng\n\n## How to convert 9950 ounce to grams?\n\n 9950 oz * 28.349523125 g = 282077.755094 g 1 oz\nA common question is How many ounce in 9950 gram? And the answer is 350.975921399 oz in 9950 g. Likewise the question how many gram in 9950 ounce has the answer of 282077.755094 g in 9950 oz.\n\n## How much are 9950 ounces in grams?\n\n9950 ounces equal 282077.755094 grams (9950oz = 282077.755094g). Converting 9950 oz to g is easy. Simply use our calculator above, or apply the formula to change the length 9950 oz to g.\n\n## Convert 9950 oz to common mass\n\nUnitMass\nMicrogram2.82077755094e+11 µg\nMilligram282077755.094 mg\nGram282077.755094 g\nOunce9950.0 oz\nPound621.875 lbs\nKilogram282.077755094 kg\nStone44.4196428572 st\nUS ton0.3109375 ton\nTonne0.2820777551 t\nImperial ton0.2776227679 Long tons\n\n## What is 9950 ounces in g?\n\nTo convert 9950 oz to g multiply the mass in ounces by 28.349523125. The 9950 oz in g formula is [g] = 9950 * 28.349523125. Thus, for 9950 ounces in gram we get 282077.755094 g.\n\n## 9950 Ounce Conversion Table",
null,
"## Alternative spelling\n\n9950 Ounces to Grams, 9950 oz to Grams, 9950 Ounces to g, 9950 Ounces in g, 9950 Ounces to Gram, 9950 Ounce to Grams, 9950 Ounce to Gram, 9950 Ounce in Gram, 9950 Ounce to g,"
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"https://ounces-to-grams.appspot.com/image/9950.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7785667,"math_prob":0.8235053,"size":901,"snap":"2023-40-2023-50","text_gpt3_token_len":313,"char_repetition_ratio":0.21850613,"word_repetition_ratio":0.0,"special_character_ratio":0.46836847,"punctuation_ratio":0.15384616,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9704739,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T00:37:39Z\",\"WARC-Record-ID\":\"<urn:uuid:cb345c66-3779-44a7-9e0b-5fb4e3f28dc9>\",\"Content-Length\":\"28492\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ac9e919d-a19b-44f6-98b9-7080328d68fa>\",\"WARC-Concurrent-To\":\"<urn:uuid:08673eb2-90bc-40c5-b572-5e4060261d6d>\",\"WARC-IP-Address\":\"142.251.16.153\",\"WARC-Target-URI\":\"https://ounces-to-grams.appspot.com/pl/9950-uncja-na-gram.html\",\"WARC-Payload-Digest\":\"sha1:2CMHI4ON6CNQW2YIO2DH3FNNWJ6WYBU5\",\"WARC-Block-Digest\":\"sha1:4NGZZETIQK35V4OS6ZOVCA7KCQ6FEI5K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510100.47_warc_CC-MAIN-20230925215547-20230926005547-00244.warc.gz\"}"} |
https://chipkit.net/archive/1132 | [
"# Problem reading&displaying QTR without the use of libraries\n\nCreated Fri, 18 Jan 2013 18:46:34 +0000 by vvysoc\n\n### vvysoc\n\nFri, 18 Jan 2013 18:46:34 +0000\n\nI have a problem reading my QTR-8A Reflectance Sensor Array from http://www.pololu.com/catalog/product/960. I'm using chipkit max 32 on my line following robot with Dual MC33926 Motor Driver Carrier from http://www.pololu.com/catalog/product/1213 and it's all connected correctly i believe. The robot is finally line following but is acting weird and part of my problem is that I'm coding it blindly because I don't exactly know the values of each sensor and position. I have tried to download and put the QTR sensor library into MPIDE under documents/mpide/libraries/QTRSensors to print the values to the serial monitor but I couldn't even verify the code because it gives me error (\nC:\\Users\\Vitaliy\\Documents\\mpide\\libraries\\QTRSensors\\QTRSensors.cpp:36:21: fatal error: Arduino.h: No such file or directory compilation terminated. ).\n\nI have tried everything from just serial print individual sensor to serialprint my \"Readsensor\" part from my code and many other combination and also researched everywhere and didnt find any fix. I have also tried to download the library on a diffrent computer which is 32 bit unlike my laptop is 64 bit and that didn't help.\n\nHere's my code for line following without a library:\n\nint LeftSensors, RightSensors, TotalSensorsAvg; int LeftVelocity, RightVelocity;\n\n//const int LEFT_MOTOR = 3, RIGHT_MOTOR = 9; #define stby 8 #define LEFTmotor1 4 #define LEFTmotor2 6 #define RIGHTmotor1 80 #define RIGHTmotor2 81\n\n//#define LEFT_MOTOR 3 //PWM //#define RIGHT_MOTOR 9 //fPWM\n\nconst int LEFT_MOTOR = 3, RIGHT_MOTOR = 9; long sensors[] = { 0, 0, 0, 0, 0, 0}; long sensors_average = 0; int sensors_sum = 0; int Position = 0; int proportional = 0; long integral = 0; int derivative = 0; int last_proportional = 0; int control_value = 0;\n\nint max_difference = 75; float Kp = .05200; float Ki = .000001100; float Kd = 1.105*300;\n\nvoid setup() {\n\npinMode(stby,OUTPUT); pinMode(LEFTmotor1,OUTPUT); pinMode(LEFTmotor2,OUTPUT); pinMode(RIGHTmotor1,OUTPUT); pinMode(RIGHTmotor2,OUTPUT);\ndigitalWrite(stby,HIGH);\n\ndigitalWrite(LEFTmotor1,HIGH); digitalWrite(LEFTmotor2,LOW); digitalWrite(RIGHTmotor1,HIGH); digitalWrite(RIGHTmotor2,LOW); Serial.begin(9600);\n\n}\n\n{\n\n``````{\nGetAverage();\nGetSum();\nGetPosition();\nGetProportional();\nGetIntegral();\nGetDerivative();\nGetControl();\nSetMotors();\n}\n``````\n\n} }\n\n//void Stop() //{ //analogWrite(LEFT_MOTOR,0); // analogWrite(RIGHT_MOTOR,0); //}\n\nvoid ReadSensors() { // read 6 sensors for (int i = 0; i < 6; i++) { sensors[i] = analogRead(i + 1);\n\n`````` // round readings less than 50 down to zero to filter surface noise\nif (sensors[i] < 50)\n{\nsensors[i] = 0;\n}\n``````\n\n} }\n\nvoid GetAverage() { // zero average variable of the sensors sensors_average = 0;\n\nfor (int i = 0; i < 6; i ++) { sensors_average += sensors[i] * i * 1000; } }\n\nvoid GetSum() { // zero variable of sum of the sensors sensors_sum = 0;\n\n// sum the total of all the sensors for (int i = 0; i < 6; i++) { sensors_sum += int(sensors[i]); } }\n\nvoid GetPosition() { // calculate the current position on the line Position = int(sensors_average / sensors_sum); }\n\nvoid GetProportional() { // caculate the proportional value proportional = Position - 2500; }\n\nvoid GetIntegral() { // calculate the integral value integral = integral + proportional; }\n\nvoid GetDerivative() { // calculate the derivative value derivative = proportional - last_proportional;\n\n// store proportional value in last_proportional for the derivative calculation on next loop last_proportional = proportional; }\n\nvoid GetControl() { // calculate the control value control_value = int(proportional * Kp + integral * Ki + derivative * Kd); }\n\nvoid AdjustControl() { // if the control value is greater than the allowed maximum set it to the maximum if (control_value > max_difference)\n\n// if the control value is less than the allowed minimum set it to the minimum if (control_value < -max_difference) }"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.59531546,"math_prob":0.9477835,"size":7034,"snap":"2023-40-2023-50","text_gpt3_token_len":1874,"char_repetition_ratio":0.17197724,"word_repetition_ratio":0.15524194,"special_character_ratio":0.28305373,"punctuation_ratio":0.16547406,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9929964,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T14:06:15Z\",\"WARC-Record-ID\":\"<urn:uuid:dbe21d8a-f37e-44b6-a332-e8f303e88d89>\",\"Content-Length\":\"21845\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e8452052-bde3-4ea6-86c0-e9f1b6ef6438>\",\"WARC-Concurrent-To\":\"<urn:uuid:03ec3edd-f47a-4bfd-8be9-61e3484d8bbb>\",\"WARC-IP-Address\":\"212.71.239.90\",\"WARC-Target-URI\":\"https://chipkit.net/archive/1132\",\"WARC-Payload-Digest\":\"sha1:XRNNVRGBTGAJNTDZN3JCZXBVYOMXZIBO\",\"WARC-Block-Digest\":\"sha1:IRKO5GBZZ5UXGJBO54OCRRTQ6VM3CDCW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233511000.99_warc_CC-MAIN-20231002132844-20231002162844-00402.warc.gz\"}"} |
https://www.physicsforums.com/threads/calculating-the-error-of-a-experimental-results.554162/ | [
"# Calculating the error of a experimental results\n\nhello everyone, ive completed a experiment regarding torsional oscillations to determin the tortional ridgity in two types of wire. The final result is about what is to be expected but im having trouble in calculating the error in my C \" torsional ridigity\" value.\n\nThe formula used is [2Pi^2M(R^2+r^2)]/(t2^2-t1^2)=C\n\nthe experiment was done by a torquing a disk of mass M connected to the end of the wire where R is the outer radius and r is the inner radius of the disc t2,t1 are the average times of the oscillations t1 being one mass and t2 being 2 masses this is to eliminate the unknown moment of inertia of the connecting bolt used to connect the disc to the end of the wires.\n\nso to calculate the error in c when R,r,M,t1and t2 all have small errors due to measurments either reading errors or stdevp/N^0.5 in the case of the T the periods.\n\ni have been calculating the error in MR^2 then Mr^2 using\n\n(dM/M)^2+2(dR/R)^2=(dmR^2/mR^2)^2=(dx/x)^2, (dx/x) for simplicity x=mR^2\n\n(dM/M)^2+2(dr/r)^2=(dmr^2/mr^2)^2=(dy/y)^2\n\nthen to add these two errors would i get:\n\nusing dQ^2=dx^2+dy^2=x^2[(dM/M)^2+2(dR/R)^2]+y^2[(dM/M)^2+2(dr/r)^2],\n\nwhere dQ would be the total error in the top line of the fraction of the formula\n\nthe bit im unsure about is when changing (dx/x)^2 to just dx^2 lets say (dx/x)^2=Z would the dx^2 to be =x^2*Z\n\ncan someone please comment if i am corrrect so far and if not please point me in the right direction as im adament to get this correct as it is vital i learn to do this for myself.\n\nThanks alot just for reading. Dan:)"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8745939,"math_prob":0.99211454,"size":2833,"snap":"2022-27-2022-33","text_gpt3_token_len":889,"char_repetition_ratio":0.11735596,"word_repetition_ratio":0.8870637,"special_character_ratio":0.30109423,"punctuation_ratio":0.04270987,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998735,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-29T16:45:28Z\",\"WARC-Record-ID\":\"<urn:uuid:529e6e39-378d-490f-bea4-172ccc80181f>\",\"Content-Length\":\"62810\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c2d5419-1def-47cc-8743-14fb79ab230c>\",\"WARC-Concurrent-To\":\"<urn:uuid:9d825b28-5420-46dc-b99e-494c031a5748>\",\"WARC-IP-Address\":\"104.26.14.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/calculating-the-error-of-a-experimental-results.554162/\",\"WARC-Payload-Digest\":\"sha1:O3C46DVC7HBKDPICQRSGAVWAFRWP6VSG\",\"WARC-Block-Digest\":\"sha1:23FXQX2G2B74RY2RKU7B7WPF2P2FMG67\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103640328.37_warc_CC-MAIN-20220629150145-20220629180145-00160.warc.gz\"}"} |
https://www.lebeausite-hotel.fr/37134/bond/work/index/calculation/mill/efficiency | [
"## bond work index calculation mill efficiency\n\n### Accurate Scale Up - IsaMill™ Advantages | Isamill\n\nAdditionally while techniques like the Bond Work Index and \"scale up factors\" are useful for coarse grinding, they can significantly underestimate grinding needs below 100 microns. Similarly Tower Mill laboratory tests typically use much finer media than can be used in full scale operation and testwork is done in \"batch\" mode.\n\n### Testwork: Bond ball mill work index - SAGMILLING.COM\n\nTestwork: Bond Ball Mill Work Index. The Bond ball mill work index is one of the most commonly used grindability tests in mining, and is often referred to as the Bond work index . The test is a 'locked-cycle' test where ground product is removed from test cycles and replaced by fresh feed. The test much achieve a steady-state before completion.\n\n### A New Approach to the Calculation of Work Index and the ...\n\nThe mill power is = 22.5 Watts, calculated by (6). Fi- P nally the product is wet screened to find the size d80. 2.4. Rod Mill Semi Continuous Process The same mill is used for the semi continuous grinding tests which is similar to the Bond test but with the exist- ing mill of known power. After time the mill product is t\n\n### Bond Work Index Procedure and Method\n\nThis Grindability Test or Bond Ball Mill Work Index Procedure is used to determine the Bond Work Index of minus six mesh or finer feed ore samples. These equation application methods are used to process <1/2″ ore samples in a Ball Mill using a standard ball charge.. Below describes in general terms the Bond Work Index Procedure used by a Professional Metallurgical Testing Laboratory.\n\n### Steam Calculators: Steam Turbine Calculator\n\nCalculation Details Step 1: Determine Inlet Properties Using the Steam Property Calculator, properties are determined using Inlet Pressure and the selected second parameter (Temperature, Specific Enthalpy, Specific Entropy, or Quality).\n\n### bond work index calculation mill portable stone crasher\n\nBond Ball Mill Work Index, BWi, kWh/t 13.4 Bond Rod Mill Work Index, RWi, kWh/t 18.1 Table 1. Example of AG/SAG Ball Mill Circuit Wio Calculations ABstrAct Optimum use of power in grinding, both in terms of grinding efficiency and use of installed capital, can have a …\n\n### Calculation of energy required for grinding in a ball mill ...\n\nThe Bond work index, W i, as an indicator of the grindability of raw materials is not a material constant but rather it changes with change of size of the grinding product.Therefore, in practice we can expect some difficulties and errors when the energy consumption is determined according to this formula in the case when, for a given size of grinding product, the value of the work index W i ...\n\n### bond grindability index of li ne\n\nBond Ball Mill Work Index (Grindability Tests) May 18, &#; This video was put together by Joshua Wright and Aldo Vasquerizo as a supplemental lecture for University. Live Chat. bond grindability index for fly ash.\n\n### 3 . 7 Brayton Cycle - MIT\n\nFigure 3.24 shows the expression for power of an ideal cycle compared with data from actual jet engines. Figure 3.24(a) shows the gas turbine engine layout including the core (compressor, burner, and turbine). Figure 3.24(b) shows the core power for a number of different engines as a function of the turbine rotor entry temperature. The equation in the figure for horsepower (HP) is the same as ...\n\n### Bond Work Index Procedure and Method\n\nThis Grindability Test or Bond Ball Mill Work Index Procedure is used to determine the Bond Work Index of minus six mesh or finer feed ore samples. These equation application methods are used to process <1/2″ ore samples in a Ball Mill using a standard ball charge.. Below describes in general terms the Bond Work Index Procedure …\n\n### Bond Work Index Tests - Grinding Solutions Ltd\n\nThe Bond Ball Mill Work Index (BBWi) test is carried out in a standardised ball mill with a pre-defined media and ore charge. The Work Index calculated from the testing can be used in the design and analysis of ball mill circuits. The test requires a minimum of 10kg of sample that has been stage-crushed to passing size of <3.35 mm.\n\n### Bond Work Index Formula-Equation\n\nThe ball mill work index laboratory test is conducted by grinding an ore sample prepared to passing 3.36 mm (6 mesh) to product size in the range of 45-150 µm (325-100 mesh), thus determining the ball mill work index (Wi B or BWi). The work index calculations across a narrow size range are conducted using the appropriate laboratory work ...\n\n### bond ball mill work index equation in wills\n\n· Grinding mill modeling has attracted the attention of a number of researchers ever since Bond published his method of energy calculation with an index called Bond work index (Bond 1961). In the 1970s, the population balance or selection and breakage function model was at the forefront of research (Fuerstenau et al. 1973).\n\n### CORRELATION BETWEEN BOND WORK INDEX AND …\n\nThe Bond's standard ball mill is used to determine the work index value of differ ent samples. The Bond work index is defined as the kilowatt-hours per short ton required to break from infinite size to a product size of 80% passing 100 µm. If the breakage characteristics of a material remain constant over all size ranges, the calcul ated work ...\n\n### How to Calculate Grinding Mill Operating Efficiency\n\nFor operating efficiency calculations, it is necessary that the efficiency factors are applied so that both work indices, used in the comparison, are on the same basis. Operating efficiency, based upon using operating work indices, is also a useful tool in comparing the variations in grinding mill operations such as: mill speed, mill size, size ...\n\n### Determination of work index in a common laboratory mill ...\n\nThe Bond work index is one of the most useful and interesting parameters used in designing grinding equipment. However, it must be obtained under restrained conditions, especially in regards to the Bond standard lab mill. The main objective of this study is to show how this index can be obtained using a Denver ball mill, which is present in most mineral processing laboratories. The …\n\n### Comminution testing - JKTech - University of Queensland\n\nA Bond Ball Mill Work Index may also be used in the simulation and optimisation of existing mill(s) and the associated grinding circuit(s). Sample requirements: A minimum of 8 kg of material crushed to nominally minus 10 mm is preferred. JKTech would stage crush the sample to minus 3.35 mm, as required for the Bond Ball Mill Work Index test feed.\n\n### GMSG GUIDELINE: DETERMINING THE BOND EFFICIENCY OF ...\n\nBond Standard Circuit Work Index: Assume the rod mill Work Index of 9.5 applies from the actual rod mill feed sizeof 19,300 mµ (although some of this work might ideally be done by crushers to achieve a rod mill F80 of 16,000 m) to a rod µ mill (circuit) product size of 1,000 µm. W Total = 2.32 + 4.77 = 7.09 very large size (FkWh/t of . 9.70 ...\n\n### SIZE REDUCTION - Universiti Teknologi Malaysia\n\nWORK INDEX Include friction in the crusher & power Material Specific gravity Work Index, W i Bauxite 2.20 8.78 Cement clinker 3.15 13.45 Cement raw material 2.67 10.51 Clay 2.51 6.30 Coal 1.4 13.00 Coke 1.31 15.13 Granite 2.66 15.13 Gravel 2.66 16.06 Gypsum rock 2.69 6.73 Iron ore (hematite) 3.53 12.84 Limestone 2.66 12.74\n\n### USING THE SMC TEST® TO PREDICT COMMINUTION …\n\n= fine ore work index (kWh/tonne) P. 1 = closing screen size in microns . Gbp = net grams of screen undersize per mill revolution . p. 80 = 80% passing size of the product in microns . f 80 = 80% passing size of the feed in microns . Note that the Bond ball work index test …\n\n### Power Calculation Of Impact Coal Crusher Based On Bond ...\n\nBond work index uses in gold processing - crusher in India. bond crushing work index of copper slag Values of Bond crushing work index will vary from a 8 kWh t for laterite hardcap through to 22 kWh t for banded iron. Power Calculation Of Impact Crusher. Bond 26 2339 3 s rod mill for work index. 19.0 MINERAL RESOURCE AND .\n\n### AMIT 135: Lesson 6 Grinding Circuit – Mining Mill Operator ...\n\nOperating data from existing mill circuit (direct proportioning) . Grinding tests in pilot scale, where the specific power consumption is determined (kWh/t dry solids) . Laboratory tests in small batch mills to determine the specific energy consumption. Energy and power calculations based on Bonds Work Index (Wi, normally expressed in kWh ...\n\n### Operating work index is not the specific energy consumption\n\nHowever, Bond Work Indeces are related to the type of equipment to be used (rod mill, ball mill, SAG uses Drop Ball parameter-Kwhr/m3-, so it is …\n\n### crushing and grinding calculations by fred c bond pdf\n\nData Base of Bond Grinding Circuit Efficiencies (under development) References . Annexes: A1. The Bond Crushing WI Test Equipment and Procedure for Bond Efficiency Determinations (Revised March 26, 2015) B1. The Bond Rod Mill WI Test Equipment and Procedure (Revised March 26, 2015) C1. The Bond Ball Mill WI Test Equipment and Procedure. More\n\n### Energy efficient mineral liberation using HPGR technology\n\nThis so-called mill energy defines an equivalent net energy in the Bond ball mill test to realise the same for a 2.4 meter wet grinding mill. Bond's empirical equation results can thus be reproduced using 60J/rev and the mill test data. Bond's original paper published in 1949 stated that the net energy input to the laboratory scale ball ...\n\n### [PDF] A quick method for Bond work index approximate value ...\n\nThe Bond work index is a measure of ore resistance to crushing and grinding and is determined using the Bond grindability test. Its value constitutes ore characteristic and is used for industrial comminution plants designing. Determining the Bond work index value is quite complicated, timeconsuming and requires trained operating personnel and therefore is subjected to errors.\n\n### bond rod mill index test\n\nIndicators of grindability and grinding efficiency. Oct 10,, SYNOPSIS Bond's Standard Work Index (SWi) indicates the gri'ldability of an ore, and tis Operamg Work Index (OWi) indicates, Bond grindability test mill is 198 x 10-7kWh, (1)primary grinding in open-circuit rod mills with.\n\n### GMSG GUIDELINE: DETERMINING THE BOND EFFICIENCY …\n\nBond Standard Circuit Work Index: Assume the rod mill Work Index of 9.5 applies from the actual rod mill feed sizeof 19,300 mµ (although some of this work might ideally be done by crushers to achieve a rod mill F80 of 16,000 m) to a rod µ mill (circuit) product size of 1,000 µm. W Total = 2.32 + 4.77 = 7.09 very large size (FkWh/t of . 9.70 ...\n\n### Orway Mineral Consultants Canada Ltd. Mississauga, ON ...\n\nDrop Weight Index (DWi) and the coarse ore grinding index (M ia). Test data from the Bond ball mill work index test is used to calculate the fine grinding index (M ib). The M ia and M ib indices are used to calculate specific energy for the coarse (W a) and fine (W b) components of the total grinding specific energy at the pinion (W\n\n### C O N S U L T I N G L T D TECHNICAL MEMORANDUM\n\nEF5BM=[ P80+10.3 1.145×P80] ( 3 ) The EF4 formula requires both the rod mill and ball mill work index (rod mill Wi is used to calculate the optimal feed size) and because this is a \"single-stage ball mill\" calculation, the F80 is actually the rod mill feed size (10,000 µm) from Table 1 and the P80 is the ball mill circuit product. The EF5 factor only applies below 75 µm to ball\n\n### Bond Work Index (Energy equation) - Grinding ...\n\nYou need a two-stage solution, first stage open-circuit mill and then second stage closed-circuit mill. First stage, will be broken into two parts as well, you use a Bond rod mill work index for the coarse component of the ore (+2.1 mm) and the Bond ball mill work index for the fine component (-2.1 mm)."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8674506,"math_prob":0.9114922,"size":10535,"snap":"2023-14-2023-23","text_gpt3_token_len":2450,"char_repetition_ratio":0.16475168,"word_repetition_ratio":0.1579241,"special_character_ratio":0.24394874,"punctuation_ratio":0.14344639,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9563386,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-20T22:09:11Z\",\"WARC-Record-ID\":\"<urn:uuid:a7e4dd9c-6c56-451b-bdb5-372ae9153711>\",\"Content-Length\":\"41099\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2912f2fa-ace2-4433-aef8-c7677c153834>\",\"WARC-Concurrent-To\":\"<urn:uuid:3824eca3-1ed6-494b-96ea-c7acdf3b40a5>\",\"WARC-IP-Address\":\"104.21.66.41\",\"WARC-Target-URI\":\"https://www.lebeausite-hotel.fr/37134/bond/work/index/calculation/mill/efficiency\",\"WARC-Payload-Digest\":\"sha1:GIBKA72SKBWVPGGZUI2RGTIBUVZGXS6B\",\"WARC-Block-Digest\":\"sha1:NILM6GWUPR6Z3YBL5ITQFQGRPIUO56PT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296943562.70_warc_CC-MAIN-20230320211022-20230321001022-00652.warc.gz\"}"} |
http://engine-heart.com/nursing-dosage-calculations-worksheets/ | [
"# 62 Good Models Of Nursing Dosage Calculations Worksheets\n\ndosage and calculations registered nurse rn this quiz on iv infusion times will test your ability to solve dosage and calculation grains nursing dosage & calculations dosage & calculations worksheets nursing dosage calculations worksheets lesson worksheets showing 8 worksheets for nursing dosage calculations worksheets are healthcare math calculating dosage fundamentals of mathematics for nursing dosage calculations\n\ndosage and calculations registered nurse rn this quiz on iv infusion times will test your ability to solve dosage and calculation grains nursing dosage & calculations dosage & calculations worksheets nursing dosage calculations worksheets lesson worksheets showing 8 worksheets for nursing dosage calculations worksheets are healthcare math calculating dosage fundamentals of mathematics for nursing dosage calculations drug dosage calculations practice exam nurseslabs practice dosage calculations for the nclex or any nursing exam with this 20 item questionnaire in the actual nclex these type of dosage calculations are\n\nnursing drug math worksheets nursing best free printable 1000 images about med math on pinterest 16 best of nursing math worksheets nursing dosage all worksheets nursing dosage calculation practice nursing math worksheet printables worksheets on 1000 images about nursing math on pinterest molarity molality mass percent mole fraction worksheet 16 best of nursing math worksheets nursing dosage medical math worksheets deployday medical best free 26 best med math for nurses images on pinterest",
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"All Worksheets Nursing Dosage Calculation Practice from nursing dosage calculations worksheets , source:snowguides.info\n\n24 best math medical images on pinterest\n\npediatric medication practice problems nursing math 24 best math medical images on pinterest nursing drug math worksheets nursing best free printable 1000 images about med math on pinterest 16 best of nursing math worksheets nursing dosage all worksheets nursing dosage calculation practice nursing math worksheet printables worksheets on 1000 images about nursing math on pinterest molarity molality mass percent mole fraction worksheet 16 best of nursing math worksheets nursing dosage medical math worksheets deployday medical best free 26 best med math for nurses images on pinterest free printable pediatric med mathml 25 psychiatric nursing mnemonics and tricks nursing math conversions worksheets medical math dimensional analysis worksheet preview dosage calculation practice worksheets tags dosage year 10 maths measurement cheat sheet geometry cheat rn med math worksheets rn best free printable worksheets metric conversions using dimensional analysis"
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https://flaviocopes.com/decimal-number-system/ | [
"In the Western world, the decimal number system is mostly what everyone knows about numbers.\n\nEveryone knows it.\n\nPost people just know that.\n\nThere are many other number systems, but the society decided to use the decimal number system as the default.\n\nWhy? I think the reason is that people have 2 hands (and 2 feet) with 5 fingers on them, and counting from 1 to 10 feels natural.\n\nWhen you reach 10, you start from scratch to reach 20.\n\nThat’s my guess, a pretty solid guess.\n\nThe decimal number system was invented by Indians and popularized by the Arabs, and it’s still called Hindu–Arabic number system.\n\nThe decimal number system is said to have base 10 because it uses 10 digits, from 0 to 9.\n\nDigits are positional, which means the digit holds a different weight (value) depending on the position.\n\nThe 1 digit in the number 10 has a different value than in the number 31, because in 10 it is put in position 2, and in 31 it is put in position 1 (counting from right).\n\nWhile this might sound obvious because you use this system since you were a child, not every number system works this way.\n\nThe roman number system, widely used in Europe since ancient Rome to the late middle ages, was still “base 10” but not positional. To represent 10 you used the letter X, to represent 100 you used C, to represent 1000 you used M.\n\nIn roman numerals, the number 243 in the decimal number system can be represented as CCXLIII.\n\nYou could not move letters around to change their meaning. Letters with a bigger value are always moved left compared to letters with less value. Except relatively to each letter, to form 4 using IV, for example (but this is another topic, let’s get back to decimal numbers).\n\nAny number in the decimal number system can be de-composed as the sum of other numbers, multiplied by the power of 10 depending on their position. Starting at position 0 from the right.\n\n$10^0$ equals to 1.\n\n$10^1$ equals to 10.\n\n$10^2$ equals to 100, and so on.\n\nIn the decimal number system:\n\n5 can be represented as $5\\times10^0$\n\n42 can be represented as $4\\times10^1 + 2\\times10^0$\n\n254 can be represented as $2\\times10^2 + 5\\times10^1 + 4\\times10^0$\n\n⭐️ install javascript into your brain with the JavaScript Masterclass. -26 days ⭐️"
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http://mathematicsmagazine.com/Articles/YupanaAdditionadnSubstraction.php | [
"",
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"Mathematics Magazine Home Articles Math Book Applications Contact Us",
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"Advertise Here. E-mail us your request for an advertising quote!\n Yupana Calculator Addition and Substractions during Inka Times by Liliana Usvat and Sascha Pugar A yupana is an abacus used to perform arithmetic operations dating back to the time of the Incas in 15 and 16 centuries. The results of these calculation were recorded on Quipu. A quipu, or knot-record (also called khipu), was a method used by the Incas and other ancient Andean cultures to keep records and communicate information. This simple and highly portable device achieved a surprising degree of precision and flexibility. It uses the Fibbonaci sequence 1, 2, 3, 5. The Inka system used seeds ( we are using coins) on the table bellow to do mathematical calculations. How the table work? We have rows of one, rows of two, rows of three and rows of five. We also have coloumns, They mean multiplication in base 10. For example one seed ( coin) in the row 2 and coloumn x1 means number 2. If we place a seed ( coin) in the row 3 and coloumn x 100 means 300. If we place a coin in the row 1 coloumn x 10,000 that number means 10,000. A coin in row 2 coloumn x 1000 means 2000. A coin in row 3 coloumn X 10 means 30. A coin in row 5 coloumn X10 means 50. The followig examples demonstrates the addtion and substraction of the followint numbers 418 + 327 = 745 We take the coins and place them on the table for 418 = 400+ 10 + 8 To write 400 : There is no 4 row on the table. we use 3 + 1 or 300 ( row 3 coloumn 100 and row 1 coloumn 100) to form 400. To write 10 : For the tens we use one coin in the row 1 coloumn x 10 To write 8 : we place 2 coins in row 5 coloumn 1 and row 3 Coloumn 1 We take the coins and place them on the table for 327 = 300 + 20 + 7 To write 300 : We place a coin on the row 3 coloumn x 100 To write 20: We place a coin on the row 2 coloumn x 10 To write 7: We place a coin on the row 5 coloumn x 1 and another coin on the row 2 Coloumn x1 To add the two numbers we do the followings: We take away the coins on the row 2 and 3 on coloumn x1 and replace it with one coin on the row 5 in coloumn x1 We have 15 wich are 3 coins worth of five in the coloumn x1 ( last coloumn) . We remove 2 coins worth of 5 and replace it with one of 10 (one coin in the row 1 coloumn x 10 ). We have 2 coins in the row 1 coloumn x 10 . We remove them and replace in with one coin in the row 2 coloumn x 10. two tens is the same as a twenty. One rule they used when they had 4 or 6 they used two different numbers that composed that number for example 4 = 3 + 1 instead of 4 =2 + 2 ot 6 = 5 + 1 instead of 6 = 3 + 3/ In the coloumn x 10 we reorganize 40 and write it as 30 + 10 so we have one coin in row 1 and another coin in row 3 for the coloumn x 10. It is easier to read that way. in the x 100 coloumn we have 1 coin on the first row and 2 coins on the row 3 that means 100 + 3000 + 300= 700. We rearange that in 500 + 200 ( one coin in row 2 and one coin in row 5, coloumn x 100). which is easier to read. The result is 745. Next addition is 1128 + 2364 = 3492 To write that we place the coins on the following positions 1128= 1000 + 100+ 20+ (5 + 3) 2364 = 2000 + 300 + (50+10) + ( 3+1) How to substract with yupana? We need two counters for this.We use pennies ( for positive numbers) and nickels for negative numbers). In the past they used two type of seeds. 212 - 139 = 73 212 = 200+ 10+ 2 One pennie on row 2 coloumn x100 , one pennie on row 1 coloumn x10, one pennie one row 2 coloumn x1 . We write the second number using nickels 139= 100 + 30 + ( 5 + 3 + 1) One nickel on row 1 coloumn x 100 , one nickel on row 3 coloumn x 10 , and one nickel in row 5, 3 and 1 on coloumn x 1. The nikels represent negative numbers and the pennies represent positive numbers. We take the pennies and breake down into smaller numbers. Two pennies break down in 2 of one and one pennie and one nickel on the coloumn x 1 cancel each other and are eliminated from the board. one 10 is equivalent to two five . On the 5 row we have one nickel and one pennie that cancel each other and are eliminated from the board. We need to eliminate all the nikels. we cannot leave any nickels on the board. 5 is broken donw in 2 and 3 and those ( coloumn x 1) 200 is broken down in 100 + 100 and one nikel and one pennie cancel each other and are eliminated from the board. 100= 50 + 50 50= 20+ 30 30 canlel out. The answer is 73. Another problem presented is : 6322 - 4816 = 1506 . First number is the positive pennies, the second number is the negative nickels. 6322 = (5000+ 1000) +300 + 20 + 2 4816= (3000+ 1000) + (500+300) +10 +( 5 + 1)",
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"Please see this attached video.\n \"Chance favors the prepared mind.\" - Louis Pasteur"
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"http://mathematicsmagazine.com/Articles/yupana_addition_Substraction.gif.jpg",
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https://km.home.focus.cn/gonglue/efdbf8e91062627a.html | [
"|\n\n# 电视墙纸怎么贴的步骤以及选择电视墙纸的技巧\n\n1、墙面处理\n\n2、测量尺寸\n\n3、切割墙板",
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"4、安装插座\n\n5、安装墙板\n\n1、市场上有很多类型的壁纸，有些是非织造材料，有些是PVC材料。对于不同的材料，价格也存在差异，铺路的整体效果也不同。从一些电视壁纸的图像，我们可以清楚地看到差异。因此，当业主选择时，应注意壁纸材料。如果要装饰样式，请选择正确的背景材质。\n\n2、市场上有很多壁纸。不同群体的不同类型和壁纸给消费者带来了许多障碍。不知道如何选择。此时，业主只需要根据房屋的装饰检查一些电视背景壁纸图案，然后结合整体效果来确定哪个壁纸最美。\n\n3、对于许多背景壁纸，选择合适的款式非常重要。一些壁纸展示了田园风格，而其他壁纸则反映了欧洲风格，而另一些则给人一种简单明了的感觉。业主必须根据背景墙纸选择正确的款式。如果它是一个现代简约的房子，绝对不可能选择结合的欧洲风格的壁纸，所以确定风格是很重要的。\n\n`声明：本文由入驻焦点开放平台的作者撰写，除焦点官方账号外，观点仅代表作者本人，不代表焦点立场错误信息举报电话： 400-099-0099，邮箱：[email protected]，或点此进行意见反馈，或点此进行举报投诉。`",
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"A B C D E F G H J K L M N P Q R S T W X Y Z\nA - B - C - D - E\n• A\n• 鞍山\n• 安庆\n• 安阳\n• 安顺\n• 安康\n• 澳门\n• B\n• 北京\n• 保定\n• 包头\n• 巴彦淖尔\n• 本溪\n• 蚌埠\n• 亳州\n• 滨州\n• 北海\n• 百色\n• 巴中\n• 毕节\n• 保山\n• 宝鸡\n• 白银\n• 巴州\n• C\n• 承德\n• 沧州\n• 长治\n• 赤峰\n• 朝阳\n• 长春\n• 常州\n• 滁州\n• 池州\n• 长沙\n• 常德\n• 郴州\n• 潮州\n• 崇左\n• 重庆\n• 成都\n• 楚雄\n• 昌都\n• 慈溪\n• 常熟\n• D\n• 大同\n• 大连\n• 丹东\n• 大庆\n• 东营\n• 德州\n• 东莞\n• 德阳\n• 达州\n• 大理\n• 德宏\n• 定西\n• 儋州\n• 东平\n• E\n• 鄂尔多斯\n• 鄂州\n• 恩施\nF - G - H - I - J\n• F\n• 抚顺\n• 阜新\n• 阜阳\n• 福州\n• 抚州\n• 佛山\n• 防城港\n• G\n• 赣州\n• 广州\n• 桂林\n• 贵港\n• 广元\n• 广安\n• 贵阳\n• 固原\n• H\n• 邯郸\n• 衡水\n• 呼和浩特\n• 呼伦贝尔\n• 葫芦岛\n• 哈尔滨\n• 黑河\n• 淮安\n• 杭州\n• 湖州\n• 合肥\n• 淮南\n• 淮北\n• 黄山\n• 菏泽\n• 鹤壁\n• 黄石\n• 黄冈\n• 衡阳\n• 怀化\n• 惠州\n• 河源\n• 贺州\n• 河池\n• 海口\n• 红河\n• 汉中\n• 海东\n• 怀来\n• I\n• J\n• 晋中\n• 锦州\n• 吉林\n• 鸡西\n• 佳木斯\n• 嘉兴\n• 金华\n• 景德镇\n• 九江\n• 吉安\n• 济南\n• 济宁\n• 焦作\n• 荆门\n• 荆州\n• 江门\n• 揭阳\n• 金昌\n• 酒泉\n• 嘉峪关\nK - L - M - N - P\n• K\n• 开封\n• 昆明\n• 昆山\n• L\n• 廊坊\n• 临汾\n• 辽阳\n• 连云港\n• 丽水\n• 六安\n• 龙岩\n• 莱芜\n• 临沂\n• 聊城\n• 洛阳\n• 漯河\n• 娄底\n• 柳州\n• 来宾\n• 泸州\n• 乐山\n• 六盘水\n• 丽江\n• 临沧\n• 拉萨\n• 林芝\n• 兰州\n• 陇南\n• M\n• 牡丹江\n• 马鞍山\n• 茂名\n• 梅州\n• 绵阳\n• 眉山\n• N\n• 南京\n• 南通\n• 宁波\n• 南平\n• 宁德\n• 南昌\n• 南阳\n• 南宁\n• 内江\n• 南充\n• P\n• 盘锦\n• 莆田\n• 平顶山\n• 濮阳\n• 攀枝花\n• 普洱\n• 平凉\nQ - R - S - T - W\n• Q\n• 秦皇岛\n• 齐齐哈尔\n• 衢州\n• 泉州\n• 青岛\n• 清远\n• 钦州\n• 黔南\n• 曲靖\n• 庆阳\n• R\n• 日照\n• 日喀则\n• S\n• 石家庄\n• 沈阳\n• 双鸭山\n• 绥化\n• 上海\n• 苏州\n• 宿迁\n• 绍兴\n• 宿州\n• 三明\n• 上饶\n• 三门峡\n• 商丘\n• 十堰\n• 随州\n• 邵阳\n• 韶关\n• 深圳\n• 汕头\n• 汕尾\n• 三亚\n• 三沙\n• 遂宁\n• 山南\n• 商洛\n• 石嘴山\n• T\n• 天津\n• 唐山\n• 太原\n• 通辽\n• 铁岭\n• 泰州\n• 台州\n• 铜陵\n• 泰安\n• 铜仁\n• 铜川\n• 天水\n• 天门\n• W\n• 乌海\n• 乌兰察布\n• 无锡\n• 温州\n• 芜湖\n• 潍坊\n• 威海\n• 武汉\n• 梧州\n• 渭南\n• 武威\n• 吴忠\n• 乌鲁木齐\nX - Y - Z\n• X\n• 邢台\n• 徐州\n• 宣城\n• 厦门\n• 新乡\n• 许昌\n• 信阳\n• 襄阳\n• 孝感\n• 咸宁\n• 湘潭\n• 湘西\n• 西双版纳\n• 西安\n• 咸阳\n• 西宁\n• 仙桃\n• 西昌\n• Y\n• 运城\n• 营口\n• 盐城\n• 扬州\n• 鹰潭\n• 宜春\n• 烟台\n• 宜昌\n• 岳阳\n• 益阳\n• 永州\n• 阳江\n• 云浮\n• 玉林\n• 宜宾\n• 雅安\n• 玉溪\n• 延安\n• 榆林\n• 银川\n• Z\n• 张家口\n• 镇江\n• 舟山\n• 漳州\n• 淄博\n• 枣庄\n• 郑州\n• 周口\n• 驻马店\n• 株洲\n• 张家界\n• 珠海\n• 湛江\n• 肇庆\n• 中山\n• 自贡\n• 资阳\n• 遵义\n• 昭通\n• 张掖\n• 中卫\n\n1室1厅1厨1卫1阳台\n\n1\n2\n3\n4\n5\n\n0\n1\n2\n\n1\n\n1\n\n0\n1\n2\n3",
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"报名成功，资料已提交审核",
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"A B C D E F G H J K L M N P Q R S T W X Y Z\nA - B - C - D - E\n• A\n• 鞍山\n• 安庆\n• 安阳\n• 安顺\n• 安康\n• 澳门\n• B\n• 北京\n• 保定\n• 包头\n• 巴彦淖尔\n• 本溪\n• 蚌埠\n• 亳州\n• 滨州\n• 北海\n• 百色\n• 巴中\n• 毕节\n• 保山\n• 宝鸡\n• 白银\n• 巴州\n• C\n• 承德\n• 沧州\n• 长治\n• 赤峰\n• 朝阳\n• 长春\n• 常州\n• 滁州\n• 池州\n• 长沙\n• 常德\n• 郴州\n• 潮州\n• 崇左\n• 重庆\n• 成都\n• 楚雄\n• 昌都\n• 慈溪\n• 常熟\n• D\n• 大同\n• 大连\n• 丹东\n• 大庆\n• 东营\n• 德州\n• 东莞\n• 德阳\n• 达州\n• 大理\n• 德宏\n• 定西\n• 儋州\n• 东平\n• E\n• 鄂尔多斯\n• 鄂州\n• 恩施\nF - G - H - I - J\n• F\n• 抚顺\n• 阜新\n• 阜阳\n• 福州\n• 抚州\n• 佛山\n• 防城港\n• G\n• 赣州\n• 广州\n• 桂林\n• 贵港\n• 广元\n• 广安\n• 贵阳\n• 固原\n• H\n• 邯郸\n• 衡水\n• 呼和浩特\n• 呼伦贝尔\n• 葫芦岛\n• 哈尔滨\n• 黑河\n• 淮安\n• 杭州\n• 湖州\n• 合肥\n• 淮南\n• 淮北\n• 黄山\n• 菏泽\n• 鹤壁\n• 黄石\n• 黄冈\n• 衡阳\n• 怀化\n• 惠州\n• 河源\n• 贺州\n• 河池\n• 海口\n• 红河\n• 汉中\n• 海东\n• 怀来\n• I\n• J\n• 晋中\n• 锦州\n• 吉林\n• 鸡西\n• 佳木斯\n• 嘉兴\n• 金华\n• 景德镇\n• 九江\n• 吉安\n• 济南\n• 济宁\n• 焦作\n• 荆门\n• 荆州\n• 江门\n• 揭阳\n• 金昌\n• 酒泉\n• 嘉峪关\nK - L - M - N - P\n• K\n• 开封\n• 昆明\n• 昆山\n• L\n• 廊坊\n• 临汾\n• 辽阳\n• 连云港\n• 丽水\n• 六安\n• 龙岩\n• 莱芜\n• 临沂\n• 聊城\n• 洛阳\n• 漯河\n• 娄底\n• 柳州\n• 来宾\n• 泸州\n• 乐山\n• 六盘水\n• 丽江\n• 临沧\n• 拉萨\n• 林芝\n• 兰州\n• 陇南\n• M\n• 牡丹江\n• 马鞍山\n• 茂名\n• 梅州\n• 绵阳\n• 眉山\n• N\n• 南京\n• 南通\n• 宁波\n• 南平\n• 宁德\n• 南昌\n• 南阳\n• 南宁\n• 内江\n• 南充\n• P\n• 盘锦\n• 莆田\n• 平顶山\n• 濮阳\n• 攀枝花\n• 普洱\n• 平凉\nQ - R - S - T - W\n• Q\n• 秦皇岛\n• 齐齐哈尔\n• 衢州\n• 泉州\n• 青岛\n• 清远\n• 钦州\n• 黔南\n• 曲靖\n• 庆阳\n• R\n• 日照\n• 日喀则\n• S\n• 石家庄\n• 沈阳\n• 双鸭山\n• 绥化\n• 上海\n• 苏州\n• 宿迁\n• 绍兴\n• 宿州\n• 三明\n• 上饶\n• 三门峡\n• 商丘\n• 十堰\n• 随州\n• 邵阳\n• 韶关\n• 深圳\n• 汕头\n• 汕尾\n• 三亚\n• 三沙\n• 遂宁\n• 山南\n• 商洛\n• 石嘴山\n• T\n• 天津\n• 唐山\n• 太原\n• 通辽\n• 铁岭\n• 泰州\n• 台州\n• 铜陵\n• 泰安\n• 铜仁\n• 铜川\n• 天水\n• 天门\n• W\n• 乌海\n• 乌兰察布\n• 无锡\n• 温州\n• 芜湖\n• 潍坊\n• 威海\n• 武汉\n• 梧州\n• 渭南\n• 武威\n• 吴忠\n• 乌鲁木齐\nX - Y - Z\n• X\n• 邢台\n• 徐州\n• 宣城\n• 厦门\n• 新乡\n• 许昌\n• 信阳\n• 襄阳\n• 孝感\n• 咸宁\n• 湘潭\n• 湘西\n• 西双版纳\n• 西安\n• 咸阳\n• 西宁\n• 仙桃\n• 西昌\n• Y\n• 运城\n• 营口\n• 盐城\n• 扬州\n• 鹰潭\n• 宜春\n• 烟台\n• 宜昌\n• 岳阳\n• 益阳\n• 永州\n• 阳江\n• 云浮\n• 玉林\n• 宜宾\n• 雅安\n• 玉溪\n• 延安\n• 榆林\n• 银川\n• Z\n• 张家口\n• 镇江\n• 舟山\n• 漳州\n• 淄博\n• 枣庄\n• 郑州\n• 周口\n• 驻马店\n• 株洲\n• 张家界\n• 珠海\n• 湛江\n• 肇庆\n• 中山\n• 自贡\n• 资阳\n• 遵义\n• 昭通\n• 张掖\n• 中卫",
null,
"",
null,
"• 手机",
null,
"• 分享\n• 设计\n免费设计\n• 计算器\n装修计算器\n• 入驻\n合作入驻\n• 联系\n联系我们\n• 置顶\n返回顶部"
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https://thriftyray.savingadvice.com/2021/09/ | [
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122.178.223.244\n)\n\n => Array\n(\n => 195.181.164.65\n)\n\n => Array\n(\n => 106.195.12.187\n)\n\n => Array\n(\n => 124.253.48.48\n)\n\n => Array\n(\n => 103.140.30.214\n)\n\n => Array\n(\n => 180.178.147.132\n)\n\n => Array\n(\n => 138.197.139.130\n)\n\n => Array\n(\n => 5.254.2.138\n)\n\n => Array\n(\n => 183.81.93.25\n)\n\n => Array\n(\n => 182.70.39.254\n)\n\n => Array\n(\n => 106.223.87.131\n)\n\n => Array\n(\n => 106.203.91.114\n)\n\n => Array\n(\n => 196.70.137.128\n)\n\n => Array\n(\n => 150.242.62.167\n)\n\n => Array\n(\n => 184.170.243.198\n)\n\n => Array\n(\n => 59.89.30.66\n)\n\n => Array\n(\n => 49.156.112.201\n)\n\n => Array\n(\n => 124.29.212.168\n)\n\n => Array\n(\n => 103.204.170.238\n)\n\n => Array\n(\n => 124.253.116.81\n)\n\n => Array\n(\n => 41.248.102.107\n)\n\n => Array\n(\n => 119.160.100.51\n)\n\n => Array\n(\n => 5.254.40.91\n)\n\n => Array\n(\n => 103.149.154.25\n)\n\n => Array\n(\n => 103.70.41.28\n)\n\n => Array\n(\n => 103.151.234.42\n)\n\n => Array\n(\n 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Array\n(\n => 39.37.185.133\n)\n\n => Array\n(\n => 123.17.79.174\n)\n\n => Array\n(\n => 180.178.146.215\n)\n\n => Array\n(\n => 41.248.83.40\n)\n\n => Array\n(\n => 103.255.4.79\n)\n\n => Array\n(\n => 103.39.119.233\n)\n\n => Array\n(\n => 85.203.44.24\n)\n\n => Array\n(\n => 93.74.18.246\n)\n\n => Array\n(\n => 95.142.120.51\n)\n\n => Array\n(\n => 202.47.42.57\n)\n\n => Array\n(\n => 41.202.219.253\n)\n\n => Array\n(\n => 154.28.188.182\n)\n\n => Array\n(\n => 14.163.178.106\n)\n\n => Array\n(\n => 118.185.57.226\n)\n\n => Array\n(\n => 49.15.141.102\n)\n\n => Array\n(\n => 182.189.86.47\n)\n\n => Array\n(\n => 111.88.68.79\n)\n\n => Array\n(\n => 156.146.59.8\n)\n\n => Array\n(\n => 119.152.62.82\n)\n\n => Array\n(\n => 49.207.128.103\n)\n\n => Array\n(\n => 203.212.30.234\n)\n\n => Array\n(\n => 41.202.219.254\n)\n\n => Array\n(\n => 103.46.203.10\n)\n\n => Array\n(\n => 112.79.141.15\n)\n\n => Array\n(\n => 103.68.218.75\n)\n\n => Array\n(\n => 49.35.130.14\n)\n\n => Array\n(\n => 172.247.129.90\n)\n\n => Array\n(\n => 116.90.74.214\n)\n\n => Array\n(\n => 180.178.142.242\n)\n\n => Array\n(\n => 111.119.183.59\n)\n\n => Array\n(\n => 117.5.103.189\n)\n\n => Array\n(\n => 203.110.93.146\n)\n\n => Array\n(\n => 188.163.97.86\n)\n\n => Array\n(\n => 124.253.90.47\n)\n\n => Array\n(\n => 139.167.249.160\n)\n\n => Array\n(\n => 103.226.206.55\n)\n\n => Array\n(\n => 154.28.188.191\n)\n\n => Array\n(\n => 182.190.197.205\n)\n\n => Array\n(\n => 111.119.183.33\n)\n\n => Array\n(\n => 14.253.254.64\n)\n\n => Array\n(\n => 117.237.197.246\n)\n\n => Array\n(\n => 172.105.53.82\n)\n\n => Array\n(\n => 124.253.207.164\n)\n\n => Array\n(\n => 103.255.4.33\n)\n\n => Array\n(\n => 27.63.131.206\n)\n\n => Array\n(\n => 103.118.170.99\n)\n\n => Array\n(\n => 111.119.183.55\n)\n\n => Array\n(\n => 14.182.101.109\n)\n\n => Array\n(\n => 175.107.223.199\n)\n\n => Array\n(\n => 39.57.168.94\n)\n\n => Array\n(\n => 122.182.213.139\n)\n\n => Array\n(\n => 112.79.214.237\n)\n\n => Array\n(\n => 27.6.252.22\n)\n\n => Array\n(\n => 89.163.212.83\n)\n\n => Array\n(\n => 182.189.23.1\n)\n\n => Array\n(\n => 49.15.222.253\n)\n\n => Array\n(\n => 125.63.97.110\n)\n\n => Array\n(\n => 223.233.65.159\n)\n\n => Array\n(\n => 139.99.159.18\n)\n\n => Array\n(\n => 45.118.165.137\n)\n\n => Array\n(\n => 39.52.2.167\n)\n\n => Array\n(\n => 39.57.141.24\n)\n\n => Array\n(\n => 27.5.32.145\n)\n\n => Array\n(\n => 49.36.212.33\n)\n\n => Array\n(\n => 157.33.218.32\n)\n\n => Array\n(\n => 116.71.4.122\n)\n\n => Array\n(\n => 110.93.244.176\n)\n\n => Array\n(\n => 154.73.203.156\n)\n\n => Array\n(\n => 136.158.30.235\n)\n\n => Array\n(\n => 122.161.53.72\n)\n\n => Array\n(\n => 106.203.203.156\n)\n\n => Array\n(\n => 45.133.7.22\n)\n\n => Array\n(\n => 27.255.180.69\n)\n\n => Array\n(\n => 94.46.244.3\n)\n\n => Array\n(\n => 43.242.178.157\n)\n\n => Array\n(\n => 171.79.189.215\n)\n\n => Array\n(\n => 37.117.141.89\n)\n\n => Array\n(\n => 196.92.32.64\n)\n\n => Array\n(\n => 154.73.203.157\n)\n\n => Array\n(\n => 183.83.176.14\n)\n\n => Array\n(\n => 106.215.84.145\n)\n\n => Array\n(\n => 95.142.120.12\n)\n\n => Array\n(\n => 190.232.110.94\n)\n\n => Array\n(\n => 179.6.194.47\n)\n\n => Array\n(\n => 103.62.155.172\n)\n\n => Array\n(\n => 39.34.156.177\n)\n\n => Array\n(\n => 122.161.49.120\n)\n\n => Array\n(\n => 103.58.155.253\n)\n\n => Array\n(\n => 175.107.226.20\n)\n\n => Array\n(\n => 206.81.28.165\n)\n\n => Array\n(\n => 49.36.216.36\n)\n\n => Array\n(\n => 104.223.95.178\n)\n\n => Array\n(\n => 122.177.69.35\n)\n\n => Array\n(\n => 39.57.163.107\n)\n\n => Array\n(\n => 122.161.53.35\n)\n\n => Array\n(\n => 182.190.102.13\n)\n\n => Array\n(\n => 122.161.68.95\n)\n\n => Array\n(\n => 154.73.203.147\n)\n\n => Array\n(\n => 122.173.125.2\n)\n\n => Array\n(\n => 117.96.140.189\n)\n\n => Array\n(\n => 106.200.244.10\n)\n\n => Array\n(\n => 110.36.202.5\n)\n\n => Array\n(\n => 124.253.51.144\n)\n\n => Array\n(\n => 176.100.1.145\n)\n\n => Array\n(\n => 156.146.59.20\n)\n\n => Array\n(\n => 122.176.100.151\n)\n\n => Array\n(\n => 185.217.117.237\n)\n\n => Array\n(\n => 49.37.223.97\n)\n\n => Array\n(\n => 101.50.108.80\n)\n\n => Array\n(\n => 124.253.155.88\n)\n\n => Array\n(\n => 39.40.208.96\n)\n\n => Array\n(\n => 122.167.151.154\n)\n\n => Array\n(\n => 172.98.89.13\n)\n\n => Array\n(\n => 103.91.52.6\n)\n\n => Array\n(\n => 106.203.84.5\n)\n\n => Array\n(\n => 117.216.221.34\n)\n\n => Array\n(\n => 154.73.203.131\n)\n\n => Array\n(\n => 223.182.210.117\n)\n\n => Array\n(\n => 49.36.185.208\n)\n\n => Array\n(\n => 111.119.183.30\n)\n\n => Array\n(\n => 39.42.107.13\n)\n\n => Array\n(\n => 39.40.15.174\n)\n\n => Array\n(\n => 1.38.244.65\n)\n\n => Array\n(\n => 49.156.75.252\n)\n\n => Array\n(\n => 122.161.51.99\n)\n\n => Array\n(\n => 27.73.78.57\n)\n\n => Array\n(\n => 49.48.228.70\n)\n\n => Array\n(\n => 111.119.183.18\n)\n\n => Array\n(\n => 116.204.252.218\n)\n\n => Array\n(\n => 73.173.40.248\n)\n\n => Array\n(\n => 223.130.28.81\n)\n\n => Array\n(\n => 202.83.58.81\n)\n\n => Array\n(\n => 45.116.233.31\n)\n\n => Array\n(\n => 111.119.183.1\n)\n\n => Array\n(\n => 45.133.7.66\n)\n\n => Array\n(\n => 39.48.204.174\n)\n\n => Array\n(\n => 37.19.213.30\n)\n\n => Array\n(\n => 111.119.183.22\n)\n\n => Array\n(\n => 122.177.74.19\n)\n\n => Array\n(\n => 124.253.80.59\n)\n\n => Array\n(\n => 111.119.183.60\n)\n\n => Array\n(\n => 157.39.106.191\n)\n\n => Array\n(\n => 157.47.86.121\n)\n\n => Array\n(\n => 47.31.159.100\n)\n\n => Array\n(\n => 106.214.85.144\n)\n\n => Array\n(\n => 182.189.22.197\n)\n\n => Array\n(\n => 111.119.183.51\n)\n\n => Array\n(\n => 202.47.35.57\n)\n\n => Array\n(\n => 42.108.33.220\n)\n\n => Array\n(\n => 180.178.146.158\n)\n\n => Array\n(\n => 124.253.184.239\n)\n\n => Array\n(\n => 103.165.20.8\n)\n\n => Array\n(\n => 94.178.239.156\n)\n\n => Array\n(\n => 72.255.41.142\n)\n\n => Array\n(\n => 116.90.107.102\n)\n\n => Array\n(\n => 39.36.164.250\n)\n\n => Array\n(\n => 124.253.195.172\n)\n\n => Array\n(\n => 203.142.218.149\n)\n\n => Array\n(\n => 157.43.165.180\n)\n\n => Array\n(\n => 39.40.242.57\n)\n\n => Array\n(\n => 103.92.43.150\n)\n\n => Array\n(\n => 39.42.133.202\n)\n\n => Array\n(\n => 119.160.66.11\n)\n\n => Array\n(\n => 138.68.3.7\n)\n\n => Array\n(\n => 210.56.125.226\n)\n\n => Array\n(\n => 157.50.4.249\n)\n\n => Array\n(\n => 124.253.81.162\n)\n\n => Array\n(\n => 103.240.235.141\n)\n\n => Array\n(\n => 132.154.128.20\n)\n\n => Array\n(\n => 49.156.115.37\n)\n\n => Array\n(\n => 45.133.7.48\n)\n\n => Array\n(\n => 122.161.49.137\n)\n\n => Array\n(\n => 202.47.46.31\n)\n\n => Array\n(\n => 192.140.145.148\n)\n\n => Array\n(\n => 202.14.123.10\n)\n\n => Array\n(\n => 122.161.53.98\n)\n\n => Array\n(\n => 124.253.114.113\n)\n\n => Array\n(\n => 103.227.70.34\n)\n\n => Array\n(\n => 223.228.175.227\n)\n\n => Array\n(\n => 157.39.119.110\n)\n\n => Array\n(\n => 180.188.224.231\n)\n\n => Array\n(\n => 132.154.188.85\n)\n\n => Array\n(\n => 197.210.227.207\n)\n\n => Array\n(\n => 103.217.123.177\n)\n\n => Array\n(\n => 124.253.85.31\n)\n\n => Array\n(\n => 123.201.105.97\n)\n\n => Array\n(\n => 39.57.190.37\n)\n\n => Array\n(\n => 202.63.205.248\n)\n\n => Array\n(\n => 122.161.51.100\n)\n\n => Array\n(\n => 39.37.163.97\n)\n\n => Array\n(\n => 43.231.57.173\n)\n\n => Array\n(\n => 223.225.135.169\n)\n\n => Array\n(\n => 119.160.71.136\n)\n\n => Array\n(\n => 122.165.114.93\n)\n\n => Array\n(\n => 47.11.77.102\n)\n\n => Array\n(\n => 49.149.107.198\n)\n\n => Array\n(\n => 192.111.134.206\n)\n\n => Array\n(\n => 182.64.102.43\n)\n\n => Array\n(\n => 124.253.184.111\n)\n\n => Array\n(\n => 171.237.97.228\n)\n\n => Array\n(\n => 117.237.237.101\n)\n\n => Array\n(\n => 49.36.33.19\n)\n\n => Array\n(\n => 103.31.101.241\n)\n\n => Array\n(\n => 129.0.207.203\n)\n\n => Array\n(\n => 157.39.122.155\n)\n\n => Array\n(\n => 197.210.85.120\n)\n\n => Array\n(\n => 124.253.219.201\n)\n\n => Array\n(\n => 152.57.75.92\n)\n\n => Array\n(\n => 169.149.195.121\n)\n\n => Array\n(\n => 198.16.76.27\n)\n\n => Array\n(\n => 157.43.192.188\n)\n\n => Array\n(\n => 119.155.244.221\n)\n\n => Array\n(\n => 39.51.242.216\n)\n\n => Array\n(\n => 39.57.180.158\n)\n\n => Array\n(\n => 134.202.32.5\n)\n\n => Array\n(\n => 122.176.139.205\n)\n\n => Array\n(\n => 151.243.50.9\n)\n\n => Array\n(\n => 39.52.99.161\n)\n\n => Array\n(\n => 136.144.33.95\n)\n\n => Array\n(\n => 157.37.205.216\n)\n\n => Array\n(\n => 217.138.220.134\n)\n\n => Array\n(\n => 41.140.106.65\n)\n\n => Array\n(\n => 39.37.253.126\n)\n\n => Array\n(\n => 103.243.44.240\n)\n\n => Array\n(\n => 157.46.169.29\n)\n\n => Array\n(\n => 92.119.177.122\n)\n\n => Array\n(\n => 196.240.60.21\n)\n\n => Array\n(\n => 122.161.6.246\n)\n\n => Array\n(\n => 117.202.162.46\n)\n\n => Array\n(\n => 205.164.137.120\n)\n\n => Array\n(\n => 171.237.79.241\n)\n\n => Array\n(\n => 198.16.76.28\n)\n\n => Array\n(\n => 103.100.4.151\n)\n\n => Array\n(\n => 178.239.162.236\n)\n\n => Array\n(\n => 106.197.31.240\n)\n\n => Array\n(\n => 122.168.179.251\n)\n\n => Array\n(\n => 39.37.167.126\n)\n\n => Array\n(\n => 171.48.8.115\n)\n\n => Array\n(\n => 157.44.152.14\n)\n\n => Array\n(\n => 103.77.43.219\n)\n\n => Array\n(\n => 122.161.49.38\n)\n\n => Array\n(\n => 122.161.52.83\n)\n\n => Array\n(\n => 122.173.108.210\n)\n\n => Array\n(\n => 60.254.109.92\n)\n\n => Array\n(\n => 103.57.85.75\n)\n\n => Array\n(\n => 106.0.58.36\n)\n\n => Array\n(\n => 122.161.49.212\n)\n\n => Array\n(\n => 27.255.182.159\n)\n\n => Array\n(\n => 116.75.230.159\n)\n\n => Array\n(\n => 122.173.152.133\n)\n\n => Array\n(\n => 129.0.79.247\n)\n\n => Array\n(\n => 223.228.163.44\n)\n\n => Array\n(\n => 103.168.78.82\n)\n\n => Array\n(\n => 39.59.67.124\n)\n\n => Array\n(\n => 182.69.19.120\n)\n\n => Array\n(\n => 196.202.236.195\n)\n\n => Array\n(\n => 137.59.225.206\n)\n\n => Array\n(\n => 143.110.209.194\n)\n\n => Array\n(\n => 117.201.233.91\n)\n\n => Array\n(\n => 37.120.150.107\n)\n\n => Array\n(\n => 58.65.222.10\n)\n\n => Array\n(\n => 202.47.43.86\n)\n\n => Array\n(\n => 106.206.223.234\n)\n\n => Array\n(\n => 5.195.153.158\n)\n\n => Array\n(\n => 223.227.127.243\n)\n\n => Array\n(\n => 103.165.12.222\n)\n\n => Array\n(\n => 49.36.185.189\n)\n\n => Array\n(\n => 59.96.92.57\n)\n\n => Array\n(\n => 203.194.104.235\n)\n\n => Array\n(\n => 122.177.72.33\n)\n\n => Array\n(\n => 106.213.126.40\n)\n\n => Array\n(\n => 45.127.232.69\n)\n\n => Array\n(\n => 156.146.59.39\n)\n\n => Array\n(\n => 103.21.184.11\n)\n\n => Array\n(\n => 106.212.47.59\n)\n\n => Array\n(\n => 182.179.137.235\n)\n\n => Array\n(\n => 49.36.178.154\n)\n\n => Array\n(\n => 171.48.7.128\n)\n\n => Array\n(\n => 119.160.57.96\n)\n\n => Array\n(\n => 197.210.79.92\n)\n\n => Array\n(\n => 36.255.45.87\n)\n\n => Array\n(\n => 47.31.219.47\n)\n\n => Array\n(\n => 122.161.51.160\n)\n\n => Array\n(\n => 103.217.123.129\n)\n\n => Array\n(\n => 59.153.16.12\n)\n\n => Array\n(\n => 103.92.43.226\n)\n\n => Array\n(\n => 47.31.139.139\n)\n\n => Array\n(\n => 210.2.140.18\n)\n\n => Array\n(\n => 106.210.33.219\n)\n\n => Array\n(\n => 175.107.203.34\n)\n\n => Array\n(\n => 146.196.32.144\n)\n\n => Array\n(\n => 103.12.133.121\n)\n\n => Array\n(\n => 103.59.208.182\n)\n\n => Array\n(\n => 157.37.190.232\n)\n\n => Array\n(\n => 106.195.35.201\n)\n\n => Array\n(\n => 27.122.14.83\n)\n\n => Array\n(\n => 194.193.44.5\n)\n\n => Array\n(\n => 5.62.43.245\n)\n\n => Array\n(\n => 103.53.80.50\n)\n\n => Array\n(\n => 47.29.142.233\n)\n\n => Array\n(\n => 154.6.20.63\n)\n\n => Array\n(\n => 173.245.203.128\n)\n\n => Array\n(\n => 103.77.43.231\n)\n\n => Array\n(\n => 5.107.166.235\n)\n\n => Array\n(\n => 106.212.44.123\n)\n\n => Array\n(\n => 157.41.60.93\n)\n\n => Array\n(\n => 27.58.179.79\n)\n\n => Array\n(\n => 157.37.167.144\n)\n\n => Array\n(\n => 119.160.57.115\n)\n\n => Array\n(\n => 122.161.53.224\n)\n\n => Array\n(\n => 49.36.233.51\n)\n\n => Array\n(\n => 101.0.32.8\n)\n\n => Array\n(\n => 119.160.103.158\n)\n\n => Array\n(\n => 122.177.79.115\n)\n\n => Array\n(\n => 107.181.166.27\n)\n\n => Array\n(\n => 183.6.0.125\n)\n\n => Array\n(\n => 49.36.186.0\n)\n\n => Array\n(\n => 202.181.5.4\n)\n\n => Array\n(\n => 45.118.165.144\n)\n\n => Array\n(\n => 171.96.157.133\n)\n\n => Array\n(\n => 222.252.51.163\n)\n\n => Array\n(\n => 103.81.215.162\n)\n\n => Array\n(\n => 110.225.93.208\n)\n\n => Array\n(\n => 122.161.48.200\n)\n\n => Array\n(\n => 119.63.138.173\n)\n\n => Array\n(\n => 202.83.58.208\n)\n\n => Array\n(\n => 122.161.53.101\n)\n\n => Array\n(\n => 137.97.95.21\n)\n\n => Array\n(\n => 112.204.167.123\n)\n\n => Array\n(\n => 122.180.21.151\n)\n\n => Array\n(\n => 103.120.44.108\n)\n\n)\n```\nArchive for September, 2021: Gramma Ray's Blog\n Layout: Blue and Brown (Default) Author's Creation\n Home > Archive: September, 2021\n\n# Archive for September, 2021\n\n## Hello Fall and all the fun that comes with it!\n\nOctober 1st, 2021 at 02:04 am\n\nI am so thankful that fall is here! With the hot, smoky summer behind us I can get out on our deck more and enjoy the hummingbirds and sunsets again! We have had some rain, which is awesome and the skies are back to blue.\n\nNow that school has started, my days are getting into a nice routine. I am able to focus more on stretching our food budget by using coupons, sales and aps like Ibotta. I am enjoying the challenge of feeding us as budget savvy as possible! (A much easier feat when I don't have a teen with me at the grocery store slipping in all the extras!!)\n\nI watch my youngest granddaughter (20 mos) every Monday. I love our Monday's together - she has so much energy and curiosity. This last Monday we went on a walk and found all the flowers and talked about the colors. She discovered some ornamental frogs in one yard and thought they were funny and pointed out an airplane overhead. I came home exhausted, but had such a happy heart by the end of the day.\n\nThankfully, the cash outflow has slowed down and we have stayed more within the budget this past several weeks- a trend I hope continues for as long as possible. It is much less stressful when the unexpected outputs aren't hitting regularly...which gives me time to breathe and rebuild the buffer account! I definitely feel more in control financially when the hub is working his three week rotation and the teen is in school.\n\nI am also finally getting back to minimalizing our home. Its been months since I have even had time to think about this but I am pulling it off the back burner now and creating a plan to use my free time to get some traction on this goal!\n\nI talked to all the kiddo's about Christmas this year and how our budget looks much different now that I am retired. I think everyone was fully on board with scaling back. With all the bio's, adopted, foster and inherited grandkids, we are at 17. My brain hurt thinking about even one gift for each. Instead we are transitioning to a family gift. Much more doable and kinder to my sanity. Instead of opening gifts, we will focus on games, food, crafts and making memories. Something we should have done years ago, actually. I don't have a clear picture of what this means, but I am excited about it none-the-less.\n\n## Breakthrough Covid\n\nSeptember 5th, 2021 at 12:09 am\n\nAugust was a blur. I got sick with Covid, even being fully vaccinated - slept lots, drank lots of water, lost all taste and smell and lost 15 lbs in two weeks. Thankfully, I am on the mend, symptoms are very mild at this point and I have now tested negative. I can honestly say, even fully vaccinated, Covid sucks - but thankfully mine stayed upper respiratory and I didnt have to deal with lower respiratory issues. The whole family got it at about the same time, all 17 of us. 4 were fully vaccinated and still got it, none of the cases became anywhere close to life threatening. (thank goodness).\n\nThings are going great with FD. We are planning to adopt her and her CASA is pushing for adoption to finish by Christmas. That is crazy fast if they can pull it off. FD turns 18 in July, so the clock is ticking. Even tho she will be 18, she wont finish high school until 2024- so she will continue to receive some services until then. In any case, the adoption is moving forward now and we are all excited to make her a permanent part of our family!\n\nFinancial wise, this has been more of a struggle than I anticipated. The hub is not allowed extra overtime at his new job, which is something we counted on from his previous job. In addition, the foster money has been cut by 2/3 since last April. These two factors leave a deficit in the budget each month of about \\$800-1000. Add to that all the extra expenses we have encountered, (water well, tires on our trailer, jacked up airline expenses, and several other unanticipated costs) and we have blown through much more of our emergency savings than I anticipated. I am considering working for my son part time to help supplement the deficit. But I am holding out to see how finances go once FD starts school. The hubs job is also saying more OT is coming this winter. Thankfully, we still have a nice cushion, but I dont want to deplete it anymore than we have above the current deficit.\n\nOtherwise, aside from Covid, retirment life has been great. I LOVE the options that the extra time allows. Its been a good summer. Altho we have had a consistent heat wave all summer added to very hazy smoke filled air. I am so ready for FALL and more energy to enjoy it."
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https://www.biostars.org/p/82605/ | [
"Question: Scatterplots Showing Correlation Between Gene Pairs\n1\nspaul850510 wrote:\n\nI have two dataframes\n\nx<-data.frame(matrix(rnorm(1000), nrow=1000, ncol=10))\ny<-data.frame(matrix(rnorm(1000), nrow=1000, ncol=10))\n\nwhere the rows are the genes and the columns are samples. I wanted to produce a scatterplot showing the correlation between all gene-pairs in \" x\" (x-axis) relative to the correlation of the same gene in \"y\" (y-axis).\n\nI transposed the dataframes to calculate gene corrleations and adopted the following code to produce the scatterplot:\n\nx<-t(x)\ny<-t(y)\n\nDF <- data.frame(x,y)\n\n# Calculate 2d density over a grid\nlibrary(MASS)\ndens <- kde2d(x,y)\n\n# create a new data frame of that 2d density grid\ngr <- data.frame(with(dens, expand.grid(x,y)), as.vector(dens\\$z))\nnames(gr) <- c(\"xgr\", \"ygr\", \"zgr\")\n\n# Fit a model\nmod <- loess(zgr~xgr*ygr, data=gr)\n\n# Apply the model to the original data to estimate density at that point DF\\$pointdens <- predict(mod, newdata=data.frame(xgr=x, ygr=y))\n\n# Draw plot\nlibrary(ggplot2)\nggplot(DF, aes(x=x,y=y, color=pointdens)) + geom_point() +scale_colour_gradientn(colours = rainbow(5)) + theme_bw()\n\nBut when I apply the following code to my transposed data, I get the error\n\n(list) object cannot be coerced to type 'double'\n\nThe plot am trying to produce look similar to this",
null,
"Are there other ways to do this?\n\nR visualization • 3.6k views\nmodified 6.0 years ago by UnivStudent380 • written 6.0 years ago by spaul850510\n1\nIrsan7.0k wrote:\n\nWhat you want to do is to plot an all-vs-all correlation matrix plot. There is a package called GGally that takes as input your matrix with genes as rows and columns as samples, calculates all the possible sample-vs-samples correlations and plots it with ggplot2. When you install it, make sure your R version is up to date, GGally depends on R version > 3.0\n\n1\nUnivStudent380 wrote:\n\nYou might also want to try using the stat_density2d function in ggplot2. It seems like it might be a simpler way of doing this. Probably would save you the trouble of doing this yourself with the 2d density. There are some good examples in the documentation which I've linked."
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https://www.arxiv-vanity.com/papers/1212.0250/ | [
"# a C0-Weak Galerkin Finite Element Method for the Biharmonic Equation\n\nLin Mu Department of Mathematics, Michigan State University, East Lansing, MI 48824 ([email protected] msu.edu) Junping Wang Division of Mathematical Sciences, National Science Foundation, Arlington, VA 22230 (). The research of Wang was supported by the NSF IR/D program, while working at National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation, Xiu Ye Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204 (). This research was supported in part by National Science Foundation Grant DMS-1115097. Shangyou Zhang Department of Mathematical Sciences University of Delaware, Newark, DE 19716 (szhang udel.edu)\n###### Abstract\n\nA -weak Galerkin (WG) method is introduced and analyzed for solving the biharmonic equation in 2D and 3D. A weak Laplacian is defined for functions in the new weak formulation. This WG finite element formulation is symmetric, positive definite and parameter free. Optimal order error estimates are established in both a discrete norm and the norm, for the weak Galerkin finite element solution. Numerical results are presented to confirm the theory. As a technical tool, a refined Scott-Zhang interpolation operator is constructed to assist the corresponding error estimate. This refined interpolation preserves the volume mass of order and the surface mass of order for the finite element functions in -dimensional space.\n\nw\n\neak Galerkin, finite element methods, weak Laplacian, biharmonic equation, triangular mesh, tetrahedral mesh, Scott-Zhang interpolation\n\n{AMS}\n\nPrimary, 65N30, 65N15; Secondary, 35B45\n\n## 1 Introduction\n\nWe consider the biharmonic equation of the form\n\n (1) Δ2u = f,inΩ, (2) u = g,on∂Ω, (3) ∂u∂n = ϕ,on∂Ω,\n\nwhere is a bounded polygonal or polyhedral domain in for . For the biharmonic problem (1) with Dirichlet and Neumann boundary conditions (2) and (3), the corresponding variational form is given by seeking satisfying and such that\n\n (4) (Δu,Δv)=(f,v)∀v∈H20(Ω),\n\nwhere is the subspace of consisting of functions with vanishing value and normal derivative on .\n\nThe conforming finite element methods for the forth order problem (4) require the finite element space be a subspace of . It is well known that constructing conforming finite elements is generally quite challenging, specially in three and higher dimensional spaces. Weak Galerkin finite element method, first introduce in (see also and for extensions), by design is to use nonconforming elements to relax the difficulty in the construction of conforming elements. Unlike the classical nonconforming finite element method where standard derivatives are taken on each element, the weak Galerkin finite element method relies on weak derives taken as approximate distributions for the functions in nonconforming finite element spaces. In general, weak Galerkin method refers to finite element techniques for partial differential equations in which differential operators (e.g., gradient, divergence, curl, Laplacian) are approximated by weak forms as distributions.\n\nA weak Galerkin method for the biharmonic equation has been derived in by using totally discontinuous functions of piecewise polynomials on general partitions of arbitrary shape of polygons/polyhedra. The key of the method lies in the use of a discrete weak Laplacian plus a stabilization that is parameter-free. In this paper, we will develop a new weak Galerkin method for the biharmonic equation (1)-(3) by redefining a weak Laplacian, denoted by , for finite element functions. Comparing with the WG method developed in , the -weak Galerkin finite element formulation has less number of unknowns due to the continuity requirement. On the other hand, due to the same continuity requirement, the -WG method allows only traditional finite element partitions (such as triangles/quadrilaterals in 2D), instead of arbitrary polygonal/polyhedral grids as allowed in .\n\nA suitably-designed interpolation operator is needed for the convergence analysis of the -weak Galerkin formulation. The Scott-Zhang operator turns out to serve the purpose well with a refinement. This paper shall introduce a refined version of the Scott-Zhang operator so that it preserves the volume mass up to order , and the surface mass up to order , when interpolating functions to the -finite element space:\n\n Q0 : H1(Ω)→C0-Pk+2, ∫T(v−Q0v)pdT =0∀p∈Pk+1−d(T), ∫E(v−Q0v)pdE =0∀p∈Pk+2−d(T),\n\nwhere is any triangle () or tetrahedron () in the finite element, and is an edge or a face-triangle of . With the operator , we can show an optimal order of approximation property of the -finite element space, under the constraints of weak Galerkin formulation. Consequently, we show optimal order of convergence in both a discrete norm and the norm, for the weak Galerkin finite element solution.\n\nThe biharmonic equation models a plate bending problem, which is one of the first applicable problems of the finite element method, cf. [9, 2, 10, 28]. The standard finite element method, i.e., the conforming element, requires a function space of piecewise polynomials. This would lead to a high polynomial degree [2, 26, 27, 24], or a macro-element [10, 6, 9, 12, 20, 25], or a constraint element (where the polynomial degree is reduced at inter-element boundary) [3, 19, 28]. Mixed methods for the biharmonic equation avoid using element by reducing the fourth order equation to a system of two second order equations, [1, 8, 11, 14, 17]. Many other different nonconforming and discontinuous finite element methods have been developed for solving the biharmonic equation. Morley element is a well known nonconforming element for its simplicity. interior penalty methods are studied in [5, 7, 15], which are similar to our -weak Galerkin method except there is no penalty parameter here.\n\n## 2 Weak Laplacian and discrete weak Laplacian\n\nLet be a bounded polyhedral domain in . We use the standard definition for the Sobolev space and their associated inner products , norms , and seminorms for any . When , we shall drop the subscript in the norm and in the inner product.\n\nLet be a triangle or a tetrahedron with boundary . A weak function on the region refers to a vector function such that and , where is the outward normal direction of on its boundary. The first component can be understood as the value of on and the second component represents the value on the boundary of . Note that may not be necessarily related to the trace of on . Denote by the space of all weak functions on ; i.e.,\n\n (5) W(T)={v={v0,vn}: v0∈L2(T),vn⋅n∈H−12(∂T)}.\n\nLet stand for the -inner product in , be the inner product in . For convenience, define as follows\n\n G2(T)={φ: φ∈H1(T), Δφ∈L2(T)}.\n\nIt is clear that, for any , we have . It follows that for any .\n\n###### Definition 2.1\n\nThe dual of can be identified with itself by using the standard inner product as the action of linear functionals. With a similar interpretation, for any , the weak Laplacian of is defined as a linear functional in the dual space of whose action on each is given by\n\n (6) (Δwv, φ)T=(v0, Δφ)T−⟨v0, ∇φ⋅n⟩∂T+⟨vn⋅n, φ⟩∂T,\n\nwhere is the outward normal direction to .\n\nThe Sobolev space can be embedded into the space by an inclusion map defined as follows\n\n iW(ϕ)={ϕ|T,∇ϕ|∂T},ϕ∈H2(T).\n\nWith the help of the inclusion map , the Sobolev space can be viewed as a subspace of by identifying each with . Analogously, a weak function is said to be in if it can be identified with a function through the above inclusion map. It is not hard to see that the weak Laplacian is identical with the strong Laplacian, i.e.,\n\n ΔwiW(v)=Δv\n\nfor smooth functions .\n\nNext, we introduce a discrete weak Laplacian operator by approximating in a polynomial subspace of the dual of . To this end, for any non-negative integer , denote by the set of polynomials on with degree no more than . A discrete weak Laplacian operator, denoted by , is defined as the unique polynomial that satisfies the following equation\n\n (7) (Δw,r,Tv, φ)T=(v0, Δφ)T−⟨v0, ∇φ⋅n⟩∂T+⟨vn⋅n, φ⟩∂T∀φ∈Pr(T).\n\nRecall that represent the on . Define . Obviously, . Since the quantity of interest is not but , we can replace by from now on to reduce the number of unknowns. Scalar represents .\n\n## 3 Weak Galerkin Finite Element Methods\n\nLet be a triangular () or a tetrahedral () partition of the domain with mesh size . Denote by the set of all edges or faces in , and let be the set of all interior edges or faces.\n\nSince with representing , obviously, is dependent on . To ensure a single values function on , we introduce a set of normal directions on as follows\n\n (8) Dh={ne: ne is unit and normal to e, e∈Eh}.\n\nThen, we can define a weak Galerkin finite element space for as follows\n\n (9) Vh={v={v0,vnne}: v0∈V0, vn|e∈Pk+1(e),e⊂∂T},\n\nwhere can be viewed as an approximation of and\n\n (10) V0={v∈H1(Ω);v|T∈Pk+2(T)}.\n\nDenote by a subspace of with vanishing traces; i.e.,\n\n V0h={v={v0,vnne}∈Vh,v0|e=0, vn|e=0, e⊂∂T∩∂Ω}.\n\nDenote by the trace of on from the component . It is easy to see that consists of piecewise polynomials of degree . Similarly, denote by the trace of from the component as piecewise polynomials of degree . Let be the discrete weak Laplacian operator on the finite element space computed by using (7) on each element for ; i.e.,\n\n (11) (Δw,kv)|T=Δw,k,T(v|T)∀v∈Vh.\n\nFor simplicity of notation, from now on we shall drop the subscript in the notation for the discrete weak Laplacian. We also introduce the following notation\n\n (Δwv,Δww)h=∑T∈Th(Δwv,Δww)T.\n\nFor any and in , we introduce a bilinear form as follows\n\n (12) s(uh,v)=∑T∈Thh−1T⟨∇u0⋅ne−un, ∇v0⋅ne−vn⟩∂T.\n\nThe stabilizer defined above is to enforce a connection between the normal derivative of along and its approximation .\n\n###### Weak Galerkin Algorithm 1\n\nA numerical approximation for (1)-(3) can be obtained by seeking satisfying and on and the following equation:\n\n (13) (Δwuh, Δwv)h+s(uh, v)=(f,v0)∀ v={v0, vnne}∈V0h,\n\nwhere and are the standard projections onto the trace spaces and , respectively.\n\n{lemma}\n\nThe weak Galerkin finite element scheme (13) has a unique solution.\n\n{proof}\n\nIt suffices to show that the solution of (13) is trivial if . To this end, assume and take in (13). It follows that\n\n (Δwuh,Δwuh)h+s(uh,uh)=0,\n\nwhich implies that on each element and on . We claim that holds true locally on each element . To this end, it follows from and (7) that for any we have\n\n 0=(Δwuh, φ)T = (u0, Δφ)T−⟨u0, ∇φ⋅n⟩∂T+⟨unne⋅n, φ⟩∂T = (Δu0,φ)T+⟨unne⋅n−∇u0⋅n, φ⟩∂T = (Δu0,φ)T,\n\nwhere we have used\n\n (15) unne⋅n−∇u0⋅n=±(un−∇u0⋅ne)=0\n\nin the last equality. The identity (3) implies that holds true locally on each element . This, together with on , shows that is a smooth harmonic function globally on . The boundary condition of and then implies that on , which completes the proof.\n\n## 4 Projections: Definition and Approximation Properties\n\nIn this section, we will introduce some locally defined projection operators corresponding to the finite element space with optimal convergent rates.\n\nLet be a special Scott-Zhang interpolation operator, to be defined in (46) in Appendix, such that for given , and for any ,\n\n (16) (Q0v, Δφ)T−⟨Q0v, ∇φ⋅n⟩∂T=(v, Δφ)T−⟨v, ∇φ⋅n⟩∂T,∀φ∈Pk(T),\n\nand for\n\n (17) (∑T∈Thh2s∥u−Q0u∥2s,T)1/2≤Chk+3∥u∥k+3.\n\nNow we can define an interpolation operator from to the finite element space such that on the element , we have\n\n (18) Qhu={Q0u,(Qn(∇u⋅ne))ne},\n\nwhere is defined in (46) and is the projection onto , for each . In addition, let be the local projection onto . For any we have\n\n (ΔwQhu, φ)T = (Q0u, Δφ)T−⟨Q0u, ∇φ⋅n⟩∂T+⟨Qn(∇u⋅ne)ne⋅n,φ⟩∂T = (u,Δφ)T−⟨u, ∇φ⋅n⟩∂T+⟨∇u⋅n, φ⟩∂T = (Δu, φ)T=(QhΔu, φ)T,\n\nwhich implies\n\n (19) ΔwQhu=Qh(Δu).\n\nThe above identity indicates that the discrete weak Laplacian of a projection of is a good approximation of the Laplacian of .\n\nLet be an element with as an edge or a face triangle. It is well known that there exists a constant such that for any function\n\n (20) ∥g∥2e≤C(h−1T∥g∥2T+hT∥∇g∥2T).\n\nDefine a mesh-dependent semi-norm in the finite element space as follows\n\n (21) |||v|||2=(Δwv, Δwv)h+s(v,v),v∈Vh.\n\nUsing (20), we can derive the following estimates which are useful in the convergence analysis for the WG-FEM (13).\n\n{lemma}\n\nLet and . Then there exists a constant such that the following estimates hold true.\n\n (22) (23) ∑T∈Thh−1T|⟨(∇Q0w)⋅ne−Qn(∇w⋅ne),∇v0⋅ne−vn⟩∂T| ≤Chk+1∥w∥k+3|||v|||.\n{proof}\n\nTo derive (22), we can use the Cauchy-Schwarz inequality, (15), the trace inequality (20), and the definition of to obtain\n\n ∑T∈Th|⟨Δw−QhΔw,(∇v0−vnne)⋅n⟩∂T| ≤C⎛⎝∑T∈Th(∥Δw−QhΔw∥2T+h2T∥∇(Δw−QhΔw)∥2T)⎞⎠12|||v||| ≤Chk+1∥w∥k+3|||v|||.\n\nAs to (23), we have from the definition of , the Cauchy-Schwarz inequality, the trace inequality (20), and (17) that\n\n ∑T∈Thh−1T|⟨(∇Q0w)⋅ne−Qn(∇w⋅ne),∇v0⋅ne−vn⟩∂T| =∑T∈Thh−1T|⟨(∇Q0w)⋅ne−∇w⋅ne,∇v0⋅ne−vn⟩∂T| ≤⎛⎝∑T∈Thh−1T∥(∇Q0w−∇w)⋅ne∥2∂T⎞⎠12⎛⎝∑T∈Thh−1T∥∇v0⋅ne−vn∥2∂T⎞⎠12 ≤C⎛⎝∑T∈Th(h−2T∥∇Q0w−∇w∥2T+∥∇Q0w−∇w∥21,T)⎞⎠12|||v||| ≤Chk+1∥w∥k+3|||v|||.\n\nThis completes the proof.\n\n## 5 An Error Equation\n\nWe first derive an equation that the projection of the exact solution, , shall satisfy. Using (7), the integration by parts, and (19), we obtain\n\n (ΔwQhu,Δwv)T = (v0,Δ(ΔwQhu))T+⟨(vnne)⋅n, ΔwQhu⟩∂T−⟨v0,∇(ΔwQhu)⋅n⟩∂T = (Δv0, ΔwQhu)T+⟨v0,∇(ΔwQhu)⋅n⟩∂T−⟨∇v0⋅n,ΔwQhu⟩∂T +⟨(vnne)⋅n,ΔwQhu⟩∂T−⟨v0,∇(ΔwQhu)⋅n⟩∂T = (Δv0,ΔwQhu)T−⟨(∇v0−vnne)⋅n,ΔwQhu⟩∂T = (Δv0,QhΔu)T−⟨(∇v0−vnne)⋅n,QhΔu⟩∂T = (Δu,Δv0)T−⟨(∇v0−vnne)⋅n,QhΔu⟩∂T,\n\nwhich implies that\n\n (24) (Δu,Δv0)T = (ΔwQhu,Δwv)T+⟨(∇v0−vnne)⋅n,QhΔu⟩∂T.\n\nNext, it follows from the integration by parts that\n\n (Δu,Δv0)T=(Δ2u,v0)T+⟨Δu,∇v0⋅n⟩∂T−⟨∇(Δu)⋅n,v0⟩∂T.\n\nSumming over all and then using the identity we arrive at\n\n ∑T∈Th(Δu,Δv0)T = (f,v0)+∑T∈Th⟨Δu,∇v0⋅n⟩∂T = (f,v0)+∑T∈Th⟨Δu,(∇v0−vnne)⋅n⟩∂T.\n\nCombining the above equation with (24) leads to\n\n (25) (ΔwQhu,Δwv)h = (f,v0)+∑T∈Th⟨Δu−QhΔu,(∇v0−vnne)⋅n⟩∂T.\n\nDefine the error between the finite element approximation and the projection of the exact solution as\n\n eh:={e0, enne}={Q0u−u0, (Qn(∇u⋅ne)−un)ne}.\n\nTaking the difference of (25) and (13) gives the following error equation\n\n (Δweh,Δwv)h+s(eh,v) = ∑T∈Th⟨Δu−QhΔu,(∇v0−vnne)⋅n⟩∂T + s(Qhu,v)∀v∈V0h.\n\nObserve that the definition of the stabilization term indicates that\n\n s(Qhu,v) = ∑T∈Thh−1T⟨(∇Q0u)⋅ne−Qn(∇u⋅ne), ∇v0⋅ne−vn⟩∂T.\n\n## 6 Error Estimates\n\nFirst, we derive an estimate for the error function in the natural triple-bar norm, which can be viewed as a discrete -norm.\n\n{theorem}\n\nLet be the weak Galerkin finite element solution arising from (13) with finite element functions of order . Assume that the exact solution of (1)-(3 ) is regular such that . Then, there exists a constant such that\n\n (27)\n{proof}\n\nBy letting in the error equation (5), we obtain the following identity\n\n = ∑T∈Th⟨Δu−QhΔu,(∇e0−enne)⋅n⟩∂T + ∑T∈Thh−1T⟨(∇Q0u⋅ne−Qn(∇u⋅ne), ∇e0⋅ne−en⟩∂T.\n\nUsing the estimates of Lemma 4, we arrive at\n\nwhich implies (27). This completes the proof of the theorem.\n\nNext, we would like to provide an estimate for the standard norm of the first component of the error function . Let us consider the following dual problem\n\n (28) Δ2w = e0inΩ, (29) w = 0,on∂Ω, (30) ∇w⋅n = 0on∂Ω.\n\nThe regularity assumption of the dual problem implies the existence of a constant such that\n\n (31) ∥w∥4≤C∥e0∥.\n{theorem}\n\nLet be the weak Galerkin finite element solution arising from (13) with finite element functions of order . Assume that the exact solution of (1)-(3) is regular such that and the dual problem (28)-(30) has the regularity. Then, there exists a constant such that\n\n (32) ∥Q0u−u0∥≤Chk+3∥u∥k+3.\n{proof}\n\nTesting (28) by error function and then using the integration by parts gives\n\n ∥e0∥2 = (Δ2w,e0) = ∑T∈Th(Δw,Δe0)T−∑T∈Th⟨Δw,∇e0⋅n⟩∂T = ∑T∈Th(Δw,Δe0)T−∑T∈Th⟨Δw,(∇e0−enne)⋅n⟩∂T.\n\nUsing (24) with in the place of , we can rewrite the above equation as follows\n\n ∥e0∥2 = (ΔwQhw,Δweh)h−∑T∈Th⟨Δw−QhΔw,(∇e0−enne)⋅n⟩∂T.\n\nIt now follows from the error equation (5) that\n\n (ΔwQhw,Δweh)h = ∑T∈Th⟨Δu−QhΔu,(∇Q0w−Qn(∇w⋅ne)ne)⋅n⟩∂T − s(eh,Qhw)+s(Qhu,Qhw).\n\nCombining the two equations above gives\n\n ∥e0∥2 = −∑T∈Th⟨Δw−QhΔw,(∇e0−enne)⋅n⟩∂T +∑T∈Th⟨Δu−QhΔu,(∇Q0w−Qn(∇w⋅ne)ne)⋅n⟩∂T −s(eh,Qhw)+s(Qhu,Qhw).\n\nUsing the estimates of Lemma 4, we can bound two terms on the right-hand side of the equation above as follows\n\n ∑T∈Th|⟨Δw−QhΔw,(∇e0−enne)⋅n⟩∂T| ≤ |s(eh,Qhw)| ≤\n\nIt follows from (15) and the definition of and that\n\n (34) ∥(∇Q0w−Qn(∇w⋅ne)ne)⋅ne∥∂T = ∥(∇Q0w−Qn(∇w⋅ne)ne)⋅n∥∂T =∥∇Q0w⋅n−Qn(∇w⋅n)∥∂T ≤ ∥∇Q0w⋅n−∇w⋅n∥∂T +∥∇w⋅n−Qn(∇w⋅n)∥∂T ≤ C∥∇Q0w⋅n−∇w⋅n∥∂T.\n\nUsing (34) and (20), we have\n\n ∑T∈Th⟨Δu−QhΔu,(∇Q0w−Qn(∇w⋅ne)ne)⋅n⟩∂T ≤C⎛⎝∑T∈Thh∥Δu−QhΔu∥2∂T⎞⎠1/2⎛⎝∑T∈Thh−1∥(∇Q0w−∇w)⋅n∥2∂T⎞⎠1/2 ≤C⎛⎝∑T∈Th(∥Δu−QhΔu∥2T+h2T∥∇(Δu−QhΔu)∥2T)⎞⎠12⋅ ⎛⎝∑T∈Th(h−2∥∇Q0w−∇w∥2T+∥∇(∇Q0w−∇w)∥2T)⎞⎠12 ≤Chk+3∥u∥k+3∥w∥4.\n\nUsing (34) and (20), we have\n\n s(Qhu,Qhw) = ∑T∈Thh−1⟨∇(Q0u)⋅ne−Qn(∇u⋅ne), ∇(Q0w)⋅ne−Qn(∇w⋅ne)⟩∂T ≤ Chk+3∥u∥k+3∥w∥4.\n\nSubstituting all above estimates into (6) and using (27) give\n\n ∥e0∥2≤Chk+3∥u∥k+3∥w∥4.\n\nCombining the above estimate with (31), we obtain the desired error estimate (32).\n\n## 7 Numerical Experiments\n\nThis section shall report some numerical results for the weak Galerkin finite element methods for the following biharmonic equation:\n\n (35) Δ2u = f in Ω, (36) u = g on ∂Ω, (37) ∂u∂n = ψ on ∂Ω.\n\nFor simplicity, all the numerical experiments are conducted by using or in the finite element space in (9).\n\nIf (i.e. ), the above equation can be simplified as\n\n (Δwv,ϕ)T=⟨vnne⋅n, ϕ⟩∂T.\n\nThe error for the -WG solution will be measured in four norms defined as follows:\n\n H1 semi-norm: ∥v−v0∥21 =∑T∈Th∫T|∇v−∇v0|2dx. Discrete H2 norm: =∑T∈Th∥Δwv∥2T+∑T∈Thh−1∥∇v0⋅ne−vn∥2"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9016449,"math_prob":0.9910634,"size":13196,"snap":"2022-27-2022-33","text_gpt3_token_len":2936,"char_repetition_ratio":0.16275015,"word_repetition_ratio":0.055107526,"special_character_ratio":0.22582601,"punctuation_ratio":0.10302535,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9962156,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-15T06:15:25Z\",\"WARC-Record-ID\":\"<urn:uuid:8b0e9177-5374-4d81-8bd5-41cde8b11576>\",\"Content-Length\":\"1049506\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:18349373-ddc8-42bb-b8fa-d1ee4739123b>\",\"WARC-Concurrent-To\":\"<urn:uuid:4999fa97-5624-40ed-b472-72ef69115bc8>\",\"WARC-IP-Address\":\"104.21.14.110\",\"WARC-Target-URI\":\"https://www.arxiv-vanity.com/papers/1212.0250/\",\"WARC-Payload-Digest\":\"sha1:NHYFT72YAISHKROE62CEHEWM6SOXGH6J\",\"WARC-Block-Digest\":\"sha1:X5YNAQMYZVJRP7IZKVDRZSRFTPRYJUCC\",\"WARC-Truncated\":\"length\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572161.46_warc_CC-MAIN-20220815054743-20220815084743-00445.warc.gz\"}"} |
https://oeis.org/A334060 | [
"The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.",
null,
"Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)\n A334060 Triangle read by rows: T(n,k) is the number of set partitions of {1..3n} into n sets of 3 with k disjoint strings of adjacent sets, each being a contiguous set of elements 1\n 1, 0, 1, 7, 3, 0, 219, 56, 5, 0, 12861, 2352, 183, 4, 0, 1215794, 174137, 11145, 323, 1, 0, 169509845, 19970411, 1078977, 30833, 334, 0, 0, 32774737463, 3280250014, 153076174, 4056764, 55379, 206, 0, 0, 8400108766161, 730845033406, 29989041076, 727278456, 10341101, 67730, 70, 0, 0 (list; table; graph; refs; listen; history; text; internal format)\n OFFSET 0,4 COMMENTS Number of configurations with k connected components (consisting of polyomino matchings) in the generalized game of memory played on the path of length 3n, see [Young]. LINKS Donovan Young, Polyomino matchings in generalised games of memory and linear k-chord diagrams, arXiv:2004.06921 [math.CO], 2020. FORMULA G.f.: Sum_{j>=0} (3*j)! * y^j * (1-(1-z)*y)^(3*j+1) / (j! * 6^j * (1-(1-z)*y^2)^(3*j+1)). EXAMPLE Triangle begins: 1; 0, 1; 7, 3, 0; 219, 56, 5, 0; 12861, 2352, 183, 4, 0; ... For n=2 and k=1 the configurations are (1,5,6),(2,3,4) and (1,2,6),(3,4,5) (i.e. configurations with a single contiguous set) and (1,2,3),(4,5,6) (i.e. two adjacent contiguous sets); hence T(2,1) = 3. MATHEMATICA CoefficientList[Normal[Series[Sum[y^j*(3*j)!/6^j/j!*((1-y*(1-z))/(1-y^2*(1-z)))^(3*j+1), {j, 0, 20}], {y, 0, 20}]], {y, z}] PROG (PARI) T(n)={my(v=Vec(sum(j=0, n, (3*j)! * x^j * (1-(1-y)*x + O(x*x^n))^(3*j+1) / (j! * 6^j * (1-(1-y)*x^2 + O(x*x^n))^(3*j+1))))); vector(#v, i, Vecrev(v[i], i))} { my(A=T(8)); for(n=1, #A, print(A[n])) } CROSSREFS Row sums are A025035. Column k=0 is column 0 of A334056. Cf. A079267, A334056, A334057, A334058, A334059, A325753. Sequence in context: A327574 A253905 A154159 * A083803 A136595 A111475 Adjacent sequences: A334057 A334058 A334059 * A334061 A334062 A334063 KEYWORD nonn,tabl AUTHOR Donovan Young, May 26 2020 STATUS approved\n\nLookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam\nContribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent\nThe OEIS Community | Maintained by The OEIS Foundation Inc.\n\nLast modified September 20 04:04 EDT 2020. Contains 337264 sequences. (Running on oeis4.)"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.5771696,"math_prob":0.9800958,"size":2044,"snap":"2020-34-2020-40","text_gpt3_token_len":892,"char_repetition_ratio":0.09607843,"word_repetition_ratio":0.006042296,"special_character_ratio":0.5797456,"punctuation_ratio":0.28224298,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9922819,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T08:09:13Z\",\"WARC-Record-ID\":\"<urn:uuid:9d2475a0-0a3c-4c91-8930-17929db0e53b>\",\"Content-Length\":\"19772\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4a48811d-5bd0-4f78-8fbd-8cc41d3d3c61>\",\"WARC-Concurrent-To\":\"<urn:uuid:092c363a-9e62-480e-8c82-214a34cbaea6>\",\"WARC-IP-Address\":\"104.239.138.29\",\"WARC-Target-URI\":\"https://oeis.org/A334060\",\"WARC-Payload-Digest\":\"sha1:AMGDXOJLVHCKANC2WCUJD2RUKSEDMJBT\",\"WARC-Block-Digest\":\"sha1:DHEU7HBOWHGGYFKGFI6NLG5MQOKCNNE5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400196999.30_warc_CC-MAIN-20200920062737-20200920092737-00078.warc.gz\"}"} |
http://esik.magtu.ru/en/18-english/no-4-25-dec-2014/108-14.html | [
"Abstract\n\nQuality management system of asynchronous electric drive assumes knowledge of exact values of its parameters. However, some of the parameters (this applies mainly to the rotor axis) can not be directly obtained. This paper describes a mathematical algorithm based on which one can estimate the physical parameters of the traction induction motor by measuring the currents and voltages of the stator windings and the rotor speed. At the base of the algorithm is the mathematical model of an asynchronous traction drive with the limitations provided in the fixed reference frame (α, β, 0). An example of a mathematical model of the traction drive was given where the values, which could not be obtained directly, were excluded. Some parameters were determined using the method of least squares. To find the remaining parameters it was proposed to use a genetic algorithm. This approach can be used to construct an observer for the correction of the existing controls in the movement control system of traction rolling stock.\n\nKeywords\n\nAsynchronous traction drive, the method of least squares, genetic algorithm.\n\nMezentsev Nickolaj Viktorovich – Ph.D. (Eng.), Associate Professor, National Technical University \"Kharkov Polytechnic Institute\", Kharkov, Ukraine.\n\nGejko Gennadij Viktorovich – Assistant Professors, postgraduate student, National Technical University \"Kharkov Polytechnic Institute\", Kharkov, Ukraine. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.63121504,"math_prob":0.7558035,"size":3209,"snap":"2020-34-2020-40","text_gpt3_token_len":825,"char_repetition_ratio":0.10858034,"word_repetition_ratio":0.004524887,"special_character_ratio":0.22156435,"punctuation_ratio":0.22861843,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95542353,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-28T09:48:59Z\",\"WARC-Record-ID\":\"<urn:uuid:26c9271c-3991-46ed-9447-0edae8f515b3>\",\"Content-Length\":\"18398\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4ee66841-f988-43b2-8ff1-d55d83772695>\",\"WARC-Concurrent-To\":\"<urn:uuid:42cd3472-2442-4841-853c-c876d5fb3cdb>\",\"WARC-IP-Address\":\"46.61.169.58\",\"WARC-Target-URI\":\"http://esik.magtu.ru/en/18-english/no-4-25-dec-2014/108-14.html\",\"WARC-Payload-Digest\":\"sha1:M7Z6Y7BIUMXBNMOVL6EDIQ7GWCOV5FFI\",\"WARC-Block-Digest\":\"sha1:6X4FB7RE7JEQJAEZZEYRM35UN4D55ATK\",\"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-20200928073028-20200928103028-00104.warc.gz\"}"} |
https://blog.xrds.acm.org/2018/01/power-bisection-logic/ | [
"# The Power of Bisection Logic\n\nBisection or Binary logic is an example of a simple yet powerful idea in computer science that has today become an integral part of every computer scientist’s arsenal. It stands synonymous to logarithmic time complexity that is no less than music to a programmer’s ears. Yet, the technique never fails to surprise us with all the creative ways it has been put to use to solve some tricky programming problems. This blog-post will endeavour to acquaint you with a few such problems and their solutions to delight you and make you appreciate it’s ingenuity and efficacy.\n\nI’d like to thank Janin Koch for her help and efforts.\n\nThe blog-post has the following flow of events:\n\n Defining the Logic Applications to Diverse Programming Problems Concluding Discussion\n\nYou can choose to skip the ‘Applications to Diverse Programming Problems’ section to directly read the problems without having to go through the preliminary discussion on the basics of the technique.\n\nPrerequisites\n\nI assume that the reader is familiar with Big-Oh notation used for describing the time complexity requirements of programs. For running and understanding the code, the reader must be familiar with programming in Python.\n\nI. Defining the Logic\n\nLet’s begin by first describing what the technique stands for and why do we use it? Consider an imaginary game with a small number of paper cups of varying heights, presented to you. Each cup has a sticker on it that tells the exact height of the cup. The sticker is however hidden from you. The cups are arranged in front of you in the order of increasing height (as depicted in Fig. 1).",
null,
"Fig. 1: A visual depiction of the paper cup game.\n\nAt a time, only a single cup can be picked and the value printed on it’s sticker can be noted. Suppose you’re asked to locate a cup having a particular height. How will you accomplish the task? (without using a measuring scale of course!)\n\nYou’ll probably begin by intuitively picking up a cup whose height you guess to be the same as the one you’re looking for. If it isn’t the case, you’ll then likely select the cup next in line to either to the left or to the right depending upon whether the selected cup’s height overshot or fell short of the target height. You might end up repeating the last step some more times till you find the cup with the correct height.",
null,
"Fig. 2: Paper cup example – the approach to locate the cup of target size (25cm).\n\nWhat is useful about the above approach? The fact that the cups are ordered by increasing height helps eliminate a portion of the cup sequence that would otherwise have to be considered, making the search space smaller (as depicted in Fig. 2).\n\nLet us now modify the game to make it more challenging – let all the cups be of the same height, with the labels representing arbitrary integers. The cups are arranged in the order of non-decreasing (described in Fig. 3) label values.\n\nFig. 3: A non-decreasing sequence of integers refers to a sequence similar to the ones depicted above.\n\nWith no obvious cue available to us such as the heights of the cups, the task now is to find a particular target label among the cups. What should our approach be? The most basic or naive approach, referred to as Linear Search, is to start picking-up cups one at a time from one end and search for the target label. If the number of cups is small (as assumed initially), it is a feasible approach. However, if it isn’t the case, then checking every cup against the target label may no longer be a feasible proposition. The amount of time to locate the desired cup will be proportional to the number of cups present, which can be a large number thus making our exercise timewise expensive.\n\nLet’s add another constraint to the target here – how will you find a particular label value in the least number of steps possible?\n\nCan we do better than Linear search? And if so, what feature of the problem can we make use of to help realize the goal?\n\nUpon pondering over it, you may observe that the cup labels are in a non-decreasing order. What does that convey to us? Simply, that the facet, which we had earlier identified as part of the initial technique i.e. elimination of cups to next consider, is still applicable. Yet how it is utilized here, is different. Think of a way to ascertain which direction (left or right) we must proceed to locate the cup with target label. We might pick any cup up, note the label and make the choice. Out of the remaining cups to consider, how will we proceed? By repeating the same step i.e. randomly choose a cup, check if it’s the desired one, if not, compare label value to ascertain in which direction to apply the step again next. Yet we ought to remember the search has to be conducted in the least number of steps. This isn’t addressed by the random choice at the beginning of the step. What can we do to regulate the behaviour? Select an element at a particular place in the sequence with the best choice being the middle-most element.\n\nThe strategy above halves the input space each time we conduct the step. It is thus called the Bisection Search or Binary Search (Illustrated in Fig. 4). Like any search strategy, we can make it return an integer value, typically -1, to indicate the absence of the target from the given sequence. Note that it is a prerequisite that the input sequence must be sorted for the Bisection Search to be applicable. The order of sort can either be non-increasing or non-decreasing.\n\nBinary Search represents an algorithm belonging to the paradigm of Divide-&-Conquer (D&C) algorithms that operate by dividing the input space into distinct, smaller spaces (referred to as the ‘Divide’ step) and repeating the process till the sub-problems obtained are small enough to be solved directly (referred to as the ‘Conquer’ step). Binary Search however does not strictly adhere to the structure of a typical D&C algorithm as it does away with the ‘Combine’ step that is responsible for combining the solutions to the sub-problems to obtain solutions to the original problem.",
null,
"Fig. 4: A sample step-wise execution of Bisection Search to locate the correct target label.\n\nPython code for Bisection Search:\n\n``````# Author - Abhineet Saxena\ndef bis_search(iseq, xkey, lidx, ridx):\n\"\"\"\nA Recursive method that performs Bisection Search over the supplied array.\n:param iseq: a sorted, non-decreasing sequence of integers.\n:param xkey: The target value to be searched for in the given sequence\n:param lidx: left index marking the left-most edge of the sub-sequence under consideration.\n:param ridx: right index marking the right-most edge of the sub-sequence under consideration.\n:return: A non-negative integer specifying the location of the target value.\n\"\"\"\nif lidx <= ridx:\nmid_idx = lidx + (ridx - lidx)//2 # Calculation of the middle index\nmid_val = iseq[mid_idx]\nif mid_val == xkey:\nreturn mid_idx\nelif mid_val < xkey:\nreturn bis_search(iseq, xkey, mid_idx + 1, ridx)\nelse:\nreturn bis_search(iseq, xkey, lidx, mid_idx - 1)\nelse:\nreturn -1\n\nprint(\"Specify a sorted integral sequence (non-decreasing):\\n\")\n# The input must be of the form “x y z ...” where the alphabets x,y,z\n# etc. represent separate integers.\n# Example sequence “-99 -3 0 2 7 10 12 56 64 89”\nip_arr = [int(elem) for elem in input().split(' ')]\nlen_arr = len(ip_arr)\nprint(bis_search(ip_arr, 78, 0, len_arr - 1))\n```\n```\n\nA peculiarity can be observed in the code above in the middle index calculation step. The statement is equivalent to ‘floor( (lidx + ridx)/2 )’ yet the specified way above takes care of addition overflows that occur when i) the number of elements in the array is very large (a billion or more) and ii) the sum of lidx and ridx exceeds the maximum positive integral value that can be represented by the programming language.\n\nII. Applications to Programming Problems\n\nNow that we’ve covered the basic algorithm, let’s take up the programming problems one by one:\n\n[Before commencing however, I’d like for the reader to try and think of a possible solution approach for each of the presented problems without immediately referring to the solution descriptions provided – even if it means writing messy pseudocode for the approach on a piece of paper. It won’t be much of a challenge if you never give it a try.]\n\n1)\n\nProblem statement:\n\nIn a sorted array ‘A’ of distinct elements, find the index of an element such that A[idx] = idx.\n\nDescription:\n\nAs an example, consider a sequence such as the one depicted below:",
null,
"We can observe that at the 8th index of the array, the value of the element is 8, i.e. A = 8. How to locate such an element programmatically in the best possible way?\n\nSolution Approach:\n\nThe most naive approach one can think of is to test every element of the array for equality with its index. But we can observe that for a large number of elements, the approach becomes infeasible. It’s complexity is O(N) in the worst case for an N element input array.\n\nFor a better approach, we need to observe a pattern that associates the indices with the stored values. In the example array above, we can see that for every index value less than 8, the value stored in A at that index is less than the index value. Eg.(value stored at idx < idx) -15 < 3; -3 < 4; 0 < 5; 2 < 6 and 5 < 7. Also, for every index value greater than 8, value stored at the index is greater than the index (27 > 9; 54 > 10).\n\nNow how can we utilize the above-found observation to arrive at the solution? Since the behaviour of the relation linking the array indices with their stored values changes at the location of the desired index, we can modify our binary search procedure to then use this change in order to seek towards the desired index location.\n\n```# Author - Abhineet Saxena\ndef mod_bsrch(iseq, lidx, ridx):\n\"\"\"\nA Recursive method that performs Modified Bisection Search to locate\nthe element such that iseq[idx] == idx.\n\"\"\"\nif lidx <= ridx:\n# Calculation of the middle element\nmid_idx = lidx + (ridx - lidx)//2\nmid_val = iseq[mid_idx]\n# Checks for the presence of the desired element\nif mid_val == mid_idx:\nreturn mid_idx\nelif mid_val < mid_idx:\n# We're to the left of the target element -> move right\nreturn mod_bsrch(iseq, mid_idx + 1, ridx)\nelse:\n# We're to the right of the target element -> move left\nreturn mod_bsrch(iseq, lidx, mid_idx - 1)\nelse:\nreturn -1\nprint(\"Specify a sorted integral sequence (non-decreasing):\\n\")\nip_arr = [int(elem) for elem in input().split(' ')]\nlen_arr = len(ip_arr)\nprint(mod_bsrch(ip_arr, 0, len_arr - 1))\n```\n\nThe complexity of the above solution approach is O(logN) for any worst-case input of size N.\n\n2)\n\nProblem Statement:\n\nIn an unsorted sequence of integers, find the position of the end of the integer array when the rest of array is populated with some symbol (eg. \\$) which is known to us such that (a) the end of the array isn’t known and (b), the problem variant, where the size of array is not specified.\n\nDescription:\n\nIn the first problem (a), the size of the array is provided to us. A sample array looks like the following:",
null,
"Here, the index 4 is the correct answer as it refers to the array index where the last integer element can be found. All elements beyond it are marked by dollar symbol. A possible input can be an array that only comprises of dollar symbols. How does our search find the desired index or report if none can be found?\n\nFor the problem variant (b), the size of the array isn’t available to us. The end of the array has been demarcated by a continuous, indefinite sequence of some symbol e.g. ‘#’. A sample input array may appear as follows:",
null,
"For the above array, the correct answer is 4.\n\nSolution:\n\n(a)\n\nTo perform better than linear search, we again need to identify a pattern that can make our bisection search feasible to apply. Although it may seem contradictory but bisection search is applicable here. The caveat being that we aren’t searching for a particular integer element. Instead, we’re trying to locate the end of the integer array.\n\nThe decision event for our search is firstly if the concerned element is an integer or not. If the element is an integer such that it’s subsequent element is the ‘\\$’ symbol, we’ve found the desired index value. If the subsequent element is not the ‘\\$’ symbol, the search then proceeds towards the right subsequence.\n\nIf the concerned element is the \\$ symbol, we first check if the prior element is an integral value. If it is so, we return the index of the element. If it is a dollar symbol, we then consider the left sub-sequence.\n\n``````# Author - Abhineet Saxena\ndef mod_bsrch_p2a(iseq, slen, lidx, ridx):\n\"\"\"\nA Recursive method that performs Modified Bisection Search to locate\nthe end of integer array over the specified input.\n\"\"\"\nif lidx <= ridx:\n# Calculation of middle index\nmid_idx = lidx + (ridx - lidx)//2\nmid_val = iseq[mid_idx]\nif mid_val != '\\$':\nif mid_idx != slen - 1:\nif iseq[mid_idx + 1] == '\\$':\nreturn mid_idx\nif iseq[mid_idx + 1] != '\\$':\nreturn mod_bsrch_p2a(iseq, slen, mid_idx + 1, ridx)\nelse:\nreturn mid_idx\nelif mid_val == '\\$':\nif mid_idx != 0:\nif iseq[mid_idx - 1] != '\\$':\nreturn mid_idx - 1\nelse:\nreturn mod_bsrch_p2a(iseq, slen, lidx, mid_idx - 1)\nelse:\nreturn -1\nelse:\nreturn -1\nprint(\"Specify the test input sequence:\\n\")\n# Sample inputs:\n# (#1) -1 0 7 8 65 23 \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$\n# (#2) \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$\n# (#3) 1 56 78 0 -3 5 -9 45\n# List comprehension to process the input\nip_arr = [int(elem) if elem != '\\$' else elem for elem in input().split(' ')]\n# Store the array length\nlen_arr = len(ip_arr)\n# Make the function call\nprint(mod_bsrch_p2a(ip_arr, len_arr, 0, len_arr - 1)) ```\n```\n\n(b)\n\nHere, we’re confronted with the problem of not knowing the size or bound of the array at the beginning. Our procedure requires the right index to mark the end of the sequence under consideration. What can we do in such a case? Firstly, we become aware of the need to delimit our search space in order for Bisection Search to be applicable. How can it be effected? Here, we use an idea called ‘Unbounded’ or ‘Exponentialbisection search. We first explore the input space by skipping elements with incremental powers of two to reach a point where the value at the current index exceeds the target value, or in our case, crosses the boundary of the integer array. We then apply Bisection Search over this reduced search space to find the desired index.",
null,
"Fig. 5: The search proceeds by exponentially moving from the indicated indices till it lands up on the 8th index whereby the while loop concludes. The lidx, ridx are supplied as indices marking the sub-array that is further evaluated using the ‘bsrch_proc()’ method.\n\n``````# Author - Abhineet Saxena\ndef bsrch_proc(iseq, lidx, ridx):\nif lidx <= ridx:\nmid_idx = lidx + (ridx - lidx) // 2 # Calculation of the middle index\nmid_val = iseq[mid_idx]\nif mid_val != '\\$' and mid_val != '#':\ntval = iseq[mid_idx + 1]\nif tval == '\\$' or tval == '#':\nreturn mid_idx\nelse:\nreturn bsrch_proc(iseq, mid_idx + 1, ridx)\nelse:\nreturn bsrch_proc(iseq, lidx, mid_idx - 1)\nelse:\nreturn -1\ndef mod_bsrch_p2b(iseq):\n\"\"\"\nA Recursive method that performs Exponential Bisection Search to locate the end of integer array\nover the specified input.\n\"\"\"\nlidx, ridx, cidx = *3\ntidx = 0\ncval = iseq[tidx]\nwhile True:\n# If considered element is an integer\nif cval != '\\$' and cval != '#':\n# If subsequent elem. not an integer\nif iseq[tidx + 1] == '\\$' or iseq[tidx + 1] == '#':\nreturn tidx\nelse:\n# Traverse input array by moving at indices at position 2^i where i is inc.’t at each iteration\ntidx = 2 ** cidx\ncval = iseq[tidx]\nlidx = ridx\nridx = tidx\ncidx += 1\nelse:\nbreak\nif ridx == 0:\nreturn -1\nelse:\nreturn bsrch_proc(iseq, lidx, ridx)\nprint(\"Specify the test input sequence:\\n\")\n# Sample inputs:\n# (#1) -1 0 7 8 65 23 \\$ \\$ \\$ \\$ # # # # # # # # # # # # # # # # # # # # #\n# (#2) \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ \\$ # # # # # # # # # # # # # # # # # # # # #\n# (#3) 1 56 78 0 -3 5 -9 45 # # # # # # # # # # # # # # # # # # # # #\n# A list comprehension to process input\nip_arr = [int(elem) if (elem != '\\$' and elem != '#') else elem for elem in input().split(' ')]\n# Store the array length\nlen_arr = len(ip_arr)\n# Make the function call\nprint(mod_bsrch_p2b(ip_arr))``````\n\nThe complexity of both the solutions above remains O(logN). The solution for problem (b) has the same complexity as that of (a). It is so due to the logarithmic nature of the initial ‘exploration’ process followed by a smaller, logarithmic cost incurred over the smaller sub-sequence that is finally searched for the target index.\n\n3)\n\nProblem Statement:\n\nThe Peak finding problem.\n\nDescription:\n\nA ‘peak’ element in a given array is an element which is no less than its neighbours. As an example, consider the below given array.",
null,
"If we plot the array elements on a graph, we’ll obtain the following:",
null,
"We can clearly observe there are two peak elements above, namely 25 and 37.\n\nAlso, for a given sequence such as {25, 10, 6} or {7, 18, 37}, the respective peak elements 25 and 37 are corner elements. If a sequence such as {12, 12, 12} is considered, then any of the elements is a peak.\n\nLet us however, consider a more strict definition for a peak element.\n\nConstraint [C1] – Let it be defined as one that is greater than its neighbours. In such a case, for the last sequence that we observed, there won’t be any peak elements. Similarly, for a sequence such as {6, 25, 25, 13}, there won’t be any peak elements possible.\n\nConstraint [C2] – We also assume that the given input sequence only consists of distinct elements.\n\nThe task at hand is thus to write a program that can locate any such element (satisfying C1) given an array ( satisfying C2) or convey the absence of such an element if none is present.\n\nSolution:\n\nAlthough C1 makes the problem appear to be a tough nut to crack, yet C2 works in our favour. If the input consists of distinct elements, the presence of a peak element is guaranteed (think about it – out of any given ‘n’ distinct elements, won’t the largest one definitely be a peak?). Since, like always, we’re looking to perform (asymptotically) better than a linear scan of the sequence, we need to identify some characteristic of the problem that can then be leveraged to possibly apply the Bisection Logic.\n\nConsider an input sequence such that we sample the middle element which is not a peak. Since all elements are distinct, it can’t be be equal to any of the neighbours. It is thus lesser in value as compared to one or both of its neighbours. Thus if we next choose a sub-array with a neighbour greater in value, only two cases can occur – either all elements are arranged monotonically (in strict increasing or decreasing order), or not (i.e. an unsorted sequence of elements is present) in the subsequence. In the former case, the corner element of the subsequence will be a peak whereas in the latter case, presence of a peak element is guaranteed (an element greater than the mid element is present in subarray – its other neighbour can either be greater in value or less than it. In either case, we’ll be able to locate a peak).\n\nThus the condition to evaluate in the procedure will be to test the element under consideration if its peak or not. The outcome will determine the choice of subarray we’ll next evaluate. Since we’ll always choose the subarray with a larger neighbour with respect to the mid, we’ll eventually converge at an element which will be a peak.\n\n``````# Author - Abhineet Saxena\ndef mod_bsrch_p3(iseq, slen, lidx, ridx):\n\"\"\"\nA recursive impl. of modified Bisection Search to find a peak element in the given array.\n\"\"\"\nif ridx - lidx <= 1: if ridx - lidx == 0 or iseq[lidx] > iseq[ridx]:\nreturn iseq[lidx]\nelse:\nreturn iseq[ridx]\nelse:\nmidx = lidx + (ridx - lidx)//2\nmidval = iseq[midx]\nif midval > iseq[midx - 1]:\nif midval > iseq[midx + 1]:\nreturn midval\nelse:\nreturn mod_bsrch_p3(iseq, slen, midx + 1, ridx)\nelse:\nreturn mod_bsrch_p3(iseq, slen, lidx, midx - 1)\nprint(\"Specify an input integral sequence:\\n\")\n\"\"\"\nSample input sequences -\n(#1) 6 15 25 19 10 22 37 31 24 16\n(#2) 2 13 26 37 45 58 69 75\n(#3) 1 76 18 -3 24 28 37 36 20 11\n\"\"\"\nip_arr = [int(elem) for elem in input().split(' ')]\nlen_arr = len(ip_arr)\nprint(mod_bsrch_p3(ip_arr, len_arr, 0, len_arr - 1))\n```\n```\n\nThe above solution can be tweaked to solve the peak finding problem for the relaxed definition of the peak element.\n\nAn interesting problem is to locate the peak (C1) in a given array where constraint C2 isn’t present. Here, bisection search based implementation is no longer applicable because ascertaining the absence of a peak element will require complete traversal of the array.\n\n4)\n\nProblem Statement:\n\nFinding frequency of elements in a sorted array with duplicates in less than O(n) time.\n\nDescription:\n\nNote – Constraint [D]: If the number of distinct elements is equal to some constant ‘c’, only then will an approach with the desired complexity be feasible.\n\nOtherwise, a Linear Scan based approach will be appropriate.\n\nFor example, consider a sequence such as {1, 1, 6, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12}. Here, the number of distinct elements is 5. It is referred to as a constant here as it is not functionally dependent on the total number of elements N in the input array i.e., c != <not equal> f(N) where f is some function. If however, every element is distinct, then c == N which means it is no longer a constant.\n\nThe approach feasibility is better understood in an asymptotic sense. For very large sized inputs ( N > 100,000), a marked difference in performance will be observed with the technique that you formulate subject to the input array satisfying [D].\n\nThe task is thus to output the frequency of all the elements present in the given array.\n\nSolution:\n\nLet’s try and identify any observable pattern that can be leveraged to apply bisection search. Consider the following example:\n\n{1, 1, 1, 1 ,1, 7, 7, 7, 7, 7, 10, 10, 10, 10, 10, 10, 10, 24, 24, 24, 24, 24, 24, 24, 24}\n\nWe have continuous runs of elements here as the input array is sorted. The length of each run is therefore equal to the difference b/w the indices on the first and last element of the run. But how to ascertain the right end index of each run? For the purpose, recall how we applied the exponential Binary Search concept to explore a sequence whose end wasn’t known. We’ll use the same concept here to find the ending index of each run. Thereafter a Python dictionary will be used to store the frequency values for all the distinct elements.\n\n``````# Author - Abhineet Saxena\ndef bsrch_util(iseq, xkey, slen, lidx, ridx):\nmidx = lidx + (ridx - lidx)//2\nmidval = iseq[midx]\nif midval == xkey:\nif midx != slen - 1:\nif iseq[midx + 1] != xkey:\nreturn midx\nelse:\nreturn bsrch_util(iseq, xkey, slen, midx + 1, ridx)\nelse:\nreturn slen - 1\nelse:\nif midx != 0:\nif iseq[midx - 1] == xkey:\nreturn midx - 1\nelse:\nreturn bsrch_util(iseq, xkey, slen, lidx, midx - 1)\nelse:\nreturn 0\ndef mod_bsrch_p4(iseq, slen):\n“””\nA modified exponential Bisection search impl. that calculates the frequency of all the elements in the array.\n“””\nelemc = iseq\niterv, delta = 0, 0\nfidx1, fidx2 = 0, 0\nfreq_dict = {}\nwhile fidx2 < slen - 1:\nfvar = 0\niterv, lidx, ridx, tidx = * 4\n# Performs exponential Bisection search\nwhile fvar == 0 and tidx + delta < slen:\nif iseq[tidx + delta] == elemc:\ntidx = 2 ** iterv\niterv += 1\nlidx = ridx\nridx = tidx + delta\nelse:\nfvar = 1\n# For single elements, the frequency is recorded differently, bypassing the call to utility function\nif iterv == 1:\nfreq_dict[elemc] = 1\nfidx1, fidx2, delta = [ridx] * 3\nif fidx2 < slen - 1:\nelemc = iseq[fidx2]\nelse:\nfreq_dict[iseq[slen - 1]] = 1\ncontinue\n# Call to Utility function for finding the right end of the run of element duplicates\nif tidx + delta <= slen - 1:\nfidx2 = bsrch_util(iseq, elemc, slen, lidx, ridx)\nelse:\nfidx2 = bsrch_util(iseq, elemc, slen, lidx, slen - 1)\n# Setting the frequency counts correctly after locating the end of duplicate element run\nif fidx2 != slen - 1:\ndelta = fidx2 + 1\nif fidx1 == 0:\nfreq_dict.setdefault(elemc, fidx2 - fidx1 + 1)\nelse:\nfreq_dict.setdefault(elemc, fidx2 - fidx1 + 1)\nelemc = iseq[delta]\nfidx1 = delta\nelse:\nfreq_dict.setdefault(elemc, fidx2 - fidx1 + 1)\nreturn freq_dict\nprint(\"Specify the test input sequence:\\n\")\n\"\"\"\nSample Inputs -\n(#1) - 1 2 2 3 3 3\n(#2) - 4 4 4 7 7 7 7 7 9 9 9 9 9 9 11 11 11 11 11 11\n(#3) - 1 1 1 1 1 1 7 7 7 7 7 7 7 7 7 10 10 10 10 10 10 10 10 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24\n(#4) - 1 1 1 3 4 4 4\n(#5) - 1 1 1 2 2 2 2 2 2 3 4 4 4 5 6 6 6 6 6 6 6 6 6 6 6 6 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 10 10\n(#6) - 1 2 3 4 5 6 7 8 9\n(#7) - 1 1 1 1 1 1 1 2\n\"\"\"\nip_arr = [int(elem) for elem in input().split(' ')] # A list comprehension to process input\nlen_arr = len(ip_arr) # Store the array length\nprint(mod_bsrch_p4(ip_arr, len_arr)) # Make the function call\n```\n```\n\nThe above solution has a logarithmic time complexity as O(c*logN) with ‘c’ as defined previously. The upper bound presented isn’t tight, yet for the purpose of describing the asymptotic behaviour of the method above, it should suffice. Note we require ‘c’ to be a constant else the complexity no longer remains logarithmic.\n\nConclusion\n\nWe experienced the versatility of Bisection Search in solving some distinct problems and realized the need to think creatively when it comes to solving programming problems (Programming, afterall, is an art form, as stated by Donald Knuth himself in his seminal books carrying a similar name). Yet the above covers only a portion of what’s possible with this technique. You can refer to for more examples of how the technique has been applied to solve problems with presenting even more challenges for you to contemplate over. A great utilization of the technique is offered by the Bisection Section for calculating roots of equations. You can learn more about it at . Some variations over the technique can be tried out at to gauge their workings and efficacy. A discussion on the time complexity of the technique has been omitted for now.\n\nI thus hope you can better appreciate programmers, engineers and computer scientists as artists who express their ideas and creativity by way of writing code. I’d like to have sparked the vision within you to become one yourself.\n\nReferences\n\nThis entry was posted in Algorithms, Computer Science Education, xrds and tagged , , , , , by Abhineet Saxena. Bookmark the permalink.",
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http://trac.clermont.cemagref.fr/wiki/SvmViabilityKernelApproximationBis | [
"Warning: Can't synchronize with repository \"(default)\" (/var/svn/SVMViabilityController does not appear to be a Subversion repository.). Look in the Trac log for more information.\n\n# SVM Viability Kernel Approximation (2/3)\n\n## SVM Viability kernel approximation algorithm\n\n### Approximating viability kernel with a classification procedure\n\nConsider a grid Kh covering the viability constraint set, with h the maximal distance between the points. At the first iteration, all the points xh of the grid are viable. We also suppose that G is mu-Lipschitz.\n\nAt iteration n+1, the algorithm remove the points that clearly go outside the generalisation of the approximation of the viability kernel at step n. If a point is viable at iteration n+1, we attribute to it a +1 label and -1 otherwise. We obtain the classification function l that define the current approximation of the viability kernel:",
null,
"Algorithm We iteratively define the sets such that:",
null,
"Then, if the classification procedure respects some conditions,",
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"The algorithm thus provides an outer approximation of viability kernels.\n\n### Approximating viability kernel with support vector machines\n\nWe consider SVMs as a relevant classification procedure in this context. The main advantage of choosing SVMs is that they provide a kind of barrier function of the viability kernel boundary, which enables one to use gradient techniques to find a viable control.\n\nInitialization: discretization of the state space and initialization of non-viable examples\n\nIteration n+1: SVMn is available\n\nIteration n+1: we use a gradient method to find a viable control (possibility to extend to several time steps)",
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"Iteration n+1: update the labels from SVMn and define SVMn+1\n\n## SVM Viability controller\n\nThe idea is to keep the same control u0 until the point at the next step reaches",
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"where Delta is a security distance on the approximation (the algorithm provides an outer approximation and it is thus necessary to reduces the approximation in order to stay within it). When the point reaches the security distance, find a viable control using the gradient descent of function f.\n\nIt is possible to define more or less cautious controller, anticipating on several time steps.\n\n## Fulfilment of algorithm convergence condition\n\nOne condition the SVMs must respect in order to proove the algorithm convergence is that the SVM produce no missclassified points. In practice, one must choose an high C-value in the SVM settings and a \"good\" alpha value (in case of using a gaussian kernel). An algorithm has been developped at LISC, in order to set automatically the SVM C-value:\n\n[Problem and viability] previous page",
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https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/03%3A_Vectors/3.12%3A_Vectors_(Summary) | [
"# 3.12: Vectors (Summary)\n\n•",
null,
"• OpenStax\n• OpenStax\n$$\\newcommand{\\vecs}{\\overset { \\rightharpoonup} {\\mathbf{#1}} }$$ $$\\newcommand{\\vecd}{\\overset{-\\!-\\!\\rightharpoonup}{\\vphantom{a}\\smash {#1}}}$$$$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\id}{\\mathrm{id}}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$ $$\\newcommand{\\kernel}{\\mathrm{null}\\,}$$ $$\\newcommand{\\range}{\\mathrm{range}\\,}$$ $$\\newcommand{\\RealPart}{\\mathrm{Re}}$$ $$\\newcommand{\\ImaginaryPart}{\\mathrm{Im}}$$ $$\\newcommand{\\Argument}{\\mathrm{Arg}}$$ $$\\newcommand{\\norm}{\\| #1 \\|}$$ $$\\newcommand{\\inner}{\\langle #1, #2 \\rangle}$$ $$\\newcommand{\\Span}{\\mathrm{span}}$$$$\\newcommand{\\AA}{\\unicode[.8,0]{x212B}}$$\n\n## Key Terms\n\n anticommutative property change in the order of operation introduces the minus sign antiparallel vectors two vectors with directions that differ by 180° associative terms can be grouped in any fashion commutative operations can be performed in any order component form of a vector a vector written as the vector sum of its components in terms of unit vectors corkscrew right-hand rule a rule used to determine the direction of the vector product cross product the result of the vector multiplication of vectors is a vector called a cross product; also called a vector product difference of two vectors vector sum of the first vector with the vector antiparallel to the second direction angle in a plane, an angle between the positive direction of the x-axis and the vector, measured counterclockwise from the axis to the vector displacement change in position distributive multiplication can be distributed over terms in summation dot product the result of the scalar multiplication of two vectors is a scalar called a dot product; also called a scalar product equal vectors two vectors are equal if and only if all their corresponding components are equal; alternately, two parallel vectors of equal magnitudes magnitude length of a vector null vector a vector with all its components equal to zero orthogonal vectors two vectors with directions that differ by exactly 90°, synonymous with perpendicular vectors parallel vectors two vectors with exactly the same direction angles parallelogram rule geometric construction of the vector sum in a plane polar coordinate system an orthogonal coordinate system where location in a plane is given by polar coordinates polar coordinates a radial coordinate and an angle radical coordinate distance to the origin in a polar coordinate system resultant vector vector sum of two (or more) vectors scalar a number, synonymous with a scalar quantity in physics scalar component a number that multiplies a unit vector in a vector component of a vector scalar equation equation in which the left-hand and right-hand sides are numbers scalar product the result of the scalar multiplication of two vectors is a scalar called a scalar product; also called a dot product scalar quantity quantity that can be specified completely by a single number with an appropriate physical unit tail-to-head geometric construction geometric construction for drawing the resultant vector of many vectors unit vector vector of a unit magnitude that specifies direction; has no physical unit unit vectors of the axes unit vectors that define orthogonal directions in a plane or in space vector mathematical object with magnitude and direction vector components orthogonal components of a vector; a vector is the vector sum of its vector components vector equation equation in which the left-hand and right-hand sides are vectors vector product the result of the vector multiplication of vectors is a vector called a vector product; also called a cross product vector quantity physical quantity described by a mathematical vector—that is, by specifying both its magnitude and its direction; synonymous with a vector in physics vector sum resultant of the combination of two (or more) vectors\n\n## Key Equations\n\n Multiplication by a scalar (vector equation) $$\\vec{B} = \\alpha \\vec{A}$$ Multiplication by a scalar (scalar equation for magnitudes) $$B = |\\alpha| A$$ Resultant of two vectors $$\\vec{D}_{AD} = \\vec{D}_{AC} + \\vec{D}_{CD}$$ Commutative law $$\\vec{A} + \\vec{B} = \\vec{B} + \\vec{A}$$ Associative law $$(\\vec{A} + \\vec{B}) + \\vec{C} = \\vec{A} + (\\vec{B} + \\vec{C})$$ Distributive law $$\\alpha_{1} \\vec{A} + \\alpha_{2} \\vec{A} = (\\alpha_{1} + \\alpha_{2}) \\vec{A}$$ The component form of a vector in two dimensions $$\\vec{A} = A_{x} \\hat{i} + A_{y} \\hat{j}$$ Scalar components of a vector in two dimensions $$\\begin{cases} A_{x} = x_{e} - x_{b} \\\\ A_{y} = y_{e} - y_{b} \\end{cases}$$ Magnitude of a vector in a plane $$A = \\sqrt{A_{x}^{2} + A_{y}^{2}}$$ The direction angle of a vector in a plane $$\\theta_{A} = \\tan^{-1} \\left(\\dfrac{A_{y}}{A_{x}}\\right)$$ Scalar components of a vector in a plane $$\\begin{cases} A_{x} = A \\cos \\theta_{A} \\\\ A_{y} = A \\sin \\theta_{A} \\end{cases}$$ Polar coordinates in a plane $$\\begin{cases} x = r \\cos \\varphi \\\\ y = r \\sin \\varphi \\end{cases}$$ The component form of a vector in three dimensions $$\\vec{A} = A_{x} \\hat{i} + A_{y} \\hat{j} + A_{z} \\hat{k}$$ The scalar z-component of a vector in three dimensions $$A_{z} = z_{e} - z_{b}$$ Magnitude of a vector in three dimensions $$A = \\sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}}$$ Distributive property $$\\alpha (\\vec{A} + \\vec{B}) = \\alpha \\vec{A} + \\alpha \\vec{B}$$ Antiparallel vector to $$\\vec{A}$$ $$- \\vec{A} = A_{x} \\hat{i} - A_{y} \\hat{j} - A_{z} \\hat{k}$$ Equal vectors $$\\vec{A} = \\vec{B} \\Leftrightarrow \\begin{cases} A_{x} = B_{x} \\\\ A_{y} = B_{y} \\\\ A_{z} = B_{z} \\end{cases}$$ Components of the resultant of N vectors $$\\begin{cases} F_{Rx} = \\sum_{k = 1}^{N} F_{kx} = F_{1x} + F_{2x} + \\ldots + F_{Nx} \\\\ F_{Ry} = \\sum_{k = 1}^{N} F_{ky} = F_{1y} + F_{2y} + \\ldots + F_{Ny} \\\\ F_{Rz} = \\sum_{k = 1}^{N} F_{kz} = F_{1z} + F_{2z} + \\ldots + F_{Nz} \\end{cases}$$ General unit vector $$\\hat{V} = \\frac{\\vec{V}}{V}$$ Definition of the scalar product $$\\vec{A} \\cdotp \\vec{B} = AB \\cos \\varphi$$ Commutative property of the scalar product $$\\vec{A} \\cdotp \\vec{B} = \\vec{B} \\cdotp \\vec{A}$$ Distributive property of the scalar product $$\\vec{A} \\cdotp (\\vec{B} + \\vec{C}) = \\vec{A} \\cdotp \\vec{B} + \\vec{A} \\cdotp \\vec{C}$$ Scalar product in terms of scalar components of vectors $$\\vec{A} \\cdotp \\vec{B} = A_{x}B_{x} + A_{y}B_{y} + A_{z}B_{z}$$ Cosine of the angle between two vectors $$\\cos \\varphi = \\frac{\\vec{A} \\cdotp \\vec{B}}{AB}$$ Dot products of unit vectors $$\\hat{i} \\cdotp \\hat{j} = \\hat{j} \\cdotp \\hat{k} = \\hat{k} \\cdotp \\hat{i} = 0$$ Magnitude of the vector product (definition) $$|\\vec{A} \\times \\vec{B}| = AB \\sin \\varphi$$ Anticommutative property of the vector product $$|\\vec{A} \\times \\vec{B} = - \\vec{B} \\times \\vec{A}$$ Distributive property of the vector product $$\\vec{A} \\times (\\vec{B} + \\vec{C}) = \\vec{A} \\times \\vec{B} + \\vec{A} \\times \\vec{C}$$ Cross products of unit vectors $$\\begin{cases} \\hat{i} \\times \\hat{j} = + \\hat{k}, \\\\ \\hat{j} \\times \\hat{l} = + \\hat{i}, \\\\ \\hat{l} \\times \\hat{i} = + \\hat{j} \\ldotp \\end{cases}$$ The cross product in terms of scalar components of vectors $$\\vec{A} \\times \\vec{B} = (A_{y}B_{z} - A_{z}B_{y}) \\hat{i} + (A_{z}B_{x} - A_{x}B_{z}) \\hat{j} + (A_{x}B_{y} - A_{y}B_{x}) \\hat{k}$$\n\n## Summary\n\n### 2.1 Scalars and Vectors\n\n• A vector quantity is any quantity that has magnitude and direction, such as displacement or velocity.\n• Geometrically, vectors are represented by arrows, with the end marked by an arrowhead. The length of the vector is its magnitude, which is a positive scalar. On a plane, the direction of a vector is given by the angle the vector makes with a reference direction, often an angle with the horizontal. The direction angle of a vector is a scalar.\n• Two vectors are equal if and only if they have the same magnitudes and directions. Parallel vectors have the same direction angles but may have different magnitudes. Antiparallel vectors have direction angles that differ by 180°. Orthogonal vectors have direction angles that differ by 90°.\n• When a vector is multiplied by a scalar, the result is another vector of a different length than the length of the original vector. Multiplication by a positive scalar does not change the original direction; only the magnitude is affected. Multiplication by a negative scalar reverses the original direction. The resulting vector is antiparallel to the original vector. Multiplication by a scalar is distributive. Vectors can be divided by nonzero scalars but cannot be divided by vectors.\n• Two or more vectors can be added to form another vector. The vector sum is called the resultant vector. We can add vectors to vectors or scalars to scalars, but we cannot add scalars to vectors. Vector addition is commutative and associative.\n• To construct a resultant vector of two vectors in a plane geometrically, we use the parallelogram rule. To construct a resultant vector of many vectors in a plane geometrically, we use the tail-to-head method.\n\n### 2.2 Coordinate Systems and Components of a Vector\n\n• Vectors are described in terms of their components in a coordinate system. In two dimensions (in a plane), vectors have two components. In three dimensions (in space), vectors have three components.\n• A vector component of a vector is its part in an axis direction. The vector component is the product of the unit vector of an axis with its scalar component along this axis. A vector is the resultant of its vector components.\n• Scalar components of a vector are differences of coordinates, where coordinates of the origin are subtracted from end point coordinates of a vector. In a rectangular system, the magnitude of a vector is the square root of the sum of the squares of its components.\n• In a plane, the direction of a vector is given by an angle the vector has with the positive x-axis. This direction angle is measured counterclockwise. The scalar x-component of a vector can be expressed as the product of its magnitude with the cosine of its direction angle, and the scalar y-component can be expressed as the product of its magnitude with the sine of its direction angle.\n• In a plane, there are two equivalent coordinate systems. The Cartesian coordinate system is defined by unit vectors $$\\hat{i}$$ and $$\\hat{j}$$ along the x-axis and the y-axis, respectively. The polar coordinate system is defined by the radial unit vector $$\\hat{r}$$, which gives the direction from the origin, and a unit vector $$\\hat{t}$$, which is perpendicular (orthogonal) to the radial direction.\n\n### 2.3 Algebra of Vectors\n\n• Analytical methods of vector algebra allow us to find resultants of sums or differences of vectors without having to draw them. Analytical methods of vector addition are exact, contrary to graphical methods, which are approximate.\n• Analytical methods of vector algebra are used routinely in mechanics, electricity, and magnetism. They are important mathematical tools of physics.\n\n### 2.4 Products of Vectors\n\n• There are two kinds of multiplication for vectors. One kind of multiplication is the scalar product, also known as the dot product. The other kind of multiplication is the vector product, also known as the cross product. The scalar product of vectors is a number (scalar). The vector product of vectors is a vector.\n• Both kinds of multiplication have the distributive property, but only the scalar product has the commutative property. The vector product has the anticommutative property, which means that when we change the order in which two vectors are multiplied, the result acquires a minus sign.\n• The scalar product of two vectors is obtained by multiplying their magnitudes with the cosine of the angle between them. The scalar product of orthogonal vectors vanishes; the scalar product of antiparallel vectors is negative.\n• The vector product of two vectors is a vector perpendicular to both of them. Its magnitude is obtained by multiplying their magnitudes by the sine of the angle between them. The direction of the vector product can be determined by the corkscrew right-hand rule. The vector product of two either parallel or antiparallel vectors vanishes. The magnitude of the vector product is largest for orthogonal vectors.\n• The scalar product of vectors is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy.\n• The cross product of vectors is used in definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations.\n\n## Contributors\n\nSamuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).\n\nThis page titled 3.12: Vectors (Summary) is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax."
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https://nursingassignmentsexpert.com/t-test-and-anova-testing-classmate-response-2-topic-5-dq-1/ | [
"# t-Test and ANOVA Testing- Classmate Response (2): Topic 5 DQ 1\n\n#### t-Test and ANOVA Testing- Classmate Response (2): Topic 5 DQ 1\n\nQUESTION-Compare the various types of ANOVA by discussing when each is most appropriate for use. Include specific examples to illustrate the appropriate use of each test and how interaction is assessed using ANOVA.\n\nClassmate (Samantha) Response-\n\nA one-way ANOVA compares the means of two or more group means to see if these means are statistically different. This test is considered a parametric test. This type of testing is used to test the statistical difference between two or more groups, two or more interventions or two or change scores. An example of its use is to compare if there is a significant time difference between sprinter times based on their smoking status. Sprint time represents the dependent status while the smoking status represents the independent variable (One-way Anova, 2021).\n\nA two-way ANOVA test seeks to evaluate if the independent variables have any affect on the dependent variable. It compares the mean differences for groups that have been split on two independent factors. An example of such comparison could be whether gender and educational level have any effect on testing anxiety of university students. Gender and educational level are the independent variables while test anxiety is the dependent variable (Two-way ANOVA, 2018).\n\nReferences:\n\nTwo-way ANOVA in SPSS Statistics. (2018). Lund Research, Ltd. Retrieved from https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php\n\nORDER A PLAGIARISM-FREE PAPER HERE !!\n\nSolution\n\nAnalysis of Variance- ANOVA\n\nHello, thank you for giving me this opportunity to respond to your post. I gladly appreciate you taking your time to contribute to the Analysis of Variance’s discussion. I will only add a few points to your post, as your contributions are agreeable to the topic. Analysis of Variance testing is very crucial in analyzing clinical research, especially public health data. Therefore, a clear understanding of the concepts and types of analysis of variance is necessary for finding the study results of a sample. Hence, it is a statistical method that focuses on comparing two or more sample means.\n\nIn addition to the one-way analysis of variance, I would like to add that it is the easiest one to use (Sureiman & Mangera,2020). The testing is done in two or more groups. These groups are normally categorically identified, thus making it easier to understand the association between independent and dependent variables in a particular sample. Based on the example provided in the post, the comparison between sprinter and smoking is observable and accurate. Therefore, the one-way approach can be used by researchers easily in articulating their work using several groups in a sample.\n\nIn the case of two-way analysis of variance, comparison can only be made between two categories of groups, thus too difficult for researchers to use (Sureiman & Mangera,2020). For instance, checking if gender and educational level affect university students is a bit too complicated and broad study for comparison and decide on a concrete conclusion. This analysis of variance tends to find out if dependent and independent variables have any effect on each other and if both variables also affect the variance in the sample study.\n\nReference\n\nSureiman, O., & Mangera, C. M. (2020). Conceptual Framework on Conducting Two-Way Analysis of Variance. Journal of the Practice of Cardiovascular Sciences, 6(3), 207. https://www.j-pcs.org/article.asp?issn=2395-5414;year=2020;volume=6;issue=3;spage=207;epage=215;aulast=Sureiman\n\nGet 20% off your first purchase\n\nX"
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https://beta.geogebra.org/m/ypJjRuU6 | [
"Do the drag test on each of the vertices. Use your knowledge of polygons to try to figure out what kind of polygon this is. Tell all you can about the figure. You may want to consider looking at sides angles and diagonals. Is one pair of opposite sides parallel? Are both? Are any sides congruent? Are the congruent sides opposite each other? Are they adjacent? Are angles congruent? Is one pair of opposite angles congruent? Are both pair of opposite angles congruent? Do diagonals bisect each other? Are diagonals congruent? Are diagonals perpendicular?"
]
| [
null
]
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http://mychaume.com/distance-formula-worksheet/ | [
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https://detailedpedia.com/wiki-Julian_date | [
"# Julian day(Redirected from Julian date)\n\nThe Julian day is the continuous count of days since the beginning of the Julian period, and is used primarily by astronomers, and in software for easily calculating elapsed days between two events (e.g. food production date and sell by date).\n\nThe Julian period is a chronological interval of 7980 years; year 1 of the Julian Period was 4713 BC (−4712). The Julian calendar year 2023 is year 6736 of the current Julian Period. The next Julian Period begins in the year AD 3268. Historians used the period to identify Julian calendar years within which an event occurred when no such year was given in the historical record, or when the year given by previous historians was incorrect.\n\nThe Julian day number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Universal Time, with Julian day number 0 assigned to the day starting at noon on Monday, January 1, 4713 BC, proleptic Julian calendar (November 24, 4714 BC, in the proleptic Gregorian calendar), a date at which three multi-year cycles started (which are: Indiction, Solar, and Lunar cycles) and which preceded any dates in recorded history. For example, the Julian day number for the day starting at 12:00 UT (noon) on January 1, 2000, was 2451545.\n\nThe Julian date (JD) of any instant is the Julian day number plus the fraction of a day since the preceding noon in Universal Time. Julian dates are expressed as a Julian day number with a decimal fraction added. For example, the Julian Date for 00:30:00.0 UT January 1, 2013, is 2456293.520833. This page was loaded at 2023-11-26 06:10:37 (UTC) – expressed as a Julian date this is 2460274.7573727. [refresh]\n\n## Terminology\n\nThe term Julian date may also refer, outside of astronomy, to the day-of-year number (more properly, the ordinal date) in the Gregorian calendar, especially in computer programming, the military and the food industry, or it may refer to dates in the Julian calendar. For example, if a given \"Julian date\" is \"October 5, 1582\", this means that date in the Julian calendar (which was October 15, 1582, in the Gregorian calendar—the date it was first established). Without an astronomical or historical context, a \"Julian date\" given as \"36\" most likely means the 36th day of a given Gregorian year, namely February 5. Other possible meanings of a \"Julian date\" of \"36\" include an astronomical Julian Day Number, or the year AD 36 in the Julian calendar, or a duration of 36 astronomical Julian years). This is why the terms \"ordinal date\" or \"day-of-year\" are preferred. In contexts where a \"Julian date\" means simply an ordinal date, calendars of a Gregorian year with formatting for ordinal dates are often called \"Julian calendars\", but this could also mean that the calendars are of years in the Julian calendar system.\n\nHistorically, Julian dates were recorded relative to Greenwich Mean Time (GMT) (later, Ephemeris Time), but since 1997 the International Astronomical Union has recommended that Julian dates be specified in Terrestrial Time. Seidelmann indicates that Julian dates may be used with International Atomic Time (TAI), Terrestrial Time (TT), Barycentric Coordinate Time (TCB), or Coordinated Universal Time (UTC) and that the scale should be indicated when the difference is significant. The fraction of the day is found by converting the number of hours, minutes, and seconds after noon into the equivalent decimal fraction. Time intervals calculated from differences of Julian Dates specified in non-uniform time scales, such as UTC, may need to be corrected for changes in time scales (e.g. leap seconds).\n\n## Variants\n\nBecause the starting point or reference epoch is so long ago, numbers in the Julian day can be quite large and cumbersome. A more recent starting point is sometimes used, for instance by dropping the leading digits, in order to fit into limited computer memory with an adequate amount of precision. In the following table, times are given in 24-hour notation.\n\nIn the table below, Epoch refers to the point in time used to set the origin (usually zero, but (1) where explicitly indicated) of the alternative convention being discussed in that row. The date given is a Gregorian calendar date unless otherwise specified. JD stands for Julian Date. 0h is 00:00 midnight, 12h is 12:00 noon, UT unless otherwise specified. Current value is as of 06:10, Sunday, November 26, 2023 (UTC) and may be cached. [refresh]\n\nName Epoch Calculation Current value Notes\nJulian date 12:00 January 1, 4713 BC proleptic Julian calendar JD 2460274.75694\nReduced JD 12:00 November 16, 1858 JD − 2400000 60274.75694\nModified JD 0:00 November 17, 1858 JD − 2400000.5 60274.25694 Introduced by SAO in 1957\nTruncated JD 0:00 May 24, 1968 floor (JD − 2440000.5) 20274 Introduced by NASA in 1979\nDublin JD 12:00 December 31, 1899 JD − 2415020 45254.75694 Introduced by the IAU in 1955\nCNES JD 0:00 January 1, 1950 JD − 2433282.5 26992.25694 Introduced by the CNES\nCCSDS JD 0:00 January 1, 1958 JD − 2436204.5 24070.25694 Introduced by the CCSDS\nLilian date day 1 = October 15, 1582 floor (JD − 2299159.5) 161115 Count of days of the Gregorian calendar\nRata Die day 1 = January 1, 1 proleptic Gregorian calendar floor (JD − 1721424.5) 738850 Count of days of the Common Era\nMars Sol Date 12:00 December 29, 1873 (JD − 2405522)/1.02749 53287.80848 Count of Martian days\nUnix time 0:00 January 1, 1970 (JD − 2440587.5) × 86400 1700979037 Count of seconds, excluding leap seconds\n.NET DateTime 0:00 January 1, 1 proleptic Gregorian calendar (JD − 1721425.5) × 864000000000 6.3836575837001E+17 Count of 100-nanosecond ticks, excluding ticks attributable to leap seconds\n• The Modified Julian Date (MJD) was introduced by the Smithsonian Astrophysical Observatory in 1957 to record the orbit of Sputnik via an IBM 704 (36-bit machine) and using only 18 bits until August 7, 2576. MJD is the epoch of VAX/VMS and its successor OpenVMS, using 63-bit date/time, which allows times to be stored up to July 31, 31086, 02:48:05.47. The MJD has a starting point of midnight on November 17, 1858, and is computed by MJD = JD − 2400000.5\n• The Truncated Julian Day (TJD) was introduced by NASA/Goddard in 1979 as part of a parallel grouped binary time code (PB-5) \"designed specifically, although not exclusively, for spacecraft applications\". TJD was a 4-digit day count from MJD 40000, which was May 24, 1968, represented as a 14-bit binary number. Since this code was limited to four digits, TJD recycled to zero on MJD 50000, or October 10, 1995, \"which gives a long ambiguity period of 27.4 years\". (NASA codes PB-1–PB-4 used a 3-digit day-of-year count.) Only whole days are represented. Time of day is expressed by a count of seconds of a day, plus optional milliseconds, microseconds and nanoseconds in separate fields. Later PB-5J was introduced which increased the TJD field to 16 bits, allowing values up to 65535, which will occur in the year 2147. There are five digits recorded after TJD 9999.\n• The Dublin Julian Date (DJD) is the number of days that has elapsed since the epoch of the solar and lunar ephemerides used from 1900 through 1983, Newcomb's Tables of the Sun and Ernest W. Brown's Tables of the Motion of the Moon (1919). This epoch was noon UT on January 0, 1900, which is the same as noon UT on December 31, 1899. The DJD was defined by the International Astronomical Union at their meeting in Dublin, Ireland, in 1955.\n• The Lilian day number is a count of days of the Gregorian calendar and not defined relative to the Julian Date. It is an integer applied to a whole day; day 1 was October 15, 1582, which was the day the Gregorian calendar went into effect. The original paper defining it makes no mention of the time zone, and no mention of time-of-day. It was named for Aloysius Lilius, the principal author of the Gregorian calendar.\n• Rata Die is a system used in Rexx, Go and Python. Some implementations or options use Universal Time, others use local time. Day 1 is January 1, 1, that is, the first day of the Christian or Common Era in the proleptic Gregorian calendar. In Rexx January 1 is Day 0.\n• The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the Sun, and thus can differ from the Julian day by as much as 8.3 minutes (498 seconds), that being the time it takes light to reach Earth from the Sun.\n\n## History\n\n### Julian Period\n\nThe Julian day number is based on the Julian Period proposed by Joseph Scaliger, a classical scholar, in 1583 (one year after the Gregorian calendar reform) as it is the product of three calendar cycles used with the Julian calendar:\n\n28 (solar cycle) × 19 (lunar cycle) × 15 (indiction cycle) = 7980 years\n\nIts epoch occurs when all three cycles (if they are continued backward far enough) were in their first year together. Years of the Julian Period are counted from this year, 4713 BC, as year 1, which was chosen to be before any historical record.\n\nScaliger corrected chronology by assigning each year a tricyclic \"character\", three numbers indicating that year's position in the 28-year solar cycle, the 19-year lunar cycle, and the 15-year indiction cycle. One or more of these numbers often appeared in the historical record alongside other pertinent facts without any mention of the Julian calendar year. The character of every year in the historical record was unique – it could only belong to one year in the 7980-year Julian Period. Scaliger determined that 1 BC or year 0 was Julian Period (JP) 4713. He knew that 1 BC or 0 had the character 9 of the solar cycle, 1 of the lunar cycle, and 3 of the indiction cycle. By inspecting a 532-year Paschal cycle with 19 solar cycles (each year numbered 1–28) and 28 lunar cycles (each year numbered 1–19), he determined that the first two numbers, 9 and 1, occurred at its year 457. He then calculated via remainder division that he needed to add eight 532-year Paschal cycles totaling 4256 years before the cycle containing 1 BC or 0 in order for its year 457 to be indiction 3. The sum 4256 + 457 was thus JP 4713.\n\nA formula for determining the year of the Julian Period given its character involving three four-digit numbers was published by Jacques de Billy in 1665 in the Philosophical Transactions of the Royal Society (its first year). John F. W. Herschel gave the same formula using slightly different wording in his 1849 Outlines of Astronomy.\n\nMultiply the Solar Cycle by 4845, and the Lunar, by 4200, and that of the Indiction, by 6916. Then divide the Sum of the products by 7980, which is the Julian Period: The Remainder of the Division, without regard to the Quotient, shall be the year enquired after.\n\n— Jacques de Billy\n\nCarl Friedrich Gauss introduced the modulo operation in 1801, restating de Billy's formula as:\n\nJulian Period year = (6916a + 4200b + 4845c) MOD 15×19×28\n\nwhere a is the year of the indiction cycle, b of the lunar cycle, and c of the solar cycle.\n\nJohn Collins described the details of how these three numbers were calculated in 1666, using many trials. A summary of Collin's description is in a footnote. Reese, Everett and Craun reduced the dividends in the Try column from 285, 420, 532 to 5, 2, 7 and changed remainder to modulo, but apparently still required many trials.\n\nThe specific cycles used by Scaliger to form his tricyclic Julian Period were, first, the indiction cycle with a first year of 313. Then he chose the dominant 19-year Alexandrian lunar cycle with a first year of 285, the Era of Martyrs and the Diocletian Era epoch, or a first year of 532 according to Dionysius Exiguus. Finally, Scaliger chose the post-Bedan solar cycle with a first year of 776, when its first quadrennium of concurrents, 1 2 3 4, began in sequence. Although not their intended use, the equations of de Billy or Gauss can be used to determined the first year of any 15-, 19-, and 28-year tricyclic period given any first years of their cycles. For those of the Julian Period, the result is AD3268, because both remainder and modulo usually return the lowest positive result. Thus 7980years must be subtracted from it to yield the first year of the present Julian Period, −4712 or 4713BC, when all three of its sub-cycles are in their first years.\n\nScaliger got the idea of using a tricyclic period from \"the Greeks of Constantinople\" as Herschel stated in his quotation below in Julian day numbers. Specifically, the monk and priest Georgios wrote in 638/39 that the Byzantine year 6149 AM (640/41) had indiction 14, lunar cycle 12, and solar cycle 17, which places the first year of the Byzantine Era in 5509/08BC, the Byzantine Creation. Dionysius Exiguus called the Byzantine lunar cycle his \"lunar cycle\" in argumentum 6, in contrast with the Alexandrian lunar cycle which he called his \"nineteen-year cycle\" in argumentum 5.\n\nAlthough many references say that the Julian in \"Julian Period\" refers to Scaliger's father, Julius Scaliger, at the beginning of Book V of his Opus de Emendatione Temporum (\"Work on the Emendation of Time\") he states, \"Iulianam vocauimus: quia ad annum Iulianum accomodata\", which Reese, Everett and Craun translate as \"We have termed it Julian because it fits the Julian year.\" Thus Julian refers to the Julian calendar.\n\n### Julian day numbers\n\nJulian days were first used by Ludwig Ideler for the first days of the Nabonassar and Christian eras in his 1825 Handbuch der mathematischen und technischen Chronologie. John F. W. Herschel then developed them for astronomical use in his 1849 Outlines of Astronomy, after acknowledging that Ideler was his guide.\n\nThe period thus arising of 7980 Julian years, is called the Julian period, and it has been found so useful, that the most competent authorities have not hesitated to declare that, through its employment, light and order were first introduced into chronology. We owe its invention or revival to Joseph Scaliger, who is said to have received it from the Greeks of Constantinople. The first year of the current Julian period, or that of which the number in each of the three subordinate cycles is 1, was the year 4713 BC, and the noon of January 1 of that year, for the meridian of Alexandria, is the chronological epoch, to which all historical eras are most readily and intelligibly referred, by computing the number of integer days intervening between that epoch and the noon (for Alexandria) of the day, which is reckoned to be the first of the particular era in question. The meridian of Alexandria is chosen as that to which Ptolemy refers the commencement of the era of Nabonassar, the basis of all his calculations.\n\nAt least one mathematical astronomer adopted Herschel's \"days of the Julian period\" immediately. Benjamin Peirce of Harvard University used over 2,800 Julian days in his Tables of the Moon, begun in 1849 but not published until 1853, to calculate the lunar ephemerides in the new American Ephemeris and Nautical Almanac from 1855 to 1888. The days are specified for \"Washington mean noon\", with Greenwich defined as 18h 51m 48s west of Washington (282°57′W, or Washington 77°3′W of Greenwich). A table with 197 Julian days (\"Date in Mean Solar Days\", one per century mostly) was included for the years –4713 to 2000 with no year 0, thus \"–\" means BC, including decimal fractions for hours, minutes and seconds. The same table appears in Tables of Mercury by Joseph Winlock, without any other Julian days.\n\nThe national ephemerides started to include a multi-year table of Julian days, under various names, for either every year or every leap year beginning with the French Connaissance des Temps in 1870 for 2,620 years, increasing in 1899 to 3,000 years. The British Nautical Almanac began in 1879 with 2,000 years. The Berliner Astronomisches Jahrbuch began in 1899 with 2,000 years. The American Ephemeris was the last to add a multi-year table, in 1925 with 2,000 years. However, it was the first to include any mention of Julian days with one for the year of issue beginning in 1855, as well as later scattered sections with many days in the year of issue. It was also the first to use the name \"Julian day number\" in 1918. The Nautical Almanac began in 1866 to include a Julian day for every day in the year of issue. The Connaissance des Temps began in 1871 to include a Julian day for every day in the year of issue.\n\nThe French mathematician and astronomer Pierre-Simon Laplace first expressed the time of day as a decimal fraction added to calendar dates in his book, Traité de Mécanique Céleste, in 1823. Other astronomers added fractions of the day to the Julian day number to create Julian Dates, which are typically used by astronomers to date astronomical observations, thus eliminating the complications resulting from using standard calendar periods like eras, years, or months. They were first introduced into variable star work in 1860 by the English astronomer Norman Pogson, which he stated was at the suggestion of John Herschel. They were popularized for variable stars by Edward Charles Pickering, of the Harvard College Observatory, in 1890.\n\nJulian days begin at noon because when Herschel recommended them, the astronomical day began at noon. The astronomical day had begun at noon ever since Ptolemy chose to begin the days for his astronomical observations at noon. He chose noon because the transit of the Sun across the observer's meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset, which vary by several hours. Midnight was not even considered because it could not be accurately determined using water clocks. Nevertheless, he double-dated most nighttime observations with both Egyptian days beginning at sunrise and Babylonian days beginning at sunset. Medieval Muslim astronomers used days beginning at sunset, so astronomical days beginning at noon did produce a single date for an entire night. Later medieval European astronomers used Roman days beginning at midnight so astronomical days beginning at noon also allow observations during an entire night to use a single date. When all astronomers decided to start their astronomical days at midnight to conform to the beginning of the civil day, on January 1, 1925, it was decided to keep Julian days continuous with previous practice, beginning at noon.\n\nDuring this period, usage of Julian day numbers as a neutral intermediary when converting a date in one calendar into a date in another calendar also occurred. An isolated use was by Ebenezer Burgess in his 1860 translation of the Surya Siddhanta wherein he stated that the beginning of the Kali Yuga era occurred at midnight at the meridian of Ujjain at the end of the 588,465th day and the beginning of the 588,466th day (civil reckoning) of the Julian Period, or between February 17 and 18 JP 1612 or 3102 BC. Robert Schram was notable beginning with his 1882 Hilfstafeln für Chronologie. Here he used about 5,370 \"days of the Julian Period\". He greatly expanded his usage of Julian days in his 1908 Kalendariographische und Chronologische Tafeln containing over 530,000 Julian days, one for the zeroth day of every month over thousands of years in many calendars. He included over 25,000 negative Julian days, given in a positive form by adding 10,000,000 to each. He called them \"day of the Julian Period\", \"Julian day\", or simply \"day\" in his discussion, but no name was used in the tables. Continuing this tradition, in his book \"Mapping Time: The Calendar and Its History\" British physics educator and programmer Edward Graham Richards uses Julian day numbers to convert dates from one calendar into another using algorithms rather than tables.\n\n## Julian day number calculation\n\nThe Julian day number can be calculated using the following formulas (integer division rounding towards zero is used exclusively, that is, positive values are rounded down and negative values are rounded up):\n\nThe months January to December are numbered 1 to 12. For the year, astronomical year numbering is used, thus 1 BC is 0, 2 BC is −1, and 4713 BC is −4712. JDN is the Julian Day Number. Use the previous day of the month if trying to find the JDN of an instant before midday UT.\n\n### Converting Gregorian calendar date to Julian Day Number\n\nThe algorithm is valid for all (possibly proleptic) Gregorian calendar dates after November 23, −4713. Divisions are integer divisions towards zero; fractional parts are ignored.\n\nJDN = (1461 × (Y + 4800 + (M − 14)/12))/4 +(367 × (M − 2 − 12 × ((M − 14)/12)))/12 − (3 × ((Y + 4900 + (M - 14)/12)/100))/4 + D − 32075\n\n### Converting Julian calendar date to Julian Day Number\n\nThe algorithm is valid for all (possibly proleptic) Julian calendar years ≥ −4712, that is, for all JDN ≥ 0. Divisions are integer divisions, fractional parts are ignored.\n\nJDN = 367 × Y − (7 × (Y + 5001 + (M − 9)/7))/4 + (275 × M)/9 + D + 1729777\n\n### Finding Julian date given Julian day number and time of day\n\nFor the full Julian Date of a moment after 12:00 UT one can use the following. Divisions are real numbers.\n\n${\\begin{matrix}J\\!D&=&J\\!D\\!N+{\\frac {{\\text{hour}}-12}{24}}+{\\frac {\\text{minute}}{1440}}+{\\frac {\\text{second}}{86400}}\\end{matrix}}$",
null,
"So, for example, January 1, 2000, at 18:00:00 UT corresponds to JD = 2451545.25 and January 1, 2000, at 6:00:00 UT corresponds to JD = 2451544.75.\n\n### Finding day of week given Julian day number\n\nBecause a Julian day starts at noon while a civil day starts at midnight, the Julian day number needs to be adjusted to find the day of week: for a point in time in a given Julian day after midnight UT and before 12:00 UT, add 1 or use the JDN of the next afternoon.\n\nThe US day of the week W1 (for an afternoon or evening UT) can be determined from the Julian Day Number J with the expression:\n\nW1 = mod(J + 1, 7)\n W1 Day of the week 0 1 2 3 4 5 6 Sun Mon Tue Wed Thu Fri Sat\n\nIf the moment in time is after midnight UT (and before 12:00 UT), then one is already in the next day of the week.\n\nThe ISO day of the week W0 can be determined from the Julian Day Number J with the expression:\n\nW0 = mod (J, 7) + 1\n W0 Day of the week 1 2 3 4 5 6 7 Mon Tue Wed Thu Fri Sat Sun\n\n### Julian or Gregorian calendar from Julian day number\n\nThis is an algorithm by Edward Graham Richards to convert a Julian Day Number, J, to a date in the Gregorian calendar (proleptic, when applicable). Richards states the algorithm is valid for Julian day numbers greater than or equal to 0. All variables are integer values, and the notation \"a div b\" indicates integer division, and \"mod(a,b)\" denotes the modulus operator.\n\nAlgorithm parameters for Gregorian calendar\nvariable value variable value\ny 4716 v 3\nj 1401 u 5\nm 2 s 153\nn 12 w 2\nr 4 B 274277\np 1461 C −38\n\nFor Julian calendar:\n\n1. f = J + j\n\nFor Gregorian calendar:\n\n1. f = J + j + (((4 × J + B) div 146097) × 3) div 4 + C\n\nFor Julian or Gregorian, continue:\n\n1. e = r × f + v\n2. g = mod(e, p) div r\n3. h = u × g + w\n4. D = (mod(h, s)) div u + 1\n5. M = mod(h div s + m, n) + 1\n6. Y = (e div p) - y + (n + m - M) div n\n\nD, M, and Y are the numbers of the day, month, and year respectively for the afternoon at the beginning of the given Julian day.\n\n### Julian Period from indiction, Metonic and solar cycles\n\nLet Y be the year BC or AD and i, m and s respectively its positions in the indiction, Metonic and solar cycles. Divide 6916i + 4200m + 4845s by 7980 and call the remainder r.\n\nIf r>4713, Y = (r − 4713) and is a year AD.\nIf r<4714, Y = (4714 − r) and is a year BC.\n\nExample\n\ni = 8, m = 2, s = 8. What is the year?\n\n(6916 × 8) = 55328; (4200 × 2) = 8400: (4845 × 8) = 38760. 55328 + 8400 + 38760 = 102488.\n102488/7980 = 12 remainder 6728.\nY = (6728 − 4713) = AD 2015.\n\n## Julian date calculation\n\nAs stated above, the Julian date (JD) of any instant is the Julian day number for the preceding noon in Universal Time plus the fraction of the day since that instant. Ordinarily calculating the fractional portion of the JD is straightforward; the number of seconds that have elapsed in the day divided by the number of seconds in a day, 86,400. But if the UTC timescale is being used, a day containing a positive leap second contains 86,401 seconds (or in the unlikely event of a negative leap second, 86,399 seconds). One authoritative source, the Standards of Fundamental Astronomy (SOFA), deals with this issue by treating days containing a leap second as having a different length (86,401 or 86,399 seconds, as required). SOFA refers to the result of such a calculation as \"quasi-JD\"."
]
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"https://images.weserv.nl/",
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https://polytope.miraheze.org/wiki/Small_ditetrahedronary_disprismatohecatonicosachoron | [
"# Small ditetrahedronary disprismatohecatonicosachoron\n\nSmall ditetrahedronary disprismatohecatonicosachoron",
null,
"Rank4\nTypeUniform\nSpaceSpherical\nNotation\nElements\nCells120 id, 720 pip, 1200 trip\nFaces2400 triangles, 3600 squares, 1440 pentagons\nEdges3600\nVertices600\nEdge figure(trip 4 pip 5 id 3 trip 4 pip 4 trip 3 id 5 pip 4)\nMeasures (edge length 1)\nCircumradius$\\frac{\\sqrt2+\\sqrt{10}}{2} \\approx 2.28825$",
null,
"Number of external pieces1357680\nLevel of complexity2836\nRelated polytopes\nArmyHi\nRegimentSidtaxhi\nAbstract & topological properties\nFlag count115200\nEuler characteristic2400\nOrientableYes\nProperties\nSymmetryH4, order 14400\nConvexNo\nNatureFeral\n\nThe small ditetrahedronary disprismatohecatonicosachoron, or sidtadphi, is a nonconvex uniform polychoron that consists of 120 icosidodecahedra, 720 pentagonal prisms, and 1200 triangular prisms. Six icosidodecahedra, twelve pentagonal prisms, and twelve triangular prisms join at each vertex.\n\n## Vertex coordinates\n\nIts vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron."
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null,
"https://static.miraheze.org/polytopewiki/thumb/6/6d/Sidtadphi_card_Bowers.jpeg/200px-Sidtadphi_card_Bowers.jpeg",
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"https://polytope.miraheze.org/w/index.php",
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https://planetmath.org/DeterminantInequalities | [
"# determinant inequalities\n\nThere are a number of interesting inequalities bounding the determinant",
null,
"",
null,
"of a $n\\times n$ complex matrix $A$, where $\\rho$ is its spectral radius:\n\n1) $\\left|\\det(A)\\right|\\leq\\rho^{n}(A)$\n2) $\\left|\\det(A)\\right|\\leq\\prod_{i=1}^{n}\\left(\\sum_{j=1}^{n}\\left|a_{ij}\\right|% \\right)=\\prod_{i=1}^{n}\\|a_{i}\\|_{1}$\n3) $\\left|\\det(A)\\right|\\leq\\prod_{j=1}^{n}\\left(\\sum_{i=1}^{n}\\left|a_{ij}\\right|% \\right)=\\prod_{j=1}^{n}\\|a_{j}\\|_{1}$\n4) $\\left|\\det(A)\\right|\\leq\\prod_{i=1}^{n}\\left(\\sum_{j=1}^{n}\\left|a_{ij}\\right|% ^{2}\\right)^{\\frac{1}{2}}=\\prod_{i=1}^{n}\\|a_{i}\\|_{2}$\n5) $\\left|\\det(A)\\right|\\leq\\prod_{j=1}^{n}\\left(\\sum_{i=1}^{n}\\left|a_{ij}\\right|% ^{2}\\right)^{\\frac{1}{2}}=\\prod_{j=1}^{n}\\|a_{j}\\|_{2}$\n6) if $A$ is Hermitian positive semidefinite",
null,
"",
null,
", $\\det(A)\\leq\\prod_{i=1}^{n}a_{ii}$, with equality if and only if $A$ is diagonal.\n\nInequalities 4)-6) are known as ”Hadamard’s inequalities”.\n\n(Note that inequalities 2)-5) may suggest the idea that such inequalities could hold: $\\left|\\det(A)\\right|\\leq\\prod_{i=1}^{n}\\|a_{i}\\|_{p}$ or $\\left|\\det(A)\\right|\\leq\\prod_{j=1}^{n}\\|a_{j}\\|_{p}$ for any $p\\in\\mathbf{N}$; however, this is not true, as one can easily see with $A=\\begin{bmatrix}1&1\\\\ -1&1\\end{bmatrix}$ and $p=3$. Actually, inequalities 2)-5) give the best possible estimate of this kind.)\n\nProofs:\n\n1) $\\left|\\det(A)\\right|=\\left|\\prod_{i=1}^{n}\\lambda_{i}\\right|=\\prod_{i=1}^{n}% \\left|\\lambda_{i}\\right|\\leq\\prod_{i=1}^{n}\\rho(A)=\\rho^{n}(A).$\n\n2) If $A$ is singular, the thesis is trivial. Let then $\\det(A)\\neq 0$. Let’s define $B=DA$, $D=diag(d_{11},d_{22},\\cdots,d_{nn})$,$d_{ii}=\\left(\\sum_{j=1}^{n}\\left|a_{ij}\\right|\\right)^{-1}$. (Note that $d_{ii}$ exist for any $i$, because $\\det(A)\\neq 0$ implies no all-zero row exists.) So $\\|B\\|_{\\infty}=\\max_{i}\\left(\\sum_{j=1}^{n}\\left|b_{ij}\\right|\\right)=1$ and, since $\\rho(B)\\leq\\|B\\|_{\\infty}$, we have:\n\n$\\left|\\det(B)\\right|=\\left|\\det(D)\\right|\\left|\\det(A)\\right|=\\left(\\prod_{i=1% }^{n}\\sum_{j=1}^{n}\\left|a_{ij}\\right|\\right)^{-1}\\left|\\det(A)\\right|\\leq\\rho% ^{n}(B)\\leq\\|B\\|_{\\infty}^{n}=1$,\n\nfrom which:\n\n$\\left|\\det(A)\\right|\\leq\\prod_{i=1}^{n}\\left(\\sum_{j=1}^{n}\\left|a_{ij}\\right|% \\right).$\n\n3) Same as 2), but applied to $A^{T}$.\n\n4)-6) See related proofs attached to ”Hadamard’s inequalities”.\n\nTitle determinant inequalities DeterminantInequalities 2013-03-22 15:34:46 2013-03-22 15:34:46 Andrea Ambrosio (7332) Andrea Ambrosio (7332) 12 Andrea Ambrosio (7332) Result msc 15A15"
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"http://mathworld.wolfram.com/favicon_mathworld.png",
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"http://planetmath.org/sites/default/files/fab-favicon.ico",
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"http://planetmath.org/sites/default/files/fab-favicon.ico",
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"http://planetmath.org/sites/default/files/fab-favicon.ico",
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http://freecomputerbooks.com/compscComputerSimulationBooks.html | [
"Processing ......",
null,
"FreeComputerBooks.com Free Computer, Mathematics, Technical Books and Lecture Notes, etc.\n\nComputational Simulations and Modeling\nRelated Book Categories:\n•",
null,
"Modeling Creativity - Case Studies in Python (Tom De Smedt)\n\nThis book is to model creativity using computational approaches in Python. The aim is to construct computer models that exhibit creativity in an artistic context, that is, that are capable of generating or evaluating an artwork (visual or linguistic), etc.\n\n•",
null,
"Modeling and Simulation in Python (Allen B. Downey)\n\nThis book is an introduction to physical modeling using a computational approach with Python. You will learn how to use Python to accomplish many common scientific computing tasks: importing, exporting, and visualizing data; numerical analysis; etc.\n\n•",
null,
"Computer Simulation Techniques - The Definitive Introduction\n\nThis book addresses all the important aspects of a computer simulation study, including modeling, simulation languages, validation, input probability distribution, and analysis of simulation output data.\n\n•",
null,
"MATLAB - Modelling, Programming and Simulations (E. P. Leite)\n\nThis is an authoritative guide to generating readable, compact, and verifiably correct MATLAB programs. It is ideal for undergraduate engineering courses in Mechanical, Aeronautical, Civil, and Electrical engineering that require/use MATLAB.\n\n•",
null,
"AMPL: A Modeling Language for Mathematical Programming\n\nThis book is a complete guide to AMPL for modelers at all levels of experience. It begins with a tutorial on widely used linear programming models, and presents all of AMPL's features for linear programming with extensive examples.\n\n•",
null,
"Modeling Reactive Systems With Statecharts (David Harel)\n\nThe book provides a detailed description of a set of languages for modelling reactive systems, which underlies the STATEMATE toolset. The approach is dominated by the language of Statecharts, used to describe behavior and activities.\n\n•",
null,
"The Nature of Code: Simulating Natural Systems with Processing\n\nA range of programming strategies and techniques behind computer simulations of natural systems, from elementary concepts in mathematics and physics to more advanced algorithms that enable sophisticated visual results, using Processing.\n\n•",
null,
"Computational and Numerical Simulations (Jan Awrejcewicz)\n\nIt presents both new theories and their applications, showing bridge between theoretical investigations and possibility to apply them by engineers of different branches of science.\n\n•",
null,
"Theory and Applications of Monte Carlo Simulations (Wai Kin Chan)\n\nThe purpose of this book is to introduce researchers and practitioners to recent advances and applications of Monte Carlo Simulation (MCS). Random sampling is the key of the MCS technique.\n\n•",
null,
"Applications of Monte Carlo Method in Science and Engineering\n\nThis book exposes the broad range of applications of Monte Carlo simulation in the fields of Quantum Physics, Statistical Physics, Reliability, Medical Physics, Polycrystalline Materials, Ising Model, Chemistry, Agriculture, Food Processing, X-ray Imaging, ...\n\n•",
null,
"From Algorithms to Z-Scores: Probabilistic and Statistical Modeling\n\nThis is a textbook for a course in mathematical probability and statistics for computer science students.\n\n•",
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"Technology and Engineering Applications of SIMULINK\n\nPresent the procedural steps required for modeling and simulating the basic dynamic system problems in SIMULINK, built on the top of MATLAB to provide a platform for engineers to plan, model, design, simulate, test and implement complex systems.\n\n•",
null,
"Modeling, Programming and Simulations Using LabVIEW™ Software\n\nIn this book a collection of applications covering a wide range of possibilities is presented. We go from simple or distributed control software to modeling done in LabVIEW to very specific applications to usage in the educational environment.\n\n•",
null,
"Learning Processing: Guide to Programming Images, Animation\n\nThis book teaches you the basic building blocks of programming needed to create cutting-edge graphics applications including interactive art, live video processing, and data visualization, using Processing..\n\n•",
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https://economics.stackexchange.com/questions/10471/quasilinear-preference-and-mrs | [
"# Quasilinear Preference and MRS\n\nDo quasi-linear indifference curves have MRS's that depend only on the nonlinear variable? For example, for a U(x) = √(x) + y, I calculated that the y would not be in the MRS. Does that mean that a consumer does not factor the consumption of a \"linear\" good y into their utility maximization?\n\nIf this is the case, can someone explain to me, practically, what it means for a good to be \"linear\" and for an MRS to exclude one variable?\n\n• The MRS is a function of $x$ and $y$. The fact that $y$ doesn't appear in the formula simply means that this function is constant in $y$. The linearity does not imply indifference. It means that an additional value of 1 is valued equally by the agent irrespective of his baseline consumption. In your example, this contrasts with the marginal utility of consuming $x$ which is decreasing with the baseline consumption. – Oliv Feb 1 '16 at 6:59\n• @Oliv I would vote for this if posted as an answer. – Giskard Feb 1 '16 at 15:14\n\nThe MRS is a function of $x$ and $y$. The fact that $y$ doesn't appear in the formula simply means that this function is constant in $y$.\n\nThe linearity does not imply indifference. It means that an additional value of $y$ is valued equally by the agent irrespective of his baseline consumption. In your example, this contrasts with the marginal utility of consuming $x$ which is decreasing with the baseline consumption since the function $u$ is concave in $x$.\n\n• A promise is a promise :) – Giskard Feb 1 '16 at 18:23\n• @denesp I was not sure it was worth an answer but your opinion lays down the law here ;-) Thanks! – Oliv Feb 1 '16 at 18:28\n\nAssume that your utility function is\n\n$$U(x,y) = \\sqrt x + y$$\n\n$$p_xx+ p_yy = M$$\n\nThe Lagrangean is\n\n$$\\Lambda = \\sqrt x + y + \\lambda[M-p_xx+ p_yy]$$\n\nand the first-order condition with respect to $y$ is\n\n$$1 =\\lambda p_y$$\n\nWe Know that $\\lambda$ is the marginal effect of an increase in Income on the maximized utility function. So (considering discrete changes) if your income increases by $1$ kudo, maximized utility will increase by $1/p_y$.\n\nIt makes sense then to treat $y$ as the numeraire good, in which case its price is undetermined, our budget constraint is $p_xx+ y = M$, and the effect on the utility function by an increase in $M$ by one unit is $1$... as is the effect of increasing $y$ by one unit! But that makes $y$ equivalent to income, it is not \"quantity\" anymore, but value.\n\nIn other words, a good entering linearly the utility function is a natural modelling choice for a composite good that represents \"all other goods\", i.e. residual income after trading for the good $x$ we want to focus on."
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http://ixtrieve.fh-koeln.de/birds/litie/document/8319 | [
"# Document (#8319)\n\nAuthor\nWorley, J.\nTitle\nIn praise of IMPRIMATUR\nSource\nMonitor. 1995, no.178, S.12-13\nYear\n1995\nAbstract\nComments generally on the European Commission Directorate General research projects in the information field and focuses briefly on the IMPRIMATUR project, which aims to balance the intellectual property rights of information producers with the access needs of users. It represents a spectrum of copyright interests, including: education, librarianship and information science, information technology and telecommunications\nTheme\nRechtsfragen\nObject\nIMPRIMATUR\n\n## Similar documents (content)\n\n1. 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https://www.hindawi.com/journals/wcmc/2021/5533399/ | [
"#### Abstract\n\nIn filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) systems, a large pilot overhead is required due to the existence of the imaginary interference. In this paper, we present an approach to reduce the pilot overhead of channel estimation. A part of pilot overhead is used for transmitting data, and compensating symbols are required and designed to remove the imaginary interference. It is worthwhile to point out that the power of compensating symbols can be helpful for data recovery; hence, the proposed approach decreases the overhead of pilots significantly without the cost of additional pilot energy. In addition, the proposed scheme is extended into multiple input multiple output systems without the performance loss. Compared with the conventional preamble consisting of columns symbols, the pilot overhead is equivalent to column symbols in the proposed preamble. To verify the proposed preamble, numerical simulations are carried out with respects to bit error ratio.\n\n#### 1. Introduction\n\nCurrently, filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has been considered as a potential alternative to the conventional orthogonal frequency division multiplexing (OFDM). In the past several years, FBMC/OQAM and other filter-based waveforms have been studied to overcome the disadvantages of OFDM. This paper focuses on the FBMC/OQAM technique and presents an effective solution to the channel estimation with low pilot overhead.\n\nUnlike in OFDM, channel estimation in FBMC/OQAM is not a straightforward mission, which is related to that the waveform synthesis and analysis of FBMC/OQAM are not same as that of OFDM. Since the orthogonality condition only is met in real field [2, 5], FBMC/OQAM systems transmit real-valued symbols obtained by the real and imaginary parts of complex-valued QAM symbols, and there exists imaginary interferences among the transmitted real-valued symbols, called the intrinsic imaginary interference . For the channel estimation, the imaginary interference has a crucial effect on the pilot design. The imaginary interference has to be eliminated to ensure the good system performance . In particular, while in OFDM receiver data/pilot symbols that are perfectly separated after applying the FFT, the signal samples from the output of the analysis filter in an FBMC/OQAM receiver are subject to intersymbol interference (ISI), both along the time and frequency/subcarriers. ISI-free symbols could be achieved after the channel equalization and the operation of taking the real parts. In the absence of the channel, ISI appears as an imaginary component that adds to the real-valued data symbols which are carried by the FBMC/OQAM waveform, which has to be considered in the pilot design.\n\nTo avert the imaginary interference, a direct method is to disable the symbols surrounding the pilots, which results in a reduced spectral efficiency. By applying the following method, this spectral efficiency loss could be avoid . One dummy symbol is set adjacent to the pilot to eliminate the imaginary interference of the FBMC/OQAM system. This dummy symbol was then called auxiliary pilot (AP) in . Although it is helpful to remove the imaginary interference to pilots, the AP method effectively increases the transmit power. A more complex approach, but more efficient in terms of transmit power, was proposed in . The data symbols surrounding pilots are performed by a linear coding so that the data symbols do not produce any imaginary interference. Nevertheless, to completely remove the imaginary interference, a long code length is required in the coding scheme, which in turn increases a large complexity at both of the transmitter and the receiver. In addition, it also introduces other complications, which are discussed in . In , the authors presented the interference approximation method (IAM), in which it was revealed that the channel estimation performance is decided by the so-called pseudopilot power consisting of pilot and the imaginary interference from adjacent data. Afterwards, the modified versions of IAM were presented to improve the pseudopilot power by employing imaginary-valued pilots, i.e., IAM-C and IAM-I . However, it should be noted that the existing IAM-based methods require columns real-valued symbols as pilot overhead to achieve the channel estimation. To reduce the pilot overhead of IAM-based schemes, the iterative algorithm was proposed to eliminate the imaginary interference for channel estimation . Nevertheless, it suffers from the problems of high computational complexity. In , the authors proposed the pairs of the real pilots (POP) method, with only columns pilots. However, by reason of the bad ability of against noise, the POP method exhibits poor channel estimation performance compared with the conventional IAM-based methods.\n\nIn this paper, we present an approach to reduce the pilot overhead of channel estimation in FBMC/OQAM systems. Compared with the conventional pilot structures, a part of pilot overhead is used for transmitting data, and compensating symbols are required and designed to eliminate the imaginary interference from data. Note that it is proven that the power of compensating symbols can be helpful for data recovery; hence, the proposed approach decreases the overhead of pilots significantly without the cost of additional pilot energy. Compared with the conventional methods with columns pilots, the proposed scheme only requires columns pilots for the channel estimation. In addition, the proposed approach is extended into multiple input multiple output- (MIMO-) based FBMC (MIMO-FBMC) systems.\n\nThe rest of this paper is organized as follows. The IAM method is briefly introduced in Section 2. The proposed approach is presented in Section 3, followed by the corresponding algorithm. Then, the proposed scheme is extended into MIMO-FBMC systems in Section 4. Section 5 shows the simulations, and Section 6 is the conclusions.\n\n#### 2. Channel Estimation with the IAM Method in FBMC/OQAM Systems\n\n##### 2.1. System Model\n\nAs depicted in Figure 1, the diagram block of FBMC/OQAM transceiver is presented, in which subcarriers are considered in the FBMC/OQAM system with the subcarrier spacing . Note that the complex-valued data symbols have the interval of samples in time, and by partitioning each complex-valued symbol, a pair of PAM symbols are obtained. The PAM symbols are denoted by , with the subchannel index and the time index. In addition, and , i.e., the real and imaginary parts of a QAM symbol, have the interval of samples in time. is the prototype filter and spans over the time interval , where is the overlapping factor and is supposed to be a positive integer. It is further assumed that the filter is even and symmetric around its center, hence, for .\n\nFollowing Figure 1, the transmitted signal is \n\nwhere stands for the subcarrier number. represents one transmitted symbol of position , with only real value.\n\nThen, the signal at the receive antenna is obtained\n\nwhere the sign is the convolution operator. represents the multipath channel, and there exists a channel noise , satisfying the Gaussian distribution with variance .\n\nThen, demodulations at the receiver can be written as\n\nThen, an operator of taking real part is required.\n\nNote that channel estimation is necessary in the FBMC/OQAM system under the multipath channel.\n\n##### 2.2. The IAM Method\n\nIn , the IAM method with 3 column pilots has been presented for the channel estimation in FBMC/OQAM systems. The estimation model of IAM can be obtained :\n\nwhere is the demodulation at the receiver of FBMC/OQAM. stands for frequency-domain channel at -th subcarrier, which is supposed quasi-invariant in the time domain in this paper, i.e.,\n\nwith the maximum channel delay spread of . The imaginary interference is written as\n\nwith , and the imaginary interference factor, , is defined as\n\nAnd the noise term is\n\nThen, the IAM channel estimation is written as \n\nFigure 2(a) depicts the existing preamble of IAM, i.e., with , , and with . Note that it is well known that the interval of an FBMC/OQAM symbol is only half of that of an OFDM symbol. Therefore, the pilot overhead in FBMC/OQAM systems is 1.5 times of that classical OFDM systems.\n\n##### 2.3. POP Method\n\nThe POP method is another preamble-based channel estimation method in . As shown in Figure 2(b), only two columns of real-valued pilots are required in the POP method, i.e., , with , and with .\n\nSuppose is the time-frequency positions of two symbols. The channel estimation by POP can be written as\n\nwhere and are the operators of taking the real part and the imaginary part, respectively. is the ratio between the imaginary part and the real part of ,\n\nThen, the channel coefficients have been estimated. This approach does not require any knowledge of the prototype function and could be adopted as preamble-based method and also as a scattered-based channel estimation method.\n\n#### 3. Proposed Channel Estimation Scheme for FBMC/OQAM Systems\n\n##### 3.1. Preamble Structure of the Proposed Scheme\n\nFigure 3 depicts the proposed preamble structure, where are pilot symbols. Different from Figure 2(a), a part time-frequency resources of the first and the third columns are used to transmit additional data symbols (ADS), i.e., with and . To eliminate the imaginary interference, compensating pilot symbols (CPS) are required, i.e., with and . According to the criteria that the imaginary interferences from ADS and CPS should be mutually canceling, can be designed by\n\nwhere represents the diagonal matrix with -th diagonal element , and\n\nThen, it is obtained as\n\nIt should be noted that (16) cannot be used to design CPS directly due to the fact that it is difficult to obtain at the transmitter.\n\nIt is proven that is a unitary matrix in the appendix. Let be the -th entry of , and it can be obtained as\n\nThus, it can be concluded that for .\n\nIn addition, define , and its -th element is , which is close to zero for . Then, it can be assumed that for or . Therefore, and can be obtained by\n\n##### 3.2. Data Recovery of ADS\n\nIn this subsection, it is proven that the CPS is helpful for data recovery of ADS. Therefore, the ADS has the similar ability to fight against the noise compared with data symbols as we can see below.\n\nAccording to (5), the demodulation of and is\n\nwhere and are the imaginary interference, respectively, i.e., , in which and , , in which and . with and . with and .\n\nAccording to (18), we have\n\nLet , and it is obtained\n\nWhen the channel noise vanishes, we have . Then, will be the input of channel equalizer instead of , since the noise variance will be reduced half after the linear combination. By this way, the ADS has similar capability to fight against the noise compared with the data symbols.\n\n#### 4. Channel Estimation in MIMO-FBMC\n\nIn this section, the proposed scheme in Section 3 can be easily extended into MIMO-FBMC systems with transmit antennas and receive antennas, as shown in Figure 4. Denote the symbol of the -th transmit antenna as , and let be the channel frequency response between the -th receive antenna and the -th transmit antenna at the -th subcarrier.\n\nWithout loss of generality, is set to 2 in this section for simplicity. As is well known, the imaginary interference exists among the FBMC/OQAM symbols . When there exists the imaginary interference between different antennas, it is difficult for one user to perform the channel estimation since the imaginary interference from other users is not available. Therefore, the key of the preamble design in MIMO-FBMC systems is the imaginary interference cancelation between antennas. Figure 5(a) depicts the conventional preambles on the two transmit antennas in MIMO-FBMC systems. Zeros are placed in the first and third columns to avert imaginary interference from data. It should be noted that nonzero pilots only locate in a part of subcarriers to ensure no imaginary interference between antennas, i.e., is a nonzero pilot for the first transmit antenna, and is a nonzero pilot for the second transmit antenna. In our proposed preambles, in Figure 5(b), the nonzero pilots in the second column are the same as the conventional preambles. Differently, half of subcarriers in the first and third columns are placed by data symbols, improving the spectral efficiency. To eliminate the imaginary interference, compensating pilot symbols are required and designed according to (16) in Section 3. Therefore, compared with the conventional preambles, the pilot overhead of the proposed preamble is reduced by 1/3.\n\nAt the receiver, the demodulation of the -th receive antenna is obtained\n\nwhere noise satisfies the Gaussian distribution with mean 0 and variance . is the imaginary interference term to the transmit symbol .\n\nAs mentioned above, the imaginary interference between antennas can be removed completely. Then, for the proposed preambles in Figure 5(b), equation (22) can be rewritten as\n\nAccordingly, the channel estimation in MIMO-FBMC systems can be obtained as\n\nThen, the simple linear interpolation is performed on and to obtain the channel estimation of all subcarriers, respectively. It should be noted that our proposed approach could decrease the overhead of pilots significantly without the cost of additional pilot energy. Although the CPS symbols consume energy, it will be completely used for symbol recovery as presented in Subsection 3.2.\n\n#### 5. Simulation Results\n\nIn this section, we evaluate the performance of the proposed channel estimation approaches that are presented in this paper through computer simulations. The FBMC/OQAM system employs the PHYDYAS filter and the overlap parameter . The multipath channel model is simulated, i.e., SUI proposed by the IEEE 802.16 broadband wireless access working group . In simulations, the following parameters are considered. (i)Subcarrier number: 2048(ii)Sampling rate (MHz): (iii)Path number: (iv)Delay of path (): 0, 0,4, 0.9(v)Power delay profile (dB): 0, -5, -10(vi)Modulation: 4QAM(vii)Channel coding: convolutional coding \n\nFor comparison, we also give the performance of POP , which only requires two columns of pilots.\n\nFigures 6 and 7 show the MSE and BER performances of the proposed approach. It can be easily seen that obvious performance loss is observed in the conventional POP method. As presented in , the performance of POP depends on a random power that could be close to zero sometimes, leading to a poor performance. In addition, the proposed scheme can achieve the same MSE and BER performances as the IAM method, which indicates that the imaginary interference between pilots and data symbols can be eliminated completely in the proposed scheme. It should be noted that only two columns pilots are needed in the proposed scheme, while the conventional preamble requires three columns of pilots. Therefore, better spectral efficiency can be achieved by our proposed channel estimation approach.\n\nFigure 8 shows BER of the proposed approach in MIMO-FBMC systems, in which both of and are set to 2. The proposed 2-column preamble can achieve similar BER compared to the conventional 3-column preamble, which demonstrates the effectiveness of the proposed scheme. It should be noted that our proposed scheme can reduce the pilot overhead significantly without the cost of additional pilot energy. Although the CPS symbols consume energy as shown in Figures 3 and 5, it will be completely used for symbol recovery as presented in Subsection 3.2.\n\n#### 6. Conclusions\n\nIn this paper, an approach was presented for the pilot overhead reduction in the channel estimation of FBMC/OQAM systems. Compared with the conventional methods with columns pilots, the proposed scheme only requires column pilots. In addition, the proposed approach was also extended into MIMO-FBMC systems. It was also proven that our proposed approach could decrease the overhead of pilots significantly without the cost of additional pilot energy and performance loss. Simulations have been done to verify the effectiveness of the proposed approach.\n\n#### Appendix\n\nFrom (8), we have and where are imaginary-valued and constant. Furthermore, when or , . Thus, (14) and (15) can be rewritten as respectively.\n\ndenote an diagonal matrix and . Therefore, we have\n\nNote that and since both of and are imaginary-valued, where is the Hermitian transpose operation. For the even subcarrier , it can be easily obtained where is the zero matrix. Then, we have\n\nBased on the equations and , we have\n\nThen,\n\nFinally, we can obtain that is a unitary matrix.\n\n#### Data Availability\n\nThe data used to support the findings of this study are available from the corresponding author upon request.\n\n#### Conflicts of Interest\n\nThe authors declare that there are no conflicts of interest regarding the publication of this paper.\n\n#### Acknowledgments\n\nThis work was financially supported in part by the National Science Foundation of China with Grant number 62001333, Nature Science Foundation of Southwest University of Science and Technology with Grant number 18zx7142, and the Scientific Research Fund of Beijing Information Science and Technology University with Grant number 2025018."
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https://network.bepress.com/physical-sciences-and-mathematics/mathematics/number-theory/page8 | [
"# Number Theory Commons™\n\n436 Full-Text Articles 426 Authors 133,476 Downloads",
null,
"76 Institutions\n\n## All Articles in Number Theory\n\n436 full-text articles. Page 8 of 17.\n\nPascal's Triangle And Mathematical Induction, 2017",
null,
"New Mexico State University\n\n#### Pascal's Triangle And Mathematical Induction, Jerry Lodder\n\n##### Number Theory\n\nNo abstract provided.\n\n2017",
null,
"Colorado State University-Pueblo\n\n#### Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett\n\n##### Number Theory\n\nNo abstract provided.\n\n2017",
null,
"The Graduate Center, City University of New York\n\n#### Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther\n\n##### Dissertations, Theses, and Capstone Projects\n\nThis thesis comes in four parts, which can be read independently of each other.\n\nIn the first chapter, we prove a generalization of Poonen's finite field Bertini theorem, and use this to show that the obvious obstruction to embedding a curve in some smooth surface is the only obstruction over perfect fields, extending a result of Altman and Kleiman. We also prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.\n\nIn the second chapter, for a fixed base curve over a finite field of characteristic at least 5 ...\n\nNeutrosophy, A Sentiment Analysis Model, 2017",
null,
"University of New Mexico\n\n#### Neutrosophy, A Sentiment Analysis Model, Florentin Smarandache, Mirela Teodorescu, Daniela Gifu\n\n##### Mathematics and Statistics Faculty and Staff Publications\n\nThis paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis. The aim of this pilot study is to find a procedure to diminish the uncertainties from public discourse induced, especially, by humans (politicians, journalists, etc.). We consider that Neutrosophy Theory is a sentiment analysis specific case regarding processing of the three states: positive, negative, and neutral. The study is intended to identify a method to answer to uncertainties solving in order to support politician's staff, NLP specialists, artificial intelligence researchers and generally the electors.\n\n2017",
null,
"The Graduate Center, City University of New York\n\n#### Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, David Seff\n\nFor any positive real number $\\theta > 1$, and any natural number $n$, it is obvious that sequence $\\theta^{1/n}$ goes to 1. Nathanson and O'Bryant studied the details of this convergence and discovered some truly amazing properties. One critical discovery is that for almost all $n$, $\\displaystyle\\floor{\\frac{1}{\\fp{\\theta^{1/n}}}}$ is equal to $\\displaystyle\\floor{\\frac{n}{\\log\\theta}-\\frac{1}{2}}$, the exceptions, when $n > \\log_2 \\theta$, being termed atypical $n$ (the set of which for fixed $\\theta$ being named $\\mcA_\\theta$), and that for $\\log\\theta$ rational, the number of atypical $n ... Algorithmic Factorization Of Polynomials Over Number Fields, 2017",
null,
"Rose-Hulman Institute of Technology #### Algorithmic Factorization Of Polynomials Over Number Fields, Christian Schulz ##### Mathematical Sciences Technical Reports (MSTR) The problem of exact polynomial factorization, in other words expressing a polynomial as a product of irreducible polynomials over some field, has applications in algebraic number theory. Although some algorithms for factorization over algebraic number fields are known, few are taught such general algorithms, as their use is mainly as part of the code of various computer algebra systems. This thesis provides a summary of one such algorithm, which the author has also fully implemented at https://github.com/Whirligig231/number-field-factorization, along with an analysis of the runtime of this algorithm. Let k be the product of the degrees of ... 2017",
null,
"Kennesaw State University #### From Simplest Recursion To The Recursion Of Generalizations Of Cross Polytope Numbers, Yutong Yang ##### KSU Journey Honors College Capstones and Theses My research project involves investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on \"Generalizations of cross-polytope numbers\". It will include the proofs of the combinatorics results in Dr. Edwards and Dr. Griffiths' recently published paper.$E(n,m)$and$O(n,m)\\$, the even terms and odd terms for Dr. Edward's original combinatorial expression, are two distinct combinatorial expressions that are in fact equal. But there is no obvious ...\n\nRoman Domination In Complementary Prisms, 2017",
null,
"East Tennessee State University\n\n#### Roman Domination In Complementary Prisms, Alawi I. Alhashim\n\n##### Electronic Theses and Dissertations\n\nThe complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number ...\n\nOn The Reality Of Mathematics, 2017",
null,
"Southeastern University - Lakeland\n\n#### On The Reality Of Mathematics, Brendan Ortmann\n\n##### Selected Student Publications\n\nMathematics is an integral cornerstone of science and society at large, and its implications and derivations should be considered. That mathematics is frequently abstracted from reality is a notion not countered, but one must also think upon its physical basis as well. By segmenting mathematics into its different, abstract philosophies and real-world applications, this paper seeks to peer into the space that mathematics seems to fill; that is, to understand how and why it works. Under mathematical theory, Platonism, Nominalism, and Fictionalism are analyzed for their validity and their shortcomings, in addition to the evaluation of infinities and infinitesimals, to ...\n\nOn Vector-Valued Automorphic Forms On Bounded Symmetric Domains, 2017",
null,
"The University of Western Ontario\n\n#### On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi\n\n##### Electronic Thesis and Dissertation Repository\n\nThe objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via Poincare series. In addition, it provides a proof of that vector-valued Poincare series on an irreducible bounded symmetric domain span the space of vector-valued automorphic forms.\n\nApplications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, 2017",
null,
"Yongsei University\n\n#### Applications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, Jongsil Lee, James Mclaughlin, Jaebum Sohn\n\n##### Mathematics Faculty Publications\n\nIn this paper we show that various continued fractions for the quotient of general Ramanujan functions G(aq, b, λq)/G(a, b, λ) may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer-Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine’s continued fraction for a ratio of 2φ1 functions, or other similar continued fraction expansions of ratios of 2φ1 functions. Further, by employing essentially the same methods, a ...\n\n2017",
null,
"West Chester University of Pennsylvania\n\n#### Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, James Mclaughlin\n\n##### Mathematics Faculty Publications\n\nThe bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of 2ψ2 series ∞ ∑n=−∞ (a, c;q)n (b,d;q)n z n . Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say χ(q), and a root ...\n\nOn P-Adic Fields And P-Groups, 2017",
null,
"University of Kentucky\n\n#### On P-Adic Fields And P-Groups, Luis A. Sordo Vieira\n\n##### Theses and Dissertations--Mathematics\n\nThe dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to ...\n\nCombinatorics Of Compositions, 2017",
null,
"Georgia Southern University\n\n#### Combinatorics Of Compositions, Meghann M. Gibson\n\n##### Electronic Theses and Dissertations\n\nInteger compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.\n\nP-Union And P-Intersection Of Neutrosophic Cubic Sets, 2017",
null,
"University of New Mexico\n\n#### P-Union And P-Intersection Of Neutrosophic Cubic Sets, Florentin Smarandache, Young Bae Jun, Chang Su Kim\n\n##### Mathematics and Statistics Faculty and Staff Publications\n\nConditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.\n\nNumbers In Base B That Generate Primes With Help The Luhn Function Of Order Ω, 2017",
null,
"University of New Mexico\n\n#### Numbers In Base B That Generate Primes With Help The Luhn Function Of Order Ω, Florentin Smarandache, Octavian Cira\n\n##### Mathematics and Statistics Faculty and Staff Publications\n\nWe put the problem to determine the sets of integers in base b ≥ 2 that generate primes with using a function.\n\nA Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, 2017",
null,
"University of New Mexico\n\n#### A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mohsin Khan\n\n##### Mathematics and Statistics Faculty and Staff Publications\n\nIn this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated.\n\n2017",
null,
"University of Central Florida\n\n#### Scaling Of Spectra Of Cantor-Type Measures And Some Number Theoretic Considerations, Isabelle Kraus\n\nWe investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number m generates a complete or incomplete Fourier basis for a Cantor-type measure with scale g.\n\nMathematics Education From A Mathematicians Point Of View, 2016",
null,
"University of Tennessee, Knoxville\n\n#### Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson\n\n##### Masters Theses\n\nThis study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.\n\nOn Sums Of Binary Hermitian Forms, 2016",
null,
"The Graduate Center, City University of New York\n\n#### On Sums Of Binary Hermitian Forms, Cihan Karabulut\n\n##### Dissertations, Theses, and Capstone Projects\n\nIn one of his papers, Zagier defined a family of functions as sums of powers of quadratic polynomials. He showed that these functions have many surprising properties and are related to modular forms of integral weight and half integral weight, certain values of Dedekind zeta functions, Diophantine approximation, continued fractions, and Dedekind sums. He used the theory of periods of modular forms to explain the behavior of these functions. We study a similar family of functions, defining them using binary Hermitian forms. We show that this family of functions also have similar properties.",
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"http://trace.tennessee.edu/assets/institution_icons/885231.png",
null,
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null
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https://andrewpwheeler.com/2014/07/13/smoothed-regression-plots-for-multi-level-data/ | [
"# Smoothed regression plots for multi-level data\n\nBruce Weaver on the SPSS Nabble site pointed out that the Centre for Multilevel Modelling has added some syntax files for multilevel modelling for SPSS. I went through the tutorials (in R and Stata) a few years ago and would highly recommend them.\n\nSomehow following the link trail I stumbled on this white paper, Visualising multilevel models; The initial analysis of data, by John Bell and figured it would be good fodder for the the blog. Bell basically shows how using smoothed regression estimates within groups is a good first step in data analysis of complicated multi-level data. I obviously agree, and previously showed how to use ellipses to the same effect. The plots in the Bell whitepaper though are very easy to replicate directly in base SPSS syntax (no extra stat modules or macros required) using just `GGRAPH` and inline `GPL`.\n\nFor illustration purposes, I will use the same data as I did to illustrate ellipses. It is the `popular2.sav` sample from Joop Hox’s book. So onto the SPSS code; first we will define a `FILE HANDLE` for where the `popular2.sav` data is located and open that file.\n\n``````FILE HANDLE data /NAME = \"!!!!!!Your Handle Here!!!!!\".\nGET FILE = \"data\\popular2.sav\".\nDATASET NAME popular2.``````\n\nNow, writing the `GGRAPH` code that will follow is complicated. But we can use the GUI to help us write the most of it and them edit the pasted code to get the plot we want in the end. So, the easiest start to get the graph with the regression lines we want in the end is to navigate to the chart builder menu (Graphs -> Chart Builder), and then create a scatterplot with `extrav` on the x axis, `popular` on the y axis, and use `class` to color the points. The image below is a screen shot of this process, and below that is the `GGRAPH` code you get when you paste the syntax.",
null,
"``````*Base plot created from GUI.\nGGRAPH\n/GRAPHDATASET NAME=\"graphdataset\" VARIABLES=extrav popular class[LEVEL=NOMINAL] MISSING=LISTWISE\nREPORTMISSING=NO\n/GRAPHSPEC SOURCE=INLINE.\nBEGIN GPL\nSOURCE: s=userSource(id(\"graphdataset\"))\nDATA: extrav=col(source(s), name(\"extrav\"))\nDATA: popular=col(source(s), name(\"popular\"))\nDATA: class=col(source(s), name(\"class\"), unit.category())\nGUIDE: axis(dim(1), label(\"extraversion\"))\nGUIDE: axis(dim(2), label(\"popularity sociometric score\"))\nGUIDE: legend(aesthetic(aesthetic.color.exterior), label(\"class ident\"))\nELEMENT: point(position(extrav*popular), color.exterior(class))\nEND GPL.``````\n\nNow, we aren’t going to generate this chart. With 100 classes, it will be too difficult to identify any differences between classes unless a whole class is an extreme outlier. Here I am going to make several changes to generate the linear regression line of extraversion on popular within each class. To do this we will make some edits to the `ELEMENT` statement:\n\n• replace `point` with `line`\n• replace `position(extrav*popular)` with `position(smooth.linear(extrav*popular))` – this tells SPSS to generate the linear regression line\n• replace `color.exterior(class)` with `split(class)` – the split modifier tells SPSS to generate the regression lines within each class.\n• make the regression lines semi-transparent by adding in `transparency(transparency.\"0.7\")`\n\nExtra things I did for aesthetics:\n\n• I added jittered points to the plot, and made them small and highly transparent (these really aren’t necessary in the plot and are slightly distracting). Note I placed the points first in the GPL code, so the regression lines are drawn on top of the points.\n• I changed the `FORMATS` of `extrav` and `popular` to `F2.0`. SPSS takes the formats for the axis in the charts from the original variables, so this prevents decimal places in the chart (and SPSS intelligently chooses to only label the axes at integer values on its own).\n• I take out the `GUIDE: legend` line – it is unneeded since we do not use any colors in the chart.\n• I change the x and y axis labels, e.g. `GUIDE: axis(dim(1), label(\"Extraversion\"))` to be title case.\n\n``````*Updated chart with smooth regression lines.\nFORMATS extrav popular (F2.0).\nGGRAPH\n/GRAPHDATASET NAME=\"graphdataset\" VARIABLES=extrav popular class[LEVEL=NOMINAL] MISSING=LISTWISE\nREPORTMISSING=NO\n/GRAPHSPEC SOURCE=INLINE.\nBEGIN GPL\nSOURCE: s=userSource(id(\"graphdataset\"))\nDATA: extrav=col(source(s), name(\"extrav\"))\nDATA: popular=col(source(s), name(\"popular\"))\nDATA: class=col(source(s), name(\"class\"), unit.category())\nGUIDE: axis(dim(1), label(\"Extraversion\"))\nGUIDE: axis(dim(2), label(\"Popularity Sociometric Score\"))\nELEMENT: point.jitter(position(extrav*popular), transparency.exterior(transparency.\"0.7\"), size(size.\"3\"))\nELEMENT: line(position(smooth.linear(extrav*popular)), split(class), transparency(transparency.\"0.7\"))\nEND GPL.``````",
null,
"So here we can see that the slopes are mostly positive and have intercepts varying mostly between 0 and 6. The slopes are generally positive and (I would guess) around 0.25. There are a few outlier slopes, and given the class sizes do not vary much (most are around 20) we might dig into these outlier locations a bit more to see what is going on. Generally though with 100 classes it doesn’t strike me as very odd as some going against the norm, and a random effects model with varying intercepts and slopes seems reasonable, as well as the assumption that the distribution of slopes are normal. The intercept and slopes probably have a slight negative correlation, but not as much as I would have guessed with a set of scores that are so restricted in this circumstance.\n\nNow the Bell paper has several examples of using the same type of regression lines within groups, but using loess regression estimates to assess non-linearity. This is really simple to update the above plot to incorporate this. One would simply change `smooth.linear` to `smooth.loess`. Also SPSS has the ability to estimate quadratic and cubic polynomial terms right within GPL (e.g. `smooth.cubic`).\n\nHere I will suggest a slightly different chart that allows one to assess how much the linear and non-linear regression lines differ within each class. Instead of super-imposing all of the lines on one plot, I make a small multiple plot where each class gets its own panel. This allows much simpler assessment if any one class shows a clear non-linear trend.\n\n• Because we have 100 groups I make the plot bigger using the `PAGE` command. I make it about as big as can fit on my screen without having to scroll, and make it 1,200^2 pixels. (Also note when you use a `PAGE: begin` command you need an accompanying `PAGE: end()` command.\n• For the small multiples, I wrap the panels by setting `COORD: rect(dim(1,2), wrap())`.\n• I strip the x and y axis labels from the plot (simply delete the `label` options within the `GUIDE` statements. Space is precious – I don’t want it to be taken up with axis labels and legends.\n• For the panel label I place the label on top of the panel by setting the opposite option, `GUIDE: axis(dim(3), opposite())`.\n\nWordPress in the blog post shrinks the graph to fit on the website, but if you open the graph up in a second window you can see how big it is and explore it easier.\n\n``````*Checking for non-linear trends.\nGGRAPH\n/GRAPHDATASET NAME=\"graphdataset\" VARIABLES=extrav popular class[LEVEL=NOMINAL] MISSING=LISTWISE\nREPORTMISSING=NO\n/GRAPHSPEC SOURCE=INLINE.\nBEGIN GPL\nPAGE: begin(scale(1200px,1200px))\nSOURCE: s=userSource(id(\"graphdataset\"))\nDATA: extrav=col(source(s), name(\"extrav\"))\nDATA: popular=col(source(s), name(\"popular\"))\nDATA: class=col(source(s), name(\"class\"), unit.category())\nCOORD: rect(dim(1,2), wrap())\nGUIDE: axis(dim(1))\nGUIDE: axis(dim(2))\nGUIDE: axis(dim(3), opposite())\nELEMENT: line(position(smooth.linear(extrav*popular*class)), color(color.black))\nELEMENT: line(position(smooth.loess(extrav*popular*class)), color(color.red))\nPAGE: end()\nEND GPL.``````",
null,
"The graph is complicated, but with some work one can go group by group to see any deviations from the linear regression line. So here we can see that most of the non-linear loess lines are quite similar to the linear line within each class. The only one that strikes me as noteworthy is class 45.\n\nHere there is not much data within classes (around 20 students), so we have to wary of small samples to be estimating these non-linear regression lines. You could generate errors around the linear and polynomial regression lines within GPL, but here I do not do that as it adds a bit of complexity to the plot. But, this is an excellent tool if you have many points within your groups and it can be amenable to quite a large set of panels."
]
| [
null,
"https://lh5.googleusercontent.com/-GeFWT0u0uBM/U8KexO9SlzI/AAAAAAAAA8A/nZ0z1yJ2GCU/w598-h629-no/CaptureScatterplot.PNG",
null,
"https://lh4.googleusercontent.com/-9_U8tv9CzOE/U8KexJhSABI/AAAAAAAAA78/W22f_RUQjYc/w625-h500-no/RegByGroup2.png",
null,
"https://lh5.googleusercontent.com/--k-xJ1xzAf4/U8KexocV5eI/AAAAAAAAA8I/myU4wMlvgak/s847-no/RegByGroup3.png",
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https://cs.stackexchange.com/questions/69962/number-of-buckets-for-bucket-sort-most-significant-bits | [
"# Number of buckets for bucket sort (most significant bits)\n\nWikipedia has this pseudocode on bucket sort:\n\nfunction bucketSort(array, n) is buckets ← new array of n empty lists for i = 0 to (length(array)-1) do insert array[i] into buckets[msbits(array[i], k)] for i = 0 to n - 1 do nextSort(buckets[i]); return the concatenation of buckets, ...., buckets[n-1]\n\nIt also explains:\n\nHere array is the array to be sorted and n is the number of buckets to use. The function msbits(x,k) returns the k most significant bits of x (floor(x/2^(size(x)-k))); different functions can be used to translate the range of elements in array to n buckets...\n\nWhat baffles me is: Why would one want to initialize buckets with n buckets when 2^k is the maximum number of values that msbits can possibly generate, given the way it's defined?\n\nThe code you found is unfortunately written and explained in a very confusing way, most notably in a way that, in my humble opinion, misses the entire point of Bucketsort.\n\nLet $A$ be an array of $n$ elements, taken from the ordered set $(S, \\le)$. Bucketsort is a sorting algorithm that sorts $A$ in linear time with probability $1$, subject to the hypothesis that the statistical distribution of the elements of $A$ over $S$ is known in advance.\n\nFor the sake of simplicity, we will assume $S$ to be the real interval $[0, 1)$ and the distribution of $A$ to be uniform over $[0, 1)$. Our second assumption is without loss of generality. In fact, should we be provided with a different probability density function $\\rho$, we could simply replace each $x \\in A$ with:\n\n$$x' =\\int_{0}^x \\rho(z) dz$$\n\nAn analogous argument holds for different choices of $S$.\n\nBucketsort works as follows:\n\n• Split $[0, 1)$ in $n$ consecutive intervals, where $n = |A|$, such that the $i$-th interval is $\\left[ \\frac{i-1}{n}, \\frac{i}{n} \\right)$\n• Create $n$ empty lists $L_1, L_2, \\dots, L_n$\n• For each element $x$ of $A$, add $x$ to the list corresponding to the interval in which it falls\n• Sort each list individually, then return the concatenation $L_1 \\circ L_2 \\circ \\dots \\circ L_n$\n\nCorrectness is obvious, but complexity isn't. The crucial hypothesis is that, by assumption, we are sorting elements uniformly distributed over $[0, 1)$. Therefore, if $n$ grows large, as it is the case in the usual asymptotic setting, at the end of our third step, each of the lists will contain a constant number of elements with probability $1$; if that weren't the case, the elements wouldn't be uniformly distributed after all. Also observe that \"with probability $1$\" is not the same as \"certainly\", although it's as close as it gets.\n\nThe choice of exactly $n$ buckets is due to the fact that we want our last step to take linear time; but that can only be achieved if each list contains a constant amount of elements. We could have chosen just as well to use $n/c$ buckets for any $c \\in \\Theta(1)$, but we couldn't have started with $k \\in o(n)$ buckets; each of them would have contained $n/k \\in \\omega(1)$ elements. The total cost of sorting them would have been:\n\n$$k \\left ( \\frac{n}{k} \\log \\frac{n}{k} \\right ) = n \\log \\omega(1) \\in \\omega(n)$$\n\n• I'm grateful for your in-depth and knowledgeable response. It probably contains the answer I'm looking for, but, unfortunately, I lack sufficient math background to follow it. Feb 11 '17 at 19:00\n• @Julian Is there anything in particular you are having problems with? I can try to clear it up. Feb 11 '17 at 20:06\n\nYes, msbits(x, k) can generate up to 2^k values. But this does not mean buckets[] array has to be length of 2^k. If buckets[] has length 2^k, each bucket has size one, and bucket sort degenerates into counting sort.\n\nSo, you want each bucket size to be more than 1. If we have n buckets, and msbits(x, k) returns 2^k values, then each bucket size is 2^k/n.\n\nOn the contrary, if we choose n = 1, then we will only have one bucket of 2^k. If we choose another sorting algorithm to this bucket, then our bucket sort will have the same order of growth as the chosen sorting algorithm."
]
| [
null
]
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https://mafiadoc.com/unconditionally-secure-multiparty-cunyedu_5b78cbca097c47aa0e8b4678.html | [
"## UNCONDITIONALLY SECURE MULTIPARTY ... - CUNY.edu\n\nparties wish to jointly compute some value based on individually held secret bits of ... What we suggest in this section is a protocol that does not require any ...\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION AND SECRET SHARING DIMA GRIGORIEV AND VLADIMIR SHPILRAIN Abstract. We suggest protocols for secure computation of the sum, product, and some other functions of three or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation, i.e., we do not let any party accumulate functions of other parties’ private numbers that would allow him to recover those numbers. Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the “two millionaires problem”. Finally, we propose a secret sharing scheme where an advantage over Shamir’s and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular player.\n\n1. Introduction Secure multi-party computation is a problem that was originally suggested by Yao in 1982. The concept usually refers to computational systems in which several parties wish to jointly compute some value based on individually held secret bits of information, but do not wish to reveal their secrets to anybody in the process. For example, two individuals who each possess some secret numbers, x and y, respectively, may wish to jointly compute some function f (x, y) without revealing any information about x or y other than what can be reasonably deduced by knowing the actual value of f (x, y). Secure computation was formally introduced by Yao as secure two-party computation. His “two millionaires problem” (cf. our Section 3) and its solution gave way to a generalization to multi-party protocols, see e.g. , . Secure multi-party computation provides solutions to various real-life problems such as distributed voting, private bidding and auctions, sharing of signature or decryption functions, private information retrieval, etc. In this paper, we offer protocols for secure computation of the sum and product of three or more elements of an arbitrary constructible ring without using encryption or any one-way functions whatsoever. We require in our scheme that there are k secure channels for communication between the k ≥ 3 parties, arranged in a circuit. We also show that less than k secure channels is not enough. Research of the first author was partially supported by the Federal Agency of the Science and Innovations of Russia, State Contract No. 02.740.11.5192. Research of the second author was partially supported by the NSF grant DMS-0914778. 1\n\n2\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\nUnconditionally secure multiparty computation was previously considered in and elsewhere (since the present paper is not a survey, we do not give a comprehensive bibliography on the subject here, but only mention what is most relevant to our paper). A new input that we offer here is that, in contrast with and other proposals, we conceal “intermediate results” of a computation. For example, when we compute a P sum of k numbers ni , only the final result ki=1 ni is known to (one of) the parties; partial Psums are not known to anybody. This is not the case in where each partial sum si=1 ni is known to at least some of the parties. This difference is important because, by the “pigeonhole principle”, at least one of the parties may accumulate sufficiently many expressions in ni to be able to recover at least some of the ni other than his own. Here we show how our method works for computing the sum (Section 2) and the product (Section 4) of private numbers. We ask what other functions can be securely computed without revealing intermediate results. Other applications of our method include voting/rating over insecure channels (Section 2.3) and a rather elegant solution of the “two millionaires problem” (Section 3). Finally, in Section 6, we propose a secret sharing scheme where an advantage over Shamir’s and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular players. The disadvantage though is that our scheme is a (k, k)-threshold scheme only. 2. Secure computation of a sum In this section, our scenario is as follows. There are k parties P1 , . . . , Pk ; each Pi has a private element ni of a fixed constructible ring R. The goal is to compute the sum of all ni without revealing any of the ni to any party Pj , j 6= i. One obvious way to achieve this is well studied in the literature (see e.g. [5, 6, 7]): encrypt each ni as E(ni ), send all E(nP i ) to some designated Pi (who does not have a decryption key), have Pi compute S = i E(ni ) and send the result to the participants for E is homomorphic, i.e., that P decryption.PAssuming that the encryption function P i E(ni ) = E( i ni ), each party Pi can recover i ni upon decrypting S. This scheme requires not just a one-way function, but a one-way function with a trapdoor since both encryption and decryption are necessary to obtain the result. What we suggest in this section is a protocol that does not require any one-way function, but involves secure communication between some of the Pi . So, our assumption here is that there are k secure channels of communication between the k parties Pi , arranged in a circuit. Our result is computing the sum of private elements ni without revealing any individual ni to any Pj , j 6= i. Clearly, this is only possible if the number of participants Pi is greater than 2. As for the number of secure channels between Pi , we will show that it cannot be less than k, by the number of parties. 2.1. The protocol (computing the sum). (1) P1 initiates the process by sending n1 +n01 to P2 , where n01 is a random element (“noise”).\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\n3\n\n(2) Each Pi , 2 ≤ i ≤ k − 1, does the following. Upon receiving an element m from Pi−1 , he adds his ni + n0i to m (where n0i is a random element) and sends the result to Pi+1 . (3) Pk adds nk + n0k to whatever he has received from Pk−1 and sends the result to P1 . (4) P 01 from what he got from Pk ; the result now is the sum S = P1 subtracts nP n + 1≤i≤k i 2≤i≤k n0i . Then P1 publishes S. (5) Now all participants Pi ,P except P1 , broadcast their n0i , possibly over insecure channels, and compute 2≤i≤k n0i . Then they subtract the result from S to P finally get 1≤i≤k ni . Thus, in this protocol we have used k (by the number of the parties Pi ) secure channels of communication between the parties. If we visualize the arrangement as a graph with k vertices corresponding to the parties Pi and k edges corresponding to secure channels, then this graph will be a k-cycle. Other arrangements are possible, too; in particular, a union of disjoint cycles of length ≥ 3 would do. (In that case, the graph will still have k edges.) Two natural questions that one might now ask are: (1) is any arrangement with less than k secure channels possible? (2) with k secure channels, would this scheme work with any arrangement other than a union of disjoint cycles of length ≥ 3? The answer to both questions is “no”. Indeed, if there is a vertex (corresponding to P1 , say) of degree 0, then any information sent out by P1 will be available to everybody, so other participants will know n1 unless P1 uses a one-way function to conceal it. If there is a vertex (again, corresponding to P1 ) of degree 1, this would mean that P1 has a secure channel of communication with just one other participant, say P2 . Then any information sent out by P1 will be available at least to P2 , so P2 will know n1 unless P1 uses a one-way function to conceal it. Thus, every vertex in the graph should have degree at least 2, which implies that every vertex is included in a cycle. This immediately implies that the total number of edges is at least k. If now a graph Γ has k vertices and k edges, and every vertex of Γ is included in a cycle, then every vertex has degree exactly 2 since by the “handshaking lemma” the sum of the degrees of all vertices in any graph equals twice the number of edges. It follows that our graph is a union of disjoint cycles. 2.2. Effect of coalitions. Suppose now we have k ≥ 3 parties with k secure channels of communication arranged in a circuit, and suppose 2 of the parties secretly form a coalition. Our assumption here is that, because of the circular arrangement of secure channels, a secret coalition is only possible between parties Pi and Pi+1 for some i, where the indices are considered modulo k; otherwise, attempts to form a coalition (over insecure channels) will be detected. If two parties Pi and Pi+1 exchanged information, they would, of course, know each other’s elements ni , but other than that, they would not get any advantage if k ≥ 4. Indeed, we can just “glue these two parties together”, i.e., consider them as one party, and then the protocol is essentially reduced to that with k −1 ≥ 3 parties. On the other hand, if k = 3, then, of course, two parties together have all the information about the third party’s element.\n\n4\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\nFor an arbitrary k ≥ 4, if n < k parties want to form a (secret) coalition to get information about some other party’s element, all these n parties have to be connected by secure channels, which means there is a j such that these n parties are Pj , Pj+1 , . . . , Pj+n−1 , where indices are considered modulo k. It is not hard to see then that only a coalition of k − 1 parties P1 , . . . , Pi−1 , Pi+1 , . . . , Pk can suffice to get information about the Pi ’s element. 2.3. Ramification: voting/rating over insecure channels. In this section, our scenario is as follows. There are k parties P1 , . . . , Pk ; each Pi has a private integer ni . There is also a computing entity B (for Boss) who shall compute the sum of all ni . The goal is to let B compute the sum of all ni without revealing any of the ni to him or to any party Pj , j 6= i. The following example from real life is a motivation for this scenario. Example 1. Suppose members of the board in a company have to vote for a project by submitting their numeric scores (say, from 1 to 10) to the president of the company. The project gets a green light if the total score is above some threshold value T . Members of the board can discuss the project between themselves and exchange information privately, but none of them wants his/her score to be known to either the president or any other member of the board. In the protocol below, we are again assuming that there are k channels of communication between the parties, arranged in a circuit: P1 → P2 → . . . → Pk → P1 . On the other hand, communication channels between B and any of the parties are not assumed to be secure. 2.4. The protocol (rating over insecure channels). (1) P1 initiates the process by sending n1 + n01 to P2 , where n01 is a random number. (2) Each Pi , 2 ≤ i ≤ k − 1, does the following. Upon receiving a number m from Pi−1 , he adds his ni + n0i to m (where n0i is a random number) and sends the result to Pi+1 . (3) Pk adds nk + n0k to whatever he has received from Pk−1 and sends the result to B. (4) Pk now starts the process of collecting the “adjustment” in the opposite direction. To that effect, he sends his n0k to Pk−1 . (5) Pk−1 adds n0(k−1) and sends the result to Pk−2 . (6) The process ends when P1 gets a number from P2 , adds his n01 , and sends the result to B. This result is the sum of all n0i . (7) B subtracts what he got from P1 from what he got from Pk ; the result now is the sum of all ni , 1 ≤ i ≤ k. 3. Application: the “two millionaires problem” The protocol from Section 2, with some adjustments, can be used to provide an elegant and efficient solution to the “two millionaires problem” introduced in :\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\n5\n\nthere are two numbers, n1 and n2 , and the goal is to solve the inequality n1 ≥ n2 ? without revealing the actual values of n1 or n2 . To that effect, we use a “dummy” as the third party. Our concept of a “dummy” is quite different from a well-known concept of a “trusted third party”; importantly, our “dummy” is not supposed to generate any randomness; he just does what he is told to. Basically, the only difference between our “dummy” and a usual calculator is that there are secure channels of communication between the “dummy” and either “real” party. One possible real-life interpretation of such a “dummy” would be an online calculator that can combine inputs from different users. Also note that in our scheme below the “dummy” is unaware of the committed values of n1 or n2 , which is useful in case the two “real” parties do not want their private numbers to ever be revealed. This suggests yet another real-life interpretation of a “dummy”, where he is a mediator between two parties negotiating a settlement. Thus, let A (Alice) and B (Bob) be two “real” parties, and D (Dummy) the “dummy”. Suppose A’s number is n1 , and B’s number is n2 . 3.1. The protocol (comparing two numbers). − − (1) A splits her number n1 as a difference n1 = n+ 1 − n1 . She then sends n1 to B. + − − (2) B splits his number n2 as a difference n2 = n2 − n2 . He then sends n2 to A. − (3) A sends n+ 1 + n2 to D. + − (4) B sends n2 + n1 to D. − + − (5) D subtracts (n+ 2 + n1 ) from (n1 + n2 ) to get n1 − n2 , and announces whether this result is positive or negative. Remark 1. Perhaps a point of some dissatisfaction in this protocol could be the fact that the “dummy” ends up knowing the actual difference n1 − n2 , so if there is a leak of this information to either party, this party would recover the other’s private number ni . This can be avoided if n1 and n2 are represented in the binary form and compared one bit at a time, going left to right, until the difference between bits becomes nonzero. However, this method, too, has a disadvantage: the very moment the “dummy” pronounces the difference between bits nonzero would give an estimate of the difference n1 − n2 to the real parties, not just to the “dummy”. We note that the original solution of the “two millionaires problem” given in , although lacks the elegance of our scheme, does not involve a third party, whereas our solution does. On the other hand, the solution in uses encryption, whereas our solution does not, which makes it by far more efficient. 4. Secure computation of a product In this section, we show how to use the same general ideas from Section 2 to securely compute a product. Again, there are k parties P1 , . . . , Pk ; each Pi has a private element ni of a fixed constructible ring R. The goal is to compute the product of all ni without revealing any of the ni to any party Pj , j 6= i. Requirements on the ring R are going to be somewhat more stringent here than they were in Section 2. Namely, we require that R does not have zero divisors and, if an element r of R is a product a · x with a known\n\n6\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\na and an unknown x, then x can be efficiently recovered from a and r. Examples of rings with these properties include the ring of integers and any constructible field. 4.1. The protocol (computing the product). (1) P1 initiates the process by sending n1 · n01 to P2 , where n01 is a random element (“noise”). (2) Each Pi , 2 ≤ i ≤ k − 1, does the following. Upon receiving an element m from Pi−1 , he multiplies m by ni · n0i (where n0i is a random element) and sends the result to Pi+1 . (3) Pk multiplies by nk · n0k whatever he has received from Pk−1 and sends the result to P1 . This result is the product P = Π1≤i≤k ni · Π2≤i≤k n0i . (4) P1 divides what he got from Pk by his n01 ; the result now is the product P = Π1≤i≤k ni · Π2≤i≤k n0i . Then P1 publishes P . (5) Now all participants Pi , except P1 , broadcast their n0i , possibly over insecure channels, and compute Π2≤i≤k n0i . Then they divide P by the result to finally get Π1≤i≤k ni . 5. Secure computation of symmetric functions In this section, we show how our method can be easily generalized to allow secure P computation of any expression of the form ki=1 nri , where ni are parties’ private numbers, k is the number of parties, and r ≥ 1 an arbitrary integer. We simplify our method here by removing the “noise”, to make the exposition more transparent. 5.1. The protocol (computing the sum of powers). (1) P1 initiates the process by sending a random element n0 to P2 . (2) Each Pi , 2 ≤ i ≤ k − 1, does the following. Upon receiving an element m from Pi−1 , he adds his nri to m and sends the result to Pi+1 . (3) Pk adds his nrk to whatever he has received from Pk−1 and sends the result to P1 . (4) P1 subtracts (n0 − nr1 ) from what he got from Pk ; the result now is the sum of all nri , 1 ≤ i ≤ k. Now that the parties can securely compute the sum of any powers of their ni , they can also compute any symmetric function of ni . However, in the course of computing a symmetric function from sums of different powers of ni , at least some of the parties will possess several different polynomials in ni , so chances are that at least some of the parties will be able to recover at least some of the ni . On the other hand, because of the symmetry of all expressions involved, there is no way to tell which ni belongs to which party. 5.2. Open problem. Now it is natural to ask: Problem 1. What other functions (other than the sum and the product) can be securely computed without revealing intermediate results to any party?\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\n7\n\nTo be more precise, we note that one intermediate result is inevitably revealed to the party who finishes computation, but this cannot be avoided in any scenario. For example, after the parties have computed the sum of their private numbers, each party also knows the sum of all numbers except his own. What we want is that no other intermediate results are ever revealed. To give some insight into this problem, we consider a couple of examples of computing simple functions different from the sum and the product of the parties’ private numbers. Example 2. We show how to compute the function f (n1 , n2 , n3 ) = n1 n2 + n2 n3 in the spirit of the present paper, without revealing (or even computing) any intermediate results, i.e., without computing n1 n2 or n2 n3 . (1) P2 initiates the process by sending a random element n0 to P3 . (2) P3 adds his n3 to n0 and sends n3 + n0 to P1 . (3) P1 adds his n1 to n0 + n3 and sends the result to P2 . (4) P2 subtracts n0 from n0 + n3 + n1 and multiplies the result by n2 . This is now n1 n2 + n2 n3 . Example 3. The point of this example is to show that functions that can be computed by our method do not have to be homogeneous (in case the reader got this impression based on the previous examples). The function that we compute here is f (n1 , n2 , n3 ) = n1 n2 + g(n3 ), where g is any function. (1) P1 initiates the process by sending a random element a0 to P2 . (2) P2 multiplies a0 by his n2 and sends the result to P3 . (3) P3 multiplies a0 n2 by a random element c0 and sends the result to P1 . (4) P1 multiplies a0 n2 c0 by his n1 , divides by a0 , and sends the result, which is n1 n2 c0 , back to P3 . (5) P3 divides n1 n2 c0 by c0 and adds g(n3 ), to end up with n1 n2 + g(n3 ). Note that in this example, the parties used more than just one loop of transmissions in the course of computation. Also, information here was sent “in both directions” in the circuit. Remark 2. Another collection of examples of multiparty computation without revealing intermediate results can be obtained as follows. Suppose, without loss of generality, that some function f (n1 , . . . , nk ) can be computed by our method in such a way that the last step in the computation is performed by the party P1 , i.e., P1 is the one who ends up with f (n1 , . . . , nk ) while no party knows any intermediate result g(n1 , . . . , nk ) of this computation. Then, obviously, P1 can produce any function of the form F (n1 , f (n1 , . . . , nk )) (for a computable function F ) as well. Examples include nr1 + n1 n2 · · · nk for any r ≥ 0; nr1 + (n1 n2 + n3 )s for any r, s ≥ 0, etc., etc. 6. Secret sharing Secret sharing refers to method for distributing a secret amongst a group of participants, each of whom is allocated a share of the secret. The secret can be reconstructed\n\n8\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\nonly when a sufficient number of shares are combined together; individual shares are of no use on their own. More formally, in a secret sharing scheme there is one dealer and k players. The dealer gives a secret to the players, but only when specific conditions are fulfilled. The dealer accomplishes this by giving each player a share in such a way that any group of t (for threshold) or more players can together reconstruct the secret but no group of fewer than t players can. Such a system is called a (t, k)-threshold scheme (sometimes written as a (k, t)-threshold scheme). Secret sharing was invented by Shamir and Blakley , independent of each other, in 1979. Both proposals assumed secure channels for communication between the dealer and each player. In our proposal here, the number of secure channels is equal to 2k, where k is the number of players, because in addition to the secure channels between the dealer and each player, we have k secure channels for communication between the players, arranged in a circuit: P1 → P2 → . . . → Pk → P1 . The advantage over Shamir’s and other known secret sharing schemes that we are going to get here is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular players. The disadvantage is that our scheme is a (k, k)-threshold scheme only. We start by describing a subroutine for distributing shares by the players among themselves. More precisely, k players want to split a given number in a sum of k numbers, so that each summand is known to one player only, and each player knows one summand only. 6.1. The Subroutine (distributing shares by the players among themselves). Suppose a player Pi receives a number M that has to be split in a sum of k private numbers. In what follows, all indices are considered modulo k. (1) Pi initiates the process by sending M − mi to Pi+1 , where mi is a random number (could be positive or negative). (2) Each subsequent Pj does the following. Upon receiving a number m from Pj−1 , he subtracts a random number mj from m and sends the result to Pj+1 . The number mj is now Pj ’s secret summand. (3) When this process gets back to Pi , he adds mi to whatever he got from Pi−1 ; the result is his secret summand. Now we get to the actual secret sharing protocol. 6.2. The protocol (secret sharing (k, k)-threshold scheme). The dealer D wants to distribute shares of a secret number N to k players Pi so that, if Pi gets a number P si , then ki=1 si = N . P (1) D arbitrarily splits N in a sum of k integers: N = ki=1 ni . (2) The loop: at Step i of the loop, D sends ni to Pi , and Pi initiates the above P Subroutine to distribute shares nij of ni among the players, so that kj=1 nij = ni . (3) After all k steps of the loop are completed, each player Pi ends up with k P P numbers nji that sum up to si = kj=1 nji . It is obvious that ki=1 si = N .\n\nUNCONDITIONALLY SECURE MULTIPARTY COMPUTATION\n\n9\n\nAcknowledgement. Both authors are grateful to Max Planck Institut f¨ ur Mathematik, Bonn for its hospitality during the work on this paper. References G. R. Blakley, Safeguarding cryptographic keys, Proceedings of the National Computer Conference 48 (1979), 313-317. D. Chaum, C. Cr´epeau, and I. Damgard, Multiparty unconditionally secure protocols (extended abstract), Proceedings of the Twentieth ACM Symposium on the Theory of Computing, ACM, 1988, pp. 11-19. I. Damgard, M. Geisler, M. Kroigard, Homomorphic encryption and secure comparison, Int. J. Appl. Cryptogr. 1 (2008), 22-31. I. Damgard, Y. Ishai, Scalable secure multiparty computation, Advances in cryptology CRYPTO 2006, 501-520, Lecture Notes in Comput. Sci. 4117, Springer, Berlin, 2006. O. Goldreich, Foundations of Cryptography: Volume 1, Basic Tools. Cambridge University Press, 2007. S. Goldwasser, S. Micali, Probabilistic encryption, J. Comput. System Sci. 28 (1984), 270-299. D. Grigoriev, I. Ponomarenko, Constructions in public-key cryptography over matrix groups, Contemp. Math., Amer. Math. Soc. 418 (2006), 103–119. A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, CRC-Press 1996. A. Shamir, How to share a secret, Comm. ACM 22 (1979), 612-613. A. C. Yao, Protocols for secure computations (Extended Abstract), 23rd annual symposium on foundations of computer science (Chicago, Ill., 1982), 160–164, IEEE, New York, 1982. ´matiques, Universite ´ de Lille, 59655, Villeneuve d’Ascq, France CNRS, Mathe E-mail address: [email protected] Department of Mathematics, The City College of New York, New York, NY 10031 E-mail address: [email protected]"
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https://www.queryhome.com/puzzle/28608/consecutive-positive-integers-individual-perfect-square | [
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"# Next three consecutive positive integers (after 1,2,3) where sum of individual cubes is equal to a perfect square?\n\n97 views\n\nIf 1^3 + 2^3 + 3^3 = m^2 where m is also an integer.\nWhat are the next three consecutive positive integers such that the sum of their individual cubes is equal to a perfect square?",
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"posted Aug 16, 2018",
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"answer Aug 17, 2018 by anonymous"
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http://businessdocbox.com/Marketing/108161820-Demand-curve-using-game-results-how-much-customers-will-buy-at-a-given-price-downward-sloping-more-demand-at-lower-prices.html | [
"# Demand curve - using Game Results How much customers will buy at a given price Downward sloping - more demand at lower prices\n\nSize: px\nStart display at page:\n\nDownload \"Demand curve - using Game Results How much customers will buy at a given price Downward sloping - more demand at lower prices\"",
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"Transcription\n\n1 31 October Bige Kahraman Class Notes First half of course (Michaelmas) is Microeconomics, second half (Hilary) is Macroeconomics Focusing on profit maximization & price formation Looking at industry level dynamics Assessment: 30% Industry Report - due 9 Dec 20% Exam - taken 9 Jan 50% Coursework Assignments - due 13 Mar Alusaf Hillside Project Supply curve - see Excel/Word docs How much outputs producers will supply at a given price Upward sloping - more supply as price goes up Can become (nearly) vertical at the industrial capacity At higher prices, more firms willing to produce Produce if price >= cost Excess industry capacity drives prices down to variable costs In the long run, new entry can hold prices down Trading game Demand curve - using Game Results How much customers will buy at a given price Downward sloping - more demand at lower prices Elasticity How sensitive supply or demand is to prices Elasticity = % change in demand / % change in price Inelastic: elasticity < 1; quantity demanded doesn t move much on price E.g. gasoline Elastic: elasticity > 1; quantity moves a lot when price changes More inelastic demand curve is associated with market power Example: Apple creating eco-system, not just devices More inelastic supply curve indicates diseconomies of scale Example: Hedge funds become more difficult to manage as they grow Equilibrium Price Where supply and demand curves intersect\n\n2 31 October Bige Kahraman In Trading Game, 63 shares demanded at \\$45 What if supply exceeds demand? Price is above equilibrium What if demand exceeds supply? Price is below equilibrium Market wants to be at equilibrium, not traders What about shifts? In Demand: Quantity supplied increases higher prices, more quantity Shift could be from movements in complementary products, wealth effect, etc. In Supply: Quantity demanded increases lower prices, more quantity Shift could be from new technology, lowered barriers to entry, etc. The Invisible Hand Mechanism for achieving equilibrium Market adapts quickly to changes in demand and supply Pursuit of self-interest leads to socially efficient outcome Gains from trade at equilibrium Surpluses from trading at equilibrium will be equal for buyers and sellers in the aggregate Equilibrium price maximizes the total gains from trade Allocative efficiency (or inefficiency) buyer/consumer surplus People willing to buy at higher prices than equilibrium seller/producer surplus People willing to sell at lower prices than equilibrium Works out to profits Price Ceiling Example Loses producer and consumer surplus in area between price ceiling and equilibrium Quantity demanded will be > quantity supplied\n\n3 Cost Functions & Profit Maximization Total Cost Function Fixed Costs (FC) Do not vary with output level Examples: rent, administrative costs, etc. Main reason Average Costs AC(Q) usually fall at first Variable Costs (VC) Increase as output increases Include materials, direct labor, etc. Average VC is a useful proxy for MC (marginal cost) Average & Marginal Costs Average cost shows how per-unit costs vary with output level AC(Q) = TC(Q)/Q Marginal cost shows how total costs increase with output Equal to slope of total cost function Additional cost of each additional unit produced: MC(Q) = TC(Q+1) - TC(Q) (Dis)economies of Scales Constant returns to scale: MC = AC Economies of scale: AC falls as output rises Due to fixed costs - spread over more units Increased productivity due to extensive specialization and experience Increased bargaining power with suppliers Diseconomies of scale: AC increase as output rises Firms become less efficient as they grow More layers of bureaucracy Difficult to coordinate multiple projects Slower in making decisions Typically firms first experience economies of scale, then diseconomies of scale Economic vs. Accounting Costs Economic costs include opportunity costs of all resources used Usually value of the best alternative choice Economic profit = Revenue - Economic Cost Zero Economic Profit does not equal Zero Accounting profit A zero economic profit = positive accounting profit\n\n4 Profit Maximization Trade off between price & quantity Optimal decision: Marginal Revenue (MR(Q)) = Marginal Cost (MC(Q)) Marginal Revenue MR(Q) = TR(Q+1) - TR(Q), where TR(Q) = p(q) x Q If MR(Q) < MC(Q) additional unit is too costly to produce If MR(Q) > MC(Q) additional unit is profitable, should produce more Rules for Profit Maximization: Market Structures Marginal Output Rule: produce until MR(Q) = MC(Q) Shutdown Rule: shut down operations if TR(Q) < TC(Q) What if there are Sunk Costs? Sunk costs can t be recovered If sunk costs are unavoidable, firms should choose optimal time based on expected future profits Firms should ignore sunk costs when optimizing, need to be forward looking Sunk cost fallacy : firms don t always ignore sunk costs, make suboptimal decisions Perfect Competition Assumes: infinitely small, equally efficient firms Homogenous products, consumers care only about price Consumers are rational Unrestricted entry and exit of firms Reasonable proxy for: Agriculture, metals, financial markets All firms take, accept the market price - price takers MR(Q) = market price, flat firm demand curve Each new unit sold at market price Profits maximized where MC(Q) = P Long Run Equilibrium p = AC(Q) Price = AC = MC firms earn normal profit (zero economic profit) Produce at lowest AC productive efficiency\n\n5 Monopoly Welfare Economics Perfectly competitive markets maximize total surplus - Allocative efficiency Perfectly competitive markets allocate demand to lowest cost sellers - Productive efficiency Market share approach Strong definition: 100% market share Many utilities Some patented products Weak definition: significant market share, no close competitor Microsoft Windows Intel in microprocessors Measure of market concentration Herfindahl Index = S S Si is market share of firm i - firm sales / total market sales Higher Herfindahl index more concentration H < 0.01 is highly competitive H < 0.15 is unconcentrated H < 0.25 is moderately concentrated H > 0.25 is highly concentrated Monopolist is a price maker Market power is the ability to charge above marginal cost MC(Q) = MR(Q) P will be higher than perfect competition, lower Q p MC 1, e is price elasticity of demand p = e What gives rise to monopolies? Barriers to entry Structural Economies of scale Large initial fixed costs Patents, high switching costs Strategic Strategic commitments Reputation Types of Monopoly Natural - economies of scale Government-created: exclusive sales rights Demand-driven: customer loyalty Deterrence to Entry Destroyer pricing: hold below AC for a period of time"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.87416923,"math_prob":0.8731184,"size":6877,"snap":"2022-40-2023-06","text_gpt3_token_len":1387,"char_repetition_ratio":0.11392405,"word_repetition_ratio":0.04074074,"special_character_ratio":0.19674277,"punctuation_ratio":0.065731816,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9548849,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-26T12:39:40Z\",\"WARC-Record-ID\":\"<urn:uuid:443956c9-7e79-4763-910a-71e73f24838f>\",\"Content-Length\":\"38208\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1c553a2f-4942-491d-8de4-8e3aba1cbe03>\",\"WARC-Concurrent-To\":\"<urn:uuid:05f629e9-48f4-4a3f-8b2f-5dcad88720a1>\",\"WARC-IP-Address\":\"144.76.236.251\",\"WARC-Target-URI\":\"http://businessdocbox.com/Marketing/108161820-Demand-curve-using-game-results-how-much-customers-will-buy-at-a-given-price-downward-sloping-more-demand-at-lower-prices.html\",\"WARC-Payload-Digest\":\"sha1:DAKNQLYJBC52PMPPIC6JAPSQIXQB4GSQ\",\"WARC-Block-Digest\":\"sha1:LXKO2VQN7OI24SXIKASMRIAMHV77UHRE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334871.54_warc_CC-MAIN-20220926113251-20220926143251-00712.warc.gz\"}"} |
https://www.teachoo.com/7903/2600/Example-10/category/Forming-Linear-Equations---Adding-subtracting-numbers/ | [
"",
null,
"",
null,
"1. Chapter 2 Class 8 Linear Equations in One Variable\n2. Concept wise\n3. Forming Linear Equations - Adding subtracting numbers\n\nTranscript\n\nExample 10 The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. What are the two numbers?Given that Ratio of two numbers is 2 : 5 Let first number be 2x & second number be 5x Given, Difference between two numbers = 66 5x − 2x = 66 3x = 66 x = 66/3 x = 22 Thus, First number = 2x = 2 × 22 = 44 Second number = 5x = 5 × 22 = 110\n\nForming Linear Equations - Adding subtracting numbers",
null,
""
]
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"https://d1avenlh0i1xmr.cloudfront.net/77e997c4-455c-4749-9a59-111fc30c66d7/slide15.jpg",
null,
"https://d1avenlh0i1xmr.cloudfront.net/3601903a-cdea-4ed0-b612-184243f625f0/slide16.jpg",
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"https://delan5sxrj8jj.cloudfront.net/misc/Davneet+Singh.jpg",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.87317556,"math_prob":1.0000019,"size":788,"snap":"2021-43-2021-49","text_gpt3_token_len":277,"char_repetition_ratio":0.14668368,"word_repetition_ratio":0.1,"special_character_ratio":0.3604061,"punctuation_ratio":0.13068181,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.000004,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,8,null,6,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-17T19:27:56Z\",\"WARC-Record-ID\":\"<urn:uuid:a186a5f6-cd9e-4698-a4f4-f23232c1c21f>\",\"Content-Length\":\"50538\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7b5dd389-cc1f-4c43-b823-857e16f7ddd0>\",\"WARC-Concurrent-To\":\"<urn:uuid:b6f1efd8-8555-4d8b-8c7f-f6d84cc43a19>\",\"WARC-IP-Address\":\"3.226.182.14\",\"WARC-Target-URI\":\"https://www.teachoo.com/7903/2600/Example-10/category/Forming-Linear-Equations---Adding-subtracting-numbers/\",\"WARC-Payload-Digest\":\"sha1:PVCR57JYBDVFFJSVWSUCY47VCF4E456S\",\"WARC-Block-Digest\":\"sha1:JMPS4G3BCG2HTYZMFFRGIIV3BBYINZJM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585181.6_warc_CC-MAIN-20211017175237-20211017205237-00132.warc.gz\"}"} |
https://www.codingprof.com/how-to-calculate-the-net-present-value-npv-in-r-examples/ | [
"# How to Calculate the Net Present Value (NPV) in R [Examples]\n\nIn this article, we discuss how to calculate the Net Present Value (NPV) in R.\n\nThe Net Present Values is a valuation method for investment projects in terms of cash inflow and cash outflow. It accounts for the time value of money by discounting all the cash flows back to today, i.e., their Present Value (PV).\n\nIn short, the Net Present Value is the difference between the present value of the cash inflows and the present value of the cash outflows. Therefore, if the NPV is greater than zero, then the investment is favorable.\n\nBut, how do you calculate the NPV in R?\n\nIn R, the easiest way to calculate the Net Present Value is by using the NPV function. This function computes the NPV given the initial cash flow, future cash flows, and the interest rate. Optionally, it shows a diagram of the cash flows.\n\nIn this article, we demonstrate how to use the NPV() function, as well as how to calculate the Net Present Value with basic R code. Additionally, we show how to calculate the NPV for a project of cash flows with different discount rates.\n\n## How to Calculate the Net Present Value (NPV) in R\n\nBelow we discuss two ways to find the NPV of a project in R.\n\nOur fictitious project has an upfront investment of \\$100. In the following years, we expect cash inflows of \\$5, \\$20, \\$25, \\$30, and \\$50. Also, we assume a constant discount rate of 5%.\n\n``````library(\"tidyverse\")\ncashflows <- tibble(time = c(0:5),\ncashflow = c(-100, 5, 20, 25, 30, 50),\ndiscount_rate = rep(0.05, 6))\ncashflows %>% print()``````\n\n### Calculate the Net Present Value with the NPV Function\n\nThe easiest way to calculate the Net Present Value in R is with the NPV() function.\n\nThis function computes the NPV of an investment given 4 mandatory arguments:\n\n1. cf0: The cash flow at moment zero, i.e., the initial investment.\n2. cf: A vector of future cash flows.\n3. times: The moments when you expect the future cash flows.\n4. i: The discount rate.\n\nThe NPV() function is part of the FinancialMath package which contains many functions for financial analysis.\n\nIf we use the NPV() function to calculate the Net Present Value of our fictitious project, we need the following R code.\n\n``````library(\"FinancialMath\")\nNPV(cf0=100, cf=c(5, 20, 25, 30, 50), times=c(1:5), i=.05)``````\n\nSince the NPV is greater than zero, this is a good investment.\n\nOptionally, the NPV() function can plot a diagram of the cash flows. By default, the plot argument is set to FALSE. However, if you use plot=TRUE, the NPV() function adds a plot of all the cash flows which can be helpful for presentations.\n\n``NPV(cf0=100, cf=c(5, 20, 25, 30, 50), times=c(1:5), i=.05, TRUE)``\n\n### Calculate the Net Present Value with Basic R Code\n\nInstead of using the NPV() function, you can also compute the NPV with Basic R Code.\n\nAlthough this method requires more coding, it might help people who are not familiar with the NPV to understand your code.\n\nBelow we show how to calculate the Net Present Value step by step.\n\nFirst, we calculate the present value of each cash flow, i.e., we discount for the time value of money.\n\n``````library(\"tidyverse\")\n\n# Calculate the Present Value of Each Cash Flow\ncashflows <- cashflows %>%\nmutate(cashflows, present_value = cashflow / (1+discount_rate)^time)``````\n\nNext, we sum the present value of each cash flow. Finally, we print the Net Present Value to the R console.\n\n``````# Sum all the Present Values\nnet_present_value <- cashflows %>%\nselect(present_value) %>%\nsum()\n\n# Print the Net Present Value (NPV)\nnet_present_value``````\n\n## How to Calculate the NPV with Different Discount Rates in R\n\nSo far, we have assumed that the discount rate is constant for each period. However, this assumption might not be valid. So, how do you calculate the Net Present Value with different discount rates?\n\nAlthough the NPV() function is convenient, it can’t calculate the Net Present Value when we deal with multiple discount rates. Therefore, you have to write your own R code.\n\nIn the example below, we expect the same initial investment and future cash flows. However, the discount rate is not stable. Instead, we will use the following scenario.\n\nThe first step to compute the NPV of a project with different discount rates is to find the correct discount factor for each period. Therefore, we will use a for-loop.\n\n``````cashflows <- cashflows %>%\nmutate(discount_factor = 1)\n\nfor (row in 2:dim(cashflows)) {\ncashflows[row,] <- mutate(cashflows[1:row,], discount_factor= lag(discount_factor,1) / (1+discount_rate))[row,]\n}\n\ncashflows``````\n\nThe for-loop is necessary because the discount factor of the current period depends on the discount factor of the previous period.\n\nFor example, the discount factor of the fourth period is:\n\nThese are the discount factors of our project.\n\nNext, we calculate the present value of each cash flow using the discount factor instead of the discount rate.\n\n``````# Calculate the Present Value of Each Cash Flow\ncashflows <- cashflows %>%\nmutate(cashflows, present_value = cashflow * discount_factor)``````\n\nFinally, we compute the sum of all the present values to find the Net Present Value\n\n``````# Sum all the Present Values\nnet_present_value <- cashflows %>%\nselect(present_value) %>%\nsum()\n\n# Print the Net Present Value (NPV)\nnet_present_value``````\n\nBecause the NPV is lower than zero, this is not a good investment."
]
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https://rdrr.io/rforge/DAMisc/man/binfit.html | [
"binfit: Scalar Measures of Fit for Binary Variable Models In DAMisc: Dave Armstrong's Miscellaneous Functions\n\nDescription\n\nCalculates scalar measures of fit for models with binary dependent variables along the lines described in Long (1997) and Long and Freese (2005).\n\nUsage\n\n `1` ``` binfit(mod) ```\n\nArguments\n\n `mod` A model of class `glm` with `family=binomial`.\n\nDetails\n\n`binfit` calculates scalar measures of fit (many of which are pseudo-R-squared measures) to describe how well a model fits data with a binary dependent variable.\n\nValue\n\nA named vector of scalar measures of fit\n\nAuthor(s)\n\nDave Armstrong (UW-Milwaukee, Department of Political Science)\n\nReferences\n\nLong, J.S. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage.\n\nLong, J.S. and J. Freese. 2005. Regression Models for Categorical Outcomes Using Stata, 2nd ed. College Station, TX: Stata Press.\n\nExamples\n\n ```1 2 3 4``` ```data(france) left.mod <- glm(voteleft ~ male + age + retnat + poly(lrself, 2), data=france, family=binomial) binfit(left.mod) ```\n\nDAMisc documentation built on May 2, 2019, 4:52 p.m."
]
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https://fr.mathworks.com/matlabcentral/cody/problems/44345-matlab-counter/solutions/1877072 | [
"Cody\n\n# Problem 44345. MATLAB Counter\n\nSolution 1877072\n\nSubmitted on 17 Jul 2019 by Evan\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\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\n\n2 Pass\nf = counter(0,1); assert(isequal(f(),0)) assert(isequal(f(),1)) assert(isequal(2,f())) assert(isequal(3,f()))\n\n3 Pass\nf = counter(1,0); assert(isequal(f(),1)) assert(isequal(f(),1)) assert(isequal(1,f())) assert(isequal(1,f()))\n\n4 Pass\nf = counter(10,2); assert(isequal(f(),10)) assert(isequal(f(),12)) assert(isequal(14,f())) assert(isequal(16,f()))\n\n5 Pass\nf = counter(0,5); y_correct = [0, 5, 10, 15, 20, 55]; assert(isequal([f() f() f() f() f() f()+f()],y_correct))\n\n6 Pass\nx0 = randi(10); b = randi(10); f = counter(x0,b); y_correct = x0 + (0:1000)*b; assert(isequal(arrayfun(@(n)f(),0:1000),y_correct))"
]
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.57988405,"math_prob":0.99995506,"size":1126,"snap":"2019-35-2019-39","text_gpt3_token_len":368,"char_repetition_ratio":0.23083779,"word_repetition_ratio":0.0,"special_character_ratio":0.38721138,"punctuation_ratio":0.18565401,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9991574,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-20T09:42:04Z\",\"WARC-Record-ID\":\"<urn:uuid:5d5fc791-16a4-45bd-a6e3-b3476bd67377>\",\"Content-Length\":\"75839\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:525cdd9c-2f96-4be4-8a32-63fd7ba526df>\",\"WARC-Concurrent-To\":\"<urn:uuid:ac7d4b4a-ea2f-4319-92bd-005541c1d16c>\",\"WARC-IP-Address\":\"104.110.193.39\",\"WARC-Target-URI\":\"https://fr.mathworks.com/matlabcentral/cody/problems/44345-matlab-counter/solutions/1877072\",\"WARC-Payload-Digest\":\"sha1:UN2TBXFD3RYXYPZE3ZEEZUWAYDYOKOQF\",\"WARC-Block-Digest\":\"sha1:42VOTPC3TNKXK5SB7UQTBOUQPSGGSKDS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573988.33_warc_CC-MAIN-20190920092800-20190920114800-00397.warc.gz\"}"} |
https://geo-python.github.io/2017/lessons/L4/functions.html | [
"# Functions¶\n\n## Sources¶\n\nThis lesson is partly based on the Software Carpentry group’s lessons on Programming with Python.\n\n## What is a function?¶\n\nA function is a block of organized, reusable code that can make your scripts more effective, easier to read, and simple to manage. You can think functions as little self-contained programs that can perform a specific task which you can use repeatedly in your code. One of the basic principles in good programming is “do not to repeat yourself”. In other words, you should avoid having duplicate lines of code in your scripts. Functions are a good way to avoid such situations and they can save you a lot of time and effort as you don’t need to tell the computer repeatedly what to do every time it does a common task, such as converting temperatures from Fahrenheit to Celsius. During the course we have already used some functions such as the print() command which is actually a built-in function in Python.\n\n## Anatomy of a function¶\n\nLet’s consider the task from the first lesson when we converted temperatures from Celsius to Fahrenheit. Such an operation is a fairly common task when dealing with temperature data. Thus we might need to repeat such calculations quite frequently when analysing or comparing weather or climate data between the US and Europe, for example.\n\n1. Let’s define our first function called celsiusToFahr:\n\nIn : def celsiusToFahr(tempCelsius):\n...: return 9/5 * tempCelsius + 32\n...:\n\n\nThe function definition opens with the keyword def followed by the name of the function and a list of parameter names in parentheses. The body of the function — the statements that are executed when it runs — is indented below the definition line.\n\nWhen we call the function, the values we pass to it are assigned to the corresponding parameter variables so that we can use them inside the function (e.g., the variable tempCelsius in this function example). Inside the function, we use a return statement to define the value that should be given back when the function is used, or called).\n\n## Calling functions¶\n\n1. Now let’s try using our function. Calling our self-defined function is no different from calling any other function such as print(). You need to call it with its name and send your value to the required parameter(s) inside the parentheses:\n\nIn : freezingPoint = celsiusToFahr(0)\n\nIn : print('The freezing point of water in Fahrenheit is:', freezingPoint)\nThe freezing point of water in Fahrenheit is: 32.0\n\nIn : print('The boiling point of water in Fahrenheit is:', celsiusToFahr(100))\nThe boiling point of water in Fahrenheit is: 212.0\n\n2. Now that we know how to create a function to convert Celsius to Fahrenheit, let’s create another function called kelvinsToCelsius:\n\nIn : def kelvinsToCelsius(tempKelvins):\n...: return tempKelvins - 273.15\n...:\n\n3. And let’s use it in the same way as the earlier one:\n\nIn : absoluteZero = kelvinsToCelsius(tempKelvins=0)\n\nIn : print('Absolute zero in Celsius is:', absoluteZero)\nAbsolute zero in Celsius is: -273.15\n\n4. What about converting Kelvins to Fahrenheit? We could write out a new formula for it, but we don’t need to. Instead, we can do the conversion using the two functions we have already created and calling those from the function we are now creating:\n\nIn : def kelvinsToFahrenheit(tempKelvins):\n...: tempCelsius = kelvinsToCelsius(tempKelvins)\n...: tempFahr = celsiusToFahr(tempCelsius)\n...: return tempFahr\n...:\n\n5. Now let’s use the function:\n\nIn : absoluteZeroF = kelvinsToFahrenheit(tempKelvins=0)\n\nIn : print('Absolute zero in Fahrenheit is:', absoluteZeroF)\nAbsolute zero in Fahrenheit is: -459.66999999999996\n\n\nFunctions such as the ones we just created can also be called from another script. In fact, quite often it is useful to create a dedicated function library for functions that you use frequently, when doing data analysis, for example. Basically this is done by listing useful functions in a single .py file from which you can then import and use them whenever needed.\n\n### Saving functions in a script file¶\n\nBefore we can import our functions we need to create a new script file and save the functions that we just created into a Python file called temp_converter.py.\n\nWe could write the functions again into our script file but we can also take advantage of the History log tab in Spyder where we should find all commands that we typed in the IPython console :\n\n1. Copy and paste (only) the functions that we wrote earlier from the History log tab and save them in the temp_converter.py script (optionally you can just write them again into the file if you want the practice ). It should look like following:",
null,
"The temp_converter.py script. Note that our function names differ slightly from those in the image.\n\n### Calling functions from another script file¶\n\nNow that we have saved our temperature conversion functions into a script file we can start using them.\n\n1. Let’s create another script file called calculator.py.\n\nImportant\n\nSave the file into the same folder where you saved the temp_converter.py file .\n\n2. Let’s now import our celsiusToFahr function from the other script by adding a specific import statement at the top of our calculator.py script. Let’s also use the function so that we can see that it is working :\n\nfrom temp_converter import celsiusToFahr\n\n# Testing that the function from another file works\nprint(\"The freezing point of water in Fahrenheit is:\", celsiusToFahr(0))\n\n3. Run the code by pressing F5 key or by pressing the play button in Spyder. We should now get following output:\n\n• It is also possible to import more functions at the same time by listing and separating them with a comma\n\nfrom my_script import func1, func2, func3\n\n4. Sometimes it is useful to import the whole script and all of its functions at once. Let’s modify the import statement in our script and test that all functions work :\n\nimport temp_converter as tc\n\n# Testing that all functions from another file work\nprint(\"The freezing point of water in Fahrenheit is:\", tc.celsiusToFahr(0))\nprint('Absolute zero in Celsius is:', tc.kelvinsToCelsius(tempKelvins=0))\nprint('Absolute zero in Fahrenheit is:', tc.kelvinsToFahrenheit(tempKelvins=0))\n\n\n### Temperature calculator (optional, advanced topic)¶\n\nSo far our functions have had only one parameter, but it is also possible to define a function with multiple parameters. Let’s now make a simple tempCalculator function that accepts temperatures in Kelvins and returns either Celsius or Fahrenheit. The new function will have two parameters:\n\n• tempK = The parameter for passing temperature in Kelvin\n• convertTo = The parameter that determines whether to output should be in Celsius or in Fahrenheit (using letters C or F accordingly)\n1. Let’s start defining our function by giving it a name and setting the parameters:\n\ndef tempCalculator(tempK, convertTo):\n\n2. Next, we need to add conditional statements that check whether the output temperature is wanted in Celsius or Fahrenheit, and then call corresponding function that was imported from the temp_converter.py file.\n\ndef tempCalculator(tempK, convertTo):\n# Check if user wants the temperature in Celsius\nif convertTo == \"C\":\n# Convert the value to Celsius using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToCelsius(tempKelvins=tempK)\nelif convertTo == \"F\":\n# Convert the value to Fahrenheit using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToFahrenheit(tempKelvins=tempK)\n\n3. Next, we need to add a return statement so that our function sends back the value that we are interested in:\n\ndef tempCalculator(tempK, convertTo):\n# Check if user wants the temperature in Celsius\nif convertTo == \"C\":\n# Convert the value to Celsius using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToCelsius(tempKelvins=tempK)\nelif convertTo == \"F\":\n# Convert the value to Fahrenheit using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToFahrenheit(tempKelvins=tempK)\n# Return the result\nreturn convertedTemp\n\n4. Lastly, as we want to be good programmers, we add a short docstring at the beginning of our function that tells what the function does and how the parameters work:\n\ndef tempCalculator(tempK, convertTo):\n\"\"\"\nFunction for converting temperature in Kelvins to Celsius or Fahrenheit.\n\nParameters\n----------\ntempK: <numerical>\nTemperature in Kelvins\nconvertTo: <str>\nTarget temperature that can be either Celsius ('C') or Fahrenheit ('F'). Supported values: 'C' | 'F'\n\nReturns\n-------\n<float>\nConverted temperature.\n\"\"\"\n\n# Check if user wants the temperature in Celsius\nif convertTo == \"C\":\n# Convert the value to Celsius using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToCelsius(tempKelvins=tempK)\nelif convertTo == \"F\":\n# Convert the value to Fahrenheit using the dedicated function for the task that we imported from another script\nconvertedTemp = kelvinsToFahrenheit(tempKelvins=tempK)\n# Return the result\nreturn convertedTemp\n\n5. That’s it! Now we have a temperature calculator that has a simple control for the user where s/he can change the output by using the convertTo parameter. Now as we added the short docstring in the beginning of the function we can use the help() function in Python to find out how our function should be used. Run the script and try following:\n\nhelp(tempCalculator)\n\n\nLet’s use it:\n\n>>> tempKelvin = 30\n>>> temperatureC = tempCalculator(tempK=tempKelvin, convertTo=\"C\")\n>>> print(\"Temperature\", tempKelvin, \"in Kelvins is\", temperatureC, \"in Celsius\")\nTemperature 30 in Kelvins is -243.14999999999998 in Celsius\n\n\nFootnotes\n\n The history log tab can be found from the same panel where we have executed our codes (bottom-right, next to IPython console).\n When communicating between script files, it is necessary to keep them in the same folder so that Python can find them (there are other ways but this is the easiest).\n Following the principles of good programming import statements that you use should always be written at the top of the script file.\n It is also possible to import functions by using specific the * character: from moduleX import * The downside of using * symbol to import all functions is that you won’t see which functions are imported, unless checking them from the script itself or using the dir() function to list them (see the lesson on modules). Warning We do not recommend importing functions using this approach as there is a risk of function name conflicts when doing this. Please use with caution"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8414523,"math_prob":0.88732344,"size":2541,"snap":"2023-14-2023-23","text_gpt3_token_len":539,"char_repetition_ratio":0.12968072,"word_repetition_ratio":0.01686747,"special_character_ratio":0.2085793,"punctuation_ratio":0.103950106,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98594534,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-01T23:48:24Z\",\"WARC-Record-ID\":\"<urn:uuid:098557e2-1cdc-4801-90bd-29d8220f5e38>\",\"Content-Length\":\"43275\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:40689fd8-6320-472f-86a0-3c3114a6fca7>\",\"WARC-Concurrent-To\":\"<urn:uuid:d0b6272d-54ab-4597-9581-3552c7d302b2>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://geo-python.github.io/2017/lessons/L4/functions.html\",\"WARC-Payload-Digest\":\"sha1:7IJC44IJW62BVQBMTSCC2HTVHQPBUQ4C\",\"WARC-Block-Digest\":\"sha1:7P3ZZVL4DUAGBVY4Y5VOTJUXF4QJFOMY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950363.89_warc_CC-MAIN-20230401221921-20230402011921-00074.warc.gz\"}"} |
https://www.excelforum.com/excel-charting-and-pivots/539304-n-a.html | [
"# #N/A\n\n1. ## #N/A\n\nSurprising Zeros in Charts\n\nMy model is built.\nUsing #N/A - my chart displays perfectly, zeros suppressed.\nThis formula is what feeds the values in my chart series.\n=IF(ISERROR(((AVERAGE(SHEET1!BE2:BM2))*(100/5))),””,((AVERAGE(SHEET1!BE2:BM2))*(100/5)))\n\nIf I alter that error handling\nto:=IF(ISERROR(((AVERAGE(SHEET1!BE2:BM2))*(100/5))),\"#N/A\",((AVERAGE(SHEET1!BE2:BM2))*(100/5)))\nZero still displays…\nIf I may ask – how would I alter this formula to function they way I hope it\nwould?\n\nSincerely,\nArturo",
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"",
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"Register To Reply\n\n2. ## RE: #N/A\n\n=IF(ISERROR(((AVERAGE(SHEET1!BE2:BM2))*(100/5))),#N/A,((AVERAGE(SHEET1!BE2:BM2))*(100/5)))\n\n\"Arturo\" wrote:\n\n> Surprising Zeros in Charts\n>\n> My model is built.\n> Using #N/A - my chart displays perfectly, zeros suppressed.\n> This formula is what feeds the values in my chart series.\n> =IF(ISERROR(((AVERAGE(SHEET1!BE2:BM2))*(100/5))),””,((AVERAGE(SHEET1!BE2:BM2))*(100/5)))\n>\n> If I alter that error handling\n> to:=IF(ISERROR(((AVERAGE(SHEET1!BE2:BM2))*(100/5))),\"#N/A\",((AVERAGE(SHEET1!BE2:BM2))*(100/5)))\n> Zero still displays…\n> If I may ask – how would I alter this formula to function they way I hope it\n> would?\n>\n> Sincerely,\n> Arturo",
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"",
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"Register To Reply"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7423113,"math_prob":0.9640001,"size":1490,"snap":"2020-34-2020-40","text_gpt3_token_len":476,"char_repetition_ratio":0.18169583,"word_repetition_ratio":0.2929293,"special_character_ratio":0.33892617,"punctuation_ratio":0.16065574,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99775183,"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\":\"2020-08-08T05:49:32Z\",\"WARC-Record-ID\":\"<urn:uuid:f4065a9e-35ea-4f9d-9c8b-6d313b0010ee>\",\"Content-Length\":\"50418\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:70ee0a70-d3f4-4776-9f5b-004c63388b53>\",\"WARC-Concurrent-To\":\"<urn:uuid:15671974-44f5-4f2e-a0f3-565b8116c360>\",\"WARC-IP-Address\":\"192.124.249.15\",\"WARC-Target-URI\":\"https://www.excelforum.com/excel-charting-and-pivots/539304-n-a.html\",\"WARC-Payload-Digest\":\"sha1:SN5QFPERZ73MNZFC5VTZN5KSU3YSNLQR\",\"WARC-Block-Digest\":\"sha1:NMVMKYKL2W6UOHIAYY4BIPIZHQXRO5FD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439737289.75_warc_CC-MAIN-20200808051116-20200808081116-00456.warc.gz\"}"} |
https://www.vub.ac.be/en/events/2008/ion-transport-concentrated-electrolyte-solutions | [
"",
null,
"Portal for\n\nWarning message\n\nAttention! This event has already passed.\n\nIon transport in concentrated electrolyte solutions\n\nTuesday, 6 May, 2008 - 16:00\nCampus: Brussels Humanities, Sciences & Engineering campus\nD\n2.01\nSteven Van Damme\nphd defence\n\nThe design and optimization of industrial electrochemical reactors can benefit from accurate electrochemical models to predict the current, potential and concentration distributions in the electrolyte solution. An electrochemical model is a set of macroscopic equations for all the relevant physical quantities, like the potential, the concentrations, the temperature and the fluid velocity, that contains all the relevant couplings between fluxes and forces. An important problem in computational electrochemistry is the determination of the coefficients in these equations. The nature of the interactions between the chemical components in the solution determines how the coefficients vary with temperature, pressure and concentrations.\n\nNowadays, the potential model is the most widely used electrochemical model. The demand for more accurate simulations and the ever‐increasing power of computers drive electrochemists to look for more advanced ‐ i.e. more general ‐ electrochemical models. Therefore, special attention is given in this work to the macroscopic equations that describe the behaviour of electrolyte solutions. A very general set of equations is presented and the couplings between fluxes and forces are discussed. The simpler electrochemical models are naturally found by treating certain quantities as constant or by neglecting certain couplings between fluxes and forces.\n\nThe answer to the question of the coefficients in the macroscopic equations lies in statistical mechanics. The basics of statistical mechanics are explained in this work. In the case of electrolyte solutions, the solvent molecules are abundant and may be modeled by a continuum. This simplification permits to treat only the ion‐ion interactions explicitly. The interest in this approach lies in the fact that the ion‐ion interactions can be modeled as hard sphere Coulomb interactions. In the mean spherical approximation (MSA), this physical model of the ion‐ion interactions leads to analytical expressions for the coefficients. This is of course of great interest for computational electrochemistry. Before this work started, only the osmotic coefficient, the activity coefficients and the electrophoretic contribution to the Onsager coefficients were known in the MSA. The relaxation contribution to the Onsager coefficients was missing. An expression for this relaxation contribution is derived here.\n\nThe charge and the diameter of the ions are microscopic parameters that characterize the ion‐ion interactions. A sensitivity study is performed to analyze how the concentration dependence of the coefficients is influenced by these parameters. This also helps to find a procedure to get the diameters from measurements of the coefficients. Several ion diameters are obtained in this way by examining the experimental data on 18 aqueous binary electrolyte solutions. The theoretical plots agree well with the experimental data. The behaviour of mixed electrolyte solutions can be predicted from those same microscopic parameters.\n\nThe multi‐ion transport and reaction model (MITReM) is to be the successor of the potential model. Different MITReM’s can be obtained by using different interaction theories for the coefficients. In the pseudo‐empirical I‐MITReM the ion‐ion interactions are treated in a crude fashion that only guarantees a correct conductivity, whereas in the MSA‐MITReM the coefficients are given by the MSA expressions. A theoretical comparative study is performed to determine the conditions under which the pseudo‐empirical I‐MITReM fails and the MSA‐MITReM is recommended. A comparison of the pseudo‐empirical I‐MITReM and the MSA‐MITReM with experiments on aqueous CuSO4 solutions is used as confirmation.\n\nAttachment:",
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https://stat.ethz.ch/pipermail/r-help/2009-May/390943.html | [
"# [R] Error in NLME (nonlinear mixed effects model)\n\nLindsay Banin l.banin05 at leeds.ac.uk\nMon May 11 19:46:34 CEST 2009\n\n```Hi there,\n\nI have been trying to fit an NLME to my data. My dataset has two category levels - one is a fixed effect (level1) and one is a random effect (level2), though so far I have only experimented with the highest level grouping (fixed, level1), with the following code:\n\nmod1 <- nlme(H ~ a*(1-exp(-b*D^c)),\ndata=sizes,\nfixed=a+b+c~factor(Loc),\nstart=c(a=75,b=0.05,c=0.7))\n\nThis returns the error:\nError in getGroups.data.frame(dataMix, eval(parse(text = paste(\"~1\", deparse(groups[]), :\nInvalid formula for groups\n\nOther points that it may be useful to note in diagnosing the problem are that:\n1) I have tried both specifying Loc=as.factor and not specifying this.\n2) I have tried other configurations of writing fixed=list(...) or fixed=c(...) and that always generates an error\n3) I have not specified groupedData\n4) My groups do not have equal sample sizes (unbalanced?)\n\nLook forward to hearing back!"
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.79490435,"math_prob":0.8190362,"size":1100,"snap":"2020-10-2020-16","text_gpt3_token_len":293,"char_repetition_ratio":0.09671533,"word_repetition_ratio":0.0,"special_character_ratio":0.27545455,"punctuation_ratio":0.15416667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9602284,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-27T05:56:50Z\",\"WARC-Record-ID\":\"<urn:uuid:02e6fafe-a9e8-4936-94b0-450a4136e555>\",\"Content-Length\":\"3751\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2f3d55fc-d1ae-4c66-b959-841b705ff72c>\",\"WARC-Concurrent-To\":\"<urn:uuid:d3a4e3c6-80de-47af-a0e6-b82fb260cd5c>\",\"WARC-IP-Address\":\"129.132.119.195\",\"WARC-Target-URI\":\"https://stat.ethz.ch/pipermail/r-help/2009-May/390943.html\",\"WARC-Payload-Digest\":\"sha1:6XTYNJAVPOZXBQ7SSJGK2QZHF7GLOMXX\",\"WARC-Block-Digest\":\"sha1:C3MPDEDYEFNZF2BO4225AU2TYR5ZRTE2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146647.82_warc_CC-MAIN-20200227033058-20200227063058-00451.warc.gz\"}"} |
http://www.baizhiedu.com/article/1104 | [
"400-616-5551\n\n# 西安python培训班：NumPy 数学函数\n\n## 发布百知教育来源：学习课程2019-12-10\n\n### NumPy 三角函数\n\nsin()数组中角度的正弦值\ncos()数组中角度的余弦值\ntan()数组中角度的正切值\narcsin()数组中角度的反正弦值\narccos()数组中角度的反余弦值\narctan()数组中角度的反正切值\ndegrees()将弧度转换成角度\n\n``import numpy as np``a = np.array([0, 30, 45, 60, 90])``print(np.char.center('不同角度的正弦值', 30, '*'))``# 通过乘 pi/180 转化为弧度``sin = np.sin(a*np.pi/180)``print(sin)``print('\\n')``print(np.char.center('不同角度的余弦值', 30, '*'))``# 通过乘 pi/180 转化为弧度``cos = np.cos(a*np.pi/180)``print(cos)``print('\\n')``print(np.char.center('不同角度的正切值', 30, '*'))``# 通过乘 pi/180 转化为弧度``tan = np.tan(a*np.pi/180)``print(tan)``print('\\n')``print(np.char.center('不同角度的反正弦值', 30, '*'))``arcsin = np.arcsin(sin)``# 将弧度转换成角度打印输出``print(np.degrees(arcsin))``print('\\n')``print(np.char.center('不同角度的反余弦值', 30, '*'))``arccos = np.arccos(cos)``# 将弧度转换成角度打印输出``print(np.degrees(arccos))``print('\\n')``print(np.char.center('不同角度的反正切值', 30, '*'))``arctan = np.arctan(tan)``# 将弧度转换成角度打印输出``print(np.degrees(arctan))``print('\\n')``# 返回``***********不同角度的正弦值***********``[0. 0.5 0.70710678 0.8660254 1. ]``***********不同角度的余弦值***********``[1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01`` 6.12323400e-17]``***********不同角度的正切值***********``[0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00`` 1.63312394e+16]``**********不同角度的反正弦值***********``[ 0. 30. 45. 60. 90.]``**********不同角度的反余弦值***********``[ 0. 30. 45. 60. 90.]``**********不同角度的反正切值***********``[ 0. 30. 45. 60. 90.]``\n\naround()四舍五入\nround()舍弃小数位\nfloor()向下取整\nceil()向上取整\n\n### numpy.around()\n\n``import numpy as np``a = np.array([1, 2.0, 30.12, 129.567])``# 四舍五入（取整）``print(np.around(a))``# 四舍五入（取一位小数）``print(np.around(a, decimals=1))``# 四舍五入（取小数点左侧第一位）``print(np.around(a, decimals=-1))``# 返回``[ 1. 2. 30. 130.]``[ 1. 2. 30.1 129.6]``[ 0. 0. 30. 130.]``\n\n### numpy.round()\n\n``mport numpy as np``a = np.array([1, 2.0, 30.12, 129.567])``# 只舍不入（取整）``print(np.around(a))``# 只舍不入（到小数点后一位）``print(np.around(a, decimals=1))``# 只舍不入（取小数点左侧第一位）``print(np.around(a, decimals=-1))``# 返回``[ 1. 2. 30. 130.]``[ 1. 2. 30.1 129.6]``[ 0. 0. 30. 130.]``\n\n### numpy.floor()\n\n``import numpy as np``a = np.array([1, 2.0, 30.12, 129.567])``# 向下取整``print(np.floor(a))``# 返回``[ 1. 2. 30. 129.]``\n\n### numpy.ceil()\n\n``import numpy as np``a = np.array([1, 2.0, 30.12, 129.567])``# 向上取整``print(np.ceil(a))``# 返回``[ 1. 2. 31. 130.]``\n\n### NumPy 算术函数\n\nmultiply()两个数组元素相乘\ndivide()两个数组元素相除\nsubtract()两个数组元素相减\npow()将第一个输入数组中的元素作为底数，计算它与第二个输入数组中相应元素的幂\nmod()计算输入数组中相应元素的相除后的余数\n\n``import numpy as np``a = np.arange(6, dtype=np.float_).reshape(2, 3)``print('第一个数组：')``print(a)``print('第二个数组：')``b = np.array([10, 10, 10])``print(b)``print('\\n')``print(np.char.center('两个数组相加', 20, '*'))``print(np.add(a, b))``print('\\n')``print(np.char.center('两个数组相减', 20, '*'))``print(np.subtract(a, b))``print('\\n')``print(np.char.center('两个数组相乘', 20, '*'))``print('两个数组相乘：')``print(np.multiply(a, b))``print('\\n')``print(np.char.center('两个数组相除', 20, '*'))``print(np.divide(a, b))``print('\\n')``# 返回``第一个数组：``[[0. 1. 2.]`` [3. 4. 5.]]``第二个数组：``[10 10 10]``*******两个数组相加*******``[[10. 11. 12.]`` [13. 14. 15.]]``*******两个数组相减*******``[[-10. -9. -8.]`` [ -7. -6. -5.]]``*******两个数组相乘*******``两个数组相乘：``[[ 0. 10. 20.]`` [30. 40. 50.]]``*******两个数组相除*******``[[0. 0.1 0.2]`` [0.3 0.4 0.5]]``\n\n### numpy.pow\n\n``import numpy as np``c = np.array([10, 100, 1000])``print('第一个数组是：')``print(c)``print('\\n')``print(np.char.center('调用 power 函数', 20, '*'))``print(np.power(c, 2))``print('\\n')``d = np.array([1, 2, 3])``print('第二个数组是：')``print(d)``print('\\n')``print(np.char.center('再次调用 power 函数', 20, '*'))``print(np.power(c, d))``# 返回``第一个数组是：``[ 10 100 1000]``****调用 power 函数*****``[ 100 10000 1000000]``第二个数组是：``[1 2 3]``***再次调用 power 函数****``[ 10 10000 1000000000]``\n\n### numpy.mod()\n\n``import numpy as np``e = np.array([10, 20, 30])``f = np.array([3, 5, 7])``print('第一个数组：')``print(e)``print('\\n')``print('第二个数组：')``print(f)``print('\\n')``print(np.char.center('调用 mod 函数', 20, '*'))``print(np.mod(e, f))``# 返回``第一个数组：``[10 20 30]``第二个数组：``[3 5 7]``*****调用 mod 函数******``[1 0 2]``\n\n### 总结\n\npython培训班：http://www.baizhiedu.com/python2019"
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null
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| {"ft_lang_label":"__label__zh","ft_lang_prob":0.6404458,"math_prob":0.99842465,"size":4941,"snap":"2019-51-2020-05","text_gpt3_token_len":2922,"char_repetition_ratio":0.20640065,"word_repetition_ratio":0.15992293,"special_character_ratio":0.44282535,"punctuation_ratio":0.23349282,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9966291,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-26T23:10:08Z\",\"WARC-Record-ID\":\"<urn:uuid:569d32d4-76ae-48c0-bb2c-1871987e31cb>\",\"Content-Length\":\"156847\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:33959c15-3f2f-4af9-a93c-0b78bfdb769a>\",\"WARC-Concurrent-To\":\"<urn:uuid:b8e27f0e-288a-4e77-bb8d-d81d8d0fd90f>\",\"WARC-IP-Address\":\"47.105.83.19\",\"WARC-Target-URI\":\"http://www.baizhiedu.com/article/1104\",\"WARC-Payload-Digest\":\"sha1:WJFZV6SBYZID62RQ6HJXUQ4SPRZZ37E7\",\"WARC-Block-Digest\":\"sha1:NQ3SSQV7MM6Q2ZFI2INJY7WRDFGQOJRA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251694071.63_warc_CC-MAIN-20200126230255-20200127020255-00524.warc.gz\"}"} |
https://bbruceyuan.com/post/8.html/ | [
"# 01之间均匀分区取两点构成三角形的概率-证明加代码实现\n\nbbruceyuan大约 3 分钟\n\n## # 3. 代码解法\n\nimport numpy as np\n\ndef can_construct_triangle(a, b):\n# 使用 任意两边之和大于第三边的性质\na, b = min(a, b), max(a, b)\n\nx = a\ny = b - a\nz = 1 - b\n\nif x + y > z and x + z > y and y + z > x:\nreturn True\nelse:\nreturn False\n\ndef main():\ntotal_cnt = 0\ncnt_be_triangle = 0\nfor _ in range(1000000):\n# 大量随机试验\na = np.random.uniform(0, 1)\nb = np.random.uniform(0, 1)\nif can_construct_triangle(a, b):\ncnt_be_triangle += 1\ntotal_cnt += 1\n\nprint(cnt_be_triangle / total_cnt)\n\nif __name__ == \"__main__\":\nmain()\n\n\n\n## # 4. 数学解法\n\n### # 4.2 转化为数学表达式\n\n$x > 0;\\ y > 0;\\ 1 - x -y > 0\\tag{1}$\n\n$x + y > 1 - x - y;\\ x + 1 - x - y > y;\\ y + 1 - x - y > x\\tag{2}$\n\n$x < 1/2;\\ y < 1/2;\\ x + y > 1/2\\tag{3}$"
]
| [
null
]
| {"ft_lang_label":"__label__zh","ft_lang_prob":0.9140458,"math_prob":0.9997125,"size":1331,"snap":"2022-40-2023-06","text_gpt3_token_len":1060,"char_repetition_ratio":0.08967596,"word_repetition_ratio":0.0,"special_character_ratio":0.27723515,"punctuation_ratio":0.14492753,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99988544,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-06T05:48:45Z\",\"WARC-Record-ID\":\"<urn:uuid:822fe478-612d-460f-b8f5-65093d9c6f25>\",\"Content-Length\":\"44476\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7c76991a-8754-40e2-9d85-af2bba576526>\",\"WARC-Concurrent-To\":\"<urn:uuid:f8957b3d-9a6d-4377-80b2-f42b836287b7>\",\"WARC-IP-Address\":\"185.199.109.153\",\"WARC-Target-URI\":\"https://bbruceyuan.com/post/8.html/\",\"WARC-Payload-Digest\":\"sha1:IBVUX77LJABHESGWG2EGLN7KWSIH7E6K\",\"WARC-Block-Digest\":\"sha1:FDOUVHVGMQLX3LRNAJQL6AWJY2TLZGL4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500304.90_warc_CC-MAIN-20230206051215-20230206081215-00445.warc.gz\"}"} |
https://avesis.deu.edu.tr/yayin/b22011b4-2ffc-4af6-9ea7-1d23c073aa39/first-order-flotation-kinetics-models-and-methods-for-estimation-of-the-true-distribution-of-notation-rate-constants | [
"## First-order flotation kinetics models and methods for estimation of the true distribution of notation rate constants\n\nINTERNATIONAL JOURNAL OF MINERAL PROCESSING, vol.58, pp.145-166, 2000 (SCI-Expanded)",
null,
"",
null,
"• Publication Type: Article / Article\n• Volume: 58\n• Publication Date: 2000\n• Doi Number: 10.1016/s0301-7516(99)00069-1\n• Journal Name:\n• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus\n• Page Numbers: pp.145-166\n• Keywords: first-order flotation kinetics models, methods for estimation, flotation rate constants\n• Dokuz Eylül University Affiliated: No\n\n#### Abstract\n\nTo improve their versatility, many first-order flotation kinetics models with distributions of flotation rate constants were redefined so that they could all be represented by the same set of three model parameters. As a result, the width of the distribution become independent of its mean, and parameters of the model and the curve fitting errors, became virtually the same, independent of the chosen distribution function. For the modified three-parameter models, the curve fitting errors were much smaller and their robustness. measured by PRESS residuals, was much better when compared to the corresponding two-parameter models. Three different methods were compared to perform flotation kinetics analysis and estimate model parameters. In Method I, recovery vs. time data were used to obtain model parameters. No significant insight into the distribution of rate constants could be obtained because the distributions were presupposed. In Method II, the froth products were fractionated into several size fractions and the data for each fraction were fitted to a model. This task was easy to perform and the method could describe the flotation kinetics reasonably well. In method III, flotation products were fractionated into many size-specific gravity fractions. The procedure involved a large amount of time and effort and it generated relatively large errors. Based on the analysis presented in this article, it was concluded the smallest errors were obtained with Method II. The overall distribution of flotation rate constants could be obtained from a weighted average of the distributions of individual size fractions. The distributions so obtained were demonstrated to be less sensitive to the choice of the model used to represent the kinetics of individual size fractions, and therefore can be assumed to be \"true\" representation of the flotation rate distribution. (C) 2000 Elsevier Science B.V. All rights reserved."
]
| [
null,
"https://avesis.deu.edu.tr/Content/images/integrations/small/integrationtype_2.png",
null,
"https://avesis.deu.edu.tr/Content/images/integrations/small/integrationtype_1.png",
null
]
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http://virtualmathmuseum.org/Surface/hyperboloid2/hyperboloid2.html | [
"# Hyperboloid of Two Sheet\n\nThe analogy of the 2-sheeted hyperboloid with the Euclidean unit sphere becomes apparent, if one sees it as the time unit sphere in Special Relativity. For visualization reasons we use only 2 space dimensions, that is, we use R^3 together with the Lorentz norm `x^2 + y^2 - z^2` .\n\nVectors for which the Lorentz norm is positive, are called “spacelike”, if vectors have negative Lorentz norm they are called “timelike”, and in case of zero Lorentz norm the name is “lightlike”.\n\nThe time unit sphere is the solution set of `x^2 + y^2 - z^2 = -1` .",
null,
"The 2-sheeted hyperboloid has a parametrization analogous to the longitude-latitude parametrization of the Euclidean sphere: (u, φ) ⟶ (sinh(u)*cos(φ), sinh(u)*sin(φ), ± cosh(u) )\n\nThe meridians (or longitudes), φ = const, are:\n\n`u ⟶ (sinh(u)*cos(φ), sinh(u)*sin(φ), ± cosh(u) )`\n\nthey have the tangent vectors: `(x,y,z) = (cosh(u)*cos(φ), cosh(u)*sin(φ), ± sinh(u) )` with Lorentz norm `x^2 + y^2 - z^2 = +1` . This means, the meridians are spacelike and parametrized by arc length.\n\nThe latitudes, `u = const`, are:\n\n`φ ⟶ (sinh(u)*cos(φ), sinh(u)*sin(φ), ± cosh(u) )` .\n\nThey are circles in planes parallel to the x-y-plane with (Euclidean) radius sinh(u) and therefore `circumference = 2*π*sinh(u)` .\n\nSince the meridian-radius, because of the arclength parametrization, has only length = u, we have: The geometry of the time unit sphere has the spectacular property:\n\n`circles of radius = u have the circumference = sinh(u)` .\n\nOne says: The Riemannian metric of this geometry is\n\n`ds^2 = du^2 + sinh(u)^2*d φ^2`\n\nThis implies: Such a circle has area `2*π*(cosh(u) - 1)` .\n\nIn short: length and area of circles grow exponentially with the radius. Differential geometers derive from this behavior of circles that the Gaussian curvature of the time unit sphere is constant = -1.\n\nRemember: the hyperbolic arclength of the meridians is much shorter than the Euclidean interpretation suggests, while the hyperbolic length of the latitude circles is in agreement with our Euclidean eyes. The circumference really grows exponentially as a function of the radius.\n\nThe next analogy with the Euclidean sphere is: There are many linear Lorentz isometries which map the hyperboloid to itsself:\n\n`(x,y,z) ⟶ cosh(u)*x + sinh(u)*z, y, sinh(u)*x + cosh(u)* z)`\n\nClearly, if `x^2 + y^2 - z^2 = -1` , then the Lorentz norm of the image is also -1.\n\nThe rotations around the z-axis:\n\n`(x,y,z) ⟶ (cos(φ)*x - sin(φ)*y, sin(φ*)x + cos(φ)*y, z)`\n\nalso leave the Lorentz norm invariant. These two families of maps are enough, to map (0, 0, 1) to any other point of the positive sheet of the hyperboloid.\n\nAnd we can exchange the two sheets:\n\n`(x,y,z) ⟶ (coshu)*x + sinh(u)*z, y, -(sinh(u)*x + cosh(u)* z))`\n\nNote that these maps are like reflections: applying them twice gives the identity. Also, (0,0,-1) can be mapped to any point on the positive sheet with one of these reflections plus a rotation.",
null,
"Anaglyph image of a hyperbolic square with 60 degree angles on the hyperboloid, and projected to the equator plane.",
null,
"A magnified view of the previous image.\n\nThe simple form of the metric implies that any curve from (0, 0, 1) to a point on the latitude circle of hyperbolic radius u has at least the length u. This implies, that the meridians are shortest connections between any two of its points. We therefore view the meridians as straight lines of our hyperbolic geometry. Note that they lie in planes through the origin, which is the midpoint of the hyperboloid. Our linear Lorentz isometries leave the origin fixed and map planes to planes. Since they also map shortest connections between points to shortest connections between the image points, we have another analogy to the Euclidean sphere: Shortest connections (or \"straight lines\" of the geometry) lie in planes through the origin.",
null,
"The white curves and the meridians are hyperbolic straight lines on the hyperboloid. The white lines bound hexagons with 90 degree angles. Stereographic projection to the x-y-plane is added.\n\nNow that we have straight lines, we can do triangle geometry. All Euclidean triangle formulas have simple hyperbolic analogues. For example the Pythagorean theorem for triangles with edge lengths a,b,c and angle π/2 opposite c reads: `cosh(c) = cosh(a)*cosh(b)` .\n\nFor very small triangles this is almost the Euclidean formula, since `cosh(x) = 1 + x^2/2 + higher order terms` .\n\nOne important result is: The angles of a hyperbolic triangle with edge lengths a,b,c are smaller than the angles of a Euclidean triangle with the same edgelengths. And there are intriguing formulas: The area of a triangle with angles α, β, γ is:\n\n`area = π - (α + β + γ)` .\n\nOne can use triangles to make regular polygons and tesselate the hyperbolic plane in many different ways. For examples there are equilateral triangles with all three angles = `π/n` for any `n ≻ 3` and squares with all four angles = `π/n for n ≻ 2` .\n\nRegular hyperbolic polygons exist with arbitrarily small angles. Even the angle zero is possible - the vertices are then at infinity and the straight lines to the same infinite vertex are called “asymptotic”. The picture shows pentagons with zero degree angles, on the hyperboloid and projected to the x-y-plane.\n\nAn anaglyph image of the previous situation. The projection rays lie on a cone which is asymptotic to the hyperboloid.\n\nStereographic projection is a very important conformal map from the Euclidean sphere to the plane. Similarly we can project the positive sheet from (0,0,-1) to the x-y-plane (which is parallel to the tangent plane at (0,0,1), opposite to the projection center).\n\nWe get as image the unit disk in the x-y-plane. We prove that this map is angle preserving (= conformal):\n\nAny two lines (in the x-y-plane) that intersect at p inside the unit disk, represent an angle at p.\n\nThe two planes through these lines and the projection center intersect the tangent plane (at (0,0,-1)) with parallel lines, i.e. with a congruent angle. The image of p in the positive sheet and (0,0,-1) can be interchanged by one of the hyperbolic reflections discussed above. This reflection maps the planes into themselves and therefore the angle at (0,0,-1) to the angle at the image point of p. This proves that this projection is conformal. Therefore the image disk is taken as the most important model of hyperbolic geometry, namely the disk model of complex analysis. The “Straight lines” of hyperbolic geometry are, in this model, circles which intersect the unit circle orthogonally.\n\n#### Conic Section Surfaces\n\nGet red/blue stereo glasses from amazon"
]
| [
null,
"http://virtualmathmuseum.org/Surface/hyperboloid2/i/hyperboloid2_dimag1.png",
null,
"http://virtualmathmuseum.org/Surface/hyperboloid2/i/hyperboloid2_square60_dots.png",
null,
"http://virtualmathmuseum.org/Surface/hyperboloid2/i/hyperboloid2_square60_magfd.png",
null,
"http://virtualmathmuseum.org/Surface/hyperboloid2/i/hyperboloid2_Hexa90_patch.png",
null
]
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https://www.edplace.com/worksheet_info/maths/keystage4/year10/topic/1237/7518/apply-the-angles-in-the-same-segment-rule | [
"",
null,
"",
null,
"# Apply the Angles in the Same Segment Rule\n\nIn this worksheet, students will focus on one specific theory relating to circles (angles in the same segment are always equal) and use this to solve related geometric problems.",
null,
"Key stage: KS 4\n\nYear: GCSE\n\nGCSE Subjects: Maths\n\nGCSE Boards: AQA, Eduqas, Pearson Edexcel, OCR,\n\nCurriculum topic: Geometry and Measures, Basic Geometry\n\nCurriculum subtopic: Properties and Constructions Circles\n\nPopular topics: Geometry worksheets\n\nDifficulty level:",
null,
"",
null,
"",
null,
"#### Worksheet Overview\n\nCircles are all around us in everyday life.\n\nHow many examples can you think of?\n\nCan you see any circular shapes in objects around you at this moment?\n\nMathematicians have investigated circles for centuries because of their love of pure mathematics.\n\nThe ability to learn, understand and apply circle theorem is an essential, but challenging, geometric skill.\n\nFor this reason, we usually only see circle theorem questions on the Higher GCSE exam paper.\n\nIt is also common for circles and angles to be linked in questions, so we may need to apply our knowledge of angle properties too.\n\nIn this activity, we will focus on one specific theory relating to circles:",
null,
"Angles in the same segment are always equal.\n\nLet's now look at how this theory works and why it is always true.",
null,
"Let's begin with a circle and mark its centre.",
null,
"We can draw two radii coming from the centre, and join them with a chord to create an isosceles triangle. Let's call the angle at the centre of the circle 2x.",
null,
"We can now use the chord as the base for a new triangle (shown in red) that touches the circumference.",
null,
"Finally, let us draw another triangle from the same base that touches the circumference (shown in blue).\n\nAngles at the circumference are alwas half the size of angles at the centre of a circle. As the angle at our centre is 2x, the two angles at the circumference created by the triangles are x. In other words, they are equal.\n\nLet's put this theory into practice now in some geometric problems.\n\n### What is EdPlace?\n\nWe're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.\n\nGet started",
null,
""
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null,
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null,
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null,
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null,
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null,
"https://www.edplace.com/userfiles/image/same%20segment%201.png",
null,
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null,
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null,
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null,
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null
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http://mptkl.tripod.com/rnd/tajuk00_2.htm | [
"",
null,
"A Catastrophe Theory Approach to Stagewise Development\n\nYEE SYE FOONG\nTechnical Teachers Training College\n\nABSTRACT\n\nWhat is Catastrophe Theory and some relevant aspects of Catastrophe Theory is discussed. The application of Catastrophe Theory to developmental research through the method of catastrophe detection, catastrophe analysis and catastrophe modelling is described. The catastrophe theoretical approach as a potential tool for studying conceptual development, specifically the development of the concept of matter and its transformations, in science education and its implications is also considered.\n\nINTRODUCTION\n\nThe concept of stages in cognitive development (Piaget & Inhelder, 1969) has come to dominate the field of education through its far-reaching educational implications. However, the debate and controversy concerning empirical criteria and methods for detecting stages and the subsequent interpretation of the results obtained continues unabated. Fischer (1983) voices this anxiety, ... Would they (developmental researchers) be able to detect the stage that was right there in front of them ? If they did notice it, how would they know what they had found ? How would they be able to tell that it was a stage ? What pattern of results would they look for ? It was then concluded that developmental researchers do not have a uniform empirical criterion to determine the existence of a stage.\n\nStage criteria such as invariant sequences, cognitive structure, integration, consolidation and equilibration has been proposed by Piaget (1960) while transition criteria such as bimodality, sudden spurts, response variability and second-order transitions has been pointed out by Flavell(1971). Unfortunately, such stage and transition criteria have seldom been investigated simultaneously. In addition to this, the rationale for each criterion was not derived from an explicit formal transition theory (van der Maas & Molenaar, 1992).\n\nConnell and Furman (1984) propose that all the transition criteria ought to be integrated within a formal model. This is because empirical evidence on the basis of any one transition criteria is insufficient to support or reject the Piagetian Stage hypothesis. A basic formal theoretical model of transition criteria would enable the integration of empirical evidence for stage transitions into a powerful argument for stagewise development. Such a formal model may be obtained through a branch of mathematics called Catastrophe Theory (Thom, 1975).\n\nCatastrophe Theory\n\nThe term Catastrophe Theory first appeared in the western press in the late sixties. It was hailed as a revolution in mathematics, comparable perhaps to Newtons invention of the differential and integral calculus (Arnold, 1992). Catastrophe Theory was applied with great diversity to areas such as the study of heart beat, geometrical and physical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology and the theory of elementary particles.\n\nThe founder of Catastrophe Theory was René Thom. The origins of Catastrophe Theory may be traced to Whitneys theory of singularities of smooth mappings and Poincaré and Andronovs theory of bifurcations of dynamical systems. Singularities, bifurcations and catastrophes are different terms used to describe the emergence of discrete structures from smooth and continuous ones. Singularity theory is a broad generalization of the study of functions at maximum and minimum points. Bifurcation means forking and is used to designate all kinds of qualitative re-organizations or metamorphoses of various entities as a result of a change in the parameters on which they depend. Catastrophes are abrupt changes which arise as a sudden response of a system to a smooth change in external conditions.\n\nCatastrophe Theory provides a universal method for the study of all discontinuities, jump transitions and sudden qualitative changes. Catastrophe Theory involves the study of the equilibrium behaviour of a large class of mathematical system functions that exhibit discontinuous jumps, that is, the points of the functions where at least the first and second derivatives are zero. The mathematical theorems of Catastrophe Theory constitute an essential contribution to the study of the singularities of families of smooth functions or infinitesimally differentiable functions.\n\nSome aspects of Catastrophe Theory\n\nStagewise or stage-by-stage development entails the concepts of stage and transition. Catastrophe Theory is capable of describing physical systems with a well-defined discontinuity. For example, boiling, which involves a transition between the liquid phase and the gaseous phase of water. Catastrophe Theory, which is part of a nonlinear dynamic system theory, may be used to model such physical systems. Such dynamic models are of sufficient complexity to transcend the dichotomy between the organismic and mechanistic paradigms (Molenaar & Oppenheimer, 1985). As a result, Catastrophe Theory has been successfully applied in psychological perception research (Stewart & Peregoy, 1983; Taéed, Taéed & Wright, 1988) and clinical psychology (Callahan & Sashin, 1990).\n\nModels derived from Catastrophe Theory relates behavioural (dependent) variables to control (independent) variables. Discontinuities in behavioural variables is modelled as a function of continuous variation in the control variables. The relationship between behavioural and control variables is in the form of mathematical expressions which represent a dynamical system which is continually seeking to reach equilibrium in varying situations. For certain fixed values of the control variables, the behavioural variable will change optimally until a stable state is attained.\n\nThe models obtained through Catastrophe Theory is also subject to a basic principle of mathematical modelling, that is, the hypothesis of structural stability or insensitivity to small perturbations. This hypothesis states that there is some kind of overall stability in any mathematical model of a real system. This stability corresponds to the inherent stability of observable phenomena in the real world. Therefore, there is the notion of stable equilibrium for a dynamical system. A dynamical system is some process which evolves continuously with time. The system is changing slowly due to changes in various parameters which describe the system. The equilibrium also changes and becomes less and less stable until for a particular value or values of the parameters, the equilibrium becomes unstable and disappears altogether. Consequently, the behaviour of the system would also undergo a sudden switch from one equilibrium state to another. The dynamical system with a continuous input thus produces a sudden discontinuity in its output.\n\nThom (1975) was able to show that for a certain fairly common kind of dynamical system, the various ways in which these discontinuous jumps in output occur may be described geometrically. It was further proven that a large class of structurally stable system functions (involving up to four control variables) exhibiting discontinuous behaviour may be classified into seven archetypical forms (the elementary catastrophe models) through a set of smooth transformations of the system variables. The catastrophe models are the fold, the cusp, the swallow-tail, the elliptic umbilic or hair, the hyperbolic umbilic or breaking wave, the butterfly and the parabolic umbilic or the mushroom. The most popular elementary catastrophe model is the cusp. All structurally system functions which show discontinuous behaviour in three dimensions may be transformed to a cusp.\n\nThe Cusp Catastrophe Model\n\nThe cusp catastrophe is denoted by\n\nV (x) = ¼ x 4 + ½ c1 x 2 + c2 x ...... (1)\n\nwhere c1 and c2 are the control parameters (or independent variables) and x is the behavioural variable (or dependent variable). Critical points occur where V1 (x) = 0 , that is,\n\nx3 + c1 x + c2 = 0 .......... (2)\n\nand they coalesce where V 11 (x) = 0 , that is,\n\n3x2 + c1 = 0 .......... (3)\n\nEliminating x gives\n\n4c1 3 + 27 c2 2 = 0 .......... (4)\n\nfor the equation of the catastrophe set K.\nThe complex behaviour of the function (that is, the relationship between x, c1 , c2 ) may be elucidated in a very revealing way by representing it geometrically in three dimensions. This is done by drawing the associated catastrophe manifold or equilibrium surface of points in the (x, c1 , c2 )-space. This space is the set M of points (x, c1 , c2 ) which satisfies Equation 2. The catastrophe manifold, M, has the appearance of a folded smooth surface as shown in Figure1.",
null,
"A clearer picture of this folded surface may be obtained from an analysis of the catastrophe map X : M C which projects points on M onto the ( c1 , c2 ) - plane or the control plane, C, according to ( x, c1 , c2 ) ( c1 , c2 ) where x c M in the neighbourhood of the origin. This projection in the control plane C is a semicubical parabola denoted by Equation 4, which is the equation of the catastrophe set K.\nThe control plane may be divided into five subsets : the shaded region I inside the curve, the region E outside it, the two branches B1 and B2 of the curve and the origin P. The points ( c1 , c2 ) which lie in I are those for which 4c1 3 + 27 c2 2 < 0 , those in E satisfy 4c1 3 + 27 c2 2 > 0 and those on the curve satisfy 4c1 3 + 27 c2 2 = 0.\nIt is now possible to give a geometrical interpretation of the nature of the equilibria of the dynamical system. For a given pair of control parameters ( c1 , c2 ), the equilibria are obtained by solving Equation 1. The roots may be described as the x-coordinates of the points at which a vertical through ( c1 , c2 ) meets the catastrophe manifold, M. Geometrically, it may be seen that\nIf ( c1 , c2 ) lies in the region I , that is, where 4c1 3 + 27 c2 2 < 0 , there are three distinct real roots. This means that there are three values of x since there are three sheets of M lying above points in I . This particular region in the control plane, C , is called the bifurcation set, B . V takes the form shown in Figure 2(a), that is, two minima on either side of a maximum.\nIf ( c1 , c2 ) lies in the region E external to the bifurcation set B, that is, where 4c1 3 + 27 c2 2 > 0 , there is one real root. This means that there is a unique value of x since only one sheet of M lies above points in E . The cusp function V takes the form shown in Figure 2(b), that is, a minimum.\nIf ( c1 , c2 ) lies on B1 , that is, where 4c1 3 + 27 c2 2 = 0 , there are three real roots; two of which are equal, with the equal pair being larger. This means that there are three values of x (of which two are equal and larger than the third). The vertical line through ( c1 , c2 ) passes through the lower sheet at a single point and is tangential to the upper sheet. The cusp function V takes the form shown in Figure 2(c), that is, a minimum and a point of inflexion to the right of the minimum.\nIf ( c1 , c2 ) lies on B2 , that is, where 4c1 3 + 27 c2 2 = 0 , there are three real roots; two of which are equal, with the equal pair being smaller. This means that there are three values of x (of which two are equal and smaller than the third). The vertical line through ( c1 , c2 ) is tangential to the lower sheet and passes through the upper sheet at a single point. The cusp function V takes the form shown in Figure 2(d), that is, a minimum and a point of inflexion to the left of the minimum.\nIf ( c1 , c2 ) lies on the cusp point, P , that is, where c1 = c2 = 0 , there are three real coincident roots (all equal to 0). This means that there are three values of x which are coincident and equal zero since the vertical line through ( c1 , c2 ) is tangential to the surface M and meets it at a single point, the origin, which passes through three sheets of M ; all at the same point. The cusp function, V , takes the form shown in Figure 2(e), that is, a minimum.\n\nMinima of V correspond to stable equilibrium while maxima or points of inflexion correspond to unstable equilibria. Hence, for control parameters in , B1 , B2 and P , there is a single equilibrium whereas for control parameters in I (that is, the bifurcation set), there are two stable equilibria and one unstable equilibrium. In other words, unstable equilibria correspond to points on M lying inside the fold curve on the middle of the three sheets while stable equiria lie outside the fold curve.",
null,
"In the bifurcation set, three modes of behaviour are possible. The middle sheet represents unstable states and is therefore called the inaccessible region. The presence of the two remaining modes implies a bimodal distribution of the behavioural variable. Phenomena such as bimodality can be used as an indicator of discontinuities. It is called a catastrophe flag by Gilmore (1981) and can be used to detect catastrophes.\n\nThe Application of Catastrophe Theory to Stagewise Development\n\nThe Catastrophe Theory approach to stagewise development may be carried out through three methods : catastrophe detection, catastrophe analysis and catastrophe modelling.\n\nCatastrophe Detection\n\nCatastrophe Theory yields a set of mathematically derived criteria to detect discontinuities or catastrophes. Gilmore (1981) refers to these criteria as catastrophe flags. Catastrophe detection provides empirical evidence for transitions in development. The occurrence of a catastrophe is invariantly associated with catastrophe flags which can be used as an indicator of discontinuities. Catastrophe flags include bimodality, inaccessibility, sudden jumps, hysteresis and divergence. The detection of catastrophe flags is quite straightforward as only behavioural measures are required. Catastrophe detection is especially useful in the initial analysis of stagewise development. These flags can be used to detect stage-to-stage transitions.\n\nModality relates to the properties of bimodal score distributions. There are three modes of behaviour possible in the bifurcation set. The maximum is not a stable state and is called the inaccessible region. The remaining two modes, represented by minima, implies a bimodal distribution of the behavioural variable. This is shown in Figure 3 and Figure 4.",
null,
"",
null,
"According to Wohlwill (1973), the occurrence of a sharp bimodal distribution of scores may be due to the high degree of interdependence among responses to different items of a test. This is indicative of discontinuous behaviour. In contrast, if the various items are independent, a uniform or normal distribution would be obtained due to continuous change. In other words, a discontinuity in cognitive level as a function of age may be translated directly into a distribution of scores. It follows then that intermediate test scores will be low in proportion.\n\nThe catstrophe flag of sudden jumps or spurts is directly coupled to bimodality and inaccessibilty. It is also a property of transitions. A sudden jump is defined as a large change in the value of the behavioural variable because of a small change in the value of a control variable. Such spurts in developmental functions may be detected using a developmental test (the yardstick) and age (the clock) for cognitive change. Fischer (1983) discussed a number of applications of this method in different fields such as speech development, brain development, object performance and classification.\n\nHysteresis refers to jumps at distinct values of the control variables when these control variables follow either an increasing or decreasing path. Hysteresis may be difficult to detect as the actual control variables have to be known in order to be manipulated effectively (that is, experimentally induced to continuous increase or decrease). Hysteresis has been successfully detected in simple neural networks that may be relevant to simulation of stagewise development (van der Maas, Verschure & Molenaar, 1990).\n\nDivergence occurs when a small change in the initial value of a path through the control plane leads to large changes in the behavioural variable. Fischer, Pipp and Bullock (1984) suggest that optimality of environmental test conditions control the discontinuity in the manner represented by the splitting control variable. Change along this splitting control variable will lead to divergence of the two modes of behaviour.\n\nThe five catastrophe flags of bimodality, inaccessibilty, sudden jumps, hysteresis and divergence occur simultaneously when the system is in transition. They occur when the values of the control variables are inside the bifurcation set.\n\nCatastrophe Analysis\n\nCatastrophe analysis involves analysing mathematically the dynamic equations which describe a transition process. These equations are repeatedly subjected to certain transformation techniques to reduce them to one of the seven archetypical or original geometrical forms specified by Thom (1975), that is, the elementary catastrophe models. Hence, catastrophe analysis requires a knowledge of the mathematical equations of the transition process.\n\nThe use of catastrophe analysis has been demonstrated in the physical sciences (Poston & Stewart, 1978). However, this variant of Catastrophe Theory is hindered in the social sciences due to the lack of knowledge of the precise dynamical equations governing the types of transitions explored. In fact, determination of the control variables of such transitions is also an obstacle. This is because discontinuities in psychological behaviour may be the result of simple discontinuous change in the independent variables and not the variables which actually controls the behaviour (that is, the control variables). This necessitates the restriction to continuous variation of the control variables as only the control variables could bring about intrinsic reorganization which constitutes a genuine stage transition.\n\nCatastrophe Modelling\n\nCatastrophe modelling is intermediate in strength between catastrophe detection and catastrophe analysis. Catastrophe modelling involves the direct specification of behavioural and control variables in one of the elementary catastrophes.\n\nThe Conflict Cusp Model, proposed by van der Maas and Molenaar (1990), relates discontinuities in conservation acquisition to the set of different strategies for solving conservation items by an appeal to the concept of cognitive conflict.\n\nThe behavioural variable, denoted by p, is defined by the quotient of the number of correct judgements of conservation items and the total number of conservation items. The test score is thus given by chance level, for example, p = 1 or 0 or 0.5. The control variables are based on conservation strategies which are classified into three types : conservation strategies (CS), nonconservation strategies (NS) and irrelevant strategies (IS). A conserver will use mainly CS and IS while a nonconserver will use NS and IS. Transitional children will have at their disposal all three types of conservation strategies whereas the remaining children (the residual group) will use predominantly IS. The Conflict Cusp Model is shown in Figure 5.",
null,
"Discontinuities can occur when both control variables are active, that is, m and n are high. A typical stage transition is illustrated by Path a. First, a nonconserver consistently uses NS. Therefore, the test score depends only on m and will be below chance level (that is, p = 0.5). With increase in the value of n corresponding to a predominance of CS, the child reaches the bifurcation set and becomes transitional. Both CS and NS are now available and the child is faced with a situation often described as a cognitive conflict (Cantor, 1983; Pinard, 1981). The middle sheet of the cusp represents a situation in which both CS and NS have equal influence. However, this region is inaccessible and consists of unstable states. This means that a transitional child will score either below or above chance level but not at the chance level. Hence, even though both predominances are equally strong, the actual application of strategies (and therefore the test scores) is biased towards only one set of strategies. On leaving the bifurcation set, the jump to a higher level takes place and the child becomes a stable conserver.\n\nThe conservation score of both conservers and nonconservers is continuously related to variation in predominances of CS and NS (or the values of m and n). Variation along the m-axis (that is, n = 0) corresponding to variation in the predominance of NS in nonconservers yields continuous changes in the test score. Variation along the n-axis (that is, m = 0) corresponding to variation in the predominance of CS in conservers will also yield continuous changes in the test score. When the values of m and n are both high, sudden jumps or transitions occur for the transitional group. The residual group is placed around the neutral point where both predominances are equal. The use of IS by these groups yields scores at the chance level. This model has not been tested empirically.\n\nCatastrophe modelling concerns the actual fitting of the model to data which requires statistical techniques. Strong evidence for the presence of a stage transition is indicated by a goodness of fit of a catastrophe model which is statistically acceptable.\n\nConclusion\n\nCatastrophe Theory provides a means to mathematically analyse the dynamics of nonlinear systems. Catastrophes mark transitions to newly emerging equilibria that is the result of endogenous reorganization or self-organization of the system dynamics.\n\nAccording to van der Maas and Molenaar (1992), catastrophes constitute formal analogues of stage transitions in Piagets theory of cognitive development. This is because the human cognitive system is one of the most complex information-processing systems in nature. Cognitive development may be characterised in a formal sense as the evolution of a nonlinear dynamic system in which the mathematical results of Catastrophe Theory are obeyed. The Catastrophe Theory approach to stagewise development as proposed by van der Maas and Molenaar (1992) gives to a straightforward methodology for detecting and modelling stage transitions. Empirical research in catastrophe detection and catastrophe modelling comprise a definite test for stage transitions.\n\nEven though the catastrophe theoretical approach was originally a formal approach to cognitive development, it cannot be denied that this approach is feasible for other forms of development, in particular the development of science concepts for students in science education. The comprehension of science concepts and its subsequent application in new situations is a form of development which requires very specific input. For example, the concept of matter and its transformations is very fundamental with ever-widening application as the study of science progresses. It is also very abstract as it involves the conceptualization of matter as being particulate and dynamic and capable of interacting with other particles. The necessary instruction such as the Particle and Kinetic Theory of Matter definitely has to be imparted to students as it is not something that is in the air which students will ultimately absorb with increasing experience and maturity. Formal instruction is required and teachers need to take students over the boundary between their haphazard and mainly narcissistic beliefs which are the result of everyday experiences to the realm of scientific knowledge.\n\nHence, instruction in the concept of matter and its transformations is a very probable control variable in students conceptual development of matter and its transformations. Research towards the determination of the exact control variables and the precise nature of this conceptual development will be invaluable in the sense that catastrophes in conceptual development of students could be customized. This holds promise for science instruction and the school science curriculum. If it can be envisaged that certain input or instruction could bring about a catastrophe or an abrupt major re-organization in the understanding of a science concept, then appropriate re-structuring of the curriculum may be better directed and more relevant. This could lead the way to the development of science concepts as a planned part of the curriculum.\n\nReferences\n\nArnold, V. I. (1992). Catastrophe theory. New York : Springer-Verlag.\nCallahan, J., & Sashin, J. I. (1990). Predictive models in psychoanalysis. Behavioural Science, 33, 97-115.\nCantor, G. N. (1983). Conflict, learning and Piaget : Comments on Zimmerman and Bloms Toward an empirical\ntest of the role of cognitive conflict in learning. Developmental Review, 3, 39-53.\nConnell, J. P., & Furman, W. (1984). The study of transitions : Conceptual and methodological issues. In R. N. Emde & R. J. Harmon (Eds.), Continuities and discontinuities in development (pp. 153-174). New York : Plenum Press.\nFischer, K. W. (1993). Developmental levels as periods of discontinuity. In K. W. Fischer (Ed.). Levels and transitions\nin childrens development: New directions for child development (Vol. 21, pp. 5-20). San Francisco : Jossey-Bass.\nFischer, K. W., Pipp, S. L., & Bullock, D. (1984). Detecting developmental discontinuities : methods and\nmeasurement. In R. N. Emde & R. J. Harmon (Eds.), Continuities and discontinuities in development\n(pp. 95-122). New York : Plenum Press.\nFlavell, J. H. (1971). Stage-related properties of cognitive development. Cognitive Psychology, 2, 421-453.\nGilmore, R. (1981). Catastrophe Theory for scientists and engineers. New York : Wiley.\nMolenaar, P. C. M., & Oppenheimer, L. (1985). Dynamic models for development and the mechanistic-\norganismic controversy. New Ideas in Psychology, 3, 233-242.\nPiaget, J. (1960). The general problems of the psychological development of the child. In J. M. Tanner & B.\nInhelder (Eds.), Discussions on child development, (Vol. 4, pp. 3-28). London : Tavistock.\nPiaget, J., & Inhelder, B. (1969). The psychology of the child. New York : Basic Books.\nPinard, A. (1981). The conservation of conservation : The childs acquisition of a fundamental concept. Chicago :\nUniversity of Chicago Press.\nPoston, T., & Stewart, I. (1978). Catastrophe theory and its applications. London : Pitman.\nStewart, I. N., & Peregoy, P. L. (1983). Catastrophe theory modelling in psychology. Psychological Bulletin,\n94, 336-362.\nTaéed, L. K., Taéed, O., & Wright, J. E. (1988). Determinants involved in the perception of the necker cube : An\napplication of catastrophe theory. Behavioural Science, 33, 97-115.\nThom, R. (1975). Structural stability and morphogenesis. Reading, MA : Benjamin.\nVan der Maas, H. L. J., & Molenaar, P. C. M. (1992). Stagewise cognitive development : An application of\ncatastrophe theory. Psychological Review, 99 (3), 395-417.\nVan der Maas, H. L. J., Verschure, P. F. M., & Molenaar, P. C. M. (1990). A note on chaotic behaviour in simple\nneural networks. Neural Networks, 3, 119-122.\nWohlwill, J. F. (1973). The study of behavioural development. San Diego, CA : Academic Press."
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https://wisc.pb.unizin.org/chem103and104/chapter/second-law-of-thermodynamics-m17q3/ | [
"# M17Q3: Second Law of Thermodynamics\n\nLearning Objectives\n\n• Calculate the entropy change for a process occurring at constant temperature.\n• Calculate the change in entropy for a chemical reaction using standard molar entropy values.\n\n## The Second Law of Thermodynamics\n\nIn the quest to identify a property that may reliably predict the spontaneity of a process, we have identified a very promising candidate: entropy. Processes that involve an increase in entropy of the systemS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, we may reach a significant conclusion regarding the relation between this property and spontaneity. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:\n\nΔSuniv = ΔSsys + ΔSsurr\n\nTo illustrate this relationship, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three reasonable possibilities for such a process:\n\n1. The objects are at different temperatures, and heat flows from the hotter to the cooler object. This always occurs spontaneously. Designating the hotter object as the system and invoking the definition of entropy yields the following:\nΔSsys =",
null,
"and ΔSsurr =",
null,
"The arithmetic signs of qrev denote the loss of heat by the system and the gain of heat by the surroundings. Since Tsys > Tsurr in this scenario, the magnitude of the entropy change for the surroundings will be greater than that for the system, and so the sum of ΔSsys and ΔSsurr will yield a positive value for ΔSuniv. This process involves an increase in the entropy of the universe.\n\n2. The objects are at different temperatures, and heat flows from the cooler to the hotter object. This is never observed to occur spontaneously. Again designating the hotter object as the system and invoking the definition of entropy yields the following:\nΔSsys =",
null,
"and ΔSsurr =",
null,
"The arithmetic signs of qrev denote the gain of heat by the system and the loss of heat by the surroundings. The magnitude of the entropy change for the surroundings will again be greater than that for the system, but in this case, the signs of the heat changes will yield a negative value for ΔSuniv. This process involves a decrease in the entropy of the universe.\n\n3. The temperature difference between the objects is infinitesimally small, TsysTsurr, and so the heat flow is thermodynamically reversible. In this case, the system and surroundings experience entropy changes that are equal in magnitude and therefore sum to yield a value of zero for ΔSuniv. This process involves no change in the entropy of the universe.\n\nThese results lead to a profound statement regarding the relation between entropy and spontaneity known as the second law of thermodynamics: all spontaneous changes cause an increase in the entropy of the universe. A summary of these three relations is provided in Table 1.\n\n ΔSuniv > 0 spontaneous ΔSuniv < 0 nonspontaneous (spontaneous in opposite direction) ΔSuniv = 0 reversible (system is at equilibrium)\n\nFor many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules reactants) to surroundings that are infinitely more massive (the earth’s atmosphere). As a result, qsurr is a good approximation of qrev, and the second law may be stated as the following:\n\nΔSuniv = ΔSsys + ΔSsurr = ΔSsys +",
null,
"We may use this equation to predict the spontaneity of a process as illustrated in Example 1.\n\n### Example 1\n\nWill Ice Spontaneously Melt?\nThe entropy change for the process\n\nH2O(s) → H2O(l)\n\nis 22.1 J/K and requires that the surroundings transfer 6.00 kJ of heat to the system. Is the process spontaneous at −10.00 °C? Is it spontaneous at +10.00 °C?\n\nSolution\nWe can calculate the spontaneity of the process by calculating the entropy change of the universe. If ΔSuniv is positive, then the process is spontaneous. At both temperatures, ΔSsys = 22.1 J/K and qsurr = −6.00 kJ.\n\nAt −10.00 °C (263.15 K), the following is true:\n\nΔSuniv = ΔSsys + ΔSsurr = ΔSsys +",
null,
"= 22.1",
null,
"+",
null,
"= -0.7",
null,
"Suniv < 0, so melting is nonspontaneous (not spontaneous) at −10.0 °C.\n\nAt 10.00 °C (283.15 K), the following is true:\n\nΔSuniv = ΔSsys +",
null,
"= 22.1",
null,
"+",
null,
"= +0.9",
null,
"Suniv > 0, so melting is spontaneous at 10.00 °C.\n\nUsing this information, determine if liquid water will spontaneously freeze at the same temperatures. What can you say about the values of Suniv?\n\nEntropy is a state function, and freezing is the opposite of melting. At −10.00 °C spontaneous, +0.7",
null,
"; at +10.00 °C nonspontaneous, −0.9",
null,
".\n\nWe can understand the relationship between entropy and enthalpy by recalling the equation just before Example 1:\n\nΔSuniv = ΔSsys +",
null,
"The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, and so this expression may be rewritten as the following:\n\nΔSuniv = ΔSsys +",
null,
"= ΔSsys",
null,
"= ΔSsys",
null,
"We will use this relationship again in the next section.\n\n## The Third Law of Thermodynamics\n\nThe previous section described the various contributions of matter and energy dispersal that contribute to the entropy of a system. With these contributions in mind, consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is only one possible location for each atom or molecule comprising the crystal, giving the system a single microstate (W = 1). According to the Boltzmann equation, the entropy of this system is zero.\n\nS = k ln W = k ln(1) = 0\n\nThis limiting condition for a system’s entropy represents the third law of thermodynamics: the entropy of a pure, perfect crystalline substance at 0 K is zero.\n\n## Standard Entropies\n\nWe can make careful calorimetric measurements to determine the temperature dependence of a substance’s entropy and to derive absolute entropy values under specific conditions. Standard entropies are given the label",
null,
"for values determined for one mole of substance at a pressure of 1 bar and a temperature of 298 K. The standard entropy change (ΔS°) for any process may be computed from the standard entropies of its reactant and product species like the following:\n\nΔSº = ∑(coefficient of product)Sº298(products) – ∑(coefficient of reactant)Sº298(reactants)\n\nFor example, ΔS° for the following reaction at room temperature:\n\nmA + nB → xC + yD\n\nis computed as the following:\n\nΔS° = [xSº298(C) + ySº298(D)] – [mSº298(A) + nSº298(B)]\n\nTable 2 lists some standard entropies at 298.15 K. You can find additional standard entropies in Appendix F.\n\nTable 2. Standard Entropies (at 298.15 K, 1 atm)\nSubstance S",
null,
"(J/mol·K)\nC(s, graphite) 5.740\nC(s, diamond) 2.377\nCO(g) 197.7\nCO2(g) 213.7\nCH4(g) 186.3\nC2H4(g) 219.6\nC2H6(g) 229.6\nCH3OH(l) 126.8\nC2H5OH(l) 160.7\nH2(g) 130.7\nH(g) 114.7\nH2O(g) 188.8\nH2O(l) 69.91\nHCl(g) 186.9\nH2S(g) 205.8\nO2(g) 205.1\n\n### Example 2\n\nDetermination of ΔS°\nCalculate the standard entropy change for the following process:\n\nH2O(g) → H2O(l)\n\nSolution\nThe value of the standard entropy change at room temperature, ΔSº298, is the difference between the standard entropy of the product, H2O(l), and the standard entropy of the reactant, H2O(g).\n\nΔSº = Sº298(H2O(l)) – Sº298(H2O(g)) =\n= (69.91",
null,
") – (188.83",
null,
") = -118.9",
null,
"The value for ΔSº298 is negative, as expected for this phase transition (condensation), which the previous section discussed.\n\nCalculate the standard entropy change for the following process:\n\nH2(g) + C2H4(g) → C2H6(g)\n\n−120.6 J/mol·K\n\n### Example 3\n\nDetermination of ΔS°\nCalculate the standard entropy change for the combustion of methanol, CH3OH:\n\n2 CH3OH(l) + 3 O2(g) → 2 CO2(g) + 4 H2O(l)\n\nSolution\nThe value of the standard entropy change is equal to the difference between the standard entropies of the products and the entropies of the reactants scaled by their stoichiometric coefficients.\n\nΔSº = [2Sº298(CO2(g)) + 4Sº298(H2O(l))] – [2Sº298(CH3OH(l)) + 3Sº298(O2(g))] = [2(213.7",
null,
") + 4(69.91",
null,
")] – [2(126.8",
null,
") + 3(205.1",
null,
")] = -161.9",
null,
"Calculate the standard entropy change for the following reaction:\n\nCa(OH)2(s) → CaO(s) + H2O(l)\n\n26.27 J/mol·K\n\n## Key Concepts and Summary\n\nThe second law of thermodynamics states that all spontaneous changes cause an increase in the entropy of the universe. These changes are temperature dependent, which is especially highlighted by the third law of thermodynamics (the entropy of a pure, perfect crystalline substance at 0 K is zero). Using standard conditions and entropies, we can calculate the change in entropy of any process by subtracting the entropy of the reactants from the entropy of the products.\n\n## Key Equations\n\n• ΔSuniv = ΔSsys + ΔSsurr\n• ΔSuniv = ΔSsys +",
null,
"• ΔSuniv = ΔSsys",
null,
"• ΔS° = [xSº298(C) + ySº298(D)] – [mSº298(A) + nSº298(B)]\n(for mA + nB → xC + yD)\n\n## Glossary\n\nsecond law of thermodynamics\nall spontaneous changes cause an increase in the entropy of the universe\n\nstandard entropies\nvalues determined for one mole of a substance at a pressure of 1 bar and a temperature of 298 K (Sº298)\n\nthird law of thermodynamics\nthe entropy of a pure, perfect crystalline substance at 0 K is zero\n\n### Chemistry End of Section Exercises\n\n1. Pure acetic acid melts at 16.6°C at 760 Torr. The molar enthaply of fusion for this process is 11.53 kJ/mol. What is the molar entropy of the system for this process. Is this enough information to determine if the process will occur spontaneously?\n2. Xylitol is sometimes used as a sugar substitute. It has a melting point of 92.0°C and and heat of fusion of 37.4 kJ/mol. Consider the process of xylitol melting at 362 K and 1.00 atm:\n1. Predict whether ΔSuniverse will be positive, negative or zero at 362 K and 1 atm, without calculations.\n2. Calculate the entropy change of the system at 362 K and 1 atm.\n3. Calculate the entropy change of the surroundings at 362 K and 1 atm.\n4. Calculate the entropy change of the universe at 362 K and 1 atm. Does this agree with your prediction in part a?\n3. Using Appendix F, calculate ΔS° at 298 K for the following changes:\n1. SnCl4(l) → SnCl4(g)\n2. CS2(g) → CS2(l)\n3. 2 H2(g) + O2(g) → 2 H2O(l)\n4. 2 HCl(g) + Pb(s) → PbCl2(s) + H2(g)\n4. Determine the entropy change for the combustion of gaseous propane, C3H8, under standard state conditions to give gaseous carbon dioxide and water.\n\n### Answers to Chemistry End of Section Exercises\n\n1. ΔS°rxn = 39.79",
null,
"; Since it is the entropy of the universe that determines spontaneity, this is not enough information on its own to determine whether the process will occur spontaneously. The entropy of the surrounding must also be known.\n1. The temperature, 362 K (89°C), is less than the melting point of xylitol so the xylitol will not melt spontaneously and ΔSuniverse is negative.\n2. 102 J/mol·K\n3. -103 J/mol·K\n4. -1 J/mol·K\n1. 107.2 J/mol·K\n2. −86.50 J/mol·K\n3. −326.7 J/mol·K\n4. −171.9 J/mol·K\n2. 100.9 J/mol·K",
null,
""
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https://in.mathworks.com/matlabcentral/answers/433705-need-help-in-optimization-problem | [
"# Need help in Optimization Problem\n\n1 view (last 30 days)\nSuraj Gurav on 4 Dec 2018\nCommented: John D'Errico on 4 Dec 2018\nHello,\nfor my Master thesis, I have done design of experiments with 25 input parameters (4 different values per parameter) and resulting 1 output parameter (which is value of inelastic strain). so in total I have 64 such combinations of input and output parameters. I want to know how do I use the Optimization Toolbox to get the optimum value of the input and output parameters. My target is to keep the output parameter (inelastic strain value) minimum.\nI am new to these MATLAB optimization tools so I read the general help document about toolbox but didn't get any clear idea.\nIt would be good if someone suggests a solution or procedure to be followed to solve the problem\nTorsten on 4 Dec 2018\nAs I said: Not MATLAB is the tool where you should try to find a solution, but in the textbook from which you got the experimental design. It should tell you how to evaluate the output of the limited number of experiments to get optimal parameters.\n\nJohn D'Errico on 4 Dec 2018\nEdited: John D'Errico on 4 Dec 2018\nI'm not sure where you get the number 64 there. And indeed, the optimization toolbox will not help you, at least not directly.\nYou tell us you have 25 input parameters, with 4 levels for each parameter to tune. So we would see\n4^25 = 2^50 = 1.12589990684262e+15\ndistinct combinations of parameters. 64 would never enter into the question.\nRegardless, this is a nonlinear integer programming problem, but the optimization toolbox does not provide such a tool. That is, you have 25 variables, each of which can effectively take on the values 1, 2, 3 or 4. Thus effectively an integer problem. It is nonlinear because the output is related in a general black box, nonlinear way to those inputs.\nThus intlinprog from the optimization toolbox solve LINEAR integer programming problems, but not nonlinear ones. And fmincon or fminunc (etc.) can solve general problems, but are not able to handle integer constraints on the parameters. So nothing in the standard optimization toolbox can help you out.\nYou will need to look in the global optimization toolbox to find a solver that can handle your problem. A quick check shows that ga can minimize a nonlinear function, AND admit integer constraints on the variables. In fact, a quick check shows that ONLY ga solves that class of problem. So you must use ga. If you don't have the global optimization toolbox, then you will need to get it.\nIf that is completely not an option, I do recall a tool called fminconset on the file exchange that will solve this class of problem, so you could try using this:\nHowever, I would note that it was last updated in the year 2000, so it is effectively 18 years out of date. It might not run by now. Since it uses fmincon itself, the odds are good that something has changed with fmincon since to prevent it from running properly. You never know with a tool that old.\n##### 2 CommentsShowHide 1 older comment\nJohn D'Errico on 4 Dec 2018\nI'm not sure where we were told your objective takes that long to run.\nFor such a problem however, GA will be infeasible. Once you have approximated the process by a low order polynomial, using that experimental design as chosen and then built a model of the system, then you can use an integer constrained optimizer like ga.\n\nR2018b\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!"
]
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https://zbmath.org/?q=an:0956.14010 | [
"# zbMATH — the first resource for mathematics\n\n$${\\mathcal D}^\\dagger$$-affinity of projective space. – With an appendix by P. Berthelot. ($${\\mathcal D}^\\dagger$$-affinité de l’espace projectif. (Avec un appendice de P. Berthelot).) (French) Zbl 0956.14010\nThe Beilinson-Bernstein theorem [A. Beilinson and J. Bernstein, C. R. Acad. Sci., Paris, Sér. I 292, 15-18 (1981; Zbl 0476.14019)] asserts that for a reductive group over a field of characacteristic 0 the flag variety $$X$$ is $${\\mathcal D}$$-affine in the following sense: Every $${\\mathcal D}_X$$-module $${\\mathcal E}$$ is generated by its global sections and $$H^i (X;{\\mathcal E})=0$$ for $$i>0$$. It follows that the global section functor induces an equivalence of categories between the category of coherent $${\\mathcal D}_X$$-modules and the category of coherent $$\\Gamma(X; {\\mathcal D}_X)$$-modules.\nIn non-zero characteristic the usual sheaf of differential operators is not finitely generated. To overcome this difficulty P. Berthelot [Ann. Sci. Éc. Norm. Supér (4) 29, No. 2, 185-272 (1996; Zbl 0886.14004)] introduced sheaves of differential operators of level $$m$$, $${\\mathcal D}_X^{(m)}$$, using a notion of partial divided power. The sheaves $${\\mathcal D}_X^{(m)}$$ are finitely generated and satisfy $${\\mathcal D}_X=\\varinjlim {\\mathcal D}_X^{(m)}$$; $${\\mathcal D}^†_{\\mathcal X}$$ is then defined as $$\\varinjlim\\widehat {\\mathcal D}_{\\mathcal X}^{(m) }$$, where $$\\widehat{\\mathcal D}_{\\mathcal X}^{(m)}$$ is the $$p$$-adic completion of $${\\mathcal D}^{(m)}_X$$, and $${\\mathcal D}^†_{{\\mathcal X}, \\mathbb{Q}}={\\mathcal D}^†_{\\mathcal X}\\otimes \\mathbb{Q}$$.\nThe aim of the paper under review is to prove a Beilinson-Bernstein theorem for the projective space in the framework of arithmetic $${\\mathcal D}$$-modules. Let $$V$$ be a discrete valuation ring of characteristics $$(0,p)$$, $${\\mathcal V}$$ its completion, and $${\\mathcal X}$$ the formal projective space of dimension $$N$$ over $$\\text{Spf} {\\mathcal V}$$. The author shows that $$\\Gamma({\\mathcal X}; {\\mathcal D}^†_{{\\mathcal X}, \\mathbb{Q}})$$ is a coherent $${\\mathcal V}$$-algebra, that coherent $${\\mathcal D}^†_{{\\mathcal X},\\mathbb{Q}}$$-modules are acyclic and that taking global sections induces equivalences between the categories of coherent $${\\mathcal D}^†_{{\\mathcal X}, \\mathbb{Q}}$$-modules and of coherent $$\\Gamma({\\mathcal X};{\\mathcal D}^†_{{\\mathcal X}, \\mathbb{Q}})$$-modules.\nIn characteristic 0 it is well known that the associated graded ring of $${\\mathcal D}_X$$ is isomorphic to the symmetric algebra of the tangent bundle of $$X$$. In the first part the author constructs the “symmetric algebra of level $$m$$” of an $${\\mathcal O}_X$$-module and shows that the associated graded ring of $${\\mathcal D}^{(m)}_X$$ is isomorphic to the symmetric algebra of level $$m$$ of the tangent bundle. Using this and the fact that the tangent bundle of the projective space is ample, she proves in the second part that, for $$n\\geq 1$$ and for any coherent $${\\mathcal D}_X^{(m)}$$-module $${\\mathcal E}$$, $$H^n(X;{\\mathcal E})$$ is of finite type and torsion.\nShe considers the behavior of cohomology when taking projective limits and obtains the vanishing of cohomology in degree greater than 1 for the $${\\mathcal D}^†_{{\\mathcal X}, \\mathbb{Q}}$$-modules. In the last two parts she gives finiteness results for the global sections and proves the equivalence of categories.\nIt should be noted that these results are given in a more general framework where the sheaf $${\\mathcal D}_X$$ is tensored by a commutative algebra with a structure of $${\\mathcal D}$$-module. In particular, for a suitable algebra associated to a divisor $$Z$$, introduced by Berthelot, this gives the sheaf of differential operators with overconvergent singularities along $$Z$$.\nVanishing results for the cohomology of this algebra are given in an appendix by P. Berthelot.\n\n##### MSC:\n 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14F30 $$p$$-adic cohomology, crystalline cohomology 14F17 Vanishing theorems in algebraic geometry\nFull Text:"
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https://gordonburgin.com/2018/04/apr-2018-challenge/?share=google-plus-1 | [
"Select Page\n\nEach month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.\n\n## MIND-Xpander numeric puzzles\n\n1. The dimensions of one box are all two-thirds of the dimensions of another. If the volume of the smaller is 64 cubic centimetres, what is the volume of the larger box?\n2. Arrange the digits 1, 2, 3, 4 and 5, using only plus & minus signs (addition & subtraction), so that they will total 111. Using the same instructions, arrange the digits for totals of 222, and 333. (Note: There may be more than one solution)\n\n## EQUATE-Sums puzzle\n\nCan you work out what each of the four symbols are worth? The totals of the three columns are given. Can you also work out the missing total?",
null,
"## EQUATE- TakeAway puzzle\n\nThe missing numbers are between 1 & 9. The three numbers in top columns, when subtracted by the lower two numbers, equals the three totals along the bottom, and the three numbers in the left rows, when subtracted by the right two numbers, equals the three totals at the far right. The top left number, when subtracted by the lower two numbers on its diagonal, equals the total in the bottom, far right box. With one number provided, solve the puzzle by finding all missing numbers that satisfy all the results as shown.",
null,
"## Feedback\n\nThere are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.\n\nIf you have a question that needs a response from me or you would like to contact me privately, please use the contact form.\n\n## Get more puzzles!\n\nIf you've enjoyed doing the puzzles, consider ordering the book; 150+ of the best puzzles in a handy pocket sized format. Click here for full details.\n\n## MIND-Xpander numeric puzzles\n\n1. If QC = 14, TJ=10 & OK = 4, what would HA = ? Solution: The numeric order of the 1st letter in the alphabet (where H=8) minus that of the 2nd letter (where A=1) gives value of 7.\n2. What do you get if you divide 40 by a half and add 20 to the result? Solution: (40 ÷ 1/2) + 20 = (40 x 2/1) + 20 = 100\n3. How can you mathematically combine six 8’s to make 1000? Solution: (888 – 88) ÷ .8 = 1000\n\n## Safety-code logic puzzle\n\nTo open this safe you must press all the buttons in the correct order. The number on each button tells you how many squares to move, and the letters tells the direction (U = up, D = down, L = left and R = right). Which is the first button you must press to open this safe?\n\nSolution: Start at ‘1R’ button in 3rd column, 2nd row",
null,
"## DARTS numeric puzzle\n\nUsing 4 darts and the following square dart board, find all combinations to score exactly 150. Numbers/boxes can be used more than once. All darts must be used, and each dart must be within one of the numbered boxes. (Note: there are several correct solutions.)",
null,
"Solutions\n\n113 + 13 + 12 + 12 = 150\n\n111 + 16 + 13 + 10 = 150\n\n108 + 16 + 16 + 10 = 150\n\n93 + 33 + 12 + 12 = 150\n\n89 + 33 + 16 + 12 = 150\n\n87 + 43 + 10 + 10 = 150\n\n79 + 49 + 12 + 10 = 150\n\n54 + 43 + 43 + 10 = 150"
]
| [
null,
"https://i1.wp.com/gordonburgin.com/wp-content/uploads/2018/04/180401-EQUATE-Sums-Puzzle.jpg",
null,
"https://i1.wp.com/gordonburgin.com/wp-content/uploads/2018/04/180401-EQUATE-TakeAway-Puzzle.jpg",
null,
"https://i1.wp.com/gordonburgin.com/wp-content/uploads/2018/04/180301-safety-code-logic-puzzle-solution.gif",
null,
"https://i1.wp.com/gordonburgin.com/wp-content/uploads/2018/03/Mar-18-Darts-Challenge.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.89895296,"math_prob":0.99435776,"size":3339,"snap":"2019-13-2019-22","text_gpt3_token_len":917,"char_repetition_ratio":0.12383808,"word_repetition_ratio":0.018018018,"special_character_ratio":0.3054807,"punctuation_ratio":0.108882524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99876845,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,6,null,3,null,3,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-18T13:58:17Z\",\"WARC-Record-ID\":\"<urn:uuid:898e8ed3-d8b0-4d3d-9ba7-7ad8e02e9971>\",\"Content-Length\":\"58261\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:189427ae-446c-4278-a53b-cb3930478dba>\",\"WARC-Concurrent-To\":\"<urn:uuid:fdd248d8-76e8-48cf-a7f0-62c57484dae8>\",\"WARC-IP-Address\":\"173.248.187.16\",\"WARC-Target-URI\":\"https://gordonburgin.com/2018/04/apr-2018-challenge/?share=google-plus-1\",\"WARC-Payload-Digest\":\"sha1:G7CIJRUHCGLJK5L43WOQRFXW3TSZUGIS\",\"WARC-Block-Digest\":\"sha1:F7GTUZ3TTL5X3UMZSBGVZTQJTG7OZXJA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912201329.40_warc_CC-MAIN-20190318132220-20190318154220-00200.warc.gz\"}"} |
https://www.geeksforgeeks.org/ugc-net-ugc-net-cs-2016-july-iii-question-11/?ref=rp | [
"Related Articles\n\n# UGC-NET | UGC NET CS 2016 July – III | Question 11\n\n• Last Updated : 27 Apr, 2018\n\nConsider the following ORACLE relations :\nR (A, B, C) = {<1, 2, 3>, <1, 2, 0>, <1, 3, 1>, <6, 2, 3>, <1, 4, 2>, <3, 1, 4> }\nS (B, C, D) = {<2, 3, 7>, <1, 4, 5>, <1, 2, 3>, <2, 3, 4>, <3, 1, 4>}.\nConsider the following two SQL queries SQ1 and SQ2 :\nSQ1 : SELECT R⋅B, AVG (S⋅B)\nFROM R, S\nWHERE R⋅A = S⋅C AND S⋅D < 7 GROUP BY R⋅B;\nSQ2 : SELECT DISTINCT S⋅B, MIN (S⋅C)\nFROM S\nGROUP BY S⋅B\nHAVING COUNT (DISTINCT S⋅D) > 1;\nIf M is the number of tuples returned by SQ1 and N is the number of tuples returned by SQ2 then\n(A) M = 4, N = 2\n(B) M = 5, N = 3\n(C) M = 2, N = 2\n(D) M = 3, N = 3"
]
| [
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.78089577,"math_prob":0.9993432,"size":711,"snap":"2021-31-2021-39","text_gpt3_token_len":349,"char_repetition_ratio":0.10749646,"word_repetition_ratio":0.036144577,"special_character_ratio":0.49226442,"punctuation_ratio":0.24170616,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9927023,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T01:11:29Z\",\"WARC-Record-ID\":\"<urn:uuid:027702e4-4e8a-4a48-9552-48d3750078a8>\",\"Content-Length\":\"99280\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:be392187-d834-43fb-a6e8-9e1ff52e6e9d>\",\"WARC-Concurrent-To\":\"<urn:uuid:90cc6e5e-9cf8-4a4b-b33f-eb65015ed8ef>\",\"WARC-IP-Address\":\"23.62.230.157\",\"WARC-Target-URI\":\"https://www.geeksforgeeks.org/ugc-net-ugc-net-cs-2016-july-iii-question-11/?ref=rp\",\"WARC-Payload-Digest\":\"sha1:L2IXKAMLADM2K4A3I66MG4NXKL6REPIM\",\"WARC-Block-Digest\":\"sha1:R6SDDT3MUPUIIZAVOERH6HSDKCKHH43D\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056656.6_warc_CC-MAIN-20210919005057-20210919035057-00230.warc.gz\"}"} |
http://thetopsites.net/article/58433503.shtml | [
"## Excel nth smallest DISTINCT value\n\nexcel second largest value duplicates\nexcel find second highest value and return adjacent cell\nexcel unique values\nfind unique values in excel multiple columns\nexcel find nth unique value\nexcel nth largest value\nindex match smallest value\ndynamic list of unique values in excel\n\nI have a set of values, the Small function gives me the ability to get the top 5 smallest values. but it doesnt take into account duplicates. I want to only see each value once. for example:\n\n1 2 2 3 4 5\n\ni want to output 1,2,3,4,5 not 1,2,2,3,4\n\nI am putting the output into 5 different columns with the formula Small(A1:A20,[1-5]) but im not sure how to tell it to only look at each distinct value in the range\n\nIf one has access to the dynamic array formulas (currently only available to office 365 insiders) one can just put this in the first cell and the results will spill across:\n\n```=SMALL(UNIQUE(A:A),SEQUENCE(,5))\n```",
null,
"Other wise we need to use some array formula in a specific manner.\n\nWe must have something besides a number in the cell directly preceding where we put the formula in the first cell. So if I am putting the formula in C1, B1 must not contain one of the numbers as we need to refer to it.\n\nPut this in C1:\n\n```=SMALL(IF(COUNTIF(\\$B\\$1:B\\$1,\\$A\\$1:\\$A\\$20)=0,\\$A\\$1:\\$A\\$20),1)\n```\n\nBeing an array formula it must be confirmed with Ctrl-Shift-enter instead of Enter when exiting edit mode. Then copy over 5 columns.",
null,
"If one cannot leave the cell B1 without a number then we must get the array another way:\n\nPut this array formula in the first cell:\n\n```=SMALL(INDEX(\\$A:\\$A,N(IF({1},MODE.MULT(IF(MATCH(\\$A\\$1:\\$A\\$20,\\$A:\\$A,0)=ROW(\\$A\\$1:\\$A\\$20),ROW(\\$A\\$1:\\$A\\$20)*{1,1}))))),COLUMN(A:A))\n```\n\nBeing an array formula it must be confirmed with Ctrl-Shift-enter instead of Enter when exiting edit mode. Then copy over 5 columns.",
null,
"Excel formula: nth largest value with duplicates, To get the nth largest value in a data set with duplicates, you can use an array formula based on the MAX and IF functions. Note: the LARGE function will easily return nth values, but LARGE will return Excel formula: nth smallest value. If you want to get the next largest value in another column, you can use a combination of the INDEX function and the MATCH function to create an excel formula.. Find the nth Smallest Value You can use the SMALL function to get the 1st, 2nd, 3rd, or nth smallest value in an array or range.\n\nHere is another option and in single formula\n\nAssume your data 1 2 2 3 4 5 put in A1:A6\n\nB1, left blank\n\nIn C1, formula copied cross right until blank\n\n```=IFERROR(1/(1/AGGREGATE(15,6,\\$A\\$1:\\$A\\$20/(\\$A\\$1:\\$A\\$20>B1),1)),\"\")\n```\n\nEdit : AGGREGATE is a function for Excel 2010 or above\n\nExcel nth smallest DISTINCT value, If one has access to the dynamic array formulas (currently only available to office 365 insiders) one can just put this in the first cell and the To get the nth largest value in a data set with duplicates, you can use an array formula based on the MAX and IF functions. Note: the LARGE function will easily return nth values, but LARGE will return duplicates when they exist in the source data.\n\nHere is another option:",
null,
"Formula in `C1`:\n\n```=SMALL(\\$A:\\$A,COUNTIF(\\$A:\\$A,\"<=\"&B1)+1)\n```\n\nDrag right...\n\nOutput the nth smallest UNIQUE number with one condition , How do I output the nth smallest unique value if column A is \"Apples\"? <b>Excel 2013</b><table cellpadding=\"2.5px\" rules=\"all\" style=\" In Excel worksheet, we can get the largest, the second largest or nth largest value by applying the Large function. But, if there are duplicate values in the list, this function will not skip the duplicates when extracting the nth largest value.\n\nHow to get the second lowest unique value if more than 1 value , Say we have data in column A like: enter image description here. In some cell, say D1 enter the array formula: =MIN(IF(\\$A\\$1:\\$A\\$20>0 To get the 2nd smallest value, 3rd smallest value, 4th smallest value, and so on, from a set of data, you can use the SMALL function. In the example shown, the formula in G5 is: = SMALL ( times , F5 ) How this formula works The SMALL function is\n\nGet nth Largest Value with Duplicates, find and get the Nth largest unique value in a range of cells in Excel. use the SMALL function to get the 1st, 2nd, 3rd, or nth smallest value How to get distinct values in Excel (unique + 1 st duplicate occurrences) As you may have already guessed from the heading of this section, distinct values in Excel are all different values in a list, i.e. unique values and first instances of duplicate values. For example: To get a distinct list in Excel, use the following formulas.\n\nReturning second smallest unique value, Hello, I'm creating a spreadsheet and have had difficultly creating a function that returns the second smallest unique value. For example if my Returns the k-th largest value in a data set ROW function: Returns the row number of a reference LEN function: Returns the number of characters in a text string INDEX function: Uses an index to choose a value from a reference or array SMALL function: Returns the k-th smallest value in a data set IF function: Specifies a logical test to perform"
]
| [
null,
"http://thetopsites.net/images/58433503-1.png",
null,
"http://thetopsites.net/images/58433503-2.png",
null,
"http://thetopsites.net/images/58433503-3.png",
null,
"http://thetopsites.net/images/58433503-4.png",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.8153613,"math_prob":0.9526861,"size":5946,"snap":"2020-45-2020-50","text_gpt3_token_len":1488,"char_repetition_ratio":0.15651296,"word_repetition_ratio":0.17134559,"special_character_ratio":0.24991591,"punctuation_ratio":0.12140078,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99276465,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-28T22:46:53Z\",\"WARC-Record-ID\":\"<urn:uuid:557f8662-d325-40d8-8679-4f5e51c88d15>\",\"Content-Length\":\"16580\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f253742d-5557-4af8-8cb4-9a730ab52ecf>\",\"WARC-Concurrent-To\":\"<urn:uuid:6fe0c102-977b-452d-a3c8-0fcc57fb6ade>\",\"WARC-IP-Address\":\"192.169.175.36\",\"WARC-Target-URI\":\"http://thetopsites.net/article/58433503.shtml\",\"WARC-Payload-Digest\":\"sha1:Y3UHY2AYM6ISBXUSEQJGLNTZOIAMHSFM\",\"WARC-Block-Digest\":\"sha1:YRCFHMZTN2IDB7S3Z6RQE5SMSKBBWAJR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107902038.86_warc_CC-MAIN-20201028221148-20201029011148-00649.warc.gz\"}"} |
http://www.woshuoba.com/%E9%87%91%E8%9E%8D%E4%BA%A7%E5%93%81%E7%BB%8F%E7%90%86%E4%B9%8B%E5%80%BA%E5%88%B8%E4%BA%A7%E5%93%81%E8%AE%BE%E8%AE%A1/ | [
"# 金融产品经理之债券产品设计\n\n## 实战\n\n### 2. 分析",
null,
"（1）分析我们设计的这款金融产品税前的融资成本。\n\n=股价×转换比率\n\n=20×(1+6%)^9×200\n\n=6757.92（元）\n\n=未来各期利息现值+到期本金现值\n\n=(10000+10000×5%)/(1+8%)\n\n=9722.22（元）\n\n10000=10000×5%×(P/A,M,9)+6757.92×(P/F,M,9)\n\n（M-6%)/(7%-6%)=(10000-7400.85)/(6933.48-7400.85)\n\n（2）分析我们设计的这款产品票面利率是否合理。\n\n10000=10000×R×(P/A,8%,9)+6757.92×(P/F,8%,9)\n\n### 3. 结论\n\n=10000×5%×(P/A,8%,10)+10000×(P/F,8%,10)\n\n=500×6.7101+4631.93\n\n=7986.98（元）\n\n10000×10.6%×(P/A,8%,10)+10000×(P/F,8%,10)\n\n=1060×6.7101+4631.93\n\n=11744.62（元）"
]
| [
null,
"http://image.woshipm.com/wp-files/2019/06/25FItmP0QADNzNCmnrRE.png!v.jpg",
null
]
| {"ft_lang_label":"__label__zh","ft_lang_prob":0.97774464,"math_prob":0.9991829,"size":3497,"snap":"2020-34-2020-40","text_gpt3_token_len":3411,"char_repetition_ratio":0.07643859,"word_repetition_ratio":0.0,"special_character_ratio":0.26365456,"punctuation_ratio":0.10973085,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9984494,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-13T08:48:04Z\",\"WARC-Record-ID\":\"<urn:uuid:7941a241-07cb-4acd-bfc7-b9b06c001f66>\",\"Content-Length\":\"48358\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1c926457-cf43-4650-b6e5-7ff6e6d495cd>\",\"WARC-Concurrent-To\":\"<urn:uuid:d9d08320-242c-4bf2-8e50-87c620c6eb83>\",\"WARC-IP-Address\":\"172.104.77.5\",\"WARC-Target-URI\":\"http://www.woshuoba.com/%E9%87%91%E8%9E%8D%E4%BA%A7%E5%93%81%E7%BB%8F%E7%90%86%E4%B9%8B%E5%80%BA%E5%88%B8%E4%BA%A7%E5%93%81%E8%AE%BE%E8%AE%A1/\",\"WARC-Payload-Digest\":\"sha1:XWGVTXVCLNVMDAVCRUPCQRXA75FDBGUB\",\"WARC-Block-Digest\":\"sha1:F53G57I3Q2IRDGW3FW45Y7ONCEKNJYIB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738964.20_warc_CC-MAIN-20200813073451-20200813103451-00081.warc.gz\"}"} |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/8470/2/a/ck/ | [
"# Properties\n\n Label 8470.2.a.ck",
null,
"Level $8470$ Weight $2$ Character orbit 8470.a Self dual yes Analytic conductor $67.633$ Analytic rank $0$ Dimension $3$ CM no Inner twists $1$\n\n# Related objects\n\n## Newspace parameters\n\n Level: $$N$$ $$=$$ $$8470 = 2 \\cdot 5 \\cdot 7 \\cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\\chi]$$ $$=$$ 8470.a (trivial)\n\n## Newform invariants\n\n Self dual: yes Analytic conductor: $$67.6332905120$$ Analytic rank: $$0$$ Dimension: $$3$$ Coefficient field: 3.3.316.1 Defining polynomial: $$x^{3} - x^{2} - 4 x + 2$$ Coefficient ring: $$\\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\\mathrm{SU}(2)$\n\n## $q$-expansion\n\nCoefficients of the $$q$$-expansion are expressed in terms of a basis $$1,\\beta_1,\\beta_2$$ for the coefficient ring described below. We also show the integral $$q$$-expansion of the trace form.\n\n $$f(q)$$ $$=$$ $$q + q^{2} + \\beta_{1} q^{3} + q^{4} - q^{5} + \\beta_{1} q^{6} + q^{7} + q^{8} + ( 2 + \\beta_{2} ) q^{9} +O(q^{10})$$ $$q + q^{2} + \\beta_{1} q^{3} + q^{4} - q^{5} + \\beta_{1} q^{6} + q^{7} + q^{8} + ( 2 + \\beta_{2} ) q^{9} - q^{10} + \\beta_{1} q^{12} + \\beta_{1} q^{13} + q^{14} -\\beta_{1} q^{15} + q^{16} + ( 4 + \\beta_{2} ) q^{17} + ( 2 + \\beta_{2} ) q^{18} + ( 2 - \\beta_{1} + \\beta_{2} ) q^{19} - q^{20} + \\beta_{1} q^{21} + ( -1 + 2 \\beta_{1} + \\beta_{2} ) q^{23} + \\beta_{1} q^{24} + q^{25} + \\beta_{1} q^{26} + ( -2 + \\beta_{1} ) q^{27} + q^{28} -2 \\beta_{2} q^{29} -\\beta_{1} q^{30} + q^{32} + ( 4 + \\beta_{2} ) q^{34} - q^{35} + ( 2 + \\beta_{2} ) q^{36} + ( 2 \\beta_{1} + 2 \\beta_{2} ) q^{37} + ( 2 - \\beta_{1} + \\beta_{2} ) q^{38} + ( 5 + \\beta_{2} ) q^{39} - q^{40} -2 \\beta_{1} q^{41} + \\beta_{1} q^{42} + ( 2 - 4 \\beta_{1} - \\beta_{2} ) q^{43} + ( -2 - \\beta_{2} ) q^{45} + ( -1 + 2 \\beta_{1} + \\beta_{2} ) q^{46} + ( 2 - 2 \\beta_{1} - 2 \\beta_{2} ) q^{47} + \\beta_{1} q^{48} + q^{49} + q^{50} + ( -2 + 6 \\beta_{1} ) q^{51} + \\beta_{1} q^{52} -\\beta_{2} q^{53} + ( -2 + \\beta_{1} ) q^{54} + q^{56} + ( -7 + 4 \\beta_{1} - \\beta_{2} ) q^{57} -2 \\beta_{2} q^{58} + ( 2 + \\beta_{1} - \\beta_{2} ) q^{59} -\\beta_{1} q^{60} + ( 4 + 2 \\beta_{1} - \\beta_{2} ) q^{61} + ( 2 + \\beta_{2} ) q^{63} + q^{64} -\\beta_{1} q^{65} + ( -4 - 3 \\beta_{2} ) q^{67} + ( 4 + \\beta_{2} ) q^{68} + ( 8 + \\beta_{1} + 2 \\beta_{2} ) q^{69} - q^{70} + ( 6 + 2 \\beta_{1} + \\beta_{2} ) q^{71} + ( 2 + \\beta_{2} ) q^{72} + ( 6 - 2 \\beta_{1} - \\beta_{2} ) q^{73} + ( 2 \\beta_{1} + 2 \\beta_{2} ) q^{74} + \\beta_{1} q^{75} + ( 2 - \\beta_{1} + \\beta_{2} ) q^{76} + ( 5 + \\beta_{2} ) q^{78} + ( -3 + 2 \\beta_{1} ) q^{79} - q^{80} + ( -1 - 2 \\beta_{1} - 2 \\beta_{2} ) q^{81} -2 \\beta_{1} q^{82} + ( 2 + \\beta_{1} ) q^{83} + \\beta_{1} q^{84} + ( -4 - \\beta_{2} ) q^{85} + ( 2 - 4 \\beta_{1} - \\beta_{2} ) q^{86} + ( 4 - 4 \\beta_{1} ) q^{87} + ( 4 - 2 \\beta_{1} ) q^{89} + ( -2 - \\beta_{2} ) q^{90} + \\beta_{1} q^{91} + ( -1 + 2 \\beta_{1} + \\beta_{2} ) q^{92} + ( 2 - 2 \\beta_{1} - 2 \\beta_{2} ) q^{94} + ( -2 + \\beta_{1} - \\beta_{2} ) q^{95} + \\beta_{1} q^{96} + ( -2 + 2 \\beta_{1} + \\beta_{2} ) q^{97} + q^{98} +O(q^{100})$$ $$\\operatorname{Tr}(f)(q)$$ $$=$$ $$3q + 3q^{2} + 3q^{4} - 3q^{5} + 3q^{7} + 3q^{8} + 5q^{9} + O(q^{10})$$ $$3q + 3q^{2} + 3q^{4} - 3q^{5} + 3q^{7} + 3q^{8} + 5q^{9} - 3q^{10} + 3q^{14} + 3q^{16} + 11q^{17} + 5q^{18} + 5q^{19} - 3q^{20} - 4q^{23} + 3q^{25} - 6q^{27} + 3q^{28} + 2q^{29} + 3q^{32} + 11q^{34} - 3q^{35} + 5q^{36} - 2q^{37} + 5q^{38} + 14q^{39} - 3q^{40} + 7q^{43} - 5q^{45} - 4q^{46} + 8q^{47} + 3q^{49} + 3q^{50} - 6q^{51} + q^{53} - 6q^{54} + 3q^{56} - 20q^{57} + 2q^{58} + 7q^{59} + 13q^{61} + 5q^{63} + 3q^{64} - 9q^{67} + 11q^{68} + 22q^{69} - 3q^{70} + 17q^{71} + 5q^{72} + 19q^{73} - 2q^{74} + 5q^{76} + 14q^{78} - 9q^{79} - 3q^{80} - q^{81} + 6q^{83} - 11q^{85} + 7q^{86} + 12q^{87} + 12q^{89} - 5q^{90} - 4q^{92} + 8q^{94} - 5q^{95} - 7q^{97} + 3q^{98} + O(q^{100})$$\n\nBasis of coefficient ring in terms of a root $$\\nu$$ of $$x^{3} - x^{2} - 4 x + 2$$:\n\n $$\\beta_{0}$$ $$=$$ $$1$$ $$\\beta_{1}$$ $$=$$ $$\\nu^{2} - 3$$ $$\\beta_{2}$$ $$=$$ $$-\\nu^{2} + 2 \\nu + 2$$\n $$1$$ $$=$$ $$\\beta_0$$ $$\\nu$$ $$=$$ $$($$$$\\beta_{2} + \\beta_{1} + 1$$$$)/2$$ $$\\nu^{2}$$ $$=$$ $$\\beta_{1} + 3$$\n\n## Embeddings\n\nFor each embedding $$\\iota_m$$ of the coefficient field, the values $$\\iota_m(a_n)$$ are shown below.\n\nFor more information on an embedded modular form you can click on its label.\n\nLabel $$\\iota_m(\\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$\n1.1\n 0.470683 −1.81361 2.34292\n1.00000 −2.77846 1.00000 −1.00000 −2.77846 1.00000 1.00000 4.71982 −1.00000\n1.2 1.00000 0.289169 1.00000 −1.00000 0.289169 1.00000 1.00000 −2.91638 −1.00000\n1.3 1.00000 2.48929 1.00000 −1.00000 2.48929 1.00000 1.00000 3.19656 −1.00000\n $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles\n\n## Atkin-Lehner signs\n\n$$p$$ Sign\n$$2$$ $$-1$$\n$$5$$ $$1$$\n$$7$$ $$-1$$\n$$11$$ $$-1$$\n\n## Inner twists\n\nThis newform does not admit any (nontrivial) inner twists.\n\n## Twists\n\nBy twisting character orbit\nChar Parity Ord Mult Type Twist Min Dim\n1.a even 1 1 trivial 8470.2.a.ck yes 3\n11.b odd 2 1 8470.2.a.cg 3\n\nBy twisted newform orbit\nTwist Min Dim Char Parity Ord Mult Type\n8470.2.a.cg 3 11.b odd 2 1\n8470.2.a.ck yes 3 1.a even 1 1 trivial\n\n## Hecke kernels\n\nThis newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\\mathrm{new}}(\\Gamma_0(8470))$$:\n\n $$T_{3}^{3} - 7 T_{3} + 2$$ $$T_{13}^{3} - 7 T_{13} + 2$$ $$T_{17}^{3} - 11 T_{17}^{2} + 24 T_{17} + 32$$ $$T_{19}^{3} - 5 T_{19}^{2} - 21 T_{19} + 17$$\n\n## Hecke characteristic polynomials\n\n$p$ $F_p(T)$\n$2$ $$( -1 + T )^{3}$$\n$3$ $$2 - 7 T + T^{3}$$\n$5$ $$( 1 + T )^{3}$$\n$7$ $$( -1 + T )^{3}$$\n$11$ $$T^{3}$$\n$13$ $$2 - 7 T + T^{3}$$\n$17$ $$32 + 24 T - 11 T^{2} + T^{3}$$\n$19$ $$17 - 21 T - 5 T^{2} + T^{3}$$\n$23$ $$-106 - 27 T + 4 T^{2} + T^{3}$$\n$29$ $$-128 - 64 T - 2 T^{2} + T^{3}$$\n$31$ $$T^{3}$$\n$37$ $$-8 - 68 T + 2 T^{2} + T^{3}$$\n$41$ $$-16 - 28 T + T^{3}$$\n$43$ $$548 - 88 T - 7 T^{2} + T^{3}$$\n$47$ $$128 - 48 T - 8 T^{2} + T^{3}$$\n$53$ $$-16 - 16 T - T^{2} + T^{3}$$\n$59$ $$83 - 13 T - 7 T^{2} + T^{3}$$\n$61$ $$316 - 13 T^{2} + T^{3}$$\n$67$ $$-992 - 120 T + 9 T^{2} + T^{3}$$\n$71$ $$-64 + 64 T - 17 T^{2} + T^{3}$$\n$73$ $$16 + 88 T - 19 T^{2} + T^{3}$$\n$79$ $$-41 - T + 9 T^{2} + T^{3}$$\n$83$ $$8 + 5 T - 6 T^{2} + T^{3}$$\n$89$ $$32 + 20 T - 12 T^{2} + T^{3}$$\n$97$ $$-128 - 16 T + 7 T^{2} + T^{3}$$"
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null,
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",
null
]
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https://www.oreilly.com/library/view/mastering-financial-calculations/9780131370388/apc.html | [
"## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.\n\nNo credit card required\n\n# Notation\n\nThe following general notation is used throughout these formulas, unless something different is specifically mentioned:\n\n D = discount rate FV = future value, or future cashflow i = interest rate or yield per annum n = number of times per year an interest payment is made N = number of years or number of coupon periods P = price (dirty price for a bond) PV = present value, or cashflow now r = continuously compounded interest rate R = coupon rate paid on a security year = number of days in the conventional year zk = zero-coupon yield for k years\n\n# Financial arithmetic basics (Chapter 1)\n\n## Effective and nominal rates\n\nIf the interest rate with n payments per year is i, the effective rate (equivalent annual rate) i* is:\n\nSimilarly:\n\n## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.\n\nNo credit card required"
]
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http://scientifictutor.org/1526/chem-college-the-relationship-between-different-equilibrium-constants/ | [
"## Chem – College: The Relationship Between Different Equilibrium Constants\n\nWhat is the relationship between different equilibrium constants?\n\nWithin the same chemical equation, questions can be asked about what happens to the equilibrium constant if we change something to that equation. There are two classic examples that pretty well illustrate the point of how it works.\n\nThe first is what happens when you multiply the chemical equation by a number like 2. Another way to say that is we double all of the coefficients in the chemical equation. If that happens then the equilibrium constant (K value) is taken to the second power (K2).\n\nThe second classic example is what happens when we flip the chemical equation over (reactants become products and products become reactants). In that case the equilibrium constant (K value) becomes 1 divided by K…(1/K).\n\nFrom there you can mix and match any combination of multiplying or flipping chemical equation over (reversing) to create problems of how K would be different.\n\nNOTE: The concept we just talked about above is different than changing the concentrations of a chemical equation. If you change the concentrations of a chemical equation by doubling all of them then you will double the equilibrium constant. If you change the concentrations of a chemical equation by dividing all of them by 2 then you will half the equilibrium constant.\n\nExample 1: Solve for the new equilibrium constant given the changing conditions.\n\nIf the equilibrium constant for the chemical equation below is K = 3M2.\n\nN2(g) + 3 H2(g) <—-> 2 NH3(g)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n2 N2(g) + 6 H2(g) <—-> 4 NH3(g)\n\nAnswer: K2 = (3M2)2 = 9M4\n\nExample 2: Solve for the new equilibrium constant given the changing conditions.\n\nIf the equilibrium constant for the chemical equation below is K = 3M2\n\nN2(g) + 3 H2(g) <—-> 2 NH3(g)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n2 NH3(g) <—-> N2(g) + 3 H2(g)\n\nAnswer: 1/K = 1/3M2 = 0.33M-2\n\nPRACTICE PROBLEMS: Solve for how the equilibrium constant changes when the reaction changes.\n\nIf the equilibrium constant for the chemical equation below is K = 1.2 * 102M\n\n2 H2O(g) <—-> 2 H2(g) + O2(g)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n2 H2(g) + O2(g) <—-> 2 H2O(g)\n\nAnswer: 1/K = 1 / (1.2 * 102M) = 8.3 * 10-3M-1\n\nIf the equilibrium constant for the chemical equation below is K = 0.6\n\nMgBr2(aq) + 2 NaI(aq) <——> MgI2(aq) + 2 NaBr(aq)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n2 MgBr2(aq) + 4 NaI(aq) <——> 2 MgI2(aq) + 4 NaBr(aq)\n\nAnswer: K2 = (0.6)2 = 0.36\n\nIf the equilibrium constant for the chemical equation below is K = 2.5 * 10-3\n\nC4(s) + 4 O2(g) <—-> 4 CO2(g)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n8 CO2(g) <—-> 2 C4(s) + 8 O2(g)\n\nAnswer: 1/K2 = 1 / (2.5 * 10-3)2 = 1.6 * 105\n\nIf the equilibrium constant for the chemical equation below is K = 9M3\n\n6 Ag+(s) + Ca3(PO4)2(s) <—-> 3 Ca2+(aq) + 2 Ag3PO4(s)\n\nThen what is the equilibrium constant for the next chemical equation at the same temperature?\n\n18 Ag+(s) + 3 Ca3(PO4)2(s) lt;—-gt; 9 Ca2+(aq) + 6 Ag3PO4(s)\n\nAnswer: K3 = (9M3)3 = 729M9",
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https://algebra-calculators.com/time-and-distance-problems/ | [
"Time and Distance Problems\n\nProblem 1: A man covers a distance of 600m in 2min 30sec. What will be the speed in km/hr?\n\nSolution:\n\nSpeed =Distance / Time\n⇒ Distance covered = 600m, Time taken = 2min 30sec = 150sec\nTherefore, Speed= 600 / 150 = 4 m/sec\n⇒ 4m/sec = (4*18/5) km/hr = 14.4 km/ hr.\n\nProblem 2: A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.\n\nSolution:\n\nIn this question, distance for both speed is constant.\n⇒ Average speed = (2xy/ x+y) km/hr, where x and y are speeds\n⇒ Average speed = (2*25*4)/ 25+4 =200/29 km/hr\nTime = 5hours 48min= 29/5 hours\nNow, Distance travelled = Average speed * Time\n⇒ Distance Travelled = (200/29)*(29/5) = 40 km\nTherefore distance of school from home = 40/2 = 20km.\n\nProblem 3: Two men start from opposite ends A and B of a linear track respectively and meet at point 60m from A. If AB= 100m. What will be the ratio of speed of both men?\n\nSolution:\n\nAccording to this question, time is constant. Therefore, speed is directly proportional to distance.\nSpeed∝Distance",
null,
"⇒ Ratio of distance covered by both men = 60:40 = 3:2\n⇒ Therefore, Ratio of speeds of both men = 3:2\n\nProblem 4: A car travels along four sides of a square at speeds of 200, 400, 600 and 800 km/hr. Find average speed.\n\nSolution:\n\nLet x km be the side of square and y km/hr be average speed\nUsing basic formula, Time = Total Distance / Average Speed\n\nx/200 + x/400 + x/600 + x/800 = 4x/y ⇒ 25x/ 2400 = 4x/ y⇒ y= 384\n⇒ Average speed = 384 km/hr"
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https://www.wiziq.com/online-tests/5701-xii_maths_integral-calculus_4 | [
"# XII_Maths_Integral Calculus_4 Online Test\n\nThe correct evaluation of \u0001 is ____.\n0\nThe value of the integral \u0001 is ____.\n3/2\n–8/3\n3/8\n8/3\n/\n0\n4\n8\n1\n\u0001 ____.\n0\n2\n1/2\n1\nThe value of \u0001 depends on ____.\nThe value of p\nThe value of q\nThe value of r\nThe value of p and q\n\u0001 ____.\n0\n2\nNone of the above\n\u0001 is equal to ____.\n\u0001 ____.\nNone of the above\n\u0001 equals to ____.\nNone of the above\n\u0001 equals ____.\nDescription:\n\nThis test consist of 10 questions.Students should ideally take 10 minutes to complete the test. This test is useful for those students who are preparing for IIT JEE, AIEEE or any other engineering entrance test. This test consist of questions from Integral Calculus and which, in general, is focused in AIEEE and IIT JEE. Last year 3 questions asked from this chapter in AIEEE. In Integral Calculus, properties of definite integration are key topics and mostly application based questions are asked.\n\nDiscussion",
null,
"76 Members Recommend\n326 Followers"
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null,
"https://wqimg.s3.amazonaws.com/ut/ust/APT-ACADEMIC-SOLUTIONS-11908.jpg",
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https://www.proofwiki.org/wiki/Category:Definitions/Complex_Modulus | [
"# Category:Definitions/Complex Modulus\n\nThis category contains definitions related to Complex Modulus.\nRelated results can be found in Category:Complex Modulus.\n\nLet $z = a + i b$ be a complex number, where $a, b \\in \\R$.\n\nThen the (complex) modulus of $z$ is written $\\cmod z$ and is defined as the square root of the sum of the squares of the real and imaginary parts:\n\n$\\cmod z := \\sqrt {a^2 + b^2}$\n\n## Pages in category \"Definitions/Complex Modulus\"\n\nThe following 2 pages are in this category, out of 2 total."
]
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https://dfc-org-production.force.com/forums/ForumsMain?id=9060G000000Bj3qQAC | [
"",
null,
"ShowAll Questionssorted byDate Posted",
null,
"Yamini Bathula\n\n# New line in String variable Adderror method in Apex Trigger\n\nHi Guys,\n\nWe have a trigger on Lead Conversion which checks for some fields (if htey are blank) and display a error message in Convert Popup(in Lightining). That is working fine. But the only issue is the new line is not working in the UI.\n\nHere is my trigger : I have added a new line every time I append the error string. but it doesn't show up in the conversion popup in Lightning.\n```trigger MandatoryFieldsLeadConversion on Lead (before Update)\n{\n\nString sBreak = '<br/>';\nBoolean hasError = false;\n{\nif (Trigger.oldMap.get(l.id).isConverted == false && Trigger.newMap.get(l.id).isConverted == true) // to check only in Lead Coversion\n{\nString erstring = 'Please Enter Below Mandatory Fields before converting this Lead \\n';\n//Skip this check for V3 and IODM Leads\nif((l.ParentAccount__c != '0019000001YHuxWAAT') && (l.ParentAccount__c != '0016F00001i2yYHQAY'))\n{\n//if Parent Account is Blank\nif((l.ParentAccount__c == null) || (l.ParentAccount__r.Name == ' '))\n{\nerstring += '\\n Parent Account' ;\nhasError = true;\n}\n//if First Name is Blank\nif((l.FirstName == null) || (l.FirstName == ' '))\n{\nerstring += '\\nFirst Name' ;\nhasError = true;\n}\n//if Email is Blank\nif((l.Email == null) || (l.Email == ' '))\n{\nerstring += '\\n Email';\nhasError = true;\n}\n//if Phone is Blank\nif((l.Phone == null) || (l.Phone == ' '))\n{\nerstring += '\\nPhone ';\nhasError = true;\n}\n//if Company is Blank\nif((l.Company == null) || (l.Company == ' '))\n{\nerstring += 'Company \\n';\nhasError = true;\n}\n//if Country is Blank\nif((l.Country__c == null) || (l.Country__c == ' '))\n{\nerstring += 'Country \\n';\nhasError = true;\n}\n//if Industry is Blank\nif((l.Industry_Ipay__c == null) || (l.Industry_Ipay__r.Name == ' '))\n{\nerstring += 'Industry \\n';\nhasError = true;\n}\n//if Parent Account is Blank\n{\nhasError = true;\n}\nif((l.Street == null) || (l.Street == ' '))\n{\nerstring += 'Street \\n';\nhasError = true;\n}\nif((l.State == null) || (l.State == ' '))\n{\nerstring += 'State \\n';\nhasError = true;\n}\nif((l.City == null) || (l.City == ' '))\n{\nerstring += 'City \\n';\nhasError = true;\n}\nif((l.PostalCode == null) || (l.PostalCode == ' '))\n{\nerstring += 'Post Code \\n';\nhasError = true;\n}\n//if Sales channel is Blank\nif((l.Sales_Channel__c == null) || (l.Sales_Channel__c == ' '))\n{\nerstring += 'Sales Channel \\n';\nhasError = true;\n}\n//if Average Transaction Amount is Blank\nif((l.Avg_Trans_Amount__c == null) || (l.Sales_Channel__c == ' '))\n{\nerstring += 'Average Transaction Amount \\n';\nhasError = true;\n}\n//ifTransactions per month is Blank\nif((l.Trans_Per_Month__c == null) )\n{\nerstring += 'Transactions per month \\n';\nhasError = true;\n}\n//if Max Singl ePay Amount is Blank\nif((l.Max_Single_Pay_Amt__c == null))\n{\nerstring += 'Maximum single payment amount \\n';\nhasError = true;\n}\n//ifDirector Details Blank\nif((l.Director_1_First_Name__c == null) || (l.Director_1_First_Name__c == ' '))\n{\nerstring += 'Director First Name \\n';\nhasError = true;\n}\nif((l.Director_1_Last_Name__c == null) || (l.Director_1_Last_Name__c == ' '))\n{\nerstring += 'Director Last Name \\n';\nhasError = true;\n}\nif((l.Director_Email__c == null) || (l.Director_Email__c == ' '))\n{\nerstring += 'Director Last Name \\n';\nhasError = true;\n}\n//if no products selected\nif(!((l.Direct_Debit_Requested__c) || (l.eCommerce__c) || (l.Video_Payment__c) || (l.Xero_Payment_Now__c) || (l.Xero_Direct_Debit__c) ))\n{\nerstring += 'One of the products Direct Debit Requested/Ecommerce/Video Payment/Xero Payment Now/Xero Direct Debit is not selected';\nhasError = true;\n}\n//Finally add the error message if any of the fields above atre blank\nif(hasError)\n{\n}\n}\n}\n}\n}```\n\nAttached the popup screenshot. Does any one have any idea what is wrong?",
null,
"",
null,
"Best Answer chosen by Yamini Bathula",
null,
"Yamini Bathula\n\nI just came through an old thread that this cannot be achived as Salesforce doesnt support HTML inputs in Lead Conversion Page due to security reasons.\nhttps://developer.salesforce.com/forums/?id=906F00000005GY3IAM\n\nsalesforce known Issue link https://success.salesforce.com/issues_view?id=a1p30000000jaTX . Thanks for your help Pawan. I am posting this so that others can benefit.\n\nThnaks,",
null,
"PawanKumar\nreplace all '\\n' with '\\r\\n'\n\nString erstring = 'Please Enter Below Mandatory Fields before converting this Lead \\r\\n';",
null,
"PawanKumar\nplease confirm whether it works for you or not?",
null,
"Yamini Bathula\nHi Pawan,\n\nI tried that. Bu it didnt work",
null,
"PawanKumar\nThanks for Reply. I think what i share you the above it works good for Long Text Area field.\n\nRoot Cause :Salesforce by default escapes any html in the addError String. To work around this, use the addError method with additional 'escape' parameter at the end. Here you are already passing false in addError method. But instead of \\n now you have to use <br/> Then you will see the new line in your page.\n\ne.g.\n\nerstring += 'Director Last Name <br/>';\n\nReference URL:",
null,
"Yamini Bathula"
]
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http://thermalscience.vinca.rs/2018/supplement--4/28 | [
"## THERMAL SCIENCE\n\nInternational Scientific Journal\n\n## Authors of this Paper\n\n,\n\n,\n\n,\n\n### A HEURISTIC OPTIMIZATION METHOD OF FRACTIONAL CONVECTION REACTION: AN APPLICATION TO DIFFUSION PROCESS\n\nABSTRACT\nThe convection differential models play an essential role in studying different chemical process and effects of the diffusion process. This paper intends to provide optimized numerical results of such equations based on the conformable fractional derivative. Subsequently, a well-known heuristic optimization technique, differential evolution algorithm, is worked out together with the Taylor’s series expansion, to attain the optimized results. In the scheme of the Taylor optimization method (TOM), after expanding the functions with the Taylor’s series, the unknown terms of the series are then globally optimized using differential evolution. Moreover, to illustrate the applicability of TOM, some examples of linear and non-linear fractional convection diffusion equations are exemplified graphically. The obtained assessments and comparative demonstrations divulged the rapid convergence of the estimated solutions towards the exact solutions. Comprising with an effective expander and efficient optimizer, TOM reveals to be an appropriate approach to solve different fractional differential equations modeling various problems of engineering.\nKEYWORDS\nPAPER SUBMITTED: 2017-07-17\nPAPER REVISED: 2017-11-15\nPAPER ACCEPTED: 2017-11-30\nPUBLISHED ONLINE: 2018-01-07\nDOI REFERENCE: https://doi.org/10.2298/TSCI170717292K\nTHERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S243 - S252]\nREFERENCES\n1. Miller, K. S., An introduction to fractional calculus and fractional differential equations, John Wiley and Sons, New York, 1993\n2. He J., H., A New Fractal Derivation, Thermal Science, 15(2011), 1, pp. S145-S147\n3. Atangana, A., Baleanu, D., New Fractional Derivatives with Nonlocal and Non-singular Kernel: Theory and application to heat transfer model, Thermal Science, 20 (2016), pp. 763-769\n4. Caputo., M., Fabrizio., M, A New Definition of Fractional Derivative without Singular Kernel, Progress in Fractional Differentiation and Application, 1(2015), 2, pp. 73-85\n5. Khalil., R., Horani., M., A, Yousef., A., Sababheh., M., A New Definition of Fractional Derivative, Journal of Computational and Applied Mathematics, 264 (2014), pp. 65-70\n6. Hosseini., K, Bekir., A, Ansari., R, New Exact Solutions of The Conformable time-Fractional Cahn- Allen and Cahn-Hilliard Equations using the Modified Kudryashov method, Optik - International Journal for Light and Electron Optics, 132 (2017), pp. 203-209\n7. Wang, K., L., Liu., S., Y., He's Fractional Derivative for Non-linear Fractional Heat Transfer Equation, Thermal Science, 20 (2016), 3, pp. 793-796\n8. Wang., K., Liu., S., Y., A New Solution Procedure for Nonlinear Fractional Porous Media Equation Based on A New Fractional Derivative, Nonlinear Science. Letters A, 7 (2016), 4, pp. 135-140\n9. Sayevand., K, Pichaghchi., K, Analysis of Nonlinear Fractional KdV Equation Based on He's Fractional Derivative, Nonlinear Science. Letters A, 7 (2016), 3, pp. 77-85\n10. Eslami., M, Rezazadeh., H., The First Integral Method for Wu-Zhang System with Conformable time-Fractional Derivative, Calcolo 53 (2016), pp. 475-485\n11. Jarad., F., Ugurlu., E., Abdelijawad., T., Baleanu., D., On A New Class of Fractional Operators, Advances in Difference Equations (2017), ArticleID 247\n12. Goufo., E., F., D., Application of The Caputo-Fabrizio Fractional Derivative Without Singular kernel to Korteweg-de Vries-Bergers Equation, Mathmatical Modelling and Analysis 21 (2016), pp. 188-198\n13. Atangana., A, Koca., I., Chaos in A Simple Nonlinear System with Atangana-Baleanu Derivatives with Fractional Order, Chaos Solitons & Fractals. 89 (2016), pp. 447-454\n14. Wu., G., C., Baleanu., D., Luo., W., H., Lyapunov Functions for Riemann-Liouville-like Fractional Difference Equations, Applied Mathematics and Computation, 314 (2017) pp. 228-236\n15. Odibat., Z., Momani., S., A Generalized Differential Transform Method for Linear Partial, Differential Equations of Fractional Order, Applied Mathematics Letters 21 (2008), pp. 194-199\n16. Abolhasani., M., Abbasbandy., S., Allahviranloo., T, A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains, Mathematics 5 (2017), 26 doi:10.3390/math5020026\n17. Chen., Y., Wu. Y, Cui., Y., Wang., Z., Jin., D, Wavelet Method for A Class of Fractional Convection-Diffusion Equation with Variable Coefficients, Journal of Computational Science 1 (2010) pp. 146-149\n18. Abbasbandya., S., Kazem., S., Alhuthali., M., S., Alsulami., H., H., Application of the Operational Matrix of Fractional-Order Legendre Functions for Solving the Time-Fractional Convection-Diffusion Equation, Applied Mathematics and Computation 266 (2015) pp. 31-40\n19. Hariharan., G., Kannan., K., Review of Wavelet Methods for the Solution of Reaction-Diffusion Problems in Science and Engineering, Applied Mathematical Modelling 38 (2014) pp. 799-813\n20. Abdusalam., H., A., Analytic and Approximate Solutions for Nagumo Telegraph Reaction Diffusion Equation, Applied Mathematics and Computation 157 (2004) pp. 515-522\n21. Wu., G., C., Baleanu., D, Luo., W. H., Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian polynomial, Thermal Science 21(2017) pp. 813-817\n22. Saruhan., H, Differential Evolution and Simulated Annealing Algorithms For Mechanical Systems Design, Engineering Science and Technology, 17 (2014) pp. 131-136\n23. Storn., R., Price., K, Differential Evolution: A Simple and Efficient Adaptive Scheme For Global Optimization Over Continuous Spaces, International Computer Science Institute, 12 (1995) pp. 1-16\n24. Storn., R., Price., K., Lampinen., J., A., Differential Evolution-A Practical Approach to Global Optimization, Springer-Natural Computing Series. Vanderplaats, 2005\n25. Bülbül, B., Sezer, M., Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method, Journal of Applied Mathematics, 2013 (2013) ArticleID 691614\n26. Aslan, B. B., Gurbuz, B., Sezer, M., A Taylor Matrix-Collocation Method Based on Residual Error for Solving Lane-Emden Type Differential Equations, New Trends Math. Sci. 224(2015), 2, pp. 219-224"
]
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https://nick-black.com/dankwiki/index.php?title=Computer_science_eponyms&oldid=7617 | [
"# Computer science eponyms\n\nComputer science needs more eponyms, in the vein of Mordenkainen. Collect them all, and impress your friends! I might make a project one day of summarizing these entries, but I'd likely sell the result as a book.\n\n• FIXME Tarjan has something like 20,004 algorithms, and all of them are outstanding\n\nExplicitly not included in this list are: general logic (Peano and Presburger arithmetic), mathematical entities not primarily associated with computer science (Markov's inequality, Chapman-Kolmogorov equation, Young tableaux), physical theories to which computer science is merely applied (Navier-Stokes equations, Taylor-Couette flow), or statistical entities not primarily associated with computer science (Ziph's Law, Pareto efficiency). Explicitly included are: terms from computer engineering (Mead-Conway rules, Ling adders) and mathematical entities primarily associated with computer science.\n\nUPDATE the threshold for inclusion is now: De Morgan's Laws. If you're not more computer sciency than De Morgan's Laws, you ain't gettin' in. Dank 12:25, 3 October 2011 (CDT)\n\n• Aanderaa–Rosenberg Conjecture suggests that non-trivial monotonicity properties of undirected graphs can only be solved by Ω(N2) algorithms on N vertices (these are all evasive decision trees on all possible edges)\n• Adam7 Algorithm is a 2D, 7-pass interlacing scheme optionally used by PNG due to Adam Costello\n• Adelson-Velskii-Landis Trees are self-height-balancing binary search trees, optimizing for lookup over modification viz. red-black trees\n• Aho-Corasick Algorithm extends the Knuth-Morris-Pratt automaton to match multiple strings in one pass of a text\n• Akra-Bazzi Method generalizes the \"master method\" of Bentley, Haken, and Saxe for subproblems of significantly different size\n• Amdahl's Law\n• Andersen's Algorithm\n• Backus-Naur Form\n• Bajard-Kla-Muller algorithm\n• Ball-Larus Heuristics\n• Banerjee Inequality\n• Barendregt convention\n• Barendregt-Geuvers-Klop Conjecture\n• Baskett, Chandy, Muntz and Palacios network\n• Batcher's Odd-Even Merge\n• Bayer Filter mosaics arrange RGB color filters on a square array of photosensors, and are used in a majority of single-chip image sensors. It uses twice as many green sensors as red or blue, to mimic the physiology of the human eye\n• Bellman-Ford Algorithm\n• Beneš network\n• Bentley-Ottman Algorithm\n• Berlekamp-Massey Algorithm\n• Berman–Hartmanis conjecture\n• Bernstein chaining\n• Bernstein conditions\n• Biba Integrity Model\n• Blom's Scheme\n• Bloom filter\n• Bluestein's FFT\n• Blum's axioms\n• Blum's Speedup Theorem\n• Blum-Blum-Shub random number generator\n• Boehm-Demers-Weiser garbage collector\n• Booth's Algorithm\n• Borůvka's Algorithm\n• Bowyer-Watson Algorithm\n• Boyer-Moore Algorithm\n• Bremermann's Limit\n• Brent's Algorithm\n• Brent's Theorem\n• Bresenham's Algorithm\n• Brewer's Theorem\n• Brodal Queue\n• Broder's Method\n• Bron-Kerbosch Algorithm\n• Brooks-Iyengar Algorithm\n• Buchberger Algorithm\n• Burrows-Wheeler Transform\n• Buzen's Algorithm\n• Callahan-Koblenz algorithm\n• Cannon's Algorithm\n• Cantor-Zassenhaus Algorithm\n• Carmack's Reverse\n• Chaff Algorithm\n• Chaitin's algorithm\n• Chaitin's Constant\n• Chaitin-Briggs algorithm\n• Chaitin–Kolmogorov random numbers\n• Chakravala's Algorithm\n• Chan's Algorithm\n• Chang-Roberts Algorithm\n• Cheney's Algorithm\n• Chew's Second Algorithm\n• Chien search\n• Cholesky decomposition expands Hermitian positive-definite matrices into products of a lower triangular matrix and its conjugate transpose. solved using the Cholesky–Crout and Cholesky–Banachiewicz algorithms.\n• Chomsky Hierarchy\n• Chomsky Normal Form\n• Chomsky-Schützenberger theorem\n• Christofides Algorithm\n• Church-Rosser Theorem\n• Church-Turing Thesis\n• Clos network\n• Cobham Axioms\n• Cobham's thesis\n• Cocke-Younger-Kasami Algorithm\n• Cohen-Sutherland algorithm\n• Coffman conditions enumerate the four conditions necessary and sufficient for deadlock within a system (mutual exclusion, hold-and-wait, a lack of preemption, and circular wait)\n• Commentz-Walter Algorithm\n• Conway's Law\n• Cook reduction\n• Cook-Levin Theorem\n• Cooley-Tukey Algorithm\n• Craig, Landin and Hagersten lock\n• Cranfield method\n• (preconditioned) Crank–Nicolson Algorithm\n• Damerau-Levenshtein distance\n• Damm Algorithm\n• Davis-Putnam Algorithm\n• Davis-Putnam-Logemann-Loveland Algorithm\n• De Bruijn presentation\n• De Bruijn string\n• Dekker's Algorithm\n• Delaunay's Triangulation\n• Dennard Scaling\n• Diffie-Hellman Key Exchange\n• Dijkstra's Algorithm\n• Dinic's Algorithm\n• DiVincenzo's criteria specify conditions necessary for a quantum computer\n• Dolev's Algorithm\n• Doo-Sabin subdivision surface\n• Duff's Device\n• Dyck Language\n• Earley Parser\n• Edmonds's matching algorithm constructs maximum matchings on graphs in O(|E||V|²)\n• Edmonds-Karp Algorithm\n• Euclid's Algorithm\n• Fagin's Theorem states that the set of all properties expressible in existential second-order logic is precisely the complexity class NP\n• Faugère F5 algorithm\n• Fiat-Shamir Heuristic\n• Fibonacci Heap\n• Fisher-Yates shuffle\n• Fletcher's Checksum\n• Floyd's Algorithm\n• Floyd-Steinberg dithering\n• Flynn Taxonomy\n• Ford-Fulkerson Algorithm\n• Fortune's Algorithm\n• Fox's Algorithm\n• Fredkin gate\n• Friedberg-Muchnik Theorem\n• Fürer's algorithm multiplies two n-digit numbers in O(nlgn*2O(lg*n))\n• Gabbay's separation theorem\n• Gabow's Algorithm\n• Gal's Accurate Tables\n• Gale-Church Algorithm\n• Gale-Shapley algorithm\n• Gilbert-Johnson-Keerthi Algorithm\n• Girvan-Newman Algorithm\n• Givens rotation\n• Glushkov Automata\n• Goldreich-Goldwasser-Halevi scheme\n• Gomory-Hu Tree\n• Gordon–Newell theorem\n• Gosper's Hack\n• Gosper's Hypergeometric Algorithm\n• Gosper's Loop Detection Algorithm\n• Graham Scan\n• Graham-Denning Model\n• Gram–Schmidt process\n• Gray codes\n• Greibach Normal Form\n• Grover's Algorithm\n• Grzegorczyk hierarchy\n• Guruswami-Sudan Algorithm\n• Gustafson's Law\n• Gutmann's Method is a 35-phase recipe for destroying data on ferromagnetic drives.\n• Guttman-Rosler transform\n• Hamming code\n• Hamming distance\n• Heckel's algorithm isolates changes between files, and is the basis for diff CACM 1978\n• Hennessy-Milner Logic\n• Herlihy's wait-free hierarchy\n• Hirschberg's Algorithm\n• Hoare logic\n• Holevo's Theorem\n• Holland's schema theorem\n• Hong-Kung bound\n• Hopcroft-Karp Algorithm\n• Hopfield net\n• Horn clauses\n• Householder transformation\n• Huet's Zipper\n• Hunt-McIlroy Algorithm\n• Iliffe vector\n• Immerman–Szelepcsényi theorem\n• Jackson network\n• Jackson's theorem\n• Jaro-Winkler distance\n• Jefferson's Time Warp\n• Jelinek-Mercer smoothing\n• Jensen's Device\n• Johnson's Algorithm\n• Kabsch Algorithm\n• Kahan Summation Algorithm\n• Kannan's Theorem\n• Karatsuba's Algorithm multiplies two n-digit numbers using nlog23 single-digit mults\n• Karger's Algorithm\n• Karn's algorithm extracts accurate TCP RTT measures, Karn-Partridge 1987\n• Karmarkar's algorithm\n• Karnaugh map\n• Karp reduction\n• Karp-Flatt metric\n• Karp-Lipton Theorem\n• Kernighan-Lin algorithm\n• Kirkpatrick-Seidel Algorithm\n• Kleene Closure\n• Kleene Plus\n• Kleene Star\n• Kneser-Ney smoothing\n• Knuth Shuffle\n• Knuth-Morris-Pratt Algorithm\n• Koenig Lookup\n• Kohonen Algorithm\n• Kohonen network\n• Kolmogorov complexity\n• Koomey's Law\n• Kosaraju's Algorithm\n• Kruskal's Algorithm\n• Kryder's Law\n• Kung-Leiserson systolic array\n• Kuroda Normal Form\n• Lamport's Bakery Algorithm\n• Lamport's Clock\n• Lamport's Hash\n• Lee-Seung algorithm\n• Lehmer random number generator\n• Lehmer's GCD Algorithm\n• Lempel-Ziv-Welch compression\n• Levenshtein automaton\n• Levenshtein distance\n• Levin reduction\n• Liang-Barsky algorithm\n• Lin-Kernighan Heuristic\n• Linde-Buzo-Gray algorithm\n• Liskov's Substitution Principle\n• Lloyd's algorithm\n• Loss-DiVincenzo machines are quantum computers based off electron spin as confined to quantum dots\n• Luby's algorithm\n• Luhn Algorithm\n• Luleå Algorithm\n• Maekawa's Algorithm\n• Mahaney's Theorem\n• Manning algorithm\n• Marzullo algorithm\n• McFarling-style branch predictor\n• Mealy machine\n• Mellor-Crummey and Scott lock\n• Merkle–Damgård construction\n• The Metropolis-Hastings algorithm for MCMC obtains samples from a probability distribution that is difficult to directly sample\n• Miller-Rabin Primality Test\n• Minsky-Fenichel-Yochelson Algorithm\n• Montgomery reduction\n• Moore machine\n• Moore's Law\n• Morgensen-Scott encoding\n• Möller-Trumbore algorithm\n• Nagle's algorithm\n• Nassi-Shneiderman diagram\n• Needham-Schroeder Protocol\n• Needleman-Wunsch Algorithm\n• Neuman-Stubblebine Protocol\n• Nevill-Manning algorithm\n• Nick's Class\n• Nisan's Generator\n• Ousterhout's dichotomy/fallacy a taxonomy of systems vs scripting languages\n• Otway-Rees Protocol\n• Paeth-Tanaka Algorithm rotates images via a method of three shears\n• Paeth Filter performs 2D image compression in PNG\n• Peterson's Algorithm\n• Petrick's method\n• Plotkin's Sticky Bit\n• Pollaczek–Khinchine formula\n• Pollard's Kangaroo Algorithm\n• Popek-Goldberg virtualization requirements\n• Post's correspondence problem\n• Postel's Law\n• Prim's Algorithm\n• Proebsting's Law claims that compiler technology doubles computing power every 18 years\n• Prüfer Coding\n• Prüfer Sequence\n• Quines\n• Quine-McLuskey algorithm\n• Rabin Automata\n• Rabin's Information Dispersal Algorithm\n• Rabin-Karp Algorithm\n• Raymond's Algorithm\n• Reed-Solomon correction code\n• Ricart-Agrawala Algorithm\n• Rice's Theorem\n• Rice-Shapiro Theorem\n• Risch Algorithm\n• Ruppert's Algorithm\n• Sattolo's Algorithm generates a 1-cyclic derangement of an array (a permutation such that every element ends up in a new position)\n• Savitch's Theorem\n• Schensted Algorithm\n• Schlick's approximation\n• The Schönhage–Strassen algorithm multiplies two n-digit numbers in O(nlgnlglgn) bit complexity using FFTs\n• Schoof's Algorithm\n• Schreier-Sims Algorithm\n• Schwartzian transform\n• Sethi-Ullman Algorithm\n• Shamir's Secret Sharing Scheme\n• Shamos-Hoey Algorithm\n• Shor's Algorithm\n• Sipser–Lautemann theorem\n• Smith's Algorithm\n• Smith-Waterman algorithm\n• Solomonoff-Levin distribution\n• Steensgaard's Algorithm\n• Stehlé-Zimmermann algorithm\n• Steinhaus-Johnson-Trotter algorithm\n• Strassen's Algorithm\n• Suurballe's Algorithm\n• Sweeney-Robertson-Tocher division algorithm\n• Tarjan's Algorithm\n• Tarjan's Dynamic Tree\n• Tarjan's Least Common Ancestors Algorithm\n• Thompson Automata\n• Timsort\n• Toda's theorem\n• Todd–Coxeter algorithm\n• Tomasulo's Algorithm\n• Tonelli-Shanks Algorithm\n• The Toom-Cook Algorithm multiplies two n-digit numbers using nlog(5)/log(3) single-digit mults\n• Turing Degree\n• Turing Machines\n• Ukkonen's Algorithm\n• Valiant-Vazirani Theorem\n• Van Jacobson Channels\n• Van Wijngaarden Grammars\n• Verhoeff Algorithm\n• Viola-Jones face detection\n• Volder's algorithm\n• von Neumann architecture\n• Wagner-Fischer Algorithm\n• Wallace Multiplier\n• Wallace tree\n• Warnsdorff's Algorithm\n• The Williams State Machine is a common parsing automaton for DEC virtual terminal input"
]
| [
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.61444044,"math_prob":0.619414,"size":11564,"snap":"2021-43-2021-49","text_gpt3_token_len":3327,"char_repetition_ratio":0.18858132,"word_repetition_ratio":0.008728179,"special_character_ratio":0.20624352,"punctuation_ratio":0.030100334,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99100876,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-08T00:27:55Z\",\"WARC-Record-ID\":\"<urn:uuid:ab56f53f-c93d-4c71-832c-e17928a02c6c>\",\"Content-Length\":\"32793\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:397c486d-077c-4b9e-bb88-77dadde33448>\",\"WARC-Concurrent-To\":\"<urn:uuid:2a7699a3-ab74-4c25-8db1-4edd0f8a6613>\",\"WARC-IP-Address\":\"173.230.130.29\",\"WARC-Target-URI\":\"https://nick-black.com/dankwiki/index.php?title=Computer_science_eponyms&oldid=7617\",\"WARC-Payload-Digest\":\"sha1:MAN32LRT7OCJRNLJPUGV6HX6AXWLWU3H\",\"WARC-Block-Digest\":\"sha1:B6FPBRAXPQE76PT3XHTIL7HNCCULJ4QJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363420.81_warc_CC-MAIN-20211207232140-20211208022140-00250.warc.gz\"}"} |
https://www.mathworks.com/matlabcentral/cody/players/13246597-sulaymon-eshkabilov/badges | [
"Cody",
null,
"# Sulaymon Eshkabilov\n\nRank\nScore\n1 – 60 of 64\n\n#### Introduction to MATLAB Master+50\n\nEarned on 24 Jul 2019 for solving all the problems in Introduction to MATLAB.\n\n#### Community Group Solver+50\n\nEarned on 13 Aug 2019 for solving a community curated groups. Has solved 2 community groups.\n\n#### Promoter+10\n\nLike a problem or solution.\n\n#### Commenter+10\n\nComment on a problem or solution.\n\n#### CUP Challenge Master+50\n\nSolve all the problems in CUP Challenge problem group.\n\n#### Creator+20\n\nCreate a problem.\n\n#### Speed Demon+50\n\nSolve a problem first.\n\nSolve a problem with a best solution.\n\n#### Quiz Master+20\n\nMust have 50 solvers for a problem you created.\n\n#### Curator+50\n\n25 solvers for the group curated by the player\n\n#### Cody Challenge Master+50\n\nSolve all the problems in Cody Challenge problem group.\n\n#### ASEE Challenge Master+50\n\nSolve all the problems in ASEE Challenge problem group.\n\n#### Tiles Challenge Master+50\n\nSolve all the problems in Tiles Challenge problem group.\n\n#### Scholar+50\n\nSolve 500 problems.\n\n#### Cody5:Easy Master+50\n\nSolve all the problems in Cody5:Easy problem group.\n\n#### Puzzler+50\n\nCreate 10 problems.\n\n#### Draw Letters Master+50\n\nSolve all the problems in Draw Letters problem group.\n\n#### Project Euler I Master+50\n\nSolve all the problems in Project Euler I problem group.\n\n#### Indexing I Master+50\n\nSolve all the problems in Indexing I problem group.\n\n#### Cody Problems in Japanese Master+50\n\nSolve all the problems in Cody Problems in Japanese problem group.\n\n#### Indexing II Master+50\n\nSolve all the problems in Indexing II problem group.\n\n#### Matrix Manipulation I Master+50\n\nSolve all the problems in Matrix Manipulation I problem group.\n\n#### Magic Numbers Master+50\n\nSolve all the problems in Magic Numbers problem group.\n\n#### Sequences & Series I Master+50\n\nSolve all the problems in Sequences & Series I problem group.\n\n#### Computational Geometry I Master+50\n\nSolve all the problems in Computation Geometry I problem group.\n\n#### Famous+20\n\nMust receive 25 total likes for the problems you created.\n\n#### Matrix Patterns I Master+50\n\nSolve all the problems in Matrix Patterns problem group.\n\n#### Strings I Master+50\n\nSolve all the problems in Strings I problem group.\n\n#### Divisible by x Master+50\n\nSolve all the problems in Divisible by x problem group.\n\n#### R2016b Feature Challenge Master+50\n\nSolve all the problems in R2016b Feature Challenge problem group.\n\n#### Number Manipulation I Master+50\n\nSolve all the problems in Number Manipulation I problem group.\n\n#### Matrix Manipulation II Master+50\n\nSolve all the problems in Matrix Manipulation II problem group.\n\n#### Matrix Patterns II Master+50\n\nSolve all the problems in Matrix Patterns II problem group.\n\n#### Cody5:Hard Master+50\n\nSolve all the problems in Cody5:Hard problem group.\n\n#### Indexing III Master+50\n\nSolve all the problems in Indexing III problem group.\n\n#### Sequences & Series II Master+50\n\nSolve all the problems in Sequences & Series II problem group.\n\n#### Functions I Master+50\n\nSolve all the problems in Functions I problem group.\n\n#### Magic Numbers II Master+50\n\nSolve all the problems in Magic Numbers II problem group.\n\n#### Likeable+20\n\nMust receive 10 likes for a problem you created.\n\n#### Matrix Patterns III Master+50\n\nSolve all the problems in Matrix Patterns III problem group.\n\n#### Indexing V Master+50\n\nSolve all the problems in Indexing V problem group.\n\n#### Celebrity+20\n\nMust receive 50 total likes for the solutions you submitted.\n\n#### Card Games Master+50\n\nSolve all the problems in Card Games problem group.\n\n#### Strings II Master+50\n\nSolve all the problems in Strings II problem group.\n\n#### Sequences & Series III Master+50\n\nSolve all the problems in Sequences & Series III problem group.\n\n#### Matrix Manipulation III Master+50\n\nSolve all the problems in Matrix Manipulation III problem group.\n\n#### Number Manipulation II Master+50\n\nSolve all the problems in Number Manipulation II problem group.\n\n#### Computational Geometry II Master+50\n\nSolve all the problems in Computational Geometry II problem group.\n\n#### Indexing IV Master+50\n\nSolve all the problems in Indexing IV problem group.\n\n#### Renowned+20\n\nMust receive 10 likes for a solution you submitted.\n\n#### Strings III Master+50\n\nSolve all the problems in Strings III problem group.\n\n#### Computational Geometry IV Master+50\n\nSolve all the problems in Computational Geometry IV problem group.\n\n#### Word Puzzles Master+50\n\nSolve all the problems in Word Puzzles problem group.\n\n#### Computational Geometry III Master+50\n\nSolve all the problems in Computational Geometry III problem group.\n\n#### Logic Master+50\n\nSolve all the problems in Logic problem group.\n\n#### Combinatorics I Master+50\n\nSolve all the problems in Combinatorics - I problem group.\n\n#### Modeling & Simulation Challenge Master+50\n\nSolve all the problems in Modeling and Simulation Challenge problem group.\n\n#### Computer Games I Master+50\n\nSolve all the problems in Computer Games I problem group.\n\n#### Board Games I Master+50\n\nSolve all the problems in Board Games I problem group."
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https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-020-00100-0 | [
"# Noisy network attractor models for transitions between EEG microstates\n\n## Abstract\n\nThe brain is intrinsically organized into large-scale networks that constantly re-organize on multiple timescales, even when the brain is at rest. The timing of these dynamics is crucial for sensation, perception, cognition, and ultimately consciousness, but the underlying dynamics governing the constant reorganization and switching between networks are not yet well understood. Electroencephalogram (EEG) microstates are brief periods of stable scalp topography that have been identified as the electrophysiological correlate of functional magnetic resonance imaging defined resting-state networks. Spatiotemporal microstate sequences maintain high temporal resolution and have been shown to be scale-free with long-range temporal correlations. Previous attempts to model EEG microstate sequences have failed to capture this crucial property and so cannot fully capture the dynamics; this paper answers the call for more sophisticated modeling approaches. We present a dynamical model that exhibits a noisy network attractor between nodes that represent the microstates. Using an excitable network between four nodes, we can reproduce the transition probabilities between microstates but not the heavy tailed residence time distributions. We present two extensions to this model: first, an additional hidden node at each state; second, an additional layer that controls the switching frequency in the original network. Introducing either extension to the network gives the flexibility to capture these heavy tails. We compare the model generated sequences to microstate sequences from EEG data collected from healthy subjects at rest. For the first extension, we show that the hidden nodes ‘trap’ the trajectories allowing the control of residence times at each node. For the second extension, we show that two nodes in the controlling layer are sufficient to model the long residence times. Finally, we show that in addition to capturing the residence time distributions and transition probabilities of the sequences, these two models capture additional properties of the sequences including having interspersed long and short residence times and long range temporal correlations in line with the data as measured by the Hurst exponent.\n\n## Introduction\n\nThe human brain is intrinsically organized into large-scale networks that can be identified when the brain is at rest [1, 2]. These networks reorganize on a sub-second temporal scale in order to allow the precise execution of mental processes . Study of the spatial and temporal aspects of the dynamics underlying this reorganization requires non-invasive measures with high temporal resolution. The electroencephalography (EEG) is a direct measure of neuronal activity which captures the temporal evolution of the scalp electrical field with millisecond resolution. Unlike local measures of EEG in channel space that vary from time-point to time-point and as a function of the reference, the global measure of EEG topography remains stable for brief periods (50–100 ms) before changing to another quasi-stable state, the so-called EEG microstates [4, 5]. Microstates have been coined the “atoms of thought” and can be considered the basic building blocks of mentation that make up the spontaneous electrophysiological activity measured at the scalp .\n\nAt rest, when the subject is not doing any task, four dominant topographies are consistently reported both in healthy individuals across the lifespan as well as in neurological and psychiatric populations . Moreover, neurological and psychiatric diseases have been shown to fundamentally alter their temporal dynamics [11, 13, 14]. This implies that the timing of the microstates and not the topography is the most crucial feature. Further evidence for the importance of the timing of the microstates comes from studies using simultaneously recorded EEG and functional magnetic resonance imaging (fMRI) that identify EEG microstates as the electrophysiological correlate of fMRI-defined resting-state networks (RSNs) . This link is surprising because EEG microstates and fMRI-RSNs are two global measures of large-scale brain activity that are observed at temporal scales two orders of magnitude apart: 50–100 ms (microstates) and 10–20 seconds (fMRI). This link could only be established because EEG microstate time-series are scale-free, i.e., they do not occur at a characteristic timescale, but show similar behavior across different temporal scales. More specifically, EEG microstate sequences have been shown to have “memory”: they are mono-fractal and have long-range temporal correlations (LRTC) over six dyadic scales that span the two orders of magnitude (256 ms to 16 s) at which EEG microstate changes and fMRI blood-oxygen-level-dependent (BOLD) oscillations can be observed . Gschwind et al. verify and expand the work of by computing scale-free behavior in EEG data using a battery of tests, including computing the power spectral density and Hurst exponents using detrended fluctuation analysis (DFA), a wavelet framework, and time-variance analysis thus corroborating the robustness of the memory of microstate time series .\n\nLRTC in microstate sequences suggest that the spatial-temporal dynamics are controlled not only by inherent structural properties of the fMRI-RSNs but also by a“sequential connectivity” that facilitates the timings and transitions between the underlying neural generators . Importantly, Van de Ville et al. demonstrate that the precise timing of the residence times but not the order of local state transitions of the microstate sequences is crucial for their fractal properties . Shuffling their state transitions without changing their timing has no effect, whereas equalizing their residence times degrades the time series to white noise. In the case that the residence times are IID and memoryless, then the residence times can be considered a “renewal process” and the whole process can be seen as Markov jump process. We note that the series of residence times and the state transition process are essentially independent. Therefore it is possible for the transitions to be Markov but the jump (residence) times to be non-Markov.\n\nEEG microstate time series models must capture and reproduce four crucial aspects: (i) the local transition probabilities between states, (ii) the distribution of residence times, (iii) the long-range temporal correlations, and (iv) that longer and shorter residence times are interspersed throughout the sequence. So far, attempts to model EEG microstate sequences have been based on Markov-type models that assume the microstate time series is a memoryless process . In particular, Gärtner et al. construct a hidden-Markov type stochastic model based on the transition probabilities between microstates extracted from the data . This approach has been criticized for the underlying assumption that the microstate transition process is independent of the underlying global field power time series and therefore does not reproduce the LRTC [19, 22]. Von Wegner et al. show that neither memoryless Markov models nor single parameter LRTC models fully capture the data . Hence, more sophisticated models need to be developed to capture the full spatiotemporal dynamics of microstate sequences.\n\nIn this paper we provide a novel modeling approach for microstate time series based on dynamical structures called noisy network attractors. These are stochastic models that exhibit heteroclinic or excitable network attractors in their noise-free dynamics . A heteroclinic network is a collection of solutions (heteroclinic orbits) to a system of ordinary differential equations that link a set of steady states that themselves are unstable. Excitable networks, in the sense introduced in , are close relations of heteroclinic networks that have a small but finite threshold of perturbation that needs to be overcome to make a transition between a number of attracting states.\n\nHeteroclinic networks have been found in models of many natural systems, for example, from population of neurons [25, 26], predator-prey dynamics , and bi-matrix game theory . The dynamics near a network attractor is generally intermittent: trajectories spend long periods of time close to one state before switching to another. Heteroclinic cycles or networks have been successfully applied to model transient dynamics in neural processes at a variety of levels of description and spatial scales . For example, from olfactory processing in the zebra fish to human working memory , episodic memory , and decision making . Time series from similar networks with noise have previously been shown to produce non-Markovian dynamics [24, 34]. These modeling techniques have also been used successfully in applications of artificial intelligence. For example, in the authors show that arbitrary Turing machines can be built from these excitable networks, and in the authors use networks of this form as the ‘brain’ for a theoretical robot that has to solve a classification task. Given the powerful capacities of network attractors to model transient dynamics at different levels, these are a promising candidate to model EEG microstate sequences.\n\nHere we demonstrate that the transitions and LRTC of EEG microstates sequences can be modeled using stochastic differential equations (SDEs) that possess such an excitable network attractor. We show that the residence time distribution of the microstate time series follows a double exponential decay. We first construct a four-node, all-to-all connected network model. The SDEs we use have low amplitude additive white noise, and the network is designed using the construction outlined in . Each node in the network represents one microstate, and the transitions between them are driven by the noise on the edges. This model captures the series of state transitions, but not the distribution of residence times. We present two extensions to this model that induce longer residence times observed in the data using two different mechanisms. The first is to add a hidden node for each microstate that acts as a trap for the transient dynamics. The second incorporates a controlling layer with two nodes representing a central switching control of faster and slower switches between the nodes or the original network. Finally, we assess the interspersion of long and short residence times by means of their autocorrelation and show that, when fitted to the data, the sequences generated with each extended model have the same extent of LRTC as measured by the Hurst exponent .\n\n## EEG data collection and analysis\n\nDetailed description of the procedures used to collect the EEG recordings and convert them into microstates are given in ; here we provide a brief summary for completeness. Nine healthy volunteers (24–33 years, mean age 28.37 years) participated for monetary compensation after giving informed consent approved by the ethics commission of the University Hospital of Geneva. None suffered from current or prior neurological or psychiatric illness or from claustrophobia. EEG was recorded from 64 sintered Ag/AgCL electrodes in an extended 10–10 system. EEG was digitized using a battery-powered and MRI-compatible EEG system (BrainAmp MR plus, Brainproducts) with a sampling frequency of 5 kHz and a hardware bandpass filter of 0.016–250 Hz with the midline fronto-central electrode as the physical reference. For each subject, we recorded one 5-minute session outside the scanner prior to recording three 5-minute runs of resting-state EEG inside the MRI scanner. Subjects were instructed to relax and rest with their eyes closed without falling asleep and to move as little as possible. Data from one subject had to be excluded due to subsequent self-report of sleep and the presence of sleep patterns in EEG. The 24 recordings from the remaining eight subjects were submitted for further processing. MRI and ballistocardiographic artifacts were removed using a sliding average, then oculomotor and myogenic artifacts were removed using independent component analysis. The data were downsampled to 125 Hz and bandpass filtered between 1 and 40 Hz.\n\nTo compute microstate sequences, first the global field power (GFP) was computed from each recording as the standard deviation of the scalp electrical field at each time point. Between the local troughs of GFP, the scalp topography remains stable and only varies in strength. EEG at all local peaks of GFP was extracted and submitted to a modified atomize-agglomerate hierarchical clustering (AAHC) algorithm . Four dominant template maps were identified as the optimal solution in each run using a cross-validation criterion, a measure of residual variance . These four dominant maps are in line with the classically identified microstates [5, 7, 12]. Finally, the microstates were fitted back onto EEG by computing the spatial correlation between the four template maps and the continuous EEG data, then the template that correlated highest with the data was assigned at each time point. Figure 1 shows a schematic of the EEG microstate procedure and the four dominant template maps. Note that at the local troughs of GFP the field strength is minimal and none of the template maps correlate well with the data; the allocation of the best template can be considered random. To avoid these brief periods being accounted as very short separate microstates, a temporal constraint criterion is required. We use a temporal constraint criterion of 32 ms (corresponding to four sample points at 125 Hz) to obtain a time-series of the dominant EEG microstates for each recording. Figure 10 in Appendix A illustrates the requirement for the temporal constraint.\n\nThe microstate time-series is a sequence that we denote by $$m(t)$$ where $$m\\in \\{1,2,3,4\\}$$ at any given sampling time point t. We classify $$m(t)$$ into epochs of the same state defined by saying that we enter a new epoch at the time point that the microstate changes, if $$m(t+1)\\neq m(t)$$; note that we enter a new epoch at the start of the sequence $$t=0$$. The average number of epochs per recording is 2010. We describe the kth epoch in terms of its state $$\\sigma (k)$$ and residence time $$\\rho (k)$$ respectively. We call the sequence of states visited $$\\sigma (k)$$ the transition process, and the sequence of residence times $$\\rho (k)$$ a residence process. These processes can, at least in principle, be independent. We define:\n\n• $$R(t)$$ is the distribution of residence times $$\\rho (k)$$ for all epochs k (regardless of state).\n\n• $$T(m,j)$$ is the probability of transition from an epoch in state m to one in state j,\n\n$$T(m,j)= \\frac{\\#\\{k: \\sigma (k)=m \\text{ and }\\sigma (k+1)=j\\}}{\\#\\{k: \\sigma (k)=m\\}}.$$\n\nNote that there are no self-transitions due to our definition of an epoch. To identify the residence distribution R from the data, we compute the histogram of residence times from each microstate sequence for bin size 40, then we find the average and standard error of each bin over all recordings. The distribution is truncated at the first empty bin. We compute the residence distribution R for the data collected inside and outside the scanner, then we use a two-sample Kolmogorov–Smirnov test and find that the histograms are from the same continuous distribution. We also calculate T for each recording and find the average and standard error for each probability over all recordings. Calculating the average T for the two groups, from inside and outside the scanner, separately we find no significant differences for any transition between the two groups using a Kruskall–Wallis test with Bonferroni correction. Therefore, we combine the recordings from inside and outside the scanner for subsequent analysis and model fitting.\n\nTo quantify the combined distribution from the data, we fit exponential curves given by\n\n$${\\mathcal{E}}^{(n)}(t)= \\sum_{i=1}^{n}a_{i} \\exp (-k_{i}t)$$\n(1)\n\nfor $$n=1,2,3$$ to the data using Matlab, and constrain $$a_{i}>0$$ and $$k_{i}\\geq 0$$. We also fit power law curves given by\n\n$${\\mathcal{P}}^{(1)}(t)= b_{1}t^{c_{1}},\\qquad { \\mathcal{P}}^{(2)}(t)= b_{2}t^{c_{2}} +d.$$\n(2)\n\nWe calculate the error χ as the least squares difference between the log of the values of each curve and the log of the data. We use an F-test (code used as written for ) with threshold $$\\alpha =0.05$$ to indicate if extra parameters are warranted to improve the fit of the data.\n\nThe residence time distribution $$R(t)$$ and transition probabilities $$T(m,j)$$ from the data are shown in Fig. 2. The distribution $$R(t)$$ is plotted on a logarithmic scale with $${\\mathcal{E}}^{(n)}(t)$$ for $$n=1,2,3$$ given by (1) and $${\\mathcal{P}}^{(n)}(t)$$ for $$n=1,2$$ given by (2). The values of the coefficients are given in Table 1. We perform a comparison of $${\\mathcal{E}}^{(1)}$$ and $${\\mathcal{E}}^{(2)}$$ and find that $$F(d_{n},d_{d}) = 1102.8(2,31)$$, which therefore rejects the null hypothesis that the distribution is $${\\mathcal{E}}^{(1)}$$. We also compare $${\\mathcal{E}}^{(3)}$$ and $${\\mathcal{E}}^{(2)}$$ and find that $$F(d_{n},d_{d}) =46.9(2,30)$$, therefore the additional parameters are warranted. Figure 2 shows that although $${\\mathcal{E}}^{(3)}$$ has smaller error, the improvement in fit is for short residence times and the tail in this case is better captured by $${\\mathcal{E}}^{(2)}$$ which lies within the error bars for large residence time values. Figure 2 also shows the cumulative distribution of residence times and the two power law curves. We perform a comparison of $${\\mathcal{P}}^{(1)}$$ and $${\\mathcal{P}}^{(2)}$$. We find that an F-test rejects the null hypothesis that the distribution is $${\\mathcal{P}}^{(1)}$$, with $$F (d_{n},d_{d}) = 1167 (2,32)$$.\n\nWe note that the error in the tail of the distribution is relatively large. There are few very long residence times $$840<\\rho <1000$$ ms, and longer recordings would be required for greater certainty about the distribution of the very long (>900 ms) residence times. The heavy tailed residence time distribution indicates non-Markovian dynamics in line with . This is supported by the best fit of the power law $${\\mathcal{P}}^{(2)}$$ with a negative slope that is synonymous with scale-free dynamics . When fitting the models to the data, we will consider residence times $$20<\\rho <900$$ ms due to the greater uncertainty for >900 ms; details of the fitting strategy are given in each section.\n\n## Single-layer excitable network model\n\nWe aim to build a model that captures the statistical properties of the transition process and residence process. To this end, we construct a model of stochastic differential equations perturbed by low amplitude additive white noise, using a general method that allows us to realize any desired graph as an attracting excitable network in phase space. This model has evolved from work in and is detailed in , and here we briefly outline the construction.\n\nWe realize the network of all possible transitions between the four canonical microstates as an excitable network with four nodes (p-cells) that represent the four microstates. There is an edge between two nodes in the network if there can be transition between the two corresponding microstates; here the network is all-to-all connected with twelve edges (y-cells).\n\nThe system is given by\n\n\\begin{aligned} & \\tau \\,\\mathrm {d}p_{j} = \\bigl[ f(p_{j},y_{k}) \\bigr]\\,\\mathrm{d}t + \\eta _{p} \\,\\mathrm {d}w_{j}, \\end{aligned}\n(3)\n\\begin{aligned} & \\tau \\,\\mathrm {d}y_{k} = \\bigl[g(p_{j},y_{k}) \\bigr] \\,\\mathrm {d}t + \\eta _{{y}_{k}} \\,\\mathrm {d}w'_{k} \\end{aligned}\n(4)\n\nfor $$j=1,\\dots,M$$ and $$k=1,\\dots,Q$$. We create a microstate model by choosing $$M=4$$ (corresponding to the number of states) and $$Q=12$$ (corresponding to the number of possible transitions between states). The $$w_{j}$$ and $$w_{k}'$$ are independent identically distributed (iid.) noise processes, and η is noise weights. We introduce the time scaling τ (which does not occur in ) because although the timescale of the p-dynamics can be scaled by the parameters, the equations for the y dynamics have a functional form in which the timescale is fixed. The $$p_{j}$$ variables classify which node of the network (i.e., which of the four microstates) is visited. The $$y_{k}$$ variables become non-zero during a transition between nodes. The functions f and g and parameters for this single-layer model are detailed in and discussed in Appendix B.1.\n\nThis network can be realized as either a heteroclinic or excitable network depending on the choice of constants in f and g . In the system with no noise, the network consists of heteroclinic connections between equilibrium solutions with $$p_{j}=1$$ and all other coordinates zero. In an excitable network, these equilibria are all stable, and small perturbations (from added noise) are required to push the trajectory from one equilibrium to another.\n\nFigure 3 shows the four microstates from the data and the coupling architecture of the network model with example time series output for the nodes and the edges in the excitable case. The transitions between nodes occur on a faster timescale than the length of time spent at each node (the residence time). Thus, the trajectory in the simulation is almost always close to one of the equilibrium solutions, where one of the $$p_{m}$$ variables is close to 1.\n\nTo determine when the trajectory is close to a given node, we define a box in phase space around that node so that when the trajectory is in the box we say it is near the node. Here we fix the box size $$h= 0.49$$ such that each box contains one node and the boxes do not overlap. The duration of time spent in the box is then the residence time for that node . The output of the model simulation is a series of k epochs where each epoch is defined by the state it is in $$\\sigma \\in \\{1,2,3,4\\}$$ and its residence time ρ. The transition rates between nodes in the model are modulated by the noise levels on the edges (rather than on the nodes) as described in . Therefore we fix the noise on the nodes $$\\eta _{p}=10^{-4}$$. The free parameters for fitting the model are the twelve noise values on the edges $$\\eta _{y_{k}} k=1,\\dots,12$$.\n\nTo fit the excitable network model output to the data, we employ the following algorithm.\n\n1. 1.\n\nInitialize: Initiate the noise values using scaled transition probabilities $$\\eta ^{0}_{y_{k}} = {\\mathcal{S}}^{0}n^{0}_{k}$$, where $$n^{0}_{k}=T(m,j)$$ and $${\\mathcal{S}}^{0}=1$$.\n\n2. 2.\n\nModel simulation and analysis: Numerically simulate the excitable network model given by system (3)–(4) with a stochastic Heun method implemented using a custom code written in Matlab. Compute ten realizations of the model using step size 0.05 up to maximum of 100,000 steps. This gives approximately 5750 epochs per realization. Calculate the transition probabilities $$T_{s}(m,j)$$ and residence distribution $$R_{s}(t)$$ from the simulations in the same way as from the data; see Sect. 2.\n\n3. 3.\n\nCost function: Compute the cost function\n\n$${\\mathcal{C}} = \\sum_{t}\\bigl( \\bigl\\vert \\log \\bigl(R(t)\\bigr) \\bigr\\vert - \\bigl\\vert \\log \\bigl(R_{s}(t)\\bigr) \\bigr\\vert \\bigr)^{2} + 100\\sum_{m,j} \\bigl(T(m,j)-T_{s}(m,j)\\bigr).$$\n(5)\n\nThis function is the weighted sum of the distance between the log of the residence times $$R(t)$$ (from the data) and $$R_{s}$$, and the distance between the transition probabilities T and $$T_{s}$$. The weighting for the transition probabilities is due to the relatively smaller magnitude of the difference. We seek to minimize this cost function.\n\n4. 4.\n\nUpdate parameters: Change $${\\mathcal{S}}^{i}$$ and $$n^{i}_{k}$$ according to the following strategy. Change $$n^{i}_{k}$$ values to minimize the least square distance between the transition probabilities T and $$T_{s}$$. Maintain the ordering between the probabilities for a given m, for example, if $$T(1,3) > T(1,2)$$ then we set $$n^{i}_{2}>n^{i}_{1}$$. In this way the excitable network model can be adjusted to produce any given set of transition probabilities, as described in . Change $${\\mathcal{S}}^{i}$$ to control the decay rate of $$R_{s}$$ and minimize the least squares distance between the log residence times R and $$R_{s}$$. If all $$\\eta _{y_{k}}$$ are large, for example, $$O(10^{-1})$$, transitions happen quickly, the residence times are short, and the decay rate of the distribution R is large (slope is steep); whereas if $$\\eta _{y_{k}}$$ are small, for example, $$O(10^{-4})$$, there are long residence times between transitions and the decay rate is small (slope is shallow). Set $$\\eta ^{i}_{y_{k}} = {\\mathcal{S}}^{i}n^{i}_{k}$$.\n\n5. 5.\n\nRepeat from 2.\n\nThe statistics of the sequences generated by the excitable network model to the data are shown in Fig. 4 with the curves $${\\mathcal{E}}^{(1)}$$ and $${\\mathcal{E}}^{(2)}$$ from Table 1. The noise weights $$\\eta _{y_{k}}$$ used here and corresponding cost function $${\\mathcal{C}}$$ are given in Table 2. Our aim is to demonstrate whether this model can produce the statistical properties of interest, and so adapting the parameters at each iteration is performed in an ad-hoc manner according to the fitting strategy. In this case the fitting algorithm is stopped when the model transition probabilities lie within the error bars of the data and residence distribution is aligned with the single exponential curve $${\\mathcal{E}}^{(1)}$$. Here, no choice of $$\\eta _{y_{k}}$$ allows the distribution to follow $${\\mathcal{E}}^{(2)}$$ as the transition process generated by the model is Markov and the residence times correspond to inter-event intervals for a Poisson process . This is further evidence that this modeling approach cannot produce a heavy tailed residence distribution observed in the data. Due to the evidence of multiscale behavior of the temporal dynamics of microstate sequences [18, 19], we now present two extensions of the model, each of which generates a residence process distribution with a heavy tail.\n\n## Hidden-node network model\n\nThe excitable network model was constructed using a general method that allows us to realize any desired graph as an attracting excitable network in phase space. We can use the same method of construction to extend the network model to a network containing 8 nodes and 20 edges (28 cell network) such that each node in the original four-node network is connected to one additional “hidden node”. Specifically, we use the system of SDEs given by (3)–(4) with $$M=8$$ and $$Q=20$$. We then modify the outputs $$(O)$$ and inputs $$(I)$$ to the p cells from the y cells so that each of the original four nodes has one additional node bidirectionally coupled to it. We introduce noise weights $$y_{\\mathrm{{out}}}$$ and $$y_{\\mathrm{{in}}}$$ on the edges connecting the hidden nodes to the network. They drive transitions out to the hidden nodes and back again, respectively.\n\nFigure 5 shows the four-node network from Fig. 3 with the additional four hidden nodes and example time series output for the nodes and the edges. Again, at almost all points in time, the trajectory is close to one of the equilibrium solutions; when the trajectory is close to a hidden node, we record the output as being at the node neighboring that particular hidden node. The transition probabilities are independent of how long it is spent at the hidden node.\n\nThe constants in f and g are fixed as in Sect. 3, so the whole network is excitable and transitions are driven by noise. We fix the noise value on all nodes $$\\eta _{p}=10^{-4}$$ as before. The free parameters for fitting the model are the twelve noise weights on the edges $$\\eta _{y_{k}}$$ and the two additional noise weights $$y_{\\mathrm{{out}}}$$ and $$y_{\\mathrm{{in}}}$$. To fit the model to the data, we use a similar procedure to that described in Sect. 3.\n\n1. 1.\n\nInitialize: Set $$\\eta ^{i}_{y_{k}} ={\\mathcal{S}}^{0} \\eta ^{0}_{y_{k}}$$ using the values from Table 2 and $$y_{\\mathrm{out}}=y_{\\mathrm{in}}=0.1$$.\n\n2. 2.\n\nModel simulation and analysis: Simulate the hidden-node model and calculate the transition probabilities $$T_{s}(m,j)$$ and residence distribution $$R_{s}(t)$$ as described in Sect. 3.\n\n3. 3.\n\nCost function: Compute the cost function $${\\mathcal{C}}$$ using (5).\n\n4. 4.\n\nUpdate parameters: For this model the shortest residence times are captured by transitions around the original four nodes. Set $${\\mathcal{S}}^{i}$$ to produce shorter residence times, then update $$n_{k}^{i}$$ as described in Sect. 3. The longer times are achieved by visits to the hidden nodes. Set $$\\eta _{y_{\\mathrm{{out}}}}$$ to control how often the hidden nodes are visited, for example, if $$\\eta _{y_{\\mathrm{{out}}}}<\\min (\\eta _{y_{k}})$$, the probability of visiting a hidden node is less than visiting a neighboring node. Set $$\\eta _{y_{\\mathrm{{in}}}}$$ to control how long it is spent at the hidden node; if $$\\eta _{y_{\\mathrm{{in}}}}$$ is large, then the time at the hidden node will be shorter than if $$\\eta _{y_{\\mathrm{{in}}}}$$ is small.\n\n5. 5.\n\nRepeat from 2.\n\nThe results of fitting the hidden-node network model with four hidden nodes to the data are shown in Fig. 6. For illustration we also show the exponential curves $${\\mathcal{E}}^{(n)}$$ for $$n=1,2$$ from Table 1. The noise weights $$\\eta _{y_{k}}$$ used and cost function are given in Table 3. The noise weights $$\\eta _{y_{\\mathrm{{in}}}}$$ and $$\\eta _{y_{\\mathrm{{out}}}}$$ are lower than the noise weights $$\\eta _{y_{k}}$$. This means that the trajectory is more likely to transition to another microstate node than to the hidden node, and when it is at a hidden node it takes longer to transfer to another node, i.e., it gets trapped. This gives longer residence times for each node than the four-node network alone.\n\nThis model allows local control at each state. However, it is not easily expandable to accommodate additional decay rates or external influences, for example, from other systems in the body. We therefore also present a more parsimonious alternative, namely a more generalizable model in which the distribution of residence times is not controlled independently at each node but by an additional controlling layer.\n\n## Multi-layer network model\n\nWe present a second extension to the excitable network model by including a controlling layer that drives the transitions around the original four-node network. To this end, we construct a system of N levels for which we set up a system of SDEs as follows:\n\n\\begin{aligned} &\\tau \\,\\mathrm {d}p_{l,j} = \\bigl[f_{l}(p_{l,j},y_{l,k}) \\bigr] \\,\\mathrm {d}t+\\eta _{p} \\,\\mathrm {d}w , \\end{aligned}\n(6)\n\\begin{aligned} &\\tau \\,\\mathrm {d}y_{l,k} = \\bigl[g_{l}(p_{l,j},y_{l,k})+ z_{l,k} \\bigr] \\,\\mathrm {d}t+\\eta _{{l,k}} \\,\\mathrm {d}w_{k}. \\end{aligned}\n(7)\n\nEach level l has $$M_{l}$$ nodes, and we assume all-to-all connections in each layer, so we have $$Q_{l}\\equiv M_{l}(M_{l}-1)$$ edges. w is independent identically distributed noise processes, η is noise weights. This system includes a general input into the y-cells $$z_{l,k}(t)$$ that linearly couples layers from the $$p_{l}$$ nodes to the $$y_{l+1,k}$$ edges by\n\n$$z_{l+1,k}= \\sum_{j=1}^{M_{l}}\\zeta _{l,j} p_{l,j}^{2}.$$\n\nThe functions f and g and parameters for this hidden-layer model are detailed in and discussed in Appendix B.2.\n\nFor the microstate model, we choose the number of levels $$N=2$$, the number of nodes in layer one $$M_{1}=2$$, in layer two $$M_{2}=4$$, the number of edges in layer one $$Q_{1}=2$$ and in layer two $$Q_{2}=12$$. The constants in functions f and g are set as in Sect. 3 for each layer, so each layer is an excitable network. Note that layer two is identical to the excitable model described in Sect. 3.\n\nLayer one with two nodes is a “controlling layer” in that we only consider the output from layer two with four nodes. As before the output is a transition process and a residence process. The two nodes in layer one affect the dynamics on the edges (and therefore the residence times) in layer two by the scalings $$\\zeta _{1,1}=\\zeta _{1}$$ and $$\\zeta _{1,2}=\\zeta _{2}$$. These scale the residence times in the output from layer two. As before we fix the noise on the nodes $$\\eta _{p}=10^{-4}$$. Figure 7 shows the coupling architecture for the two-layer model with time series of the nodes and edges in each layer. Note that layer two is the same as in Fig. 3(B). For illustrative purposes, in Fig. 7 we choose $$\\zeta _{1}=10^{-1}$$ and $$\\zeta _{2}=10^{-3}$$ here. Panels (B)–(E) clearly show that when $$p_{1,2}=1$$ in layer one the residence times at each node in layer two $$p_{2,j}$$ are longer (transitions between nodes are less frequent) as the edges in layer two $$y_{2,k}$$ are scaled by $$\\zeta _{2}$$. Note that if $$\\zeta _{1}=\\zeta _{2}$$ layer one would be redundant as the residence times would be consistent (drawn from the same distribution) in either node and the residence process would again be exponential.\n\nThe free parameters for fitting the model are the two noise values on the edges in layer one $$\\eta _{1,k}$$ for $$k=1,2$$, the 12 noise values on the edges in layer two $$\\eta _{2,k}$$ for $$k=1,\\dots,12$$, and the two transfer parameters $$\\zeta _{l}$$ for $$l=1,2$$. To fit the multi-layer model, we employ the fitting algorithm as for the other two models.\n\n1. 1.\n\nInitialize: Set $$\\eta ^{i}_{2,k}$$ using the values from Table 2. Set $$\\eta _{1,k}=10^{-2}$$, $$\\zeta _{1}=10^{-1}$$, and $$\\zeta _{2}=10^{-3}$$.\n\n2. 2.\n\nModel simulation and analysis: Simulate the multi-layer model and calculate the transition probabilities $$T_{s}(m,j)$$ and residence distribution $$R_{s}(t)$$, as described in Sect. 3, from the output of layer two only.\n\n3. 3.\n\nCost function: Compute the cost function $${\\mathcal{C}}$$ using (5).\n\n4. 4.\n\nUpdate parameters: Update the parameters according to the following strategy. Update $$\\eta _{2,k}$$ in the same way as for $$n_{k}^{i}$$ in Sect. 3 to fit the transition probabilities. Adjust the transfer parameters $$\\zeta _{j}$$ to change the dynamics on the edges of layer two in a homogeneous way (equivalent to changing $${\\mathcal{S}}$$ in the previous models). If ζ is increased, the residence times decrease and the decay rate of the distribution becomes quicker; if ζ is decreased, the decay rate is decreased. The residence distribution of the output from layer two is a linear combination of the decay rates governed by ζs. The proportion of each distribution (the mixing) is controlled by the noise on the edges in layer one $$\\eta _{1,k}$$. In the two-node case, for example, if $$\\eta _{1,1}< \\eta _{1,2}$$ transitions along $$y_{1,2}$$ will occur more frequently than along $$y_{1,1}$$ and so the trajectory will spend longer in node $$p_{1,1}$$ than $$p_{1,2}$$.\n\n5. 5.\n\nRepeat from 2.\n\nThe results of fitting the multi-layer model with two nodes in layer one to the data are shown in Fig. 8 with the exponential curves $${\\mathcal{E}}^{(1)}$$ and $${\\mathcal{E}}^{(2)}$$ from Table 1. The parameters for the simulations and the value of the cost function $${\\mathcal{C}}$$ are shown in Table 4. The distribution of the simulations agree closely with $${\\mathcal{E}}^{(2)}$$. Note that the magnitude of the noise on the edges of layer two $$\\eta _{2,i}$$ is much smaller than for the excitable network model. This is due to the additive nature of the transition parameters given by (7).\n\nIn the limit $$N \\to \\infty$$ of number of nodes in the controlling layer the distribution would be the sum of infinitely many exponentials, i.e., a power law. However, it is interesting that only two nodes in the controlling layer are sufficient to capture the dynamics. This suggests that the microstate dynamics might be driven by oscillations in other bodily rhythms such as the cardiac or respiratory cycles.\n\n## Comparison of hidden-node and multi-layer network models\n\nSo far, we have shown that the hidden-node model and the two-layer model are extensions of the excitable model that both reproduce the transition probabilities and the residence time distributions found in the data. Yet another crucial feature of microstate residence time is that the long and short residence times are interspersed throughout the time-series. For the hidden-node model, the trajectory getting ‘trapped’ at one hidden node should be independent of getting trapped at another hidden node. For the two-layer model, however, the first layer drives the residence times of the second layer, which can lead to clear blocks of short residence times driven by node $$p_{1,1}$$ with blocks of long residence times driven by node $$p_{1,2}$$; see, for example, Fig. 7, panel (D).\n\nWe now examine the role of the noise weights on the residence times produced by each version of the model. We consider two sets of noise values: exemplar noise values used in Figs. 5 and 7 and the noise values used to fit the models to the data, used in Figs. 6 and 8. The exemplar noise weights on all edges for the hidden-node model are $$\\eta _{y_{k}}=5\\times 10^{-2}$$. For the two-layer model, the edge weights are $$\\eta _{l,k}=10^{-2}$$ for $$l=1,2$$ and all k, with transfer parameters $$\\zeta _{1} = 10^{-1}$$ and $$\\zeta _{2} =10^{-3}$$. The noise weights used for the models fitted to the data are shown in Table 3 for the hidden-node model and in Table 4 for the two-layer model.\n\nWe assess the generated sequences from the hidden-node and two-layer models by computing the autocorrelation of the signal and the Hurst exponent . Autocorrelation identifies any correlation between the signal and a lagged copy of itself. We compute the autocorrelation by computing the Pearson correlation coefficient between 400 consecutive epochs $$\\rho (k)$$ and $$\\rho (k+i)$$, $$k=1,\\dots,400$$ for 100 lag times $$i=1,\\dots,100$$. The Hurst exponent H is a measure of the extent of the LRTC in a time series. For white noise $$H=0.5$$, whereas $$0.5< H<1$$ is indicative of LRTC. We compute H using wavelet fractal analysis with the code written for . For the data, we use all 24 EEG microstate sequences to compute the Hurst exponent. For each model and set of parameters, we use ten simulations to compute the Hurst exponent.\n\nFigure 9 shows the residence times, autocorrelation, and Hurst exponent from the data, the two-layer, and hidden-node network model simulations. In each panel two sequences are shown, for the data these are the durations from two subjects, for the models these are two simulations. The Hurst exponent is shown as a violin plot with the mean value (over all 24 subjects, or over 10 model simulations) marked. The durations from the data show short residence times interspersed with some very long residence times, and the autocorrelation is noisy around zero. The mean Hurst exponent for the data is $$H= 0.6374$$ as reported in indicating scale-free behavior with LRTC. The hidden-node model with exemplar noise weights has some very large residence times, note that the y-axis scale is from 0 to 800 and a mean Hurst exponent of $$H=0.8444$$. However, when the hidden-node model is fitted to the data, the longest residence times are in line with the data, the autocorrelation is noisy around zero, and $$H=0.6485$$. The two-layer model residence times with exemplar noise weights show clear blocks alternating between longer residence times and shorter residence times. This is reflected in the oscillatory structure of the autocorrelation and $$H=0.7730$$. Importantly, fitting the two-layer model to the data abolishes this clustering and renders the long and short residence times interspersed with a corresponding autocorrelation that is again noisy around zero and $$H=0.6259$$ closer to the value for the data. Finally, we note that the Hurst exponent for sequences generated by the excitable four-node network model (not shown in Fig. 9) is $$H\\approx 0.5$$ indicating no LRTC.\n\n## Discussion\n\nIn this article we demonstrate novel mathematical models for EEG microstate sequences constructed using excitable networks that overcome the main caveats of previous modeling approaches that consider microstate sequences as memoryless Markov processes. Resting state brain activity has been shown to visit four canonical EEG microstates with variable durations. The residence times can be considered a residence process that contains interspersed long and short times. Microstate-sequences are mono-fractal and have long range temporal correlations (LRTC) that span two orders of magnitude ; the EEG microstate sequences can be thought of as having “memory”. This means that models with memoryless Markov switching between states at times given by a Poisson process will not capture the full temporal dynamics of microstate sequences; more sophisticated modeling approaches are required. Here we demonstrate that excitable network models can capture the crucial features of microstate sequences: the local transition probabilities; the distribution of residence times; the interspersion of long and short residence times; and the LRTC.\n\nWe investigate the distribution of residence times of resting state EEG microstate sequences from healthy subjects and show that the distribution has a heavy tail. We show that although the residence time distribution can be fit by a power law, it can also be captured by a sum of exponentials, where each exponential adds a characteristic decay rate to the distribution. We show that a sum of two exponentials is sufficient to capture the heavy tail of the distribution, indicating the data has two characteristic decay rates. We show that the microstate sequences from the data have interspersed long and short residence times giving an autocorrelation of the signal around zero. Finally, we compute the Hurst exponent, a measure of LRTC in time series in line with .\n\nWe aim to design models that capture the local transitions and residence time distributions observed in the data. To this end, we split each microstate sequence into a local state transition process that gives the probabilities of switching between states and a residence process that produces the timings of microstate transitions. Using the construction outlined in , we build systems of stochastic differential equations that each have a noisy network attractor. Specifically, we construct a series of excitable network models and compare these to the data. The simplest, discussed in Sect. 3, simply has four (stable) nodes that represent the four classic microstates. The nodes are all-to-all connected because transitions between any two microstates are possible. Dynamics around the network are driven by noise on the edges, where the level of noise on a given edge governs the probability of transition along that edge. We fit the model to the data by changing the noise on the edges of the network. In this way the model captures the local transition process between microstates. However, this construction produces statistics that are well modeled by a Markov transition process and switching times that are Poisson. In this case the residence time distribution is a single exponential with fast decay rate and no heavy tail. Correspondingly, the Hurst exponent for the simulated sequences is $$H\\approx 0.5$$ indicating no LRTC.\n\nIn order to capture the heavy tail of the residence time distribution that appears crucial for the LRTC of the microstate sequences, we extend the single-layer excitable network model using the two following approaches.\n\nFirst, in Sect. 4, we add one hidden node onto each of the original four nodes, that acts as a ‘trap’ for the trajectories. This creates long residence times at each node. We add two additional noise parameters, one out to the hidden node and one back from it, in order to control the durations of these longer residence times. The local transitions between the original four nodes are unaffected by the hidden nodes and the transition probabilities remain unchanged. With this extension, this model produces residence time distributions with heavy tails, and the simulated microstate sequences show long and short residence times that are interspersed giving an autocorrelation around zero. Moreover, we show that when the model is fitted to the data, simulated sequences have a mean Hurst exponent in line with the data indicating LRTC.\n\nThe second extension, in Sect. 5, is the addition of a controlling layer that acts on the edges in the original four-node network, making transitions slower or faster, leading to longer or shorter residence times respectively. The residence time distribution from the data is captured by the sum of two exponentials, therefore two decay rates. Accordingly, we use two nodes in the controlling layer with two corresponding transfer parameters: one that captures the short times and one that captures the long times. The noise on the edges in the controlling layer controls the level of mixing between long and short times in the distribution. When the model is simulated using exemplar noise values and transfer parameters, as shown in Fig. 8, the microstate sequences show clusters of short residence times followed by clusters of long residence times, giving a sinusoidal autocorrelation. The Hurst exponent value of these sequences is higher than the data indicating a smoother trend. When the noise values and transfer parameters of the model are set to produce the correct distribution of residence times, the long and short residence times are interspersed and the autocorrelation decays to noise around zero. Similarly, the Hurst exponent for the fitted sequences is in line with the data. The clustering of long and short times disappears here because the switching between nodes in the controlling layer is faster than the switching between nodes in the original layer when modulated by the slow transfer parameter. Therefore, no transitions occur in the original layer, it remains at one node under the influence of the slow transfer parameter, until the controlling layer switches and the dynamics on the edges in the original layer are modulated by the fast transfer parameter.\n\nThe purpose of this paper is to demonstrate that excitable network models can generate sequences that exhibit the features of microstate sequences. The ad-hoc fitting procedure used here demonstrates that these models capture the temporal properties of the switching dynamics more thoroughly than existing statistical models. For further fitting and application of these models to data, a suitable parameter fitting algorithm and systematic parameter space exploration should be employed.\n\nThroughout this paper we use four nodes for the four canonical microstates from and consistently reproduced in the literature . Additional nodes could be added to either of these network constructions to extend the model for larger numbers of microstates, for example, seven or fifteen . The hidden-node network model has $$d\\times N$$ nodes where d is the number of decay rates required and N is the number of states, whereas the multi-layer model has $$d+N$$ nodes. Therefore, for larger systems, the multi-layer mode provides a more parsimonious and generalizable modeling approach.\n\nIn line with current microstate literature [43, 46] we consider the group level statistics rather than for each individual. We note that while the mean Hurst exponents from the two-layer and hidden-node models align with the data, the spread of the distribution of the Hurst exponent does not. In particular when the models are fitted to the data, the distributions are narrow around the mean; see Fig. 9. The spread of the distribution for the Hurst exponents from the data is likely due to inter-individual variability. We do not fit the models to each individual and do not capture this variability. We leave it to future research to developing the models to explore inter- and intra-individual differences.\n\nThese new models support classic microstate analysis and provide insight into the spatial temporal structure of EEG microstate sequences and therefore into the switching dynamics of the underlying neural neural networks. From a neuroscientific perspective, a centrally controlled switching of microstates as in the two-layer model is more parsimonious than a decentralized control of switching as in the hidden-node model. In the former, the switching between the nodes is modulated in the same way for the whole network at once, and in the latter, the switching between nodes happens more independently from one to another. Note that both models capture the data from healthy subjects similarly well. One could consider this difference in locus of switching control as a difference between health and pathology.\n\nInterestingly, neurological and psychiatric conditions rarely affect all microstates similarly, but they generally selectively target only one or two microstates [8, 1013, 46]. A way to consider the physiological plausibility of the hidden-node model is that altering the connection between a single node-hidden node pair represents a change at the individual microstate level. We plot the individual distributions for each microstate and model with the data in Appendix C. We note that the distributions of the residence times for each microstate produced by the hidden-node and two-layer models give a good fit to the data, as measured by the error values given in Table 5. For the hidden-node model, the noise values governing frequency of visits to the hidden nodes ($$y_{\\mathrm{out}}$$) and duration spent there ($$y_{\\mathrm{in}}$$) are the same for all nodes. Changing the $$y_{\\mathrm{in}}$$ and $$y_{\\mathrm{out}}$$ values allows adaptation of the hidden-node model to describe differences between healthy and pathological groups.\n\nThe modeling techniques described in this paper are widely applicable to other physiological and synthetic signals. For example, in task situations, the microstate immediately before a stimulus has been shown to predict stochastically occurring variations in the perceptual fate of upcoming stimuli; this pertains to hemispheric lateralization of word processing, perceptual switching of multi-stable stimuli, and perceptual awareness at the sensory threshold . The models presented here, in particular the two-layer model, could be extended and used to investigate the relationship between brain activity and perception.\n\nA way to consider the physiological plausibility of the two-layer model would be to relate EEG microstates to other bodily rhythms such as the cardiac or respiratory cycle. The cardiac cycle can be subdivided into the systole (contraction of the heart muscles) and diastole (relaxation of the heart muscles). The systole is shorter and less variable than the diastole, and they could be likened to the two nodes in the controlling layer of the two-layer model. Similarly, brain activity (local field potential (LFP) activity in limbic networks implied in memory formation) is tightly coupled to the respiratory cycle both in rodents and humans . Hence, simultaneous recordings of EEG, electrocardiogram (ECG), and respiration could provide an interesting way of testing the physiological plausibility of the two-layer model by relating the different layers to different physiological processes.\n\nFuture research could pit the performance of the different models against each other by applying them to data from patients with pathologies of different aetiologies: while the hidden-node model should better capture the changes due to psychiatric diseases that affect only one or two microstates, the two-layer model should capture potential differences in microstate sequences in patients with pathologies affecting, for example, their cardiac rhythm.\n\n## Availability of data and materials\n\nThe data used in this paper are published in and are available from JB on reasonable request.\n\n1. 1.\n\nhttp://brainmapping.unige.ch/Cartool.htm\n\n## Abbreviations\n\nEEG:\n\nElectroencephalogram\n\nMRI:\n\nMagnetic resonance imaging\n\nfMRI:\n\nFunctional magnetic resonance imaging\n\nRSNs:\n\nResting-state networks\n\nLRTC:\n\nLong-range temporal correlations\n\nBOLD:\n\nBlood-oxygen-level-dependent\n\nDFA:\n\nDetrended fluctuation analysis\n\nSDEs:\n\nStochastic differential equations\n\nGFP:\n\nGlobal field power\n\nAAHC:\n\nAtomize-agglomerate hierarchical clustering\n\nLFP:\n\nLocal field potential\n\nECG:\n\nElectrocardiogram\n\n## References\n\n1. 1.\n\nDamoiseaux JS, Rombouts S, Barkhof F, Scheltens P, Stam CJ, Smith SM et al.. 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NeuroImage. 2016;141:442–51.\n\n24. 24.\n\nAshwin P, Postlethwaite C. Designing heteroclinic and excitable networks in phase space using two populations of coupled cells. J Nonlinear Sci. 2016;26(2):345–64.\n\n25. 25.\n\nAshwin P, Karabacak Ö, Nowotny T. Criteria for robustness of heteroclinic cycles in neural microcircuits. J Math Neurosci. 2011;1(1):13.\n\n26. 26.\n\nChossat P, Krupa M. Heteroclinic cycles in Hopfield networks. J Nonlinear Sci. 2016;26(2):315–44.\n\n27. 27.\n\nGonzález-Díaz LA, Gutiérrez ED, Varona P, Cabrera JL. Winnerless competition in coupled Lotka–Volterra maps. Phys Rev E. 2013;88(1):012709.\n\n28. 28.\n\nAguiar MA. Is there switching for replicator dynamics and bimatrix games? Phys D, Nonlinear Phenom. 2011;240(18):1475–88.\n\n29. 29.\n\nHutt A, Graben P. Sequences by metastable attractors: interweaving dynamical systems and experimental data. Frontiers Appl Math Stat. 2017;3:11.\n\n30. 30.\n\nFriedrich RW, Laurent G. Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science. 2001;291(5505):889–94.\n\n31. 31.\n\nBick C, Rabinovich MI. Dynamical origin of the effective storage capacity in the brain’s working memory. Phys Rev Lett. 2009;103(21):218101.\n\n32. 32.\n\nAfraimovich VS, Zaks MA, Rabinovich MI. Mind-to-mind heteroclinic coordination: model of sequential episodic memory initiation. Chaos, Interdiscip J Nonlinear Sci. 2018;28(5):053107.\n\n33. 33.\n\nRabinovich MI, Huerta R, Varona P, Afraimovich VS. Transient cognitive dynamics, metastability, and decision making. PLoS Comput Biol. 2008;4(5):e1000072.\n\n34. 34.\n\nArmbruster D, Stone E, Kirk V. Noisy heteroclinic networks. Chaos, Interdiscip J Nonlinear Sci. 2003;13(1):71–9.\n\n35. 35.\n\nAshwin P, Sensitive PC. Finite-state computations using a distributed network with a noisy network attractor. IEEE Trans Neural Netw Learn Syst. 2018;29(12):5847–58.\n\n36. 36.\n\nEgbert MD, Jeong V, Where PCM. Computation and Dynamics Meet: heteroclinic Network-Based Controllers in Evolutionary Robotics. IEEE Trans Neural Netw Learn Syst. 2019.\n\n37. 37.\n\nHurst HE. Methods of using long-term storage in reservoirs. In: Proceedings of the institution of civil engineers. vol. 5. 1956. p. 519–43.\n\n38. 38.\n\nTibshirani R, Cluster WG. Validation by prediction strength. J Comput Graph Stat. 2005;14(3):511–28.\n\n39. 39.\n\nPascual-Marqui RD, Michel CM, Lehmann D. Segmentation of brain electrical activity into microstates: model estimation and validation. IEEE Trans Biomed Eng. 1995;42(7):658–65.\n\n40. 40.\n\nAnderson KB, Conder JA. Discussion of multicyclic Hubbert modeling as a method for forecasting future petroleum production. Energy Fuels. 2011;25(4):1578–84.\n\n41. 41.\n\nHe BJ, Zempel JM, Snyder AZ, Raichle ME. The temporal structures and functional significance of scale-free brain activity. Neuron. 2010;66(3):353–69.\n\n42. 42.\n\nAshwin P, Postlethwaite C. On designing heteroclinic networks from graphs. Phys D, Nonlinear Phenom. 2013;265:26–39.\n\n43. 43.\n\nMichel CM, Koenig T. EEG microstates as a tool for studying the temporal dynamics of whole-brain neuronal networks: a review. NeuroImage. 2018;180:577–93.\n\n44. 44.\n\nCusto A, Van De Ville D, Wells WM, Tomescu MI, Brunet D, Michel CM. Electroencephalographic resting-state networks: source localization of microstates. Brain Connect. 2017;7(10):671–82.\n\n45. 45.\n\nSeitzman BA, Abell M, Bartley SC, Erickson MA, Bolbecker AR, Hetrick WP. Cognitive manipulation of brain electric microstates. NeuroImage. 2017;146:533–43.\n\n46. 46.\n\nKhanna A, Pascual-Leone A, Michel CM, Farzan F. Microstates in resting-state EEG: current status and future directions. Neurosci Biobehav Rev. 2015;49:105–13.\n\n47. 47.\n\nMohr C, Michel CM, Lantz G, Ortigue S, Viaud-Delmon I, Landis T. Brain state-dependent functional hemispheric specialization in men but not in women. Cereb Cortex. 2005;15(9):1451–8.\n\n48. 48.\n\nBritz J, Landis T, Michel CM. Right parietal brain activity precedes perceptual alternation of bistable stimuli. Cereb Cortex. 2009;19(1):55–65.\n\n49. 49.\n\nBritz J, Michel CM. State-dependent visual processing. Front Psychol. 2011;2:370.\n\n50. 50.\n\nBritz J, Pitts MA, Michel CM. Right parietal brain activity precedes perceptual alternation during binocular rivalry. Hum Brain Mapp. 2011;32(9):1432–42.\n\n51. 51.\n\nBritz J, Díaz Hernàndez L, Ro T, Michel CM. EEG-microstate dependent emergence of perceptual awareness. Front Behav Neurosci. 2014;8:163.\n\n52. 52.\n\nTort ABL, Brankačk J, Draguhn A. Respiration-entrained brain rhythms are global but often overlooked. Trends Neurosci. 2018;41(4):186–97.\n\n53. 53.\n\nCorcoran AW, Pezzulo G, Hohwy J. Commentary respiration-entrained brain rhythms are global but often overlooked. Front Syst Neurosci. 2018;12:25.\n\n54. 54.\n\nVarga S, Heck DH. Rhythms of the body, rhythms of the brain: respiration, neural oscillations, and embodied cognition. Conscious Cogn. 2017;56:77–90.\n\n## Acknowledgements\n\nJC would like to thank Mauro Copelli for informative discussions about criticality and power law scaling in the data. The software package CartoolFootnote 1 was developed by Denis Brunet from the Functional Brain Mapping Laboratory, Geneva, Switzerland.\n\n## Funding\n\nJC and PA gratefully acknowledge the financial support of the EPSRC Centre for Predictive Modeling in Healthcare, via grant EP/N014391/1. JC acknowledges funding from MRC Skills Development Fellowship MR/S019499/1. CMP and PA acknowledge funding from the Marsden Fund, Royal Society of New Zealand.\n\n## Author information\n\nAuthors\n\n### Contributions\n\nPA, CMP, JB, JC conceived and designed study. JB provided the experimental data. JC, PA, CMP, JB analyzed the data. PA, CMP, and JC developed the models and performed computations. JC fit the models to the data. JC wrote the paper with input from PA, CMP, JB. All authors read and commented on the final version of manuscript.\n\n### Corresponding author\n\nCorrespondence to Jennifer Creaser.\n\n## Ethics declarations\n\n### Ethics approval and consent to participate\n\nThe data used in this paper are published in . Nine healthy right-handed individuals participated for monetary compensation after giving informed consent approved by the University Hospital of Geneva Ethics Committee.\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\nNot applicable.\n\n## Appendices\n\n### Appendix A: Illustration of microstate back-fitting procedure\n\nMicrostate analysis comprises two steps: identifying the microstate template maps (cluster analysis) and determining the microstate parameters underlying their strength and timing (back-fitting). The latter comprises a time-point wise spatial correlation between the template maps identified in the cluster analysis and the continuous data, and labels are assigned in a winner-takes-all fashion, i.e., the template that correlates highest with the data is assigned at that time point. At the local troughs of GFP, where the field strength is minimal and the global dissimilarity is high, none of the template maps correlate well with the data, and the allocation of the best template can be considered random. Without applying a temporal constraint criterion, these brief periods will be accounted as very short separate microstates, and microstates could never be longer as the period between the local GFP troughs. In other words, a temporal constraint criterion is necessary in order to ‘jump across’ the GFP troughs and ignore the polarity. Without this temporal constraint, one would obtain a peak around 2–3 sampling periods corresponding to the local GFP troughs and corresponding to 16–24 ms (at a sampling rate of 125 Hz) in our case.\n\nFigure 10 shows and example series of maps from consecutive times points of the EEG. The maps corresponding to troughs in GFP are marked. The first 24 time point maps were assigned to microstate map 2 (orange) and the remaining time point maps to microstate 3 (yellow). The temporal constraint ensures that the toughs within each period are not assigned to different microstates. It is important to note that microstates are characterized by topography alone, i.e., the polarity of the topography is irrelevant for characterizing a microstate, and a given microstate can undergo several polarity changes, which occur at the local troughs of GFP. Note that each microstate period undergoes several polarity changes.\n\n### Appendix B: Network models with heteroclinic/excitable networks\n\nWe briefly specify the dynamical models used to flexibly construct heteroclinic or excitable networks with arbitrary transition probabilities and waiting times. The models, and why they robustly have attracting networks of connections between equilibria in phase space, are detailed in .\n\n### B.1 Single-layer network model\n\nWe use the following functions to define the network dynamic model presented in (3, 4), and for the generalization to include additional hidden nodes:\n\n\\begin{aligned} &f(p_{j},y_{k}) = p_{j} \\bigl(F \\bigl(1- p^{2} \\bigr)+ D \\bigl(p_{j}^{2}p^{2}-p^{4} \\bigr) \\bigr)+ E \\bigl(-Z^{(O)}_{j}(p,y)+Z^{(I)}_{j}(p,y) \\bigr), \\end{aligned}\n(8)\n\\begin{aligned} &g(p_{j},y_{k}) = -y_{k} \\bigl( \\bigl(y_{k}^{2}-1\\bigr)^{2}+ A-B p_{\\alpha (k)}^{2} +C \\bigl(y^{2}-y_{k}^{2} \\bigr) \\bigr), \\end{aligned}\n(9)\n\nwhere $$j=1,\\ldots,M$$, $$k=1,\\ldots,Q$$ and\n\n$$p^{2}=\\sum_{j=1}^{M} p_{j}^{2},\\qquad p^{4}=\\sum _{j=1}^{M} p_{j}^{4},\\qquad y^{2}=\\sum_{j=1}^{Q} y_{j}^{2}.$$\n\nThe outputs $$(O)$$ and inputs $$(I)$$ to the p cells from the y cells are determined by\n\n\\begin{aligned} &Z^{(O)}_{j}(p,y) = \\sum_{\\{k: \\alpha (k)=j\\}} y_{k}^{2}p_{\\omega (k)}p_{j}, \\end{aligned}\n(10)\n\\begin{aligned} &Z^{(I)}_{j}(p,y) = \\sum_{\\{k': \\omega (k')=j\\}} y_{k'}^{2}p_{ \\alpha (k')}^{2}. \\end{aligned}\n(11)\n\nTo ensure the network is in the excitable regime, we fix the constants in functions f and g throughout as follows:\n\n$$A=0.5,\\qquad B=1.49,\\qquad C=2,\\qquad D=10, \\qquad E=4, \\qquad F=2$$\n\nalthough the behavior is robust to small enough changes to these parameters. See for more details and justification of how the model exhibits an excitable network where trajectories explore a set of N nodes along M possible directed edges.\n\n### B.2 Multi-layer network model\n\nThe functions f and g in the multi-layer model (6, 7) are defined by\n\n\\begin{aligned} &f_{l}(p_{l,j},y_{l,k}) = p_{l,j} \\bigl(F\\bigl(1- p_{l}^{2}\\bigr)+ D\\bigl(p_{l,j}^{2}p_{l}^{2}-p_{l}^{4} \\bigr) \\bigr) + E \\bigl(-Z^{(O)}_{l,j}(p,y)+Z^{(I)}_{l,j}(p,y) \\bigr), \\end{aligned}\n(12)\n\\begin{aligned} &g_{l}(p_{l,j},y_{l,k}) = -y_{l,k} \\bigl(\\bigl(y_{l,k}^{2}-1\\bigr)^{2}+A - B p_{l, \\alpha (k)}^{2} +C\\bigl(y_{l}^{2}-y_{l,k}^{2} \\bigr) \\bigr) \\end{aligned}\n(13)\n\nfor $$j=1,\\dots,M_{l}$$ and $$k=1,\\dots,Q_{l}$$. The outputs $$(O)$$ and inputs $$(I)$$ to the p cells from the y cells are as follows:\n\n\\begin{aligned} &Z^{(O)}_{l,j}(p,y) = \\sum_{\\{k: \\alpha (k)=j\\}} y_{l,k}^{2}p_{l, \\omega (k)}p_{l,j}, \\end{aligned}\n(14)\n\\begin{aligned} &Z^{(I)}_{l,j}(p,y) = \\sum_{\\{k': \\omega (k')=j\\}} y_{l,k'}^{2}p_{l, \\alpha (k')}^{2}, \\end{aligned}\n(15)\n\nand\n\n$$p_{l}^{2}=\\sum_{j=1}^{M_{l}} p_{l,j}^{2},\\qquad p_{l}^{4}=\\sum _{j=1}^{M_{l}} p_{l,j}^{4},\\qquad y_{l}^{2}=\\sum_{k=1}^{Q_{l}} y_{l,k}^{2}.$$\n\nThe default parameters AF are as in Appendix B.1.\n\n### Appendix C: Individual microstate distributions\n\nThe individual microstate distributions for each model are shown in Fig. 11. The error χ is the least squares difference between the log of the values of each curve and the log of the data and the measure of fit, given in Table 5. In line with the main results, the one layer model does not capture the distributions of the individual microstates and the errors χ are large. The distributions of the two-layer and hidden-node models have a smaller error $$\\chi <20$$ for all microstates. The agreement shown here further demonstrates the potential for this model to capture properties of interest in microstate analysis.",
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"https://mathematical-neuroscience.springeropen.com/track/article/10.1186/s13408-020-00100-0",
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https://plantpot.works/8182 | [
"# How to Use the Ruby downto Method\n\n09/24/2021\n\nContents\n\nIn this article, you will learn how to use the Ruby downto method.\n\n## Using the downto Method\n\nThe downto method is a built-in method in the Ruby programming language. It is used to iterate downwards from a given number to a specified limit, performing a block of code at each step.\n\n### Syntax\n\nThe syntax for using the downto method is as follows:\n\n``````start.downto(stop) do |variable|\n# Code to be executed\nend\n``````\n\n### Parameters\n\n• `start`: The starting number.\n• `stop`: The stopping number.\n• `variable`: The variable used to represent the current iteration value.\n\n### Examples\n\n#### Printing numbers from 10 to 1\n\n``````10.downto(1) do |i|\nputs i\nend\n``````\n\nOutput:\n\n``````10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n``````\n\nIn the above example, we start at 10 and iterate downwards until we reach 1. At each step, we print the current value of the iterator variable i.\n\n#### Summing up numbers from 1 to 10\n\n``````sum = 0\n10.downto(1) do |i|\nsum += i\nend\nputs sum\n``````\n\nOutput:\n\n``55``\n\nIn the above example, we start at 10 and iterate downwards until we reach 1. At each step, we add the current value of the iterator variable i to the variable sum. After the loop has completed, we print the value of sum.\n\n#### Using a range object with downto\n\n``````(1..10).downto(1) do |i|\nputs i\nend\n``````\n\nOutput:\n\n``````10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n``````\n\nIn the above example, we use a range object (1..10) as the starting value for the downto method. This allows us to iterate over the range of values from 1 to 10 in a descending order."
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https://postgrespro.com/docs/enterprise/10/rowtypes | [
"## 8.16. Composite Types\n\nA composite type represents the structure of a row or record; it is essentially just a list of field names and their data types. Postgres Pro allows composite types to be used in many of the same ways that simple types can be used. For example, a column of a table can be declared to be of a composite type.\n\n### 8.16.1. Declaration of Composite Types\n\nHere are two simple examples of defining composite types:\n\n```CREATE TYPE complex AS (\nr double precision,\ni double precision\n);\n\nCREATE TYPE inventory_item AS (\nname text,\nsupplier_id integer,\nprice numeric\n);\n```\n\nThe syntax is comparable to `CREATE TABLE`, except that only field names and types can be specified; no constraints (such as `NOT NULL`) can presently be included. Note that the `AS` keyword is essential; without it, the system will think a different kind of `CREATE TYPE` command is meant, and you will get odd syntax errors.\n\nHaving defined the types, we can use them to create tables:\n\n```CREATE TABLE on_hand (\nitem inventory_item,\ncount integer\n);\n\nINSERT INTO on_hand VALUES (ROW('fuzzy dice', 42, 1.99), 1000);\n```\n\nor functions:\n\n```CREATE FUNCTION price_extension(inventory_item, integer) RETURNS numeric\nAS 'SELECT \\$1.price * \\$2' LANGUAGE SQL;\n\nSELECT price_extension(item, 10) FROM on_hand;\n```\n\nWhenever you create a table, a composite type is also automatically created, with the same name as the table, to represent the table's row type. For example, had we said:\n\n```CREATE TABLE inventory_item (\nname text,\nsupplier_id integer REFERENCES suppliers,\nprice numeric CHECK (price > 0)\n);\n```\n\nthen the same `inventory_item` composite type shown above would come into being as a byproduct, and could be used just as above. Note however an important restriction of the current implementation: since no constraints are associated with a composite type, the constraints shown in the table definition do not apply to values of the composite type outside the table. (A partial workaround is to use domain types as members of composite types.)\n\n### 8.16.2. Constructing Composite Values\n\nTo write a composite value as a literal constant, enclose the field values within parentheses and separate them by commas. You can put double quotes around any field value, and must do so if it contains commas or parentheses. (More details appear below.) Thus, the general format of a composite constant is the following:\n\n```'( `val1` , `val2` , ... )'\n```\n\nAn example is:\n\n```'(\"fuzzy dice\",42,1.99)'\n```\n\nwhich would be a valid value of the `inventory_item` type defined above. To make a field be NULL, write no characters at all in its position in the list. For example, this constant specifies a NULL third field:\n\n```'(\"fuzzy dice\",42,)'\n```\n\nIf you want an empty string rather than NULL, write double quotes:\n\n```'(\"\",42,)'\n```\n\nHere the first field is a non-NULL empty string, the third is NULL.\n\n(These constants are actually only a special case of the generic type constants discussed in Section 4.1.2.7. The constant is initially treated as a string and passed to the composite-type input conversion routine. An explicit type specification might be necessary to tell which type to convert the constant to.)\n\nThe `ROW` expression syntax can also be used to construct composite values. In most cases this is considerably simpler to use than the string-literal syntax since you don't have to worry about multiple layers of quoting. We already used this method above:\n\n```ROW('fuzzy dice', 42, 1.99)\nROW('', 42, NULL)\n```\n\nThe ROW keyword is actually optional as long as you have more than one field in the expression, so these can be simplified to:\n\n```('fuzzy dice', 42, 1.99)\n('', 42, NULL)\n```\n\nThe `ROW` expression syntax is discussed in more detail in Section 4.2.13.\n\n### 8.16.3. Accessing Composite Types\n\nTo access a field of a composite column, one writes a dot and the field name, much like selecting a field from a table name. In fact, it's so much like selecting from a table name that you often have to use parentheses to keep from confusing the parser. For example, you might try to select some subfields from our `on_hand` example table with something like:\n\n```SELECT item.name FROM on_hand WHERE item.price > 9.99;\n```\n\nThis will not work since the name `item` is taken to be a table name, not a column name of `on_hand`, per SQL syntax rules. You must write it like this:\n\n```SELECT (item).name FROM on_hand WHERE (item).price > 9.99;\n```\n\nor if you need to use the table name as well (for instance in a multitable query), like this:\n\n```SELECT (on_hand.item).name FROM on_hand WHERE (on_hand.item).price > 9.99;\n```\n\nNow the parenthesized object is correctly interpreted as a reference to the `item` column, and then the subfield can be selected from it.\n\nSimilar syntactic issues apply whenever you select a field from a composite value. For instance, to select just one field from the result of a function that returns a composite value, you'd need to write something like:\n\n```SELECT (my_func(...)).field FROM ...\n```\n\nWithout the extra parentheses, this will generate a syntax error.\n\nThe special field name `*` means all fields, as further explained in Section 8.16.5.\n\n### 8.16.4. Modifying Composite Types\n\nHere are some examples of the proper syntax for inserting and updating composite columns. First, inserting or updating a whole column:\n\n```INSERT INTO mytab (complex_col) VALUES((1.1,2.2));\n\nUPDATE mytab SET complex_col = ROW(1.1,2.2) WHERE ...;\n```\n\nThe first example omits `ROW`, the second uses it; we could have done it either way.\n\nWe can update an individual subfield of a composite column:\n\n```UPDATE mytab SET complex_col.r = (complex_col).r + 1 WHERE ...;\n```\n\nNotice here that we don't need to (and indeed cannot) put parentheses around the column name appearing just after `SET`, but we do need parentheses when referencing the same column in the expression to the right of the equal sign.\n\nAnd we can specify subfields as targets for `INSERT`, too:\n\n```INSERT INTO mytab (complex_col.r, complex_col.i) VALUES(1.1, 2.2);\n```\n\nHad we not supplied values for all the subfields of the column, the remaining subfields would have been filled with null values.\n\n### 8.16.5. Using Composite Types in Queries\n\nThere are various special syntax rules and behaviors associated with composite types in queries. These rules provide useful shortcuts, but can be confusing if you don't know the logic behind them.\n\nIn Postgres Pro, a reference to a table name (or alias) in a query is effectively a reference to the composite value of the table's current row. For example, if we had a table `inventory_item` as shown above, we could write:\n\n```SELECT c FROM inventory_item c;\n```\n\nThis query produces a single composite-valued column, so we might get output like:\n\n``` c\n------------------------\n(\"fuzzy dice\",42,1.99)\n(1 row)\n```\n\nNote however that simple names are matched to column names before table names, so this example works only because there is no column named `c` in the query's tables.\n\nThe ordinary qualified-column-name syntax `table_name``.``column_name` can be understood as applying field selection to the composite value of the table's current row. (For efficiency reasons, it's not actually implemented that way.)\n\nWhen we write\n\n```SELECT c.* FROM inventory_item c;\n```\n\nthen, according to the SQL standard, we should get the contents of the table expanded into separate columns:\n\n``` name | supplier_id | price\n------------+-------------+-------\nfuzzy dice | 42 | 1.99\n(1 row)\n```\n\nas if the query were\n\n```SELECT c.name, c.supplier_id, c.price FROM inventory_item c;\n```\n\nPostgres Pro will apply this expansion behavior to any composite-valued expression, although as shown above, you need to write parentheses around the value that `.*` is applied to whenever it's not a simple table name. For example, if `myfunc()` is a function returning a composite type with columns `a`, `b`, and `c`, then these two queries have the same result:\n\n```SELECT (myfunc(x)).* FROM some_table;\nSELECT (myfunc(x)).a, (myfunc(x)).b, (myfunc(x)).c FROM some_table;\n```\n\n### Tip\n\nPostgres Pro handles column expansion by actually transforming the first form into the second. So, in this example, `myfunc()` would get invoked three times per row with either syntax. If it's an expensive function you may wish to avoid that, which you can do with a query like:\n\n```SELECT (m).* FROM (SELECT myfunc(x) AS m FROM some_table OFFSET 0) ss;\n```\n\nThe `OFFSET 0` clause keeps the optimizer from flattening the sub-select to arrive at the form with multiple calls of `myfunc()`.\n\nThe `composite_value``.*` syntax results in column expansion of this kind when it appears at the top level of a `SELECT` output list, a `RETURNING` list in `INSERT`/`UPDATE`/`DELETE`, a `VALUES` clause, or a row constructor. In all other contexts (including when nested inside one of those constructs), attaching `.*` to a composite value does not change the value, since it means all columns and so the same composite value is produced again. For example, if `somefunc()` accepts a composite-valued argument, these queries are the same:\n\n```SELECT somefunc(c.*) FROM inventory_item c;\nSELECT somefunc(c) FROM inventory_item c;\n```\n\nIn both cases, the current row of `inventory_item` is passed to the function as a single composite-valued argument. Even though `.*` does nothing in such cases, using it is good style, since it makes clear that a composite value is intended. In particular, the parser will consider `c` in `c.*` to refer to a table name or alias, not to a column name, so that there is no ambiguity; whereas without `.*`, it is not clear whether `c` means a table name or a column name, and in fact the column-name interpretation will be preferred if there is a column named `c`.\n\nAnother example demonstrating these concepts is that all these queries mean the same thing:\n\n```SELECT * FROM inventory_item c ORDER BY c;\nSELECT * FROM inventory_item c ORDER BY c.*;\nSELECT * FROM inventory_item c ORDER BY ROW(c.*);\n```\n\nAll of these `ORDER BY` clauses specify the row's composite value, resulting in sorting the rows according to the rules described in Section 9.23.6. However, if `inventory_item` contained a column named `c`, the first case would be different from the others, as it would mean to sort by that column only. Given the column names previously shown, these queries are also equivalent to those above:\n\n```SELECT * FROM inventory_item c ORDER BY ROW(c.name, c.supplier_id, c.price);\nSELECT * FROM inventory_item c ORDER BY (c.name, c.supplier_id, c.price);\n```\n\n(The last case uses a row constructor with the key word `ROW` omitted.)\n\nAnother special syntactical behavior associated with composite values is that we can use functional notation for extracting a field of a composite value. The simple way to explain this is that the notations `field(table)` and `table.field` are interchangeable. For example, these queries are equivalent:\n\n```SELECT c.name FROM inventory_item c WHERE c.price > 1000;\nSELECT name(c) FROM inventory_item c WHERE price(c) > 1000;\n```\n\nMoreover, if we have a function that accepts a single argument of a composite type, we can call it with either notation. These queries are all equivalent:\n\n```SELECT somefunc(c) FROM inventory_item c;\nSELECT somefunc(c.*) FROM inventory_item c;\nSELECT c.somefunc FROM inventory_item c;\n```\n\nThis equivalence between functional notation and field notation makes it possible to use functions on composite types to implement computed fields. An application using the last query above wouldn't need to be directly aware that `somefunc` isn't a real column of the table.\n\n### Tip\n\nBecause of this behavior, it's unwise to give a function that takes a single composite-type argument the same name as any of the fields of that composite type. If there is ambiguity, the field-name interpretation will be preferred, so that such a function could not be called without tricks. One way to force the function interpretation is to schema-qualify the function name, that is, write `schema.func(compositevalue)`.\n\n### 8.16.6. Composite Type Input and Output Syntax\n\nThe external text representation of a composite value consists of items that are interpreted according to the I/O conversion rules for the individual field types, plus decoration that indicates the composite structure. The decoration consists of parentheses (`(` and `)`) around the whole value, plus commas (`,`) between adjacent items. Whitespace outside the parentheses is ignored, but within the parentheses it is considered part of the field value, and might or might not be significant depending on the input conversion rules for the field data type. For example, in:\n\n```'( 42)'\n```\n\nthe whitespace will be ignored if the field type is integer, but not if it is text.\n\nAs shown previously, when writing a composite value you can write double quotes around any individual field value. You must do so if the field value would otherwise confuse the composite-value parser. In particular, fields containing parentheses, commas, double quotes, or backslashes must be double-quoted. To put a double quote or backslash in a quoted composite field value, precede it with a backslash. (Also, a pair of double quotes within a double-quoted field value is taken to represent a double quote character, analogously to the rules for single quotes in SQL literal strings.) Alternatively, you can avoid quoting and use backslash-escaping to protect all data characters that would otherwise be taken as composite syntax.\n\nA completely empty field value (no characters at all between the commas or parentheses) represents a NULL. To write a value that is an empty string rather than NULL, write `\"\"`.\n\nThe composite output routine will put double quotes around field values if they are empty strings or contain parentheses, commas, double quotes, backslashes, or white space. (Doing so for white space is not essential, but aids legibility.) Double quotes and backslashes embedded in field values will be doubled.\n\n### Note\n\nRemember that what you write in an SQL command will first be interpreted as a string literal, and then as a composite. This doubles the number of backslashes you need (assuming escape string syntax is used). For example, to insert a `text` field containing a double quote and a backslash in a composite value, you'd need to write:\n\n```INSERT ... VALUES ('(\"\\\"\\\\\")');\n```\n\nThe string-literal processor removes one level of backslashes, so that what arrives at the composite-value parser looks like `(\"\\\"\\\\\")`. In turn, the string fed to the `text` data type's input routine becomes `\"\\`. (If we were working with a data type whose input routine also treated backslashes specially, `bytea` for example, we might need as many as eight backslashes in the command to get one backslash into the stored composite field.) Dollar quoting (see Section 4.1.2.4) can be used to avoid the need to double backslashes.\n\n### Tip\n\nThe `ROW` constructor syntax is usually easier to work with than the composite-literal syntax when writing composite values in SQL commands. In `ROW`, individual field values are written the same way they would be written when not members of a composite."
]
| [
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https://www.jobilize.com/physics/section/problems-exercises-maxwell-s-equations-electromagnetic-by-openstax?qcr=www.quizover.com | [
"# 24.1 Maxwell’s equations: electromagnetic waves predicted and (Page 2/10)\n\n Page 2 / 10\n\nSince changing electric fields create relatively weak magnetic fields, they could not be easily detected at the time of Maxwell’s hypothesis. Maxwell realized, however, that oscillating charges, like those in AC circuits, produce changing electric fields. He predicted that these changing fields would propagate from the source like waves generated on a lake by a jumping fish.\n\nThe waves predicted by Maxwell would consist of oscillating electric and magnetic fields—defined to be an electromagnetic wave (EM wave). Electromagnetic waves would be capable of exerting forces on charges great distances from their source, and they might thus be detectable. Maxwell calculated that electromagnetic waves would propagate at a speed given by the equation\n\n$c=\\frac{1}{\\sqrt{{\\mu }_{0}{\\epsilon }_{0}}}.$\n\nWhen the values for ${\\mu }_{0}$ and ${\\epsilon }_{0}$ are entered into the equation for $c$ , we find that\n\n$c=\\frac{1}{\\sqrt{\\left(8\\text{.}\\text{85}×{\\text{10}}^{-\\text{12}}\\phantom{\\rule{0.25em}{0ex}}\\frac{{\\text{C}}^{2}}{\\text{N}\\cdot {\\text{m}}^{2}}\\right)\\left(4\\pi ×{\\text{10}}^{-7}\\phantom{\\rule{0.25em}{0ex}}\\frac{\\text{T}\\cdot \\text{m}}{\\text{A}}\\right)}}=\\text{3}\\text{.}\\text{00}×{\\text{10}}^{8}\\phantom{\\rule{0.25em}{0ex}}\\text{m/s},$\n\nwhich is the speed of light. In fact, Maxwell concluded that light is an electromagnetic wave having such wavelengths that it can be detected by the eye.\n\nOther wavelengths should exist—it remained to be seen if they did. If so, Maxwell’s theory and remarkable predictions would be verified, the greatest triumph of physics since Newton. Experimental verification came within a few years, but not before Maxwell’s death.\n\n## Hertz’s observations\n\nThe German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that not only confirmed the existence of electromagnetic waves, but also verified that they travel at the speed of light.\n\nHertz used an AC $\\text{RLC}$ (resistor-inductor-capacitor) circuit that resonates at a known frequency ${f}_{0}=\\frac{1}{2\\pi \\sqrt{\\text{LC}}}$ and connected it to a loop of wire as shown in [link] . High voltages induced across the gap in the loop produced sparks that were visible evidence of the current in the circuit and that helped generate electromagnetic waves.\n\nAcross the laboratory, Hertz had another loop attached to another $\\text{RLC}$ circuit, which could be tuned (as the dial on a radio) to the same resonant frequency as the first and could, thus, be made to receive electromagnetic waves. This loop also had a gap across which sparks were generated, giving solid evidence that electromagnetic waves had been received.",
null,
"The apparatus used by Hertz in 1887 to generate and detect electromagnetic waves. An RLC size 12{ ital \"RLC\"} {} circuit connected to the first loop caused sparks across a gap in the wire loop and generated electromagnetic waves. Sparks across a gap in the second loop located across the laboratory gave evidence that the waves had been received.\n\nHertz also studied the reflection, refraction, and interference patterns of the electromagnetic waves he generated, verifying their wave character. He was able to determine wavelength from the interference patterns, and knowing their frequency, he could calculate the propagation speed using the equation $\\upsilon =\\mathrm{f\\lambda }$ (velocity—or speed—equals frequency times wavelength). Hertz was thus able to prove that electromagnetic waves travel at the speed of light. The SI unit for frequency, the hertz ( $1 Hz=\\text{1 cycle/sec}$ ), is named in his honor.\n\n## Section summary\n\n• Electromagnetic waves consist of oscillating electric and magnetic fields and propagate at the speed of light $c$ . They were predicted by Maxwell, who also showed that\n$c=\\frac{1}{\\sqrt{{\\mu }_{0}{\\epsilon }_{0}}},$\n\nwhere ${\\mu }_{0}$ is the permeability of free space and ${\\epsilon }_{0}$ is the permittivity of free space.\n\n• Maxwell’s prediction of electromagnetic waves resulted from his formulation of a complete and symmetric theory of electricity and magnetism, known as Maxwell’s equations.\n• These four equations are paraphrased in this text, rather than presented numerically, and encompass the major laws of electricity and magnetism. First is Gauss’s law for electricity, second is Gauss’s law for magnetism, third is Faraday’s law of induction, including Lenz’s law, and fourth is Ampere’s law in a symmetric formulation that adds another source of magnetism—changing electric fields.\n\n## Problems&Exercises\n\nVerify that the correct value for the speed of light $c$ is obtained when numerical values for the permeability and permittivity of free space ( ${\\mu }_{0}$ and ${\\epsilon }_{0}$ ) are entered into the equation $c=\\frac{1}{\\sqrt{{\\mu }_{0}{\\epsilon }_{0}}}$ .\n\nShow that, when SI units for ${\\mu }_{0}$ and ${\\epsilon }_{0}$ are entered, the units given by the right-hand side of the equation in the problem above are m/s.\n\nwhat is Andromeda\nwhat is velocity\ndisplacement per unit time\nMurlidhar\nthe ratec of displacement over time\nJamie\nthe rate of displacement over time\nJamie\nthe rate of displacement over time\nJamie\ndid you need it right now\nPathani\nup to tomorrow\nSantosh\ni need a description and derivation of kinetic theory of gas\nSantosh\npls the sum of change in kinetic and potential energy is always what ?\nFaith\ni need a description and derivation of kinetic theory of gas\nSantosh\ndid you need it right now\nPathani\nA few grains of table salt were put in a cup of cold water kept at constant temperature and left undisturbed. eventually all the water tasted salty. this is due to?\nAunt Faith,please i am thinking the dissolution here from the word \"solution\" exposed the grains of salt to be dissolved in the water.Thankyou\nJunior\nJunior\nAunt Faith,please i am thinking the dissolution here from the word \"solution\" exposed the grains of salt to be dissolved in the water.Thankyou\nJunior\nit is either diffusion or osmosis. just confused\nFaith\ndue to solvation....\nPathani\nwhat is solvation pls\nFaith\nwater molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.\nPathani\nokay thanks\nFaith\nmy pleasure\nPathani\nwhat is solvation pls\nFaith\nwater act as a solvent and salt act as solute\nPathani\nokay thanks\nFaith\nits ok\nPathani\ndue to solvation....\nPathani\nwater molecule surround the salt molecules . solute solute attraction break in the same manner solvent solvent interaction also break. as a result solute and solvent attraction took place.\nPathani\nwhat is magnetism\nphysical phenomena arising from force caused by magnets\nis the phenomenon of attracting magnetic substance like iron, cobalt etc.\nFaith\nwhat is heat\nHeat is a form of energy where molecules move\nsaran\ntopic-- question\nSalman\nI know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.\n20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T\nwhy is a body moving at a constant speed able to accelerate\n20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T\nLilian\nbecause it changes only direction and the speed is kept constant\nJustice\nWhy is the sky blue...?\nIt's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic\nMike\nA heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel\nA thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to\nBe raised until its distance from d lens is 27cm find d radius of curvature\nAzummiri\nwhat happens when a nuclear bomb and atom bomb bomb explode add the same time near each other\nA monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question\nv2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.\nRamonyai\nwhy is the north side is always referring to n side of magnetic",
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null,
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https://ch.mathworks.com/help/stats/predict-class-labels-using-classificationsvm-predict-block.html | [
"# Predict Class Labels Using ClassificationSVM Predict Block\n\nThis example shows how to use the ClassificationSVM Predict block for label prediction. The block accepts an observation (predictor data) and returns the predicted class label and class score for the observation using a trained support vector machine (SVM) classification model.\n\n### Train Classification Model\n\nThis example uses the `ionosphere` data set, which contains radar return qualities (`Y`) and predictor data (`X`) of 34 variables. Radar returns are either of good quality (`'g'`) or bad quality (`'b'`).\n\nLoad the `ionosphere` data set. Determine the sample size.\n\n```load ionosphere n = numel(Y)```\n```n = 351 ```\n\nSuppose that the radar returns are detected in sequence, and you have the first 300 observations, but you have not received the last 51 yet. Partition the data into present and future samples.\n\n```prsntX = X(1:300,:); prsntY = Y(1:300); ftrX = X(301:end,:); ftrY = Y(301:end);```\n\nTrain an SVM model using all presently available data. Specify predictor data standardization.\n\n`svmMdl = fitcsvm(prsntX,prsntY,'Standardize',true);`\n\n`svmMdl` is a `ClassificationSVM` model.\n\nCheck the negative and positive class names by using the `ClassNames` property of `svmMdl`.\n\n`svmMdl.ClassNames`\n```ans = 2×1 cell {'b'} {'g'} ```\n\nThe negative class is `'b'`, and the positive class is `'g'`. The output values from the Score port of the ClassificationSVM Predict block have the same order. The first and second elements correspond to the negative class and positive class scores, respectively.\n\nThis example provides the Simulink model `slexIonosphereClassificationSVMPredictExample.slx`, which includes the ClassificationSVM Predict block. You can open the Simulink model or create a new model as described in this section.\n\nOpen the Simulink model `slexIonosphereClassificationSVMPredictExample.slx`.\n\n```SimMdlName = 'slexIonosphereClassificationSVMPredictExample'; open_system(SimMdlName)```",
null,
"The `PreLoadFcn` callback function of `slexIonosphereClassificationSVMPredictExample` includes code to load the sample data, train the SVM model, and create an input signal for the Simulink model. If you open the Simulink model, then the software runs the code in `PreLoadFcn` before loading the Simulink model. To view the callback function, on the Modeling tab, in the Setup section, select Model Settings > Model Properties. Then, on the Callbacks tab, select the `PreLoadFcn` callback function in the Model callbacks pane.\n\nTo create a new Simulink model, open the Blank Model template and add the ClassificationSVM Predict block. Add the Inport and Outport blocks and connect them to the ClassificationSVM Predict block.\n\nDouble-click the ClassificationSVM Predict block to open the Block Parameters dialog box. Specify the Select trained machine learning model parameter as `svmMdl`, which is the name of a workspace variable that contains the trained SVM model. Click the action button (with three vertical dots) or click Update Model on the Modeling tab. The dialog box displays the classification type and the options used to train the SVM model `svmMdl` under Trained Machine Learning Model. Select the Add output port for predicted class scores check box to add the second output port Score.",
null,
"The ClassificationSVM Predict block expects an observation containing 34 predictor values. Double-click the inport block, and set the Port dimensions to 34 on the Signal Attributes tab.\n\nCreate an input signal data in the form of a structure array for the Simulink model. The structure array must contain these fields:\n\n• `time` — The points in time at which the observations enter the model. In this example, the duration includes the integers from 0 through 50. The orientation must correspond to the observations in the predictor data. So, in this case, `time` must be a column vector.\n\n• `signals` — A 1-by-1 structure array describing the input data and containing the fields `values` and `dimensions`, where `values` is a matrix of predictor data, and `dimensions` is the number of predictor variables.\n\nCreate an appropriate structure array for future radar returns.\n\n```radarReturnInput.time = (0:50)'; radarReturnInput.signals(1).values = ftrX; radarReturnInput.signals(1).dimensions = size(ftrX,2);```\n\nTo import signal data from the workspace:\n\n• Open the Configuration Parameters dialog box. On the Modeling tab, click Model Settings.\n\n• In the Data Import/Export pane, select the Input check box and enter `carsmallInput` in the adjacent text box.\n\n• In the Solver pane, under Simulation time, set Stop time to `radarReturnInput.time(end)`. Under Solver selection, set Type to `Fixed-step`, and set Solver to `discrete (no continuous states)`.\n\nSimulate the model.\n\n`sim(SimMdlName);`\n\nWhen the inport block detects an observation, it directs the observation into the ClassificationSVM Predict block. You can use the Simulation Data Inspector (Simulink) to view the logged data of the Outport blocks."
]
| [
null,
"https://ch.mathworks.com/help/examples/stats/win64/PredictClassLabelsUsingClassificationSVMPredictBlockExample_01.png",
null,
"https://ch.mathworks.com/help/examples/stats/win64/PredictClassLabelsUsingClassificationSVMPredictBlockExample_02.png",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.67649186,"math_prob":0.82666886,"size":4884,"snap":"2020-45-2020-50","text_gpt3_token_len":1095,"char_repetition_ratio":0.15717213,"word_repetition_ratio":0.0054719565,"special_character_ratio":0.20004095,"punctuation_ratio":0.1296729,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9557184,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-24T08:19:09Z\",\"WARC-Record-ID\":\"<urn:uuid:c6f82e68-4b81-4dea-9425-4a5035ddf226>\",\"Content-Length\":\"77254\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f3a16b41-9ccd-409e-affa-bea8d5c63140>\",\"WARC-Concurrent-To\":\"<urn:uuid:76a0ac89-774c-45cc-92ab-1a761ae379d3>\",\"WARC-IP-Address\":\"23.223.252.57\",\"WARC-Target-URI\":\"https://ch.mathworks.com/help/stats/predict-class-labels-using-classificationsvm-predict-block.html\",\"WARC-Payload-Digest\":\"sha1:UIYQPEQS2TFAREW667IYRCDFZJ77FC6J\",\"WARC-Block-Digest\":\"sha1:VMCBLSCUN67HPPROUOETLFOBTJZCVASX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141171126.6_warc_CC-MAIN-20201124053841-20201124083841-00612.warc.gz\"}"} |
https://edurev.in/course/quiz/attempt/18497_Test-Buoyancy-And-Floatation/e89e96fe-842e-4aef-bcd7-3c9e11a28ed8 | [
"Courses\n\n# Test: Buoyancy And Floatation\n\n## 10 Questions MCQ Test Topicwise Question Bank for GATE Civil Engineering | Test: Buoyancy And Floatation\n\nDescription\nThis mock test of Test: Buoyancy And Floatation for Civil Engineering (CE) helps you for every Civil Engineering (CE) entrance exam. This contains 10 Multiple Choice Questions for Civil Engineering (CE) Test: Buoyancy And Floatation (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Buoyancy And Floatation quiz give you a good mix of easy questions and tough questions. Civil Engineering (CE) students definitely take this Test: Buoyancy And Floatation exercise for a better result in the exam. You can find other Test: Buoyancy And Floatation extra questions, long questions & short questions for Civil Engineering (CE) on EduRev as well by searching above.\nQUESTION: 1\n\n### A floating body is in stable equilibrium when\n\nSolution:\n\nFloating body will be under stable equilibrium when metacentre is positive",
null,
"QUESTION: 2\n\nSolution:\nQUESTION: 3\n\n### A small plastic boat loaded with nuts and bolts is floating in a bath tub. if the cargo is dumped into the water, allowing the boat to float empty, then the water level in the tub will\n\nSolution:\nQUESTION: 4\n\nThe line of action of the buoyant force acts through the\n\nSolution:\nQUESTION: 5\n\nA body is floating as shown in the given figure. The centre of buoyancy, centre of gravity and metacentre are labelled respectively as B, G and M. The body is",
null,
"Solution:\n\nSince metacentre is below centre of gravity the body is in unstable equilibrium in rotation.\n\nQUESTION: 6\n\nA metal cube of size 15 cm x 15 cm x 15 cm and specific gravity 8.6 is submerged in a twolayered liquid, the bottom layer being mercury and the top layer being water. The percentage of the volume of the cube remaining above the interface will be, approximately",
null,
"Solution:",
null,
"",
null,
"QUESTION: 7\n\nThe centre of gravity of the volume of liquid displaced is called\n\nSolution:\nQUESTION: 8\n\nWhen a block of ice floating on,water in a container melts, the level of water in the container\n\nSolution:\nQUESTION: 9\n\nA metal block is thrown into a deep lake. As it sinks deeper in water, the buoyant force acting on it\n\nSolution:\nQUESTION: 10\n\nA rectangular floating body is 20 m long and 5 m wide. The water line is 1.5 m above the bottom. If the centre of gravity is 1.8 m from the bottom, then its metacentric height will be approximately\n\nSolution:",
null,
"",
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""
]
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null,
"https://cdn3.edurev.in/ApplicationImages/Temp/ba7a62b4-d017-4fcc-a0e2-edb282dbf7da_lg.jpg",
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"https://cdn3.edurev.in/ApplicationImages/Temp/274067d0-08ee-4aa4-9756-eb9bd5c9fdd8_lg.jpg",
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"https://cdn3.edurev.in/ApplicationImages/Temp/7d64e520-3074-4960-b53d-866392a7c847_lg.jpg",
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"https://cdn3.edurev.in/ApplicationImages/Temp/d72d3590-bcaa-403f-ba2f-b95417f7340a_lg.jpg",
null,
"https://cdn3.edurev.in/ApplicationImages/Temp/6d1b563a-d90e-48f1-8c4b-a86136141f23_lg.jpg",
null,
"https://cdn3.edurev.in/ApplicationImages/Temp/dd9ab910-7eea-42d9-9906-44f9da464ceb_lg.jpg",
null,
"https://cdn3.edurev.in/ApplicationImages/Temp/c4b01882-53ee-4278-906e-14141f866ed6_lg.jpg",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.8518045,"math_prob":0.72766393,"size":1702,"snap":"2021-04-2021-17","text_gpt3_token_len":414,"char_repetition_ratio":0.12485277,"word_repetition_ratio":0.0815047,"special_character_ratio":0.23854288,"punctuation_ratio":0.076246336,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9735131,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-19T22:28:48Z\",\"WARC-Record-ID\":\"<urn:uuid:f7e1287d-0fa5-4473-93dc-b3ec7998dcef>\",\"Content-Length\":\"308473\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:77a32927-9a28-47c3-97de-f9b2f971ef45>\",\"WARC-Concurrent-To\":\"<urn:uuid:72a73493-4233-4935-ab77-1de5a7568d0f>\",\"WARC-IP-Address\":\"35.198.207.72\",\"WARC-Target-URI\":\"https://edurev.in/course/quiz/attempt/18497_Test-Buoyancy-And-Floatation/e89e96fe-842e-4aef-bcd7-3c9e11a28ed8\",\"WARC-Payload-Digest\":\"sha1:JCP56KUKWVJRHFQ64KAHTGJZZ3LT37E7\",\"WARC-Block-Digest\":\"sha1:5QLZVYBYW6C2YKG2EP7BNCLQUYDTANZE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038917413.71_warc_CC-MAIN-20210419204416-20210419234416-00525.warc.gz\"}"} |
https://mathcracker.com/profitability-index-calculator | [
"# Profitability Index Calculator\n\nInstructions: Use this step-by-step Profitability Index Calculator to compute the profitability index ($$PI$$) of a stream of cash flows by indicating the yearly cash flows ($$F_t$$), starting at year $$t = 0$$, and the discount rate ($$r$$) (Type in the cash flows for each year from $$t=0$$ to $$t = n$$. The first cash flow must be negative. Type '0' if there is no cash flow for a year):",
null,
"Interest Rate $$(r)$$ =",
null,
"Type the yearly cash flows (comma or space separated)\n\n## Profitability Index Calculator\n\nMore about the this PI calculator so you can better understand how to use this solver\n\nThe profitability index of a stream of cash flows $$F_t$$ depends on the discount interest rate $$r$$, and the cash flows themselves. It is computed as the present value ($$PV$$) after the initial investment $$I$$.\n\n### How do you calculate the profitability index (PI)?\n\nFirst, we let:\n\n$PV = \\displaystyle \\sum_{i=1}^n \\frac{F_i}{(1+i)^i}$\n\nbe the present value ($$PV$$) after the initial investment. The profitability index is therefore:\n\n$PI = \\frac{PV}{I}$\n\nOther ways to evaluate a project include using instead a NPV calculator or also a IRR calculator . Those two metrics are the most common ones used to evaluate and make the decision of whether or not a project should be undertaken.",
null,
"### Example of the calculation of the profitability index\n\nQuestion: Assume that you act as the manager company, and you are asked to evaluate a project. This project requires a payment of $10,000 to get started. Then, it is expected that the project will bring a revenue of$3,000 at the end of the first year, and then another \\$4,000 at the end of the following 3 years. Suppose that the discount rate is 4.5%, compute the profitability index of the project.\n\nSolution:\n\nThis is the information we have been provided with:\n\n• The cash flows provided are: -10000, 3000, 4000, 4000, 4000 and the discount rate is $$r = 0.045$$.\n\nTherefore, the initial investment is $$I = 10000$$, and the present value (PV) of cash flows after the initial investment associated to these cash flows are computed using the following formula\n\n$PV = \\displaystyle \\sum_{i=1}^n {\\frac{F_i}{(1+i)^i}}$\n\nThe following table shows the cash flows and discounted cash flows:\n\n Period Cash Flows Discounted Cash Flows 1 3000 $$\\displaystyle \\frac{ 3000}{ (1+0.045)^{ 1}} = \\text{\\textdollar}2870.81$$ 2 4000 $$\\displaystyle \\frac{ 4000}{ (1+0.045)^{ 2}} = \\text{\\textdollar}3662.92$$ 3 4000 $$\\displaystyle \\frac{ 4000}{ (1+0.045)^{ 3}} = \\text{\\textdollar}3505.19$$ 4 4000 $$\\displaystyle \\frac{ 4000}{ (1+0.045)^{ 4}} = \\text{\\textdollar}3354.25$$ $$Sum = 13393.16$$\n\nBased on the cash flows provided the PV is computed as follows:\n\n$\\begin{array}{ccl} PV & = & \\displaystyle \\frac{ 3000}{ (1+0.045)^{ 1}}+\\frac{ 4000}{ (1+0.045)^{ 2}}+\\frac{ 4000}{ (1+0.045)^{ 3}} +\\frac{ 4000}{ (1+0.045)^{ 4}} \\\\\\\\ \\\\\\\\ & = & \\text{\\textdollar}2870.81+\\text{\\textdollar}3662.92+\\text{\\textdollar}3505.19+\\text{\\textdollar}3354.25 \\\\\\\\ \\\\\\\\ & = & \\text{\\textdollar}13393.16 \\end{array}$\n\nTherefore, the profitability index is ($$PI$$) computed as.\n\n$\\begin{array}{ccl} PI & = & \\displaystyle \\frac{PV}{I} \\\\\\\\ \\\\\\\\ & = &\\displaystyle \\frac{13393.17}{10000} \\\\\\\\ \\\\\\\\ & = & 1.3393 \\end{array}$\n\nTherefore, the profitability indexe associated to the provided cash flows and the discount rate of $$r = 0.045$$ is $$PI =1.3393$$."
]
| [
null,
"https://mathcracker.com/images/arrow.png",
null,
"https://mathcracker.com/images/arrow.png",
null,
"https://mathcracker.com/images/profitability-index-calculator.jpg",
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]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.8348843,"math_prob":0.99946815,"size":3323,"snap":"2023-14-2023-23","text_gpt3_token_len":1022,"char_repetition_ratio":0.14432058,"word_repetition_ratio":0.04016064,"special_character_ratio":0.36984652,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999852,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-24T22:33:17Z\",\"WARC-Record-ID\":\"<urn:uuid:a3709d12-cca3-4311-8d9c-bd6f2a095f6c>\",\"Content-Length\":\"119865\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19283346-f9c0-4d09-87d8-cb8bb8532e33>\",\"WARC-Concurrent-To\":\"<urn:uuid:0a1fe99d-45ba-48ed-b794-e35813608314>\",\"WARC-IP-Address\":\"34.230.232.255\",\"WARC-Target-URI\":\"https://mathcracker.com/profitability-index-calculator\",\"WARC-Payload-Digest\":\"sha1:5432DS4OKSYIBYU2RMJXK7HE6WSPQCJY\",\"WARC-Block-Digest\":\"sha1:FZNRTFDSRBMOEZS6T3F6G2DEX46UZHKX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945289.9_warc_CC-MAIN-20230324211121-20230325001121-00753.warc.gz\"}"} |
https://ie.boun.edu.tr/tr/content/advances-defective-parameters-graphs | [
"# Advances on defective parameters in graphs\n\n Başlık Advances on defective parameters in graphs Publication Type Journal Article Year of Publication 2015 Authors Akdemir, A., and T. Ekim Journal Discrete Optimization Volume 16 Pagination 62-69 ISSN 1572-5286 Anahtar kelimeler Cocritical graphs, Defective cocoloring, Defective Ramsey numbers, Efficient graph generation Abstract We consider the generalization of Ramsey numbers to the defective framework using k-dense and k-sparse sets. We construct the first tableaux for defective Ramsey numbers with exact values whenever it is known, and lower and upper bounds otherwise. In light of defective Ramsey numbers, we consider the defective cocoloring problem which consists of partitioning the vertex set of a given graph into k-sparse and k-dense sets. By the help of efficient graph generation methods, we show that c0(4)=12,c1(3)=12 and c2(2)=10 where ck(m) is the maximum order n such that all n-graphs can be k-defectively cocolored using at most m colors. We also give the numbers of k-defective m-cocritical graphs of order n (until n=10) for different levels of defectiveness and m=2,3 and 4. URL https://www.sciencedirect.com/science/article/pii/S1572528615000031 DOI 10.1016/j.disopt.2015.01.002"
]
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http://nmarkou.blogspot.com/2018/04/ | [
"## Saturday, April 21, 2018\n\n### The \"No Free Lunch\" Theorem\n\nThe \"No Free Lunch\" theorem was first published by David Wolpert and William Macready in their 1996 paper \"No Free Lunch Theorems for Optimization\".\n\nIn computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method. No solution therefore offers a 'short cut'.\n\nA model is a simplified version of the observations. The simplifications are meant to discard the superfluous details that are unlikely to generalize to new instances. However, to decide what data to keep , you must make assumptions. For example, a linear model makes the assumption that the data is fundamentally linear and the distance between the instances and the straight line is just noise, which can safely be ignored.\n\nDavid Wolpert demonstrated that if you make absolutely no assumption about the data, then there is no reason to prefer one model over any other. This is called the \"No Free Lunch Theorem\" (NFL).\n\nNFL states that no model is a priori guaranteed to work better. The only way to know for sure which model is the best is to evaluate them all. Since this is not possible, in practice you make some reasonable assumptions about the data and you evaluate only a few reasonable models.\n\n## Sunday, April 15, 2018\n\n### Review : Focal Loss for Dense Object Detection\n\nThe paper Focal Loss for Dense Object Detection introduces a new self balancing loss function that aims to address the huge imbalance problem between foreground/background objects found in one-step object detection networks.\n\ny : binary class {+1, -1}\np : probability of input correctly classified to binary class\n\nGiven Cross Entropy (CE) loss for binary classification:\nCE(p, y) =\n-log(p) , if y = 1\n-log(1 - p), if y = -1\n\nThe paper introduces the Focal Loss (FL) term as follows\nFL(p,y) =\n-(1-p)^gamma * log(p), if y = +1\n-(p)^gamma * log(1-p), if y = -1\n\nWith gamma values ranging from 0 (disabling focal loss, default CE) to 2.\nIntuitively, the modulating factor reduces the loss contribution from easy examples and extends the range in which an example receives loss.\nEasy examples are those that achieve p close to 0 and close to 1.\n\nExample 1\ngamma = 2.0\np = 0.9\ny = +1\nFL(0.9, +1) = - ( 1 - 0.9 ) ^ 2.0 * log(0.9) = 0.00045\nCE(0.9, +1) = - log(0.9) = 0.0457\n\nExample 2\ngamma = 2.0\np = 0.99\ny = +1\nFL(0.99, +1) = - ( 1 - 0.99 ) ^ 2.0 * log(0.99) = 0.000000436\nCE(0.9,9 +1) = - log(0.99) = 0.00436\n\nThat means a near certainty (a very easy example) will have a very small FL compared cross entropy loss and an ambiguous result (close to p ~ 0.5) will have a much higher effect.\n\nIn practice the authors use an a-balanced variance of FL:\n\nFL(p,y) =\n-a(y) * ( 1 - p ) ^ gamma * log(p), if y = +1\n-a(y) * ( p ) ^ gamma * log(1 - p), if y = -1\n\nWhere a(y) is a multiplier term fixing the class imbalance. This form yields slightly improved accuracy over the non-a-balanced form.\n\nThe authors then go and build a network to show off the capabilities of their loss function. The network is called RetinaNet and it's a standard Feature Pyramid Network (FPN) Backbone with two subnets's (one object classification, one box regression) attached at each feature map. It's a very common implementation for a one stage detector, similar to SSD (edit, exactly the same as SSD) and YOLO. A slight differentiation is the prior addition when initializing the bias for the object classification network and sparse calculation when adding the total cost."
]
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https://virtualpiano.net/artists/camila-cabello/ | [
"",
null,
"# Camila Cabello\n\n3 Music Sheets\n\n• ###### Birth Name:\n\nKarla Camila Cabello Estrabao\n\n• ###### Born:\n\n3rd March 1997\n\n• ###### Genres:\n\nKarla Camila Cabello Estrabao is a Cuban-American singer and songwriter. She rose to prominence as a member of the girl group Fifth Harmony, formed on The X Factor USA in 2012, signing a joint record deal with Syco Music and Epic Records. While in Fifth Harmony, Cabello began to establish herself as a solo artist with the release of the collaborations \"I Know What You Did Last Summer\" with Shawn Mendes, and \"Bad Things\" with Machine Gun Kelly, the latter reaching number four on the US Billboard Hot 100. After leaving the group in late 2016, Cabello released several other collaborations, including \"Hey Ma\" by Pitbull and J Balvin for The Fate of the Furious soundtrack, and her debut solo single \"Crying in the Club\".\n\n## Artist's Music Sheets\n\n•",
null,
"k l k j k l | h | f | l k | h | h l k j k l | h | f | l k h | h l k j h g l l l | g g l l l | k | l k l k h | k | l k l k | j k l | h | f | l k | h | h l k j k l | h | f | l k h | h l k j h g l l l | g g l l l | k | k l k l k | h | k | l k l k h j j | f d f d s | f d f d s a o p f d f d s | f d f g f d s p f f f | o o o o d d d | s a | o p | f d f d s | f d f d s s a p f d f d s | f d f g f d s p | f f f | o o o o | d d d | d s a | k l k j k l | h | f | l k | h | h l k j k l | h | f | l k h | h l k j h g l l l | g g l l l | k | l k l k h | k | l k l k | j k l | h | f | l k | h | h l k j k l | h | f | l k h | h l k j h g l l l | g g l l l | k | k l k l k | h | k | l k l k h j j | f d f d s | f d f d s s a p f d f d s | f d f g f d s p | f f f | hhjffdfdfd fd d s d s d s d h | j h f | d s | j f | h g f d s j f | h g j f | h g f d s f | k l k j k l | h | f | l k | h | h l k j k l | h | f | l k h | h l k j h g l l l | g g l l l | k | k l k l k | h | k | l k l k h j j\nLevel: 3\nLength: 03:30\nEasy\n\n#### Camila Cabello\n\n•",
null,
"E y y E E w | y t y Y y t E y y E E w | y t y Y y t E y y E E w | y t y Y y t E y E | y t y t E y e | E e E e E w | oooy y Y y t y | y t y t w | oooy y Y y t y | y t y t w E o o o y y Y y t y | y t y t w | y t y Y y t E y y E E w | y t y Y y t E y y E E w | y t y Y y t E y E | y t y t E y e | E e E e E w\nLevel: 2\nLength: 01:15\nEasy\n\n#### Camila Cabello\n\n•",
null,
"k l k j k l | h | f | l k h | k l k j k l | h | f | l k h | k l k j h g l l [sgl] | g l l [sgl] | k l k [fl] k h | [hk] | l k l k [dj] | p f d f d [sup] | f d f [ed] s [ws] a p f d f [suo] | [suo] | f d f [eg] f d s [qp] | [qsfp] | [qsfp] [qsfp] o o o [uo] | [uod] | [uod] [uod] | [yoa] | f d f d [sup] | f d f [ed] s [ws] a p f d f d [suo] f d f [eg] f d s [qp] | [qsfp] | [qsfp] [qsfp] | o o o [uo] | [uod] | [uod] [uod] | [yoa] | l l k j k [fjl] | j | f | l k | h | h l k j k [fhl] h | f | l k | h | a s a p o [ti] | [sti] [sti] [sti] | [ti] [ti] | [sti] [sti] [sti] | k | l k l k h | [dhk] | l k l l k j k [fjl] | j | f | l k | h | k l k j k [fhl] | h | f | l k | h | k l k j h [sg] | [sgl] [sgl] [sgl] | [sg] [sg] | [sgl] [sgl] [sgl] | k | l k l [ak] h | [dhk] | l k l k | j f d f d [sup] | f d f [ed] s [ws] a p f d f [suo] | [suo] | f d f [eg] f d s [qp] | [qsfp] | [qsfp] [qsfp] o o o [uo] | [uod] | [uod] [uod] | [yoa] [tup] | u o i u y t [tup] | u o i | [tup] | u o i u y t [wtu] | u a s a p a [sup] | p | u | s a | o | a s a p a s | o |u | s a o | a s a p o [ti] | [sti] [sti] [sti] | [ti] [ti] | [sti] [sti] [sti] k | l k l k h | [dhk] | l k l l k j k [fjl] | j | f | l k | h | a s a p a [sup] | p | u | s a | o | o s a p o [ti] | [sti] [sti] [sti] | [ti] [ti] | [sti] [sti] [sti] k | [tip] | p a s | d | s a | o o [tuo] | p a s | d | s a | p p [tip] | p a s | d s a p p [ruo] | a o o [ryo] | [sup] | p | u | s a | o | o s a p a s | o u | s a | o | o s a p o [ti] | [sti] [sti] [sti] | [ti] [ti] | [sti] [sti] [sti] a |s a s a o | [ayo] | s a s a | p [tup]\nLevel: 6\nLength: 04:12\nIntermediate"
]
| [
null,
"https://virtualpiano.net/wp-content/uploads/2020/08/Camila-Cabello-Artist-on-Virtual-Piano-Play-Piano-Online.jpg",
null,
"https://virtualpiano.net/wp-content/uploads/2020/09/Senorita-–-Shawn-Mendes-feat-Camila-Cabello-Virtual-Piano.jpg",
null,
"https://virtualpiano.net/wp-content/uploads/2020/08/Havana-Camila-Cabello-Best-Online-Piano-Keyboard-Virtual-Piano.jpg",
null,
"https://virtualpiano.net/wp-content/uploads/2020/08/Senorita-–-Shawn-Mendes-Camila-Cabello-Virtual-Piano.jpg",
null
]
| {"ft_lang_label":"__label__en","ft_lang_prob":0.566713,"math_prob":0.97179,"size":3864,"snap":"2020-45-2020-50","text_gpt3_token_len":1760,"char_repetition_ratio":0.25051814,"word_repetition_ratio":0.69645494,"special_character_ratio":0.49534163,"punctuation_ratio":0.022065314,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9943949,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,4,null,3,null,1,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-23T22:15:22Z\",\"WARC-Record-ID\":\"<urn:uuid:9218cbd2-0555-416f-b565-96959eec2325>\",\"Content-Length\":\"160915\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f40128c2-ae01-457c-9e37-dfa1cd45ece2>\",\"WARC-Concurrent-To\":\"<urn:uuid:239819cc-b726-4fa3-8c31-b41717e1cc02>\",\"WARC-IP-Address\":\"104.26.6.54\",\"WARC-Target-URI\":\"https://virtualpiano.net/artists/camila-cabello/\",\"WARC-Payload-Digest\":\"sha1:EOLIN5F3NSVSPSVKOCDCJLKCCPUR5MAN\",\"WARC-Block-Digest\":\"sha1:BQVCR6XBU2DPSYPBWTWUPFGEXH4T66QC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141168074.3_warc_CC-MAIN-20201123211528-20201124001528-00426.warc.gz\"}"} |
https://pureportal.strath.ac.uk/en/publications/riordan-graphs-ii-spectral-properties | [
"# Riordan graphs II\n\n## spectral properties\n\nGi-Sang Cheon, Ji-Hwan Jung, Sergey Kitaev, Seyed Ahmad Mojallal\n\nResearch output: Contribution to journalArticle\n\n1 Citation (Scopus)\n\n### Abstract\n\nThe authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in . Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.\n\nOriginal language English 174-215 42 Linear Algebra and its Applications 575 12 Apr 2019 https://doi.org/10.1016/j.laa.2019.04.011 Published - 15 Aug 2019\n\n### Fingerprint\n\nSpectral Properties\nFractals\nStructural properties\nGraph in graph theory\nDeterminant\nSignless Laplacian\nLaplacian Eigenvalues\nGraph Invariants\nNullity\nPascal\nOtto Toeplitz\nInertia\nStructural Properties\nFractal\nEigenvalue\n\n### Keywords\n\n• Riordan graph\n• Laplacian eigenvalue\n• signless Laplacian eigenvalue\n• intertia\n• nullity\n• Rayleigh-Ritz quotient\n• Pascal graph\n• Catalan graph\n\n### Cite this\n\nCheon, Gi-Sang ; Jung, Ji-Hwan ; Kitaev, Sergey ; Mojallal, Seyed Ahmad. / Riordan graphs II : spectral properties. In: Linear Algebra and its Applications. 2019 ; Vol. 575. pp. 174-215.\n@article{0894563681f5446b8cb61d6271fcd870,\ntitle = \"Riordan graphs II: spectral properties\",\nabstract = \"The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in . Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.\",\nkeywords = \"Riordan graph, adjacency eigenvalue, Laplacian eigenvalue, signless Laplacian eigenvalue, intertia, nullity, Rayleigh-Ritz quotient, Pascal graph, Catalan graph\",\nauthor = \"Gi-Sang Cheon and Ji-Hwan Jung and Sergey Kitaev and Mojallal, {Seyed Ahmad}\",\nyear = \"2019\",\nmonth = \"8\",\nday = \"15\",\ndoi = \"10.1016/j.laa.2019.04.011\",\nlanguage = \"English\",\nvolume = \"575\",\npages = \"174--215\",\njournal = \"Linear Algebra and its Applications\",\nissn = \"0024-3795\",\n\n}\n\nRiordan graphs II : spectral properties. / Cheon, Gi-Sang; Jung, Ji-Hwan; Kitaev, Sergey; Mojallal, Seyed Ahmad.\n\nIn: Linear Algebra and its Applications, Vol. 575, 15.08.2019, p. 174-215.\n\nResearch output: Contribution to journalArticle\n\nTY - JOUR\n\nT1 - Riordan graphs II\n\nT2 - spectral properties\n\nAU - Cheon, Gi-Sang\n\nAU - Jung, Ji-Hwan\n\nAU - Kitaev, Sergey\n\nPY - 2019/8/15\n\nY1 - 2019/8/15\n\nN2 - The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in . Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.\n\nAB - The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in . Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.\n\nKW - Riordan graph\n\nKW - Laplacian eigenvalue\n\nKW - signless Laplacian eigenvalue\n\nKW - intertia\n\nKW - nullity\n\nKW - Rayleigh-Ritz quotient\n\nKW - Pascal graph\n\nKW - Catalan graph\n\nUR - https://www.sciencedirect.com/journal/linear-algebra-and-its-applications\n\nUR - https://arxiv.org/abs/1801.07021\n\nU2 - 10.1016/j.laa.2019.04.011\n\nDO - 10.1016/j.laa.2019.04.011\n\nM3 - Article\n\nVL - 575\n\nSP - 174\n\nEP - 215\n\nJO - Linear Algebra and its Applications\n\nJF - Linear Algebra and its Applications\n\nSN - 0024-3795\n\nER -"
]
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https://socratic.org/questions/an-isosceles-triangle-has-its-base-along-the-x-axis-with-one-base-vertex-at-the- | [
"# An isosceles triangle has its base along the x-axis with one base vertex at the origin and its vertex in the first quadrant on the graph of y = 6-x^2. How do you write the area of the triangle as a function of length of the base?\n\nJan 16, 2017\n\n$\\text{Area, expressed as the function of base-length \"l,\" is } \\frac{1}{8} l \\left(24 - {l}^{2}\\right)$.\n\n#### Explanation:\n\nWe consider an Isosceles Triangle $\\Delta A B C$ with base vertices\n\n$B \\left(0 , 0\\right) \\mathmr{and} C \\left(l , 0\\right) , \\left(l > 0\\right) \\in \\text{ the X-axis=} \\left\\{\\left(x , 0\\right) | x \\in \\mathbb{R}\\right\\}$\n\nand the third vertex\n\nA in G={(x,y)|y=6-x^2; x,y in RR} sub Q_I......(star).\n\nObviously, the length $B C$ of the base is $l$.\n\nLet $M$ be the mid-point of the base $B C . \\therefore M \\left(\\frac{l}{2} , 0\\right)$.\n\n$\\Delta A B C \\text{ is isosceles, } \\therefore A M \\bot B C .$ So, if $h$ is the height of\n\n$\\Delta A B C , \\text{ then,} \\because , B C$ is the X-Axis, $A M = h .$\n\nClearly, $A = A \\left(\\frac{l}{2} , h\\right) .$\n\nNow, the Area of $\\Delta A B C = \\frac{1}{2} l h \\ldots \\ldots \\ldots \\ldots \\ldots \\ldots . \\left(\\ast\\right)$\n\nBut, $A \\left(\\frac{l}{2} , h\\right) \\in G \\therefore \\left(\\star\\right) \\Rightarrow h = 6 - {l}^{2} / 4$\n\nTherefore, the Area of $\\Delta A B C = \\frac{1}{2} l \\left(6 - {l}^{2} / 4\\right) \\ldots \\left[\\because , \\left(\\ast\\right)\\right] ,$ or,\n\n$\\text{Area, expressed as the function of base-length \"l,\" is } \\frac{1}{8} l \\left(24 - {l}^{2}\\right)$."
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https://help.altair.com/flux/Flux/Help/english/UserGuide/English/topics/TransitionDePhase.htm | [
"# Phase transition\n\n## Definition\n\nA phase transition is a metallurgical transformation of the material produced by a modification of a particular exterior parameter (such as temperature, magnetic field…).\n\nSuch a transformation can be:\n\n• a modification of the state of the material:\n• the transitions between the solid, liquid and gaseous phases\n• a modification of the crystalline microstructure (see the example of iron below)\n• a modification of the magnetic behavior:\n• the transition from a ferromagnetic to the paramagnetic behavior of magnetic materials at the Curie point.\n• a modification of the electric behavior\n• certain ceramics become superconducting below a critical temperature\n\nThe notion of order of a phase transition.\n\n• First-order phase transitions are those that involve a latent heat. During such a transition, the system either absorbs, or releases a fixed quantity of energy.\n• Second-order phase transitions, also called “continuous phase” transitions, which are not associated with latent heat.\n\n## Example of an iron body\n\nLet us look at the dependence on temperature of the heat capacity of an iron body in the figure below.\n\nThis figure demonstrates:\n\n• a second-order phase transition:\n• T= 1033 K: ferromagnetic iron / paramagnetic iron transformation (at the Curie point)\n• first-order phase transitions:\n• T= 1183 K: iron α (cc) / iron γ (cfc) transformation\n• T= 1673 K: iron γ (cfc) / iron α (cc) transformation\n• T= 1812 K: iron α (cc) / liquid iron transformation\n\nDependence of the heat capacity of an iron body on temperature:",
null,
""
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null,
"https://help.altair.com/flux/Flux/Help/english/UserGuide/English/topics/Images/TransitionDePhase_0.svg",
null
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https://conceptispuzzles.com/index.aspx?uri=puzzle/calcudoku | [
" CalcuDoku\n Log inBecome a member",
null,
"# CalcuDoku\n\n## Addition, subtraction, multiplication and division will never be the same again\n\n• The math teaching puzzle from Japan\n• Fun, addictive and fascinating\n• Simple rules, very easy to learn\n• Requires no language skills\n• Wide range of logic and difficulty levels\n• Develops logical deduction and reasoning\n\n# SingleOp CalcuDoku\n\nPlay new puzzles each week\n\nEach puzzle consists of a grid containing blocks surrounded by bold lines. The object is to fill all empty squares so that the numbers 1 to N (where N is the number of rows or columns in the grid) appear exactly once in each row and column and the numbers in each block produce the result shown in the top-left corner of the block according to the math operation appearing on the top of the grid. In CalcuDoku a number may be used more than once in the same block.\n\nSingleOp CalcuDoku 4x4.a.n\nDifficulty: Ultra easy\nSingleOp CalcuDoku 5x5.m.n\nDifficulty: Very easy\nSingleOp CalcuDoku 6x6.a.n\nDifficulty: Medium\n\n# DualOp CalcuDoku\n\nPlay new puzzles each week\n\nEach puzzle consists of a grid containing blocks surrounded by bold lines. The object is to fill all empty squares so that the numbers 1 to N (where N is the number of rows or columns in the grid) appear exactly once in each row and column and the numbers in each block produce the result of the math operation shown in the top-left corner of the block. In CalcuDoku a number may be used more than once in the same block.\n\nDualOp CalcuDoku 4x4.as.a\nDifficulty: Ultra easy\nDualOp CalcuDoku 5x5.as.a\nDifficulty: Easy\nDualOp CalcuDoku 6x6.md.a\nDifficulty: Medium\n\n# QuadOp CalcuDoku\n\nPlay new puzzles each week\n\nEach puzzle consists of a grid containing blocks surrounded by bold lines. The object is to fill all empty squares so that the numbers 1 to N (where N is the number of rows or columns in the grid) appear exactly once in each row and column and the numbers in each block produce the result of the math operation shown in the top-left corner of the block. In CalcuDoku a number may be used more than once in the same block.\n\nQuadOp CalcuDoku 4x4.asmd.a\nDifficulty: Ultra easy\nQuadOp CalcuDoku 5x5.asmd.a\nDifficulty: Easy\nQuadOp CalcuDoku 6x6.asmd.a\nDifficulty: Medium"
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"https://conceptispuzzles.com/picture/3/1635.gif",
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https://software.intel.com/content/www/us/en/develop/documentation/mkl-developer-reference-c/top/lapack-routines/lapack-least-squares-and-eigenvalue-problem-routines/lapack-least-squares-and-eigenvalue-problem-driver-routines/generalized-symmetric-definite-eigenvalue-problems-lapack-driver-routines/sbgv.html | [
"Contents\n\n# ?sbgv\n\nComputes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with banded matrices.\n\n## Syntax\n\nInclude Files\n• mkl.h\nDescription\nThe routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form\nA\n*\nx\n=\nλ\n*\nB\n*\nx\n. Here\nA\nand\nB\nare assumed to be symmetric and banded, and\nB\nis also positive definite.\nInput Parameters\nmatrix_layout\nSpecifies whether matrix storage layout is row major (\nLAPACK_ROW_MAJOR\n) or column major (\nLAPACK_COL_MAJOR\n).\njobz\nMust be\n'N'\nor\n'V'\n.\nIf\njobz\n=\n'N'\n, then compute eigenvalues only.\nIf\njobz\n=\n'V'\n, then compute eigenvalues and eigenvectors.\nuplo\nMust be\n'U'\nor\n'L'\n.\nIf\nuplo\n=\n'U'\n, arrays\nab\nand\nbb\nstore the upper triangles of\nA\nand\nB\n;\nIf\nuplo\n=\n'L'\n, arrays\nab\nand\nbb\nstore the lower triangles of\nA\nand\nB\n.\nn\nThe order of the matrices\nA\nand\nB\n(\nn\n0\n).\nka\nThe number of super- or sub-diagonals in\nA\n(\nka\n0\n).\nkb\nThe number of super- or sub-diagonals in\nB\n(\nkb\n0).\nab\n,\nbb\nArrays:\nab\n(size at least max(1,\nldab\n*\nn\n) for column major layout and max(1,\nldab\n*(\nka\n+ 1)) for row major layout)\nis an array containing either upper or lower triangular part of the symmetric matrix\nA\n(as specified by\nuplo\n) in band storage format.\nbb\n(size at least max(1,\nldbb\n*\nn\n) for column major layout and max(1,\nldbb\n*(\nkb\n+ 1)) for row major layout)\nis an array containing either upper or lower triangular part of the symmetric matrix\nB\n(as specified by\nuplo\n) in band storage format.\nldab\nThe leading dimension of the array\nab\n; must be at least\nka\n+1\nfor column major layout and at least max(1,\nn\n) for row major layout\n.\nldbb\nThe leading dimension of the array\nbb\n; must be at least\nkb\n+1\nfor column major layout and at least max(1,\nn\n) for row major layout\n.\nldz\nThe leading dimension of the output array\nz\n;\nldz\n1\n. If\njobz\n=\n'V'\n,\nldz\nmax(1,\nn\n)\n.\nOutput Parameters\nab\nOn exit, the contents of\nab\nare overwritten.\nbb\nOn exit, contains the factor\nS\nfrom the split Cholesky factorization\nB\n=\nS\nT\n*S\n, as returned by pbstf / pbstf .\nw\n,\nz\nArrays:\nw\n, size at least max(1,\nn\n).\nIf\ninfo\n= 0\n, contains the eigenvalues in ascending order.\nz\n(size at least max(1,\nldz\n*\nn\n))\n.\nIf\njobz\n=\n'V'\n, then if\ninfo\n= 0\n,\nz\ncontains the matrix\nZ\nof eigenvectors, with the\ni\n-th column of\nz\nholding the eigenvector associated with\nw\n(\ni\n). The eigenvectors are normalized so that\nZ\nT\n*B\n*\nZ\n= I\n.\nIf\njobz\n=\n'N'\n, then\nz\nis not referenced.\nReturn Values\nThis function returns a value\ninfo\n.\nIf\ninfo\n=0\n, the execution is successful.\nIf\ninfo\n=\n-i\n, the\ni\n-th parameter had an illegal value.\nIf\ninfo\n> 0\n, and\nif\ni\nn\n, the algorithm failed to converge, and\ni\noff-diagonal elements of an intermediate tridiagonal did not converge to zero;\nif\ninfo\n=\nn\n+\ni\n, for\n1\ni\nn\n, then pbstf / pbstf returned\ninfo\n=\ni\nand\nB\nis not positive-definite. The factorization of\nB\ncould not be completed and no eigenvalues or eigenvectors were computed.\n\n#### Product and Performance Information\n\n1\n\nIntel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.\n\nNotice revision #20110804"
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https://quant.stackexchange.com/questions/15559/why-gamma-for-atm-option-decreases-as-volatility-increases | [
"# Why gamma for ATM option decreases as volatility increases\n\nWhy is the gamma for an at the money option less when volatility increases. Intuitively ,I thought that increasing volatility means more uncertainty,hence the option price will be more sensitive to the underlying price. Hence more volTility in my mind would mean a higher gamma for ATM option.\n\nBut the reverse is true. What am I missing?\n\n## 3 Answers\n\nThink of moving volatility in the other direction.\n\nAs volatility approaches zero, any call strike strictly smaller than the ATM strike, $K<K_{ATM}$, will have zero probability of ending in the money, and the corresponding option value will be zero. An infinitesimally small change in stock price will not move $K$ past $K_{ATM}$, so the option value remains zero nearby. Thus, the sensitivity is zero.\n\nSimilarly for $K>K_{ATM}$, all options end up in the money, so the $\\Gamma$ is also zero (though for the ITM options $\\Delta=1$ rather than 0, ignoring interest and dividend rates).\n\nOnly strikes very close to $ATM$ have any likelihood of changing between $\\Delta=0$ and $\\Delta=1$.\n\nNow, note that that $\\Gamma = \\frac{\\partial}{\\partial S}\\Delta$ for any volatility. Furthermore, for a call $\\Delta(S) \\rightarrow 1$ as $S \\rightarrow \\infty$.\n\nThus\n\n$$\\int_0^\\infty \\Gamma(S) dS = 1$$\n\nThat is to say, the area under the gamma curve is always 1.\n\nIn high-volatility cases, the $\\Gamma$ is \"spread out\" over a wide range of $S$, so it never gets very big yet adds up to 1. When volatility is low, the $\\Gamma$ is all concentrated near $K_{ATM}$ so it has to get very big.\n\nWe conclude that as volatility increases, $\\Gamma$ decreases near $K_{ATM}$ and increases for other strikes.\n\n(This is a more formal version of SolitonK's answer, which I have upvoted)\n\nVictor123, let's start from $\\Delta$. This is the expected change in the price of an option if the underlying asset moves by a currency unit, say 1 USD. For the case of a call option, the Delta varies between 0 and 1. Everything else been equal, the Delta of OTM calls will approach to 0 as the price moves out of the target barrier. Conversely for the case where ITM, Delta will approach to 1. It is thus safe to assume that the delta of an ATM option (i.e $S=K$) equals around 0.5. Relaxing any language formalisms, we can say that at the ATM point, the Stock has around 50% chance of going up or down.\n\nThe $\\Gamma$ of an option, shows the Delta's sensitivity to changes in the price of the underlying -or how volatile the option is relative to the underlying asset movements. Following the above, given that the expiration doesn't change, ATM options exhibit maximum Gamma value which washes out as we move away from $K$.\n\nIncrease in volatility increases the price of options which in turn increases the IV. Increase in IV is equivalent to pushing out the expiry date with the old IV. You know ATM Gamma increases as you get closed to expiry. Assume your DTE increases now .. Gamma has to decrease :)"
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https://wiki.fysik.dtu.dk/gpaw/tutorialsexercises/electronic/dos/dos.html | [
"# Density of states¶\n\nTake a look at the dos.py program and try to get a rough idea of what it can do for you. Use it to plot the density of states (DOS) for the three Fe configurations from the Electron spin and magnetic structure exercise (on the x-axis you have the energy relative to the Fermilevel).\n\n• Do the DOS plots integrate to the correct numbers? (i.e. number of bands).\n\n• The DOS for the anti-ferromagnetic phase looks a bit like that for the non-magnetic phase - is it magnetic at all?! Calculate the magnetization like this:\n\n```from ase.io import write\nfrom gpaw import GPAW\ncalc = GPAW('anti.gpw')\natoms = calc.get_atoms()\nup = calc.get_pseudo_density(0)\ndown = calc.get_pseudo_density(1)\nzeta = (up - down) / (up + down)\nwrite('magnetization.cube', atoms, data=zeta)\n```\n\nand look at it.\n\n• Calculate the DOS for bulk Aluminum and compare it (qualitatively) to the DOS for the non-magnetic calculation. The DOS for a simple metal has this shape: g(E) ~ E1/2. Explain the qualitative difference.\n\n• Plot also the DOS for bulk Si and the CO molecule. Identify the bandgap between valence and conduction bands for Si and the HOMO-LUMO gap for CO. Make sure that your k-point mesh for Si is dense enough to sample the band structure.\n\n## Projected Density of states (PDOS)¶\n\nThe projected density of states is useful for for analyzing chemical bonding. There exist several studies where the density projected onto the d states of a given surface atom is used. This short exercise demonstrates how to construct the PDOS of Fe.\n\nWe will get a feel for the local density of states by plotting the PDOS for the ferro-magnetic Fe crystal. Look at pdos.py. Use it to plot the s, p, and d-states on one of the Fe atoms."
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https://learn.microsoft.com/en-us/dotnet/api/system.threading.tasks.task.whenall?redirectedfrom=MSDN&view=net-7.0 | [
"## Definition\n\nCreates a task that will complete when all of the supplied tasks have completed.\n\n WhenAll(IEnumerable) Creates a task that will complete when all of the Task objects in an enumerable collection have completed. WhenAll(Task[]) Creates a task that will complete when all of the Task objects in an array have completed. WhenAll(IEnumerable>) Creates a task that will complete when all of the Task objects in an enumerable collection have completed. WhenAll(Task[]) Creates a task that will complete when all of the Task objects in an array have completed.\n\nCreates a task that will complete when all of the Task objects in an enumerable collection have completed.\n\n``````public:\n``public static System.Threading.Tasks.Task WhenAll (System.Collections.Generic.IEnumerable<System.Threading.Tasks.Task> tasks);``\n``static member WhenAll : seq<System.Threading.Tasks.Task> -> System.Threading.Tasks.Task``\n``Public Shared Function WhenAll (tasks As IEnumerable(Of Task)) As Task``\n\n#### Parameters\n\nThe tasks to wait on for completion.\n\n#### Returns\n\nA task that represents the completion of all of the supplied tasks.\n\n#### Exceptions\n\nThe `tasks` argument was `null`.\n\nThe `tasks` collection contained a `null` task.\n\n### Examples\n\nThe following example creates a set of tasks that ping the URLs in an array. The tasks are stored in a `List<Task>` collection that is passed to the WhenAll(IEnumerable<Task>) method. After the call to the Wait method ensures that all threads have completed, the example examines the Task.Status property to determine whether any tasks have faulted.\n\n``````using System;\nusing System.Collections.Generic;\nusing System.Net.NetworkInformation;\n\npublic class Example\n{\npublic static void Main()\n{\nint failed = 0;\nString[] urls = { \"www.adatum.com\", \"www.cohovineyard.com\",\n\"www.contoso.com\" };\n\nforeach (var value in urls) {\nvar url = value;\ntry {\nif (! (reply.Status == IPStatus.Success)) {\nInterlocked.Increment(ref failed);\nthrow new TimeoutException(\"Unable to reach \" + url + \".\");\n}\n}\ncatch (PingException) {\nInterlocked.Increment(ref failed);\nthrow;\n}\n}));\n}\ntry {\nt.Wait();\n}\ncatch {}\n\nConsole.WriteLine(\"All ping attempts succeeded.\");\nConsole.WriteLine(\"{0} ping attempts failed\", failed);\n}\n}\n// The example displays output like the following:\n// 5 ping attempts failed\n``````\n``````open System\nopen System.Net.NetworkInformation\n\nlet mutable failed = 0\n\nlet urls =\n\"www.cohovineyard.com\"\n\"www.cohowinery.com\"\n\"www.contoso.com\" ]\n\nurls\n|> List.map (fun url ->\nlet png = new Ping()\n\ntry\n\nInterlocked.Increment &failed |> ignore\nraise (TimeoutException \\$\"Unable to reach {url}.\")\nwith :? PingException ->\nInterlocked.Increment &failed |> ignore\nreraise ()))\n\ntry\nt.Wait()\nwith _ ->\n()\n\nprintfn \"All ping attempts succeeded.\"\nprintfn \\$\"{failed} ping attempts failed\"\n\n// The example displays output like the following:\n// 5 ping attempts failed\n``````\n``````Imports System.Collections.Generic\nImports System.Net.NetworkInformation\n\nModule Example\nPublic Sub Main()\nDim failed As Integer = 0\nDim urls() As String = { \"www.adatum.com\", \"www.cohovineyard.com\",\n\"www.contoso.com\" }\n\nFor Each value In urls\nDim url As String = value\nDim png As New Ping()\nTry\nIf Not reply.Status = IPStatus.Success Then\nInterlocked.Increment(failed)\nThrow New TimeoutException(\"Unable to reach \" + url + \".\")\nEnd If\nCatch e As PingException\nInterlocked.Increment(failed)\nThrow\nEnd Try\nEnd Sub))\nNext\nTry\nt.Wait()\nCatch\nEnd Try\n\nConsole.WriteLine(\"All ping attempts succeeded.\")\nConsole.WriteLine(\"{0} ping attempts failed\", failed)\nEnd If\nEnd Sub\nEnd Module\n' The example displays output like the following:\n' 5 ping attempts failed\n``````\n\n### Remarks\n\nThe overloads of the WhenAll method that return a Task object are typically called when you are interested in the status of a set of tasks or in the exceptions thrown by a set of tasks.\n\nNote\n\nIf any of the supplied tasks completes in a faulted state, the returned task will also complete in a Faulted state, where its exceptions will contain the aggregation of the set of unwrapped exceptions from each of the supplied tasks.\n\nIf none of the supplied tasks faulted but at least one of them was canceled, the returned task will end in the Canceled state.\n\nIf none of the tasks faulted and none of the tasks were canceled, the resulting task will end in the RanToCompletion state.\n\nIf the supplied array/enumerable contains no tasks, the returned task will immediately transition to a RanToCompletion state before it's returned to the caller.\n\n### Applies to\n\nCreates a task that will complete when all of the Task objects in an array have completed.\n\n``````public:\n``public static System.Threading.Tasks.Task WhenAll (params System.Threading.Tasks.Task[] tasks);``\n``static member WhenAll : System.Threading.Tasks.Task[] -> System.Threading.Tasks.Task``\n``Public Shared Function WhenAll (ParamArray tasks As Task()) As Task``\n\n#### Parameters\n\nThe tasks to wait on for completion.\n\n#### Returns\n\nA task that represents the completion of all of the supplied tasks.\n\n#### Exceptions\n\nThe `tasks` argument was `null`.\n\nThe `tasks` array contained a `null` task.\n\n### Examples\n\nThe following example creates a set of tasks that ping the URLs in an array. The tasks are stored in a `List<Task>` collection that is converted to an array and passed to the WhenAll(IEnumerable<Task>) method. After the call to the Wait method ensures that all threads have completed, the example examines the Task.Status property to determine whether any tasks have faulted.\n\n``````using System;\nusing System.Collections.Generic;\nusing System.Net.NetworkInformation;\n\npublic class Example\n{\n{\nint failed = 0;\nString[] urls = { \"www.adatum.com\", \"www.cohovineyard.com\",\n\"www.contoso.com\" };\n\nforeach (var value in urls) {\nvar url = value;\ntry {\nif (! (reply.Status == IPStatus.Success)) {\nInterlocked.Increment(ref failed);\nthrow new TimeoutException(\"Unable to reach \" + url + \".\");\n}\n}\ncatch (PingException) {\nInterlocked.Increment(ref failed);\nthrow;\n}\n}));\n}\ntry {\nawait t;\n}\ncatch {}\n\nConsole.WriteLine(\"All ping attempts succeeded.\");\nConsole.WriteLine(\"{0} ping attempts failed\", failed);\n}\n}\n// The example displays output like the following:\n// 5 ping attempts failed\n``````\n``````open System\nopen System.Net.NetworkInformation\n\nlet mutable failed = 0\n\nlet urls =\n\"www.cohovineyard.com\"\n\"www.cohowinery.com\"\n\"www.contoso.com\" |]\n\nurls\n|> Array.map (fun url ->\nlet png = new Ping()\n\ntry\n\nInterlocked.Increment &failed |> ignore\nraise (TimeoutException \\$\"Unable to reach {url}.\")\nwith :? PingException ->\nInterlocked.Increment &failed |> ignore\nreraise ()))\n\nlet main =\n\ntry\ndo! t\nwith _ ->\n()\n\nprintfn \"All ping attempts succeeded.\"\nprintfn \\$\"{failed} ping attempts failed\"\n}\n\nmain.Wait()\n// The example displays output like the following:\n// 5 ping attempts failed\n``````\n``````Imports System.Collections.Generic\nImports System.Net.NetworkInformation\n\nModule Example\nPublic Sub Main()\nDim failed As Integer = 0\nDim urls() As String = { \"www.adatum.com\", \"www.cohovineyard.com\",\n\"www.contoso.com\" }\n\nFor Each value In urls\nDim url As String = value\nDim png As New Ping()\nTry\nIf Not reply.Status = IPStatus.Success Then\nInterlocked.Increment(failed)\nThrow New TimeoutException(\"Unable to reach \" + url + \".\")\nEnd If\nCatch e As PingException\nInterlocked.Increment(failed)\nThrow\nEnd Try\nEnd Sub))\nNext\nTry\nt.Wait()\nCatch\nEnd Try\n\nConsole.WriteLine(\"All ping attempts succeeded.\")\nConsole.WriteLine(\"{0} ping attempts failed\", failed)\nEnd If\nEnd Sub\nEnd Module\n' The example displays output like the following:\n' 5 ping attempts failed\n``````\n\n### Remarks\n\nThe overloads of the WhenAll method that return a Task object are typically called when you are interested in the status of a set of tasks or in the exceptions thrown by a set of tasks.\n\nNote\n\nIf any of the supplied tasks completes in a faulted state, the returned task will also complete in a Faulted state, where its exceptions will contain the aggregation of the set of unwrapped exceptions from each of the supplied tasks.\n\nIf none of the supplied tasks faulted but at least one of them was canceled, the returned task will end in the Canceled state.\n\nIf none of the tasks faulted and none of the tasks were canceled, the resulting task will end in the RanToCompletion state.\n\nIf the supplied array/enumerable contains no tasks, the returned task will immediately transition to a RanToCompletion state before it's returned to the caller.\n\n### Applies to\n\nCreates a task that will complete when all of the Task<TResult> objects in an enumerable collection have completed.\n\n``````public:\ngeneric <typename TResult>\n``public static System.Threading.Tasks.Task<TResult[]> WhenAll<TResult> (System.Collections.Generic.IEnumerable<System.Threading.Tasks.Task<TResult>> tasks);``\n``static member WhenAll : seq<System.Threading.Tasks.Task<'Result>> -> System.Threading.Tasks.Task<'Result[]>``\n``Public Shared Function WhenAll(Of TResult) (tasks As IEnumerable(Of Task(Of TResult))) As Task(Of TResult())``\n\n#### Type Parameters\n\nTResult\n\nThe type of the completed task.\n\n#### Parameters\n\nThe tasks to wait on for completion.\n\n#### Returns\n\nA task that represents the completion of all of the supplied tasks.\n\n#### Exceptions\n\nThe `tasks` argument was `null`.\n\nThe `tasks` collection contained a `null` task.\n\n### Examples\n\nThe following example creates ten tasks, each of which instantiates a random number generator that creates 1,000 random numbers between 1 and 1,000 and computes their mean. The Delay(Int32) method is used to delay instantiation of the random number generators so that they are not created with identical seed values. The call to the WhenAll method then returns an Int64 array that contains the mean computed by each task. These are then used to calculate the overall mean.\n\n``````using System;\nusing System.Collections.Generic;\n\npublic class Example\n{\npublic static void Main()\n{\nfor (int ctr = 1; ctr <= 10; ctr++) {\nint delayInterval = 18 * ctr;\nvar rnd = new Random();\n// Generate 1,000 random numbers.\nfor (int n = 1; n <= 1000; n++)\ntotal += rnd.Next(0, 1000);\n}\ntry {\ncontinuation.Wait();\n}\ncatch (AggregateException)\n{ }\n\nlong grandTotal = 0;\nforeach (var result in continuation.Result) {\ngrandTotal += result;\nConsole.WriteLine(\"Mean: {0:N2}, n = 1,000\", result/1000.0);\n}\n\nConsole.WriteLine(\"\\nMean of Means: {0:N2}, n = 10,000\",\ngrandTotal/10000);\n}\n// Display information on faulted tasks.\nelse {\nforeach (var t in tasks) {\n}\n}\n}\n}\n// The example displays output like the following:\n// Mean: 506.34, n = 1,000\n// Mean: 504.69, n = 1,000\n// Mean: 489.32, n = 1,000\n// Mean: 505.96, n = 1,000\n// Mean: 515.31, n = 1,000\n// Mean: 499.94, n = 1,000\n// Mean: 496.92, n = 1,000\n// Mean: 508.58, n = 1,000\n// Mean: 494.88, n = 1,000\n// Mean: 493.53, n = 1,000\n//\n// Mean of Means: 501.55, n = 10,000\n``````\n``````open System\n\n[| for i = 1 to 10 do\nlet delayInterval = 18 * i\n\nlet mutable total = 0L\nlet rnd = Random()\n\nfor _ = 1 to 1000 do\ntotal <- total + (rnd.Next(0, 1000) |> int64)\n\n} |]\n\ntry\ncontinuation.Wait()\n\nwith :? AggregateException ->\n()\n\nfor result in continuation.Result do\nprintfn \\$\"Mean: {float result / 1000.:N2}, n = 1,000\"\n\nlet grandTotal = continuation.Result |> Array.sum\n\nprintfn \\$\"\\nMean of Means: {float grandTotal / 10000.:N2}, n = 10,000\"\n\n// Display information on faulted tasks.\nelse\n\n// The example displays output like the following:\n// Mean: 506.34, n = 1,000\n// Mean: 504.69, n = 1,000\n// Mean: 489.32, n = 1,000\n// Mean: 505.96, n = 1,000\n// Mean: 515.31, n = 1,000\n// Mean: 499.94, n = 1,000\n// Mean: 496.92, n = 1,000\n// Mean: 508.58, n = 1,000\n// Mean: 494.88, n = 1,000\n// Mean: 493.53, n = 1,000\n//\n// Mean of Means: 501.55, n = 10,000\n``````\n``````Imports System.Collections.Generic\n\nModule Example\nPublic Sub Main()\nFor ctr As Integer = 1 To 10\nDim delayInterval As Integer = 18 * ctr\nDim total As Long = 0\nDim rnd As New Random()\n' Generate 1,000 random numbers.\nFor n As Integer = 1 To 1000\ntotal += rnd.Next(0, 1000)\nNext\nEnd Function))\nNext\nTry\ncontinuation.Wait()\nCatch ae As AggregateException\nEnd Try\n\nDim grandTotal As Long = 0\nFor Each result in continuation.Result\ngrandTotal += result\nConsole.WriteLine(\"Mean: {0:N2}, n = 1,000\", result/1000)\nNext\nConsole.WriteLine()\nConsole.WriteLine(\"Mean of Means: {0:N2}, n = 10,000\",\ngrandTotal/10000)\n' Display information on faulted tasks.\nElse\nNext\nEnd If\nEnd Sub\nEnd Module\n' The example displays output like the following:\n' Mean: 506.34, n = 1,000\n' Mean: 504.69, n = 1,000\n' Mean: 489.32, n = 1,000\n' Mean: 505.96, n = 1,000\n' Mean: 515.31, n = 1,000\n' Mean: 499.94, n = 1,000\n' Mean: 496.92, n = 1,000\n' Mean: 508.58, n = 1,000\n' Mean: 494.88, n = 1,000\n' Mean: 493.53, n = 1,000\n'\n' Mean of Means: 501.55, n = 10,000\n``````\n\nIn this case, the ten individual tasks are stored in a List<T> object. List<T> implements the IEnumerable<T> interface.\n\n### Remarks\n\nThe call to WhenAll<TResult>(IEnumerable<Task<TResult>>) method does not block the calling thread. However, a call to the returned Result property does block the calling thread.\n\nIf any of the supplied tasks completes in a faulted state, the returned task will also complete in a Faulted state, where its exceptions will contain the aggregation of the set of unwrapped exceptions from each of the supplied tasks.\n\nIf none of the supplied tasks faulted but at least one of them was canceled, the returned task will end in the Canceled state.\n\nIf none of the tasks faulted and none of the tasks were canceled, the resulting task will end in the RanToCompletion state. The Task<TResult>.Result property of the returned task will be set to an array containing all of the results of the supplied tasks in the same order as they were provided (e.g. if the input tasks array contained t1, t2, t3, the output task's Task<TResult>.Result property will return an `TResult[]` where `arr == t1.Result, arr == t2.Result, and arr == t3.Result)`.\n\nIf the `tasks` argument contains no tasks, the returned task will immediately transition to a RanToCompletion state before it's returned to the caller. The returned `TResult[]` will be an array of 0 elements.\n\n### Applies to\n\nCreates a task that will complete when all of the Task<TResult> objects in an array have completed.\n\n``````public:\ngeneric <typename TResult>\n``public static System.Threading.Tasks.Task<TResult[]> WhenAll<TResult> (params System.Threading.Tasks.Task<TResult>[] tasks);``\n``static member WhenAll : System.Threading.Tasks.Task<'Result>[] -> System.Threading.Tasks.Task<'Result[]>``\n``Public Shared Function WhenAll(Of TResult) (ParamArray tasks As Task(Of TResult)()) As Task(Of TResult())``\n\n#### Type Parameters\n\nTResult\n\nThe type of the completed task.\n\n#### Parameters\n\nThe tasks to wait on for completion.\n\n#### Returns\n\nA task that represents the completion of all of the supplied tasks.\n\n#### Exceptions\n\nThe `tasks` argument was `null`.\n\nThe `tasks` array contained a `null` task.\n\n### Examples\n\nThe following example creates ten tasks, each of which instantiates a random number generator that creates 1,000 random numbers between 1 and 1,000 and computes their mean. In this case, the ten individual tasks are stored in a `Task<Int64>` array. The Delay(Int32) method is used to delay instantiation of the random number generators so that they are not created with identical seed values. The call to the WhenAll method then returns an Int64 array that contains the mean computed by each task. These are then used to calculate the overall mean.\n\n``````using System;\nusing System.Collections.Generic;\n\npublic class Example\n{\npublic static void Main()\n{\nfor (int ctr = 1; ctr <= 10; ctr++) {\nint delayInterval = 18 * ctr;\ntasks[ctr - 1] = Task.Run(async () => { long total = 0;\nvar rnd = new Random();\n// Generate 1,000 random numbers.\nfor (int n = 1; n <= 1000; n++)\ntotal += rnd.Next(0, 1000);\n\n}\ntry {\ncontinuation.Wait();\n}\ncatch (AggregateException)\n{}\n\nlong grandTotal = 0;\nforeach (var result in continuation.Result) {\ngrandTotal += result;\nConsole.WriteLine(\"Mean: {0:N2}, n = 1,000\", result/1000.0);\n}\n\nConsole.WriteLine(\"\\nMean of Means: {0:N2}, n = 10,000\",\ngrandTotal/10000);\n}\n// Display information on faulted tasks.\nelse {\n}\n}\n}\n// The example displays output like the following:\n// Mean: 506.38, n = 1,000\n// Mean: 501.01, n = 1,000\n// Mean: 505.36, n = 1,000\n// Mean: 492.00, n = 1,000\n// Mean: 508.36, n = 1,000\n// Mean: 503.99, n = 1,000\n// Mean: 504.95, n = 1,000\n// Mean: 508.58, n = 1,000\n// Mean: 490.23, n = 1,000\n// Mean: 501.59, n = 1,000\n//\n// Mean of Means: 502.00, n = 10,000\n``````\n``````open System\n\n[| for i = 1 to 10 do\nlet delayInterval = 18 * i\n\nlet mutable total = 0L\nlet rnd = Random()\n\nfor _ = 1 to 1000 do\ntotal <- total + (rnd.Next(0, 1000) |> int64)\n\n} |]\n\ntry\ncontinuation.Wait()\n\nwith :? AggregateException ->\n()\n\nfor result in continuation.Result do\nprintfn \\$\"Mean: {float result / 1000.:N2}, n = 1,000\"\n\nlet grandTotal = Array.sum continuation.Result\n\nprintfn \\$\"\\nMean of Means: {float grandTotal / 10000.:N2}, n = 10,000\"\n\n// Display information on faulted tasks.\nelse\n\n// The example displays output like the following:\n// Mean: 506.38, n = 1,000\n// Mean: 501.01, n = 1,000\n// Mean: 505.36, n = 1,000\n// Mean: 492.00, n = 1,000\n// Mean: 508.36, n = 1,000\n// Mean: 503.99, n = 1,000\n// Mean: 504.95, n = 1,000\n// Mean: 508.58, n = 1,000\n// Mean: 490.23, n = 1,000\n// Mean: 501.59, n = 1,000\n//\n// Mean of Means: 502.00, n = 10,000\n``````\n``````Imports System.Collections.Generic\n\nModule Example\nPublic Sub Main()\nFor ctr As Integer = 1 To 10\nDim delayInterval As Integer = 18 * ctr\nDim total As Long = 0\nDim rnd As New Random()\n' Generate 1,000 random numbers.\nFor n As Integer = 1 To 1000\ntotal += rnd.Next(0, 1000)\nNext\nEnd Function)\nNext\nTry\ncontinuation.Wait()\nCatch ae As AggregateException\nEnd Try\n\nDim grandTotal As Long = 0\nFor Each result in continuation.Result\ngrandTotal += result\nConsole.WriteLine(\"Mean: {0:N2}, n = 1,000\", result/1000)\nNext\nConsole.WriteLine()\nConsole.WriteLine(\"Mean of Means: {0:N2}, n = 10,000\",\ngrandTotal/10000)\n' Display information on faulted tasks.\nElse\nNext\nEnd If\nEnd Sub\nEnd Module\n' The example displays output like the following:\n' Mean: 506.38, n = 1,000\n' Mean: 501.01, n = 1,000\n' Mean: 505.36, n = 1,000\n' Mean: 492.00, n = 1,000\n' Mean: 508.36, n = 1,000\n' Mean: 503.99, n = 1,000\n' Mean: 504.95, n = 1,000\n' Mean: 508.58, n = 1,000\n' Mean: 490.23, n = 1,000\n' Mean: 501.59, n = 1,000\n'\n' Mean of Means: 502.00, n = 10,000\n``````\n\n### Remarks\n\nThe call to WhenAll<TResult>(Task<TResult>[]) method does not block the calling thread. However, a call to the returned Result property does block the calling thread.\n\nIf any of the supplied tasks completes in a faulted state, the returned task will also complete in a Faulted state, where its exceptions will contain the aggregation of the set of unwrapped exceptions from each of the supplied tasks.\n\nIf none of the supplied tasks faulted but at least one of them was canceled, the returned task will end in the Canceled state.\n\nIf none of the tasks faulted and none of the tasks were canceled, the resulting task will end in the RanToCompletion state. The Result of the returned task will be set to an array containing all of the results of the supplied tasks in the same order as they were provided (e.g. if the input tasks array contained t1, t2, t3, the output task's Result will return an `TResult[]` where `arr == t1.Result, arr == t2.Result, and arr == t3.Result)`.\n\nIf the supplied array/enumerable contains no tasks, the returned task will immediately transition to a RanToCompletion state before it's returned to the caller. The returned `TResult[]` will be an array of 0 elements."
]
| [
null
]
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https://edboost.org/node/1673 | [
"# Writing Decimals as Words/Numerals\n\nPacket includes:\n6 worksheets, with 15 problems each (90 problems per packet)\n\nOne of the key aspects of understanding decimals is understanding place value -- and learning how to translate decimals to words and words to numerals is a good way to practice decimal place value.\n\nSample Problem(s):\n\nWrite the decimal in words:\n\n.07\n\n.567\n\nWrite the words as a decimal:\n\nfour hundreds\n\ntwo hundred sixty-one thousands\n\n## Decimals: writing it out in words 2 | Decimals | Pre-Algebra | Khan Academy",
null,
"",
null,
"Words to Numerals Up to 3 Decimal Digits.pdf",
null,
"Words to Numerals Up to 3 Decimal Digits Answer Key.pdf"
]
| [
null,
"https://edboost.org/sites/edboost.org/files/media-youtube/G7QiIkYfeME.jpg",
null,
"https://edboost.org/modules/file/icons/application-pdf.png",
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"https://edboost.org/modules/file/icons/application-pdf.png",
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.7622827,"math_prob":0.9134515,"size":586,"snap":"2019-51-2020-05","text_gpt3_token_len":135,"char_repetition_ratio":0.14261168,"word_repetition_ratio":0.06666667,"special_character_ratio":0.22525597,"punctuation_ratio":0.11504425,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95557284,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,10,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-15T03:01:37Z\",\"WARC-Record-ID\":\"<urn:uuid:069a9e6d-7022-46a0-b107-806497880106>\",\"Content-Length\":\"25520\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7705613d-902a-409e-aa5d-29f5446f4ad1>\",\"WARC-Concurrent-To\":\"<urn:uuid:576dd4b8-4c18-434d-93c3-bed87f79fb98>\",\"WARC-IP-Address\":\"192.252.156.35\",\"WARC-Target-URI\":\"https://edboost.org/node/1673\",\"WARC-Payload-Digest\":\"sha1:FFE33YPWU44YONHALHO75SNHUGVI6B6A\",\"WARC-Block-Digest\":\"sha1:WLR4L5ISGL6PBLJR7WLEDMD6QKZ47RJY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541301014.74_warc_CC-MAIN-20191215015215-20191215043215-00009.warc.gz\"}"} |
https://www.webqc.org/molecularweightcalculated-190824-1.html | [
"",
null,
"#### Chemical Equations Balanced on 08/24/19\n\n Molecular weights calculated on 08/23/19 Molecular weights calculated on 08/25/19\nCalculate molecular weight\n 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\nMolar mass of ca is 40.078\nMolar mass of f is 18.9984032\nMolar mass of Cr(NO3)3 is 238.0108\nMolar mass of H3PO4 is 97.995182\nMolar mass of (NH4)2CO3 is 96.08582\nMolar mass of C2H5o is 45.0605\nMolar mass of N2O5 is 108,0104\nMolar mass of C4H10O3 is 106.1204\nMolar mass of CaF2 is 78.0748064\nMolar mass of C6H12O6 is 180,15588\nMolar mass of ammonia is 17.03052\nMolar mass of [H2][O2][N2][CH4][CO][CO2][C1][C2][C3][C4][C5][C6][C7][C8] is 582,47534\nMolar mass of NaC12H25SO4 is 288.37926928\nMolar mass of NaH2PO4 is 119.97701128\nMolar mass of phenol is 94.11124\nMolar mass of CaCO3 is 100.0869\nMolar mass of C12 is 144.1284\nMolar mass of C12 is 144.1284\nMolar mass of Zn2(AsO4)(OH) is 286.68654\nMolar mass of Ni (CH3COO) 2·4H2O is 248.84256\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of Co (CH3COO) 2·4H2O is 249.082355\nMolar mass of NiSO4 (NH4)2SO4 6H2O is 976.8856\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Mn (CH3COO) 2·4H2O is 245.087205\nMolar mass of Ni is 58.6934\nMolar mass of NaC12H25SO4 is 288.37926928\nMolar mass of Ar is 39.948\nMolar mass of Ca2Al3(SiO4)(Si2O7)O(OH) is 454.3572558\nMolar mass of SF6(ion) is 146.0554192\nMolar mass of SF6 is 146.0554192\nMolar mass of sucrose is 342.29648\nMolar mass of sucrose is 342.29648\nMolar mass of *5o2 is 159.994\nMolar mass of SF6(ion) is 146.0554192\nMolar mass of NiCo is 117.626595\nMolar mass of c is 12.0107\nMolar mass of H2 is 2.01588\nMolar mass of H2O is 18.01528\n 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\nCalculate molecular weight\n Molecular weights calculated on 08/23/19 Molecular weights calculated on 08/25/19\nMolecular masses on 08/17/19\nMolecular masses on 07/25/19\nMolecular masses on 08/24/18\nBy using this website, you signify your acceptance of Terms and Conditions and Privacy Policy."
]
| [
null,
"https://www.webqc.org/pictures/webqclogo2.png",
null
]
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https://cran.fhcrc.org/web/packages/decido/vignettes/decido.html | [
"Constrained triangulation of polygons\n\nDecido aims to provide very fast constrained triangulations for polygons using a robust C++ library created by Mapbox.\n\nConstrained triangulation by ear clipping is an important low-cost method for decomposing a polygon into triangles, used for 3D visualization and many analytical techniques. Here constrained means shape-preserving, in the sense that every edge of the polygon will be included as the edge of a triangle in the result.\n\nEar clipping (or cutting) must be applied to a path-based polygon that consists of only one island, with zero or more holes. Any multiple island polygons must be triangulated separately by this method.\n\nThe better-known Delaunay triangulation is generally not shape-preserving as it works only on points, without knowledge of input line segments or polygon edges. Shape-preserving Delaunay or more commonly near-Delaunay triangulation is performed on a set of edges rather than paths, and can be performed on multiple polygons at once. Holes require careful trimming of triangles after the decomposition is performed in this approach. (See the anglr package for the DEL0() function for high-quality triangles, with control over size, angle, and the Delaunay criterion).\n\nExample\n\nThis is a basic example of triangulating a single-ring polygon. The output is a vector of triplet indices defining each triangle.\n\nlibrary(decido)\nx <- c(0, 0, 0.75, 1, 0.5, 0.8, 0.69)\ny <- c(0, 1, 1, 0.8, 0.7, 0.6, 0)\n(ind <- earcut(cbind(x, y)))\n#> 2 1 7 7 6 5 5 4 3 2 7 5 5 3 2\n\nplot_ears(cbind(x, y), ind)",
null,
"Support for holes is provided by the argument holes. The values are the starting index of each hole, here in R's 1-based convention.\n\n## polygon with a hole\nx <- c(0, 0, 0.75, 1, 0.5, 0.8, 0.69,\n0.2, 0.5, 0.5, 0.3, 0.2)\ny <- c(0, 1, 1, 0.8, 0.7, 0.6, 0,\n0.2, 0.2, 0.4, 0.6, 0.4)\nind <- earcut(cbind(x, y), holes = 8)\nplot_ears(cbind(x, y), ind)",
null,
"The hole-specification is a little subtle, since usually R's functions (polygon and polypath, and others) expect NA values to separate paths.\n\nNotice how the hole begins at index 8, hence holes = 8 above, and holes = c(8, 13) below.\n\nplot_ears(cbind(x, y), ind, col = \"grey\", border = NA)\ntext(x, y, labels = seq_along(x), pos = 2)",
null,
"The method is subtle.\n\nThis example adds a third polygon, a second hole in the island.\n\nx <- c(0, 0, 0.75, 1, 0.5, 0.8, 0.69,\n0.2, 0.5, 0.5, 0.3, 0.2,\n0.15, 0.23, 0.2)\ny <- c(0, 1, 1, 0.8, 0.7, 0.6, 0,\n0.2, 0.2, 0.4, 0.6, 0.4,\n0.65, 0.65, 0.81)\nind <- earcut(cbind(x, y), holes = c(8, 13))\nplot_ears(cbind(x, y), ind, col = \"grey\")",
null,
"Performance for developers\n\nThere is a headers API for decido.\n\n## this code is not run in the vignette\n## but can be run as is with decido installed\nlibrary(Rcpp)\n\ncppFunction(\ndepends = \"decido\"\n, includes = '#include \"decido/decido.hpp\"'\n, code = '\nRcpp::IntegerVector earcut0( SEXP polygon ) {\nreturn decido::api::earcut( polygon );\n}\n'\n)\n\npoly <- list(matrix(c(0,0,0,1,1,1,1,0,0,0), ncol = 2, byrow = T))\nearcut0( poly )\n# 1 4 3 3 2 1\n\nOrientation\n\nTriangles are returned in counter-clockwise order, as is proper and good in a world where area is positive (I'm kidding, it's just a convention that folks use … see fortunes::fortune(\"illogical\")).\n\nFirst a function so I can show this with a plot.\n\n## plot triangles (input is triplets of xy coordinates)\n## with one side an oriented arrow\nplot_tri <- function(x, add = TRUE) {\nif (!add) plot(x, asp = 1, type = \"n\")\nidx <- c(1:3, 1)\nfor (i in seq_len(nrow(x)/3)) {\n#print(idx)\n## plot only the first arrow\narrows(x[idx, 1], x[idx, 2],\nx[idx, 1], x[idx, 2], length = 0.25, lwd = 2, col = \"firebrick\")\n## segments the rest\nsegments(x[idx[2:3], 1], x[idx[2:3], 2],\nx[idx[3:4], 1], x[idx[3:4], 2])\n\nidx <- idx + 3\n\n}\n}\n\nSee how each triangle has its first edge (the first two indexes) shown as an arrow. They're all counter-clockwise. I've checked this on very large sets of real-world inputs, you can get 0-area polygons and very small negative-epsilon area polygons when the 3 points are collinear or so close to it that numeric precision fails us.\n\nplot_tri(cbind(x, y)[ind, ], add = FALSE)",
null,
"(See this discussion for more on the topic where I was exactly backwards on the counter-clockwise thing, but airing the topic was very helpful).\n\nOrientation is not really important in planar contexts, though you'll find very little consensus on this. (Would it not be handy if all holes in polygons had negative area …). It really matters in 3D because the orientation has a more definite meaning when the triangles are representing surfaces.\n\nComparing paths and triangles\n\nThis example defines a much simpler shape, the minimal shape able to be decomposed to triangles (and not stay a triangle).\n\nA quadrilateral, with two holes that are open to each other allows the use of the same data, and we can tweak whether we wanted one hole or two. This is an important example used for validating early versions of this package.\n\nx <- c(0, 0, 1, 1,\n0.4, 0.2, 0.2, 0.4,\n0.6, 0.8, 0.8, 0.6\n)\ny <- c(0, 1, 1, 0,\n0.2, 0.2, 0.4, 0.4,\n0.6, 0.6, 0.4, 0.4\n)\nind <- decido::earcut(cbind(x, y), holes = c(5, 9))\nplot_ears(cbind(x, y), ind, col = \"grey\")\ntitle(\"triangle plot, two holes\")",
null,
"plot_holes(cbind(x, y), holes = c(5, 9), col = \"grey\")\ntitle(\"path plot, two holes\")",
null,
"ind <- decido::earcut(cbind(x, y), holes = 5)\nplot_ears(cbind(x, y), ind, col = \"grey\")\ntitle(\"triangle plot, two holes as one\")",
null,
"plot_holes(cbind(x, y), holes = 5, col = \"grey\")\ntitle(\"path plot, two holes as one\")",
null,
"A geographic example\n\nFor good measure we include a geographic example, a triangulation of the mainland part of Tasmania from the oz package.\n\nlibrary(oz)\noz_ring <- oz::ozRegion(states = FALSE)\nring <- oz_ring\\$lines[]\nindices <- earcut(ring[c(\"x\", \"y\")])\nplot_ears(cbind(ring\\$x, ring\\$y), indices)",
null,
"Variants\n\nThe actual triangulation obtained depends on where the polygons start. This is complicated, because of the sheer number of possible variants, combinations of starting points among the island and its holes.\n\nImportant “edge” cases are degeneracies, holes touching the island or each other, duplicated edges, intersecting edges, zero-length edges, holes actually external to islands, already existing triangles, and existing quadrilaterals (amongst others). We aren't going to explore those here, and we are reasonably confident that Mapbox has been presented with a rich enough pool of variant polygons to make its library pretty robust. There's no uniquely “correct” here either, different systems and standards will apply different rules and allow or choose differently.\n\nFirst a function to “rotate” coordinates to different start/end.\n\nvecrot <- function(x, k) {\nif (k < 0 || k > length(x)) warning(\"k out of bounds of 'x' index\")\nk <- k %% length(x)\n## from DescTools::VecRot\nrep(x, times = 2)[(length(x) - k + 1):(2 * length(x) - k)]\n}\n\nNow plot each possible variant of defining the polygon ring by traversing the boundary anti-clockwise from a different starting vertex, shown as a filled point symbol.\n\nx <- c(0, 0, 0.75, 1, 0.5, 0.8, 0.69)\ny <- c(0, 1, 1, 0.8, 0.7, 0.6, 0)\n(ind <- earcut(cbind(x, y)))\n#> 2 1 7 7 6 5 5 4 3 2 7 5 5 3 2\n\nplot_ears(cbind(x, y), ind)\npoints(x, y, pch = 19, col = \"firebrick\")\ntitle(\"original\")",
null,
"op <- par(mfrow = c(2, 3))\nfor (rot in head(seq_along(x), -1)) {\nxx <- vecrot(x, rot); yy <- vecrot(y, rot)\nind <- earcut(cbind(xx, yy))\nplot_ears(cbind(xx, yy), ind)\ntitle(sprintf(\"rot %i\", rot))\npoints(xx, yy, pch = 19, col = \"firebrick\")\n}",
null,
"par(op)\n\nCompare this to constrained Delaunay triangulation from the RTriangle package (not illustrated here but the result is that the constrained triangulation is different from all variants above, and the conforming triangulation inserts two points not included in the original data - these are called Steiner points).\n\nlibrary(sfdct)\nlibrary(sf)\nxsf <- st_sfc(st_polygon(list(cbind(x, y)[c(seq_along(x), 1), ])))\nplot(ct_triangulate(xsf, Y = TRUE), col = NA)\n\n## now a conforming Delaunay triangulation\nplot(ct_triangulate(xsf, D = TRUE), col = NA)\n\nPerformance\n\nCompare timing of C++ versus JS implementations, the original C++ decido was born from the Javascript version 'rearcut'. With version 0.3.0 decido gained a C++ headers API thanks to David Cooley.\n\nring <-\nremotes::install_github(\"hypertidy/rearcut\")\n\nlibrary(Rcpp)\n## some people love to see the world burn by\n## ignoring indexes and working purely in coordinates ...\ncppFunction(\ndepends = \"decido\"\n, includes = '#include \"decido/decido.hpp\"'\n, code = '\nRcpp::IntegerVector earcut0( SEXP polygon ) {\nreturn decido::api::earcut( polygon );\n}\n'\n)\n\ndim(ring <- decido:::ant_cont )\n\nrbenchmark::benchmark(js = rearcut::earcut(ring),\ndecido = decido::earcut(ring),"
]
| [
null,
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8BodvS0W2otrO7TRzyZXwwZzYapM+y3h9J9GoknA24DDWdhQ+oFVcPnPp3EC5hImUzU6UZ9yNynk3iyRMBESpqBf3DeHyb3aSWelFwPHDCZORNci4TGfXqJb8jeCBwxiV3dvZQKh/v0Ek/Wgi17aUuux9uDIXCfZuLJhe6tMQejHvZcVHX36SY+XvAieMwuFvlaYE9p9+kmnmwSNpGStC2d7bOCuu7TTjy5xpLzEpCi7b6rKOo+/cSToidERG3n8pkstVR0n4bid0TFTaRc35+xonLu01A8uXuwkLAGjndtnVHLfTqKJ/3miYnbSvE6ntoKuU9L8buzhOWNnsW74JIq7rnFb91Fmv71jDPmHTTvkCiePNFLUGBSW8gfQwn33OJP2kZmnrrsN0MtKSBliien3Swqcg7IbJr6FVdIds8t/uivSdFuQr4oMu+QKr5B2ETKEqhH+yS75/+Lf5X0aL18qrc8iShVPFndXdDsxoUj4WLJdM8t/pkezz40au3a0hvMO+SKJ2OmiInb6PeurTPS3POP6l8e9oNIpNsdSg3uSNtEyioxgY/dCRxQjnuIy7mDH9tliJEsnmzMPSAk7kSITOYmOt0f+Pdr7q1zLQ5BWl7HtzP5PCFhX4JOh9OO4b6+bMXuqhECl+7rAkp81VzzFuniRU2kzBYSlbS5Hzmo9e/+P8Xdd6SAEr+sK+HrmuEGhWXutYSKFzWRst8fRUQ1WLRs0cnk058Ji0+Rxk09ITNPFxH1xskiohpsmhU/jzzzmLD4FGktnvReKCDo+5Z7VXDcMG3c/Rc0iYvfBb/4zbGSwSWxzZbtKojflfWJgKjZYi4XDOZNeSWYtdS4xVdGY4tXLi6PVpp3qCCeLGB9cMKJM58UEDTBnVvExU6CW3yPauNly3HmHUqIJ4N+AR9zwTnwMTu4KKgV1bjFH1NvvOzNNO9QQ3xd9D3wmPvywEN2IvD/VDLc4qeUbW440lBdZtGshniyVMCyl92ELZj99RWiIpvhFr8/lhGJRDLL95t3KCKejLgOPOTF4BmNO3hD6Or7NACXc82122qbrZtVEX8gdwN0yDWDoCN2sPBlUZHNpPd1vME68ImULVHggJ1c86moyGY0EE/GXwwdsa+o2dilRwQFtqCD+Hg3l5UsfFMuaLnsQx6+3wBCB/GkOroPNuB7lrsWMPyPsGdELWghnkwvAQ6YLeZ++splQsLaoYd40msRbLzTl8LGSzBnq5CwdmgifkfU7ukwdu4fAxqug3ECv/4xoYl4cvdA0HD1+aDhOhgtJKotuogn/e8DDVewGzRcO3s8fGRQaCP+80z/i1k4MM4+ySwfVQ8KCJoCbcSTJ0EvwVadAhktwYL1AoKmQB/xZPjPAYPFRTxre5XohdcpNBLfkP02YLTemwCDJSiFD5kSjcST5yAnUk6/Bi5WgoPj3MuAoZN4UnY5XKytx8PFSlAj4DGxlGglPl6wFi5YFHzV3KefgY7ogFbiyZs5cLfGhoJP0LplG3REB/QST6bC3Ru7dyxYqARlgcykSKCZ+Jaip6FC1RVAReogwBu22okn2+AmUuYDT2fePQ02njO6iSe3D4WKVAZ795+88ivYeM54E39Ljf/IioonfR4ACvT0aUCBEvzba7DxnPEmflb3gQ9+5jOyquLBJlIeAr5rOzmQlTA68NjUx1+Zmjlmua95XaqKJwtS5w30Ry/YtfRGgUZzw3sf//4pkWOm+/gWWlnxZAjQ8kVXgyY7+/5CyGiueBS/b+k5ueXVn832MYVEXfH1UbvswP6p7gMSJsE7wuZl2eJN/OUZP/1d292FFsuc2NSoK56sAppImRUHCdPOU78FDOaON/G/6nhU8XvvkRUWT0ZdDRJmyHMgYdq5SXBiXBPaXccbNOW+DhHmLshu+TybiacC0VM8eRVkIuXn3QCCJDgS6A1bbcWTiSAPPeTBLT/6Mfw0fkd0FR8vWAUQZfR8gCDt/MevwUJ5QlfxZGs2wETKJWfwx0hw35/AQnlCW/Gk3FeeWHsOWdIzMHNZPVgoT+grnhz/OH+MnjC3gkiAy10l0Fj8ziz+x9inzgA4kTb2jwcK5BWNxZN7+Fee3wD1hc9/iZiS5YTO4kkx/+1xjpSjSTz5e5g4ntFafF2U+zbpQKDldSp2wMTxjNbiSWVP3ghzJkCcR+snEcya1V3oLZ78pIIzwK7uIOfRImaFDQc0F9+Q8xZnhFyQp3Z3lkNE8YPm4smafM7v1Ec9DHIaiyGi+EF38eQCzrzgiwBuABIy15rhQzDai48XvMRVvwkk5egE4BUY3dFePNmU08hVvwgiE0IpQAx/oHgyrZSr+qSZ/KewbyJ/DJ+g+Na/Wa6JlOsB8h39+V/5Y/gExROyPco1hwXgru1jL3CH8AuKb+VOrrXLitdxn8D1H3KH8AuQ+D7Wv5kQiSd9eVLBzOa8IGxlNHzCJDe4xY8zOHqM5eHFMInfncWRV6q2kPfwh4PLT9AJf965UQ+1kjX3IfOOMIknj/TlqJzDmyRwO+TSix7hFv/p+AmfEFL4pWVHqMSTobPZ6454lPPgz1nys4oHoI9/qXheU+jF78tmn/P865GcBw8soSwFxODu+ztOzgi7eLKafdnLRt67toEllKWAGdVvr/yHZVvIxJPRVzJXPZbz8Zmgn7BtA6/jO2jKY16DZiLfSgvBJZSlgBJfNbfz7d4ag6smuddSSTxZn8c6kXIt3+O6wSWUpYASv6zrOv6NCoNTPExLVEo8uex81ppZXMddCLjCrmewqe+ipZB1edp+VTzHDS6hLAWKp6jJZnyA7sbJPIcNLqEsBb/4zbGSwSUx66NDIRRPZjDOft1exHHQZgk3bAHEV0Zji1cuLo9abj6FUTzpzThLnWc59PeCSyhLwS2+R7XxssWS4ymU4ndm7mKqd+YT7McMMKEsBf+XNO3zuvdaFkILpXgyv5ip2oJS9kMGmFCWglv8lLLNDUcaqsssmsMpngyYw1JrXx77EQNMKEvBLX5/LCMSiWSW7zfvCKl4xomU3di/0A94uasEAJdzzbXbam3WaAupeLKEaSLlxbexHi/IhLIUeB1voYRlbeI1Plb5TSbIhLIUKN5CY3Sj/0otUdbDBZlQlgLFW1nLsuxlX4b/LQZBJpSlQPE2XMSw2kH5VYwHK2WsxwmKtyFe8KLvOu8xZikPNKEsBYq3g2UiZTZbusBAE8pSoHhbrj3bd5XTlzIdKdCEshQo3p4i3zff72dbxibQhLIUKN6eHdE97oWSqM9nOtDYIBPKUqD4FNw92G+NAh8purqQc8MWxaem3zyfFcaxrEoabEJZChSfit1Ztf4qrGKZbB1sQlkKFJ+SJ3r5Kx9nSTkabEJZChSfmtN8PhPVe5P/YwSbUJYCxaemIfttX+WnX+P/GMEmlKVA8Q48528i5dbjfR8h4ISyFCjeiTFTfBWP+v5WL+CEshQo3ommPF9TZIb6nokTcEJZChTvyMZcP09C3jvWb/yAE8pSoHhnJp/no3Bdgd/wYyAynTKB4p3xN5Ey3+fFWdAJZSlQvAs1UR8TKcvu8xc86ISyFCjejZnDvJddfpq/2EEnlKVA8a70Xui56CGfd22DTihLgeJd2ZX1ieeyvfwtmhZ0QlkKFO/Ogn6ei17tbzKGjOWuEqB4Dwzy/EDkW338xA08oSwFivdAXdRz+pGon6RWgSeUpUDxXlh6rNdva4as9hE28ISyFCjeEyOv9VjwLj9ftwWeUJYCxXviQO4GbwX3dPMRNfCEshQo3hvrvE6kzKvzHDP4hLIUKN4j4y/2Vu7cBzyHDD6hLAWK90i8m7dM8UuGew4ZfEJZChTvleqopzSgh3I8Rww+oSwFivfM9BJPxXq+6zVg8AllKVC8d3o97qXUlRVe45UynwkAKN47O7K8TKTccILHcBISylKgeB/cPdBLKa8pRyUklKVA8X446V4PhQZ5G/6Tx4NPKEuB4v3weeZ290K3efzOTUJCWQoU74snPSxxtKu7t1gSEspSoHh/DPeQDTTX0+OZMhLKUqB4f3iZSDnqYS+RZCSUpUDxPvEwkXLRWZ4CSUgoS4Hi/TL2crcSTZ7u2spIKEuB4v0SL3BNE1fk5UktGQllKVC8b950zTw0aaaHMBKfsG0DxftnqtuMt/X93YNISShLgeL901L0tEsJD3dt3/glzMmwwi/+w+f/3vrz8KPm7ekrnmyLusyAKV7nGkNKQlkKbvFrf9z/RzMPkyZLyTQWT24f6rx/9qWuIaQklKXgFn/qErLn3MnNeoknfZyfrKstdI0gJaEsBX/Cwa8JOTj+ku/0Er8ry/lzy3G7VpOTUJaCW/wJNa0/Dk0co5d48vCJjrtHWIY8JuQklKXgFn/TrLaf8SmaiSdDbnXa++uRLtXlJJSl4BZ/qD3F5OFPzTvSXHx91OmhysZcl+pyEspS4HU8K6scJ1Ie6zItTk5CWQoo8VVzO99+8JRBmYccXmEWT0Zd7bBzomNPIC8/QSdQ4pd1ZdHSRXxT7uupd6492bGupISyFNjUs/Oq00TKLMeqkhLKUqB4DiY6JAvs57gKrqSEshT84jfHSgaXxKzTwDQQHy9YlXLfjZOdakpKKEvBLb4yGlu8cnF51PIgkQbiydbslNPfthc5VSwFPxW/cIvvUW28bLE8d6yDeFJ+ZspdTo9rHLxAwLn4g/9effs3lHszzTu0EE+OTzmR8kyHXJU1Lhd7AcAtfkrZ5oYjDdVlFs16iN+Zlaq3XlCaupashLIU3OL3xzIikUhm+X7zDj3Ek3uKU+zYl5e6kqyEshQAl3PNtdtqm62bNRFPilOlleme+qOVlVCWAq/jeamLpkgvMv62lHWk37BF8QBU9rTfvmZQqhrSEspSoHh+zrRftqwlmqqCtISyFCien4act2y3n7AxRQVpCWUpUDwAa/Jt16yuuDJFeWkJZSlQPAQX2D5O/V6Kzl9eQlkKFA9BvOBFu81R+7u28hLKUqB4EDblNNpsHb7UtrC8hLIUKB6GaaU2Gx+w//fJSyhLgeKBKLJ5Xro+37aovISyFCgeiO1ZNkP1gt12ReUllKVA8VDceYp12zi7bEMSE8pSoHgwTrjfsmm1zX8GmQllKVA8GLutEynjdilHJSaUpUDxcDzS17Kp9yZrsXnyEspSoHhAhs4yb5l+jbWUxISyFCgekH3Z5pzCNb2spSQvd5UAxUOy2rLsZdRy6SYzoSwFigdltPkLuaHLzUVkJpSlQPGgNOWZvmq/d6y5iMyEshQoHpb1eclte12BuYTMhLIUKB6Yy0x/4vnmO7kyE8pSoHhgWgqfTfq97F7TfpkJZSlQPDQ12UkJKpab1kKUmlCWAsWDM+MM+rdDpru2UhPKUqB4eHon3YzvlXxTZ67NTVwZoHh4dmZ+Qv129fVJOyfsDfZkUoHiBfDgSdQvb/VJ2lca6JmkBsWLYMAc6pco/dC93ISyFCheBHVRKivNkNXUnjelJpSlQPFCWELNpbiLfoxebkJZChQvhpKuId2ebtR2uQllKVC8GBqzu2ZM5tV1bZebUJYCxQtiXdeyl+d2pbOQnFCWAsWL4qLOtXyXDO/cKDmhLAWKF0XXRMpDXSlHJSeUpUDxwuiaSNmzM6eB5ISyFCheHNd25Ce5sqJjk+SEshQoXiC9EotbbjihY4saT9i2geIFsiO6p/1NR8pR2QllKVC8SO5OrHg26A/tr7ITylKgeKH0m2e83JZ4ll52QlkKFC+U3Vm1bS+7urf/KjuhLAWKF8sT7XOoctufwztHckJZChQvmGEz236WPtz2s9kyu0IeKF4wDdlvt/584qy299ITylKgeNE81zaRsslIOSo9oSwFihfOmCmtP4raHsmRnlCWAsULpymvipBJbV299ISyFChePBtzD5Cq/kSJ/ASdYMLBAJh8HiHZLQoklKXAhIMB0FK4nBSvVSChLAUmHAyCbdFvZ1+qQEJZCkw4GAgzh9UWKpBQlgITDgZDn4U5DaWyT4JGasLBz4Z941omTdiVNeRGFRJTdCIx4eCRiiv6lC3ycIC0YNpRuYMuwev4NlbMb23qJ6mwdnsA7CsdeNTyF/5F9ml0ASW+am7n2zcqDE75qfuh+1SUjarQgvHDp/7gj+pMp4ATv2xc59u9NQYPuGXVu/0dsqPmjodqtOB3U2teO7xXlTnSRGRT//yTLgXeH7uHvHf2d+xHCBOHz99A9l/5iuzT6EKieLJl4ujrPnErlC58c8von74s+yQoxN2rdxePSETcvXoUrzTi7tWjeKURd68exSuNuHv1KF5pxN2rR/FKI+5ePYpXGpnX8YhEULymoHhNESf+j0PHupKZz09uBkCQaBQgSEYuQJB/AoiRn+v+0Z/8hSjxXoB49OpvlvSODDzzDECQWX8DCALyNBp/EBTvAxTvGRRvAcV7BcWLCILifYDiPYPiLeghHmJpkA9mAwRZuRIgyOwPAIKArJbCH0SweMs3OwwcaXQv48ohS7ZvBhohljaC+EgAgggWj6gKitcUFK8pKF5TULymoHhNQfGaguI1RYz4/VMzjqu0ec8a5NDME485lWliWvLRPz1mnENZb0FWFB9dzLKAJR1k+5isojkMmQkfO+2HM2xPyj9ixJeP+Xpz1mbre9Yg+2/+S92SH7Mk70w++vhRTOLpIK8Urqv7y6ecQYbFDtT2Weo/xgvrpnWKZ/5c2xEivjlzEyGxmOU9cxCDk57nDfLShIdYxCcFGfYMQwRzkNzW9+VMX0HM7BDP/LkmECK+NtJAyOISy3vmIG18+aO/cwb5vvhjJvF0kIM/eKhn0awmzjP5ZfmBD0+oYjiVLvHMn2sCIeK3RY4QsnKw5T1zkFYOnjuT80zIHfMIk3g6yMeRUV/tPvVezjP5y8mRCNvS9p3imT/XBGH5i2++ZPJhzjPZXtzEJp4OsieylpDfnMEX5EDB/KbdIx5wqWGL2n/xzRnVrX1YzPKeOQiJXz7BZhKXvyCVGYWFWUf34TyTbi+ziaeDfBhpbJV2tv8gdB/P+rkmEDOqj52/9+3s1hHnsqqu9zxBDk8d811TE8eYBzMAAAFESURBVMufPBXkH19++eXcMV/xBSG3l9Z/cdo8viDxYxc07zn7Jv8x4k0/L2+Kc36u7Qi6jp+S0aPtGnPc3K73PEE+jbTxKOeZtMLU1CcFOVieXTj7IGeQd0ZGu0/b5z/G3LaP4U7Oz7UdvHOnKSheU1C8pqB4TUHxmoLiNQXFawqK1xQUrykoXlNQvKageE1B8ZqC4jUFxWsKitcUFK8pKF5TULymoHhNQfGaguI1BcW381HeX8kXBX+WfRrBgeITLB1w4II5sk8iQFB8BxOGnMIyTyKsoPgO1kUYVioILyg+QeOJsZ7fyj6JAEHxCa6fTG6YLPskAgTFt7O29c+9sd9vZZ9GcKB4TUHxmoLiNQXFawqK1xQUrykoXlNQvKageE1B8ZqC4jUFxWsKitcUFK8pKF5TULymoHhNQfGaguI15f8B0K1bTxEam2IAAAAASUVORK5CYII=",
null,
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",
null,
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aQfgmIRT8+pLaKR+AVhEn9G/hWQi0S85itlaUNa/Jw0w2fNcU9oFe9/KDpsIc3EL4D8dedmLksyqm6Ze6JoxBu5joZypMXvuqT6A8cp35s3oUB87fgvpC4O/vK8ihHj7ldX3PIpw25ObTtrSsY2EGIGhze/EAy/45+fuKRbj/glS2enxL8wr+FffnjCU8qKW7vhmrT4xKwDLaNaCDkDw5tfCI4Xd5/edVaJFvHNzfOq+0en36Owt9qU+J7SV5P9xGlBg8H+A/jD86r+nYbP8vapFb922MqBvR+LpRQnLb4t1uE49ZXEpEHgji9CxM7j+8VvmjJvYOeLc/voMT1Ji98WSy67alJ6x1uzmRx7wpxeCC7xjXXZYfubaa6+0v+7Ald0TPzL07/5Sk5vC94XjSlI3iP+zt+F4FM4WeESv2LgPH7zTWkm553Z5xO4ooz4zRdMezm3th9vFY0pSOZ3fElr8gVe5nd84j2IF0XBU/3mpuq5TZubX5k1ZWNTU/Yh73RN76bH9KC3+5ZEd2+ym4vaXzsx/areeep+iBdFgfhrY0mubn4mtYnV9u+9e+Zmekov6lLL3508j59fUtGQ2dX3199llp0Lb3wx5MW3xCsnVcZb8vZre+fu9S7/A8nzvyxZPdERPw9p8Q1l8fpV9YmyBveENvH+h2GBJavJH2Aw0uIrWtObLWPdExAfsh9gMPL/SHMwvWnP+yA0iA/ZDzAYafHzq1o6+jpaq2rcExAfsh9gMNLiO+MlydfApYlO9wTEhyu/C4bTuZ62bW09+bshPlz5XUTqPN5ocSxZDeZ3AfGisGQ1mN8FxIvCktVgfhcQLwpLVoP5XUC8KCxZzcV3A/GisGQ1F98NxIvCktVcfDcQLwpLVnPx3UC8KCxZzcV3A/GisGQ1lj4PiBeFJaux9HlAvCgsWY2lzwPiRWHJaix9HhAvCktWY+nzgHhRWLIaS58HxIvCktVU+HwgXhSWrKbC5wPxorBkNRU+H4gXhSWrqfD5QLwoLFlNhc8H4kVhyWoouwcQLwpLVkPZPYB4UViyGsruAcSLwpLVUHYPIF4UlqyGsnsA8aKwZDWU3QOIF4Ulq5noXkC8KCxZzUT3AuJFYclqJroXEC8KS1Yz0b2AeFFYspqJ7gXEi8KS1UhyTyBeFJasRpJ7AvGisGQ1ktwTiBeFJauR5J5AvCgsWY0k9wTiRWHJaiK4NxAvCktWE8G9gXhRWLKaCO4NxIvCktVEcG8gXhSWrCaCewPxorBkNRHcG4gXhSWrgdwFgHhRWLIayF0AiBeFJauB3AWAeFFYshrIXQCIF4Ulq4HcBYB4UViy6o9dCIgXhSWr/tiFgHhRWLLqj10IefE7V7+b/Hr0Qfd+iA9F7EJIi183YvwJtUed7rx7QnwoYhdCWvw5jzh7LryqB+JDGrsQ8hccPOA4hy+59BOd4ldOGTlm/r8qb/C/vlU6brVs1kIoSy2ItPgz30x+OXLZLJ3iJ/xl46ryxaor7D3r7q5/H/W2ZNZCqEotirT4WxelvvbO1yl+1PLm5rlX9N/ivXj8ADuO/8xxrvyRZNZCKAotjLT4I5lLTB7d5Z5QKP7GuY1PVTzQf+s7F/+n/5EIvH188j+pK2dnbjRUMgnvR0nkAETyPL7hK7HYvIEKP7iglx6zMD1frTvy25Lp6fGmBUd5fA+kNgyX+Ma67HDHo2mqqv2/i9ZZ44nxpme/9v2BChdtF40ZiB3fGjM9Pj89rN3B/FSvJHAQuMSvmJMdKhf/VOzF5ubbz+Y1UYCpt6hZV7RXZUTxqX7z6IUvrzn7Ml4THjy0Zs2Ck19Ssza9VyaiKL754Uklo2dvYBXhxXWjhp+3UtHa9F6ZkBffEq+cVBlvyduv7Z27SOLfjWKkxTeUxetX1SfKGtwTED8U/t0oRlp8RWt6s2WsewLih8C/GtXIv1d/ML1pL3VPQPwQ+FejGmnx86taOvo6Wqtq3BMQPwT+1ahGWnxnvCQWi5UmOt0TED8E/tWohuF0rqdtW1tP/m6IHwKBWhUTyfP4yENvlQ2INwG9VTYg3gT0VtmAeBPQW2UD4k1Ab5UNiDcBvVU2IN4A9FL5gHgD0EvlA+INQC+VD4g3AL1UPiDeAPRS+YB4/dA7ZQTi9UPvlBGI1w+9U0YgXj/0ThmBeP3QO2UE4vVD75QRiNcOvVJOIF479Eo5gXjt0CvlBOK1Q6+UE4jXDr1STiBeN/RGWYF43dAbZQXidUNvlBWI1w29UVYgXjf0RlmBeM3QC+UF4jVDL5QXiNcMvVBeIF4z9EJ5gXjN0AvlBeI1Qy+UF4jXC71PZiBeL/Q+mYF4vdD7ZAbi9ULvkxmI1wu9T2YgXiv0OrmBeK3Q6+QG4rVCr5MbiNcKvU5uIF4r9Dq5gXit0OvkBuJ1Qm+THYjXCb1NdiBeJ/Q22YF4ndDbZAfidUJvkx2I1wi9TH5wwUGN+BeiD1xwUCP+hegDFxzUiH8h+tB9wcHlU4bdPHDLtAnFbI6luCJ727dMjei+4ODaDdfYI765qalp/chfZG/6lqkR/RccrB0Q/6E5Jdr4SUV2+N++ZWpE/wUHs+L7brpiiMKKhak3Zoc3XtolUKcm9J/HZ8U/ubTon+qbm589/pns2Fn7N/Q6ueES31iXHW6+Kc3ki73vmRWfPLRBI5pYMGVg7BytEq1TPVziV8zJDtvfTHPfz7zvmRV/5+vJLw+tFj1CNBn/RGb71qLkl/bLjGYZhLqn+tUPe+3t7b4l0d2bHm6fvcd5a8Yn9CNEgJZRn2YGRy96xen83kazaXLRLb4udWZ7d2a85bJv3vAB/QBRIH5j/+gPt3/z4vUmo7hQ9169t3gQEtS9Vw/xoUbde/UQH2rUvVcP8aFG3Xv1EB9q1L1XD/GhRt179RAfanSfx4OQAPGWAvGWok5807mzfSkdI8/oEoZFysoYFikZzbDIHzGsMWa0f/VnfaRKvAgXMqzx9iKGRVauZFhk0dsMi3BUwrAIxAcA4oWB+DwgXhSIV7EIxAcA4oWB+DzsED+bYY0ddzAssmoVwyJ37GBYhKMShkUUi8/7lx0CfYcYFjlyhGGRQ30Mi3BUwrCIYvEgrEC8pUC8pUC8pUC8pUC8pUC8pUC8pagR31lTMrbBY0xd5EjtuJHnkP4wbfDRd42cM8R9xRZ5cuLwiW9ILvLOrFGnLf48+Bq5HzBE7jWDGvGJWQdaRrXkj6mLdN62df8jI3ZKJnGcS2aSxOcusrF8w/6tuyQXmRrvajvjseBr5H7AELnXDErE95S+6jjxeN6YvEiaCYS/tB+8yPPVyyjiBy0ylfivPYMWGZ0cJ0j/BJH98AFyr8dQIr4t1uE49ZV5Y/IiKfae8K7kIp9OfJ8kPneRw8ct+/Jpi7olk/w00bXzzEZClAHx5F6PoUT8tlif46yalDcmL5Lk8IW1kkmcu5Y4JPG5i7wfm7lv9zn3SCbZelYsdhshSY54cq/HiMojvufSq45KJnlnYjdNfO4ie2LrHOfx8+UW6Tp5affuafcRooT8Ed9T0pr8HRbPG5MXcXovr/b4I65gizSUlJePGn6GZJIvraeJz11kZ+xQUtqM4Ivk/o6n9noMNa/q4xe1v3Zi8hXnisaBscwiR2tmfdLdTXnI5yzy2d69e+tm7ZNbxLnzgoMfTVkit0jvqQ/07Jlxa/A1+j9gSKrXDIrO4+eXVKTOMefUDYxlFtmV/szYByWTJCE91Q9a5HDixPI7Dksu8vr0slOu+Tj4Gv0fMCTVawa8c2cpEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEG8pEJ/hvZP+w/no5H8zHUMfEH+Mx/6k69uLTYfQCMT3U332ZMrfSUQViO9nQ4zwSQXRBeKPcWhc/Mv/ZzqERiD+GN+/yll4lekQGoH4DOuSD/dDX/1n0zH0AfGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGWAvGW8v9hCF70TqWa+wAAAABJRU5ErkJggg==",
null,
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",
null,
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",
null,
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TWP7o4+8HLCe0tepa5PqXkMd/SBlxPeW/IKdX1KzWO4Ywy8pPDeklel69NqHscdY+AlhfeWvCJdn1bzOO44Ay8pvLfk1ej6tJrHcscZeEnhK0tega5PrXksd6yBlxXeW/Lyd31qzeO5Yw28rPDekpe+61NrHs8db+Blha8sebm7Pr3mMd3xBl5W+MqSl7rr02se0x1z4KWF95a8zF2fXvO47pgDLy18ZclL2/UZNY/rjjvw0sJXlrysXZ9R89juuAMvLXxlyUva9Rk1j+2OPfDywleWvIxdn1Xz+O7YAy8vfGXJS9j1WTWP744/8PLCV5a8fF2fVfME7vgDLy98dclL1vWZNU/gTjDwEsNXlrxcXZ9Z8yTuBAMvMXxlyUvV9Zk1T+JOMvASw1eXvDxdn13zRO4kAy8xfHXJS9P12TVP5E408DLDV5Z86Vg5uj675snciQZeZvjqkr9Ahq5HqHkyd7KBlxm+uuRl6HqEmid0Jxt4meGrS16CrkeoeUJ3woGXGr665Ive9Sg1T+pOOPBSw1eXfMG7HqXmSd1JB15q+OqSL3bXo9Q8sTvpwEsN7y/5Anc9Us0TuxMPvNzw1SVf3K5Hqnlyd+KBlxu+uuQL2/VINU/uTj7wcsP7S76YXY9W8xTu5AMvN7y/5AvZ9Wg1T+FOMfCSw1eXfBG7Hq3madwpBl5yeH/JF67rEWuexp1m4CWH95d80boeseap3GkGXnJ4f8kXrOsRa57KnWrgZYf3l3yRuh615uncqQZednh/yReo61Frns6dbuBlh/eXfHG6HrXmKd3pBl52+MCSL0jXI9c8pTvlwEsP7y/5YnQ9cs3TulMOvPTw/pIvRNcj1zytO+3ASw8fWPL5dz16zVO70w68EPjf/snq/cdzzrn9MHyAAXxgyefe9eg1T+1OPfBC4D+5w1o6Zc3aqTfBB1jA+0s+765Hr3l6d+qBFwI/+C/WiW9a1t4T4QMs4ANLPteux6h5enf6gRcz8c9Zo9+xrH3D4QMs4ANLPs+ux6h5Bu70Ay8E/pHRj97dsmnTnBvhAyzgA0s+x67HqHkG7gwGXsxH9U9PrwHghBVcPrgLLvm8uh6n5lm4Mxh4UU/nDr/2VsytTOADSz6nrsepeRbuLAZe+ufxoSWfT9fj1DwTdxYDLxJ+80r4FibwwSWfQ9dj1TwTdyYDLxJ+zdzqqxub3Yxqy36vbPjAkhff9Q83LkGv+S23njS+uaGZKief3jx4HYMHLn/VB5e88K7HqfkXvjt56sUv/+4L5NfLya+WWaey6DUF4INLXmzX49S8w/54ad63Z75Jfr3c3LisiUWvCYHvbp8xeUZ7d+R2NvDBJS+06zE+mi+zl0rz7vkw+5+ckV83seg1EfBdDe2d6zo7GrrgA4zgA0teZNej13yF3YZ/OftfnJmLWPSaCPjRW90X28bABxjBB5e8sK5Hr3mfnRU8i14TAV+7z32xvx4+wAg+uORFdT1yzQfZWcGz6DUR8PPbunv6e7a2RZgZwQeXvKCuR635MDszeAa9JgL+QHsdAKC+4wB8gBV8cMmL6HrUmofZmcEz6DUxT+f6du3Y1Re9mRV8cMkL6HrEmo+yM4Nn0GsKPI8PL3n+XY9W83Hs7ODpe00J+NCS59z1aDUfz84Onr7X1IAPLnm+XY9U80ns7ODpe00N+OCS59r1KDWfzM4QnrrX1IAPLXl+XY9S82nsDOGpe00N+NCS59b1CDWfzs4QnrrXFIEPLnleXZ9d81nsLOFpe00R+NCS59L12TWfzc4SnrbXFIEPLXkeXZ9Z8yjsLOFpe00R+NCS59D1WTWPxs4UnrLXVIEPLXnWXZ9V86jsTOEpe00V+NCSZ9z1GTWPzs4UnrLXVIEPLXm2XZ9e8zjsbOHpek0V+PCSZ9j16TWPx84Wnq7XlIEPLXl2XZ9a87jsbOHpek0Z+NCSZ9b1aTWPz84YnqrXlIEPL3k2XZ9W8yTsjOGpek0Z+PCSZ9L1KTVPxs4YnqrX1IEPLXkWXZ9c86TsrOFpek0d+PCSp+765JonZ2cNT9Nr6sCHlzxt1yfWPA07a3iaXmMG//Xt+P8CpvDhJU/Z9Uk1T8fOHJ6i15jBLxs58XtvYP4L2MKHlzxN1yfVPC07c3iKXmNX9UefXVDf+nAPzr+ALXx4yVNck4Sap2dnDk/Ra0x3/M6zQO0NGD//zRY+vOTJr0l8zbNgZw9P3mvs4P/60AWNHVvfWD4J/V/AFh5a8oTXJL7m2bCzhyfvNWbwV9Vd9tNe++XHkZ+JTQ5j+PCSJ7smsTXPip09PHmvMYO/p/KL7DB+5QNj+PCSJ7omcTXPjp0DPHHXq/M8PrLk8a9JXM2zZOcAT9z1KsFDSx77msTUPFt2DvDEXa8UfHjJ416TaM2zZucBT9r1SsFDSx7rmkRrnj07D3jSrlcKHlryONckUvM82HnAk3a9UvDQkse4JnDN82HnAk/Y9WrBQ0se9ZrANc+LnQs8YderBQ8tecRrAtU8P3Yu8IRdrxY8tOTRrkm45nmy84En63q14OElj3BNwjXPl50PPFnXKwYPLfnsaxKqed7sfODJul4xeGjJZ16TYM3zZ+cET9T1isHDSz79mgRrXgQ7J3iirlcMHl7yqdckUPNi2DnBE3W9avDQkk+7Jn7Ni2LnBU/S9arBw0s+8Zr4NS+OnRc8SderBg8v+aRrUq15key84Em6XjV4eMknXJNKzYtl5wZP0PXKwcNLPu6aVGpeNDs3eIKuVw4eXvIx18SrefHs3OAJul45eHjJR69JuebzYOcHj9/1ysFHljx0Tco1nw87P3j8rhcHP+6dyE1c4OElH74mbs3nxc4PHr/rRcDPdTO4dS58gAs8vORD18Sp+fzYOcJjd72QvzvXcredYSvvhg9wgY8sef+aODWfJztHeOyuFwG/5/IrXresUW9HDnCBjyz56jWxa35Lruwc4bG7XsyOf2rC7b3C4OElX7kmSyb+MGd2nvC4XS/og7sPV5xRJwo+suTda/L8ebO+kTc7T3jcrhf2Uf3vu/4WuY0PfGTJO9fk4eGnTzr7Cexzsc68mRvQLldyXr22MfbUmF2v3vP46JK3r8mS44/NfdqdzPvtDZTy+2e/EjvxuF0vEH7zSv/Rb3ez8Ors9yKAjyz5C04aMe77D1Km89sMcs7j/zlrO1W+963tZ8f+qzG7XiD8Gv95/JZFbs6KPLOPhgD+WnjJ39l4w5R5i2jSMXbRRdMuL0ROB0PXxv6z8bpexaqPLvllh2b1kj9MJ3//+iMr8B8J+6w6afbqVa2xh/C6XkX46DP55pYt5I/Szf+1XFoAeIfdfjEyduTxul4IfHf7jMkz2rsjt/OCj3y6/ppD2XeUkY/uyB3eY7dfiR95rK4XAd/V0N65rrOjoQs+wAs+8jX5Zdn3k5m8q77KXkoaeayuFwE/eqv7YtsY+AAv+Mg33skPH2RPGnmsrhfyRZp97ov9kV+Exgs+8t31ssOH2UtJI4/T9SLg57d19/T3bG2LMHODh3+ETm74CHvSyON0vQj4A+11AID6jgPwAW7w8M/Jywwfw15KGHmcrhfzdK5v145dfdGbucHDvwxHXvh49qSRx+h6JZ/HR37jnazwSeylhJHH6HpF4aFfaysnfAp7wshjdL2i8NDvrpcRPpW9lDDy6F2vKDz0B2rkg89iTxh59K5XFB76K3SywWezl+JHHr3rVYUP/6lZueCR2BNGHrnrVYUP/z15meAR2UvxI4/c9arCh5a8RPDo7PEjj9z1qsKHlrw08DjspfiRR+16ZeGDS14SeEz2+JFH7Xpl4YNLXgp4bPZS7Mijdr2y8MElLwE8CXv8yCN2vbLwwSVfeHgy9lLsyCN2vbrwgSVfcHhi9tiRR+x6deEDS77Q8BTspdiRR+t6deEDS77A8HTssSOP1vXqwgeWfGHhadlLcSOP1vUKw/tLvqDwDNhjRx6p6xWG95d8IeGZsJfiRh6p6xWG95d8AeFZsceNPFLXKwzvL/nCwbNjL8WNPErXqwxfXfIFg2fKHjfyKF2vMnx1yRcKnjF7KWbkUbpeZfjqki8QPHv2uJFH6HqV4atLvjDwPNhLMSOP0PVKw1eWfEHgObHHjDxC1ysNX1nyhYDnxl6KGfnsrlcavrLkCwDPkz1m5LO7Xmn4ypLPHZ4veyk68tldrza8t+RzhufOHjPymV2vNry35HOFF8Beio58ZterDe8t+RzhxbBHRz6z69WG95Z8bvCi2EvRkc/qesXhy0s+J3iB7NGRz+p6xeHLSz4XeKHspcjIZ3W94vDlJZ8DvGj26MhndL3i8OUlLxxePHspMvIZXa86vLvkBcPnwh4Z+YyuVx3eXfJC4XNiL0VGPr3rVYd3l7xA+PzYIyOf3vWqw7tLXhh8nuwleOTTu155eGfJC4LPmT0y8qldrzy8s+SFwOfOXoJHPrXrlYd3lrwA+CKwwyOf2vXKwztLnjt8MdhL8Mindb368PaS5wxfGHZ45NO6Xn14e8lzhS8Qewka+bSuVx/eXvIc4YvFDo98SterD28veW7wRWMvQSOf0vUawDd1cYIvIDs08ildLwR+94Y/2P/96D74djHwCxdzgS8kewka+eSuFwG/aUjToKUfWb2RtxQDv34mB/iiskMjn9z1IuCnPGi9ddE1fXnBl+pXs4YvLnspPPLJXS/kDw7+xbIOX/7ZD/KCb7qFLXyh2aGRT+x6EfCnbrf/c+TK1rzgF17KEr7g7KXwyCd2vQj4Je51Pzo/L/j1o5Zk309m1rrwxWcPj3xi14uAP1L+E5Mf7YEPCIIvDR132f9m31Nq3l8waYUc7KXwyCd1vQbP4+0lP//1OUfJH6aThaVHVkjCHh75pK4XCL95ZfXVV1a7absi+71YwF/btLr1u6tp0jVx9dwhF8b+CeciJjDySV0vEH7N3OqrYuGfm9r6TdpcPGBm06TPdb5A/2hE5J8DI5/Q9RpU/XPTF9Gewiv5VVOnXPVDKewDI5/Q9erD07sHd7sk9oEtn9D1QuC722dMntHeHbldBDy1e+RDOinsAyMf3/Ui4Lsa2jvXdXY0dMEHBMDTusd/JF98+8DIx3e9CPjRW90X28bAB/jDU7qnPIErur0/8vFdL+Rz9fvcF/vr4QPc4encs563F9o+MPKxXS8Cfn5bd09/z9a2CDNveCp3pE/XFNjeH/nYrhcBf6C9DgBQ33EAPsAZnsYd/bN0RbX3Rz6268U8nevbtWNXX/RmvvAU7pifnC2mvT/ycV2v7vN4cneSz8kX0N4f+biuVxae2J34SzGFs6+OfFzXqwpP6k73Fbhi2fsjH9P1isITujP4wmuR7KsjH9P1asKTubP6enth7KsjH9P1SsITuTP9NouC2FdHPtr1KsKTuLP/7poi2FdHPtr1CsITuHP6pqr87SsjH+169eDx3Xl+L13O9tWRb4C7Xjl4bHfu30KZq31l5CNdrxo8rruY75zNz74y8pGuVwwe013gN0znZV8Zebjr1YLHcxf9ffK52FdGHu56peCx3HP58Ygc7L2Rh7teJXgc9/x+Kka0fWXkoa5XCB7DPecfhhJr74081PXqwKO7F+Fn4ATaeyMPdb0y8MjuRWB3I8zeG/lw16sCj+peGHY3Yuy9kQ93vSLwiO7FYncjwr488uGuVwMezb2A7G6423sjH+p6JeCR3IvK7oazfXnkQ12vAjyKe6HZ3fC0L498qOsVgEdwLz67G3725ZEPdr388NnukrC74WRfHvlg10sPn+kuE7sbLvbuyAe7Xnb4LHfp2N2wty+PfKDrJYfPcJeT3Q1re3fk5/hdLzd8urvE7G6Y2rsjH+h6qeFT3WVnd8PQ3h15v+tlhk9zV4LdDSt7d+T9rpcYPsVdHXY3bOydkfe7Xl74ZHfF2N0wsHdHvtr10sInuqvI7oba3hn5atfLCp/kriy7Gzp7Z+SrXS8pfIK72uxuaOydka90vZzw8e4asLshtndGvtL1UsLHuuvC7obQ3h75StfLCB/nrhW7GxJ7Z+S9rpcQPsZdP3Y3+Pb2yHtdLx981F1TdjeY9vbIe10vHXzEXWd2N1j29siXu142eNhde3Y36Pb2yJe7XjJ4yN2wV4NqP3Jtuevlgg+7G/ZwkOztkXe7Xir4kLthjwmC/ci1btfLBB90N+xJybJf1ep2vUTwAXfDnpp0+5Frna6XB953N+zZSbFf1ep0vTTwVXfDjphE+5HfaZHnDw5W3A07TuLtV7XaXS/JHxz03A07duLsR066TZI/OFh2N+xkidivmtQixx8cdN0NO0Ug+5GDnpXhDw467oadNkH7VTW3Ff0PDr4xzXE37Ezi2x/fMv29zGuf4x8c7F/0uWnPTW817Mzi2a8aMLbt/iy1HJ/HP3aXNWHiIMPONK79sFOsq3dmXH1W8JtXVl/dssjNWZdl3/WgmkmXm7DNZ0aDE46xHo88vY5e/bQgw6+ZW311/3Y3q+7JeJdbXrR+sX3F3dtN2OaLj770M+uBDRlXn1/Vb/hRxhvsvOQt63ezPyC/B5PYoF3XHOGtbVdeeP3r5HdgkhCk68rvc/XZ8CY5ht/n6g18ocPvc/UGvtDh97l6A1/o8PtcvYEvdPh9rt7AFzr8Pldv4AudPJ/Hm+QYA69pDLym4Qf/s6mXZKb+OPo01jE4SUMDg5PUNTI4yVAG5ziuMfvSn7GXFzxKEL5FKDMvL2NwkkceYXCSZS8zOAmLS8LgJAYeIwYeOQY+EgOPGgPP4yQGHiMGHjkGPhI94C9hcI5XljM4ybp1DE6y/BUGJ2FxSRichDN85Cs7BOk/yOAkR44wOMnBfgYnYXFJGJyEM7xJUWPgNY2B1zQGXtMYeE1j4DWNgdc0Bl7T8IE/sKBuTFfM66QnObL0tNopT9M+EsvaUzs35W3RTvLYhMETfkt5kt+3Djvx5o/xz/GDaccsjn1Q+OED39H6l+5h3dHXSU9y4GsvvfvgkN2Uj8SyLm8hgg+e5NlRz7z70h7Kk0xvP7Rr3EP453jymbePhFIAAAJqSURBVOuq8MTXtRwu8H31v7Ks9vbI68QncfPJrJ8IzzzJU1fcTQIfOsl0wq/2hE7SaL/eQfQliKUVeOLr6oUL/C7QY1mdMyKvE5/EyduD/kB5kg8nvEYEHzzJ4Zq7TzpxWS/lI7mj49DuUzcTPBQfnvi6euECvwP0W9a6yZHXiU9i5/BFSykfibXidosIPniS10DLO29O+SfKR/LSGQB8jeCRBOCJr6sXWSa+77PXfET5SH4/oZcMPniSt8Amy1p7Dt1JDh1/V++bM1cRPJSCT3xf3VZ7h7VHXic+iXX0qitifogL7yRddaNGDRs8jvKRnPA0GXzwJLvBQRttNv5Jgjue9Lp64fNRffun9v/XsfZHnGs2+6/TnOSjBa0f9PaSjHzgJH97++23V7a+Q3cS65Y5+/ZOu53uJEc/8f2+t2YvwT/H0d6vdPQepbyu5XB6Hj+/brTzHHPuSv91mpPsAU7uo3wkdoiqPnSSwx3Hjlp+mPIkL85qGHndX/HPsdK5DLdSXtdyzGfuNI2B1zQGXtMYeE1j4DWNgdc0Bl7TGHhNY+A1jYHXNAZe0xh4TWPgNY2B1zQGXtMYeE1j4DWNgdc0Bl7TGHhNY+A1jYHXNAa+nFdH/Le19/hf5v0wxMXAe3nozEOX3pz3gxAYA1/JFX93FsnPScgaA1/JM4DgNxXIGwPv5eBp7Se9n/eDEBgD7+XL11g3XpP3gxAYA1/OJnvcD57+k7wfhrgYeE1j4DWNgdc0Bl7TGHhNY+A1jYHXNAZe0xh4TWPgNY2B1zQGXtMYeE1j4DWNgdc0Bl7TGHhNY+A1jYHXNP8Pl/eF/BIJJhMAAAAASUVORK5CYII=",
null,
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",
null,
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",
null,
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",
null,
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VlNT7pLv5PLg+pZxpG7f+71wwBGdl05UfqrH4xc0f+dE/8fnvpdj/dJ4nVXKPlRoTKZVBEW58+GUNK9h3hw7294sAuLw+FLpGG5kzeeMp9wdn6KLDg30ai9MaDz5WANiCu6+tO+H2nfoM2EH1kW0l0JS4AmzGLXV8TanmBl3C1ILykcXP1gEQ9Kx5qiN/kBOAsSbT6eUCIZyo0c14eyoHLH48+AIHxpyZu9PjP+dfVo/fzxPZNDRCxA/KMButoCRRjx9T5TX6XXKmRafWXtAfKwE9U6kVwiILQ3BnSQmrM7vO+iQbSrULXeOnd2wqcPGh6ISSKBoJd5Q4PMJuZqY9wtyBrUpygbLRzuzYeificJd2euXohBY2AHTyvcN37eqFu/vNbOU7Qa3v8Pbfrgb3uONP76+tHGu6A4LSC59KB587X9C3pqecZ/kSMVKfyyq9Tzm86x0f/NYUFsAP3vXKVIOnsMK0jPuIpmvEbzRq23zp2N8DeHayPTwPDoybgq2rxpdC+r/XbG3ULgtwPvcvbmR0rFkF+4n3y5SQwB+cFo8mW1Wl2vx6YM+Mflvd8+zuXMXJL7BnX7joLa+3QFS6cGYeWmDWfqq4vCBcbhSlL0ws0VV1AunzCIF5WL7c5t0n94WZIcQnkXfrkOVOWG3Doyi/I+rbLOnRkb4dc/Pm2lEKhCcv3FctMW8zC8CYpxN5Ow60CYi/f/dowMsDOIzu7VqX4m6bGPi9Jno++n3o2+2Xl7n3vH71/5Kfrn9a52M01/e/W17H/RubS7b/XllB+ordQH8DGyaYekCwOwsOXkKPtrfQxT71ARPtwvstV0V771xdqxPYJkYjZ5JgbT+1dsf2UZzXGtsM6dGRvhx33/mVwXGJ7zVWAwx9RDaxqGpzXuZgqXILHz0UWSU+NkkBVb14hupQYR/y4E/AT/lN614VGDV00aftPl6a3GA0Mcvn8eerXLgqxue6237cpfMTb48znZsRIRYJO9VAhwsULIIpSHgj4fWx86T/YtQt9L65FDGj9eMSqN+N6AhSdG5fxMc0AbrXM3+xBK5QXjP50JHAaMJeqah+FpjbuZ0ZNQ6nqXt0BeZIIC4lE15x/sQfTsceI5kXZ9pyx3xnOHV8x77hMmF2gFPpiA0Gcjx9u/f8Nb9c8+n31YOWB5+Vm9VZjihv4f9FE4zjcGpQAUxvfKjeKTX2MsqJqSfLBRcgShLyW7nN/B5qcbAT82eild2kobrXP3be632cKctNozga+aovXh5pVuHRh3M/NK0GPZLm/BxI/VwRALrj7XpzoaGj+6II0wZ5q269OTR9+e/t0Tuz5PHJ4u7z7J5v0vGWZ06ToyWtxjj0BdEV5cYaSsuCArVurHMVoqKO97f3xpKMfYyPOz62kz6HaLidbiqGiP0zu4nHUE8vCKpydMoO5rq3XuThRhsl/fCTkT2IiTS51uCzVtdmTczdSnoauU8laOuVgTgkFFSmZpnnFQGsZmv57aD6GFjseoWoOvn6nbsIcwx4+lGIpjy+cvnVO2iDC9+zcSz13Dng15Mys+aEz3F0Bu3MJpmszYIKlAKOYYG3bIDtBLk4urwo2dNgxg6krHPsohEdEUfig56PAAkrOToRLGrT78IHWuaRv14/8pmY0l3ItUewNRQASyDMM7Nu5mjoYSnv1Rd971EqE9EJcf0QUY+3dyccgdlz6+391794TlgyoSuj6Q90HFwJSBI+RY96D4h1JHXS+ZXT/u3iv5D8SIBskTwwDEubzI7vGxizYuHBZDWidRUqW+9n/7YyOFxtYdAk78Qudp5CelRNP5lsSF+8rSBIpTpvamDsy3Xk0aG+FXbkDYtxOX5IZLjw3hm4fhnRl3M9cVhJ0fw/QezFyuCcWAICTOHyc9pKj9uU9PWVW7+pCbV2kJ36x9/uovxXsSX/pPZXdOrEbME4bfEQqVG1fOm0BmiU/Mn5g7tWcWDmQDvx7xw+vlyd3CeRBytH1qjhN7D4xXE74JR8jlsjGhwYnfZuG83zSEdopPOj2ILxjiH/GfROriI61Xk8ZG+Dt+QKzKLsVdMd6YobCRHIZ3btwtEO38cUpH0TU36hJxwBUbQsieUBRrUqo+d+o49y/jJuv7b6vLeKZPbvcoY6oIXyJhiVhsQs3gCGFWUcW+WHWMxE8KoGJ036rgEC7EJIkTd5Odlot1xWocsMQKmYAvEPhXOteyiSshwwmjKXOqoIKdUAcrQtIq7f2cNmrq5+5Dn4ZDTl4059F4WJ0zzJVxt0AaeGmLVsEgtGcBTB5Exj7ES9GDr0+bWztveWs+959EzH9008d5IUdjpKrwVfppFbnxAVwWhosjg3gQk0Wx/QOfGiaAmJRoyFkh/VZfMJ51okYvIf5WBAZIpX4ycVKtG/HmGzqi5VyrcDYeHYKtigeSkmkPvm63o42E/znj4MXu6QE4BOn+WDh7lCvjbkF5CaGsx1p4Bw11SSzCepLSK9Ir4/vE5RRPcTxO6Skb8hLSAiIJVy0A4t3jcr4wb76sX/tsVWAvSZiS0BtTEdZdHW3e1/jGmCgeACxt91ilJDLKX15sr44rGg0JDahWccHxEfFQoQZBWLVhkd0ObwnfQAkL2nr1Z2cMyjww+bOpKYArBQLO0wwvG0k8omsphaqZ01Cn5xrDeQCK0l96pvvqMZ8h9MfaR4+0/JJ2fP/4itPfLFv50z+ZZxSNk/QjMK4cxOTENK/S9NucgfN+R2cnEE4n9E8PTYycQbbuF1b29CN8EE5YcYlOEqOPl2qr6EfRXDA47Bpa5Od4LNoAHhBBjmpH8X12O7wl/HXKkZREjO8z6ruFFvphOIgoeIvhZfVEn+WGhOlN0LNVwjZqD7FIfU/DFnQ6Y8veMfaB7payt2jX7sRur76Ut/nOT0PCZLh/175YyeGcz22PulStAphWu6Hb/UV1ZbeI1l1BmH5uxKAJepl/6YAIQVItTSoSMyarzqH7gxzOKRsOVoqAJnFg4ny7HR4LP8nEhOYj/1NlJIEylH52VllgiXrXd6A26LDL65ooIxuSsP0Mj3bA7wt6SI3DHFj42/Gb0Miv0K8rQscv/NCzq6Iflz78yanwBZ+jHkmLaz81FF7qMperPVgSIBg1/Tvr467UaCEWWnOV/P+LirJjZBwuh68bX1OsEuvH9vNXF7/p6B0YQYZvJ2gdBbangUE4b0H3wbXb7HZ4LDxr5F0kk5uPvPq9kbGDaY7+OrNrmh5w05g+8VPJbMy76K7kLhvEpPY4OzBXXpTh/6hf6oRRyz264Pu5r7ydG5P8VhBHwIlbWpg0+76k3viTBSMxG5+8oa4rhgXXkB7bhbpif4FIKBDrqrdUaoW6qQv1kohqzyeEkOHbIV0cTJNcAhSAPS396Xz7sUqPhU8yDfYyaOoJLi2fHNKdECCN6SSIx8nq5Kf9GB7tlAuZKWo2GdDDQrTFmp7nMmuCjS3JZ/PmuzcZ61ztA3t/emR2t98JC9oj65EJPMAb98g03revpMaKZr6NzbY6dHc3FhZIqk607kqJXCGRJFV/VKtXaSufr9KK9XXMVy5xBhm+LUuk37cF8IAgqfIJii3wWPgnTEuWNDgP4Jj4Rb/jSBlHSfg0Li9rZq+O/Cn3ygzJX/S7vpgcJDX5eri/6ImKfisQeqH/u+/2dRVIsuabzN0fjgja80Hg9CmZXC4OH83GuVxlZnjhvrl9BiO/Lk0HfljIgZoHr6IDVTq5MjRUIdHXnK4vJpr2+peLFcryj528h5uQ4dvcVLo9N7oBIBQ/UUS1BG2aXn3PYXSwaCAZUHuE4UXO+pM/i2pafhtWXHz07vqb6HC5iHzsAdAb/sr+B2URbeB1pgNBJCMIh71f71++94MsmQgalsmw4C4cLNF/ZNiUwLX3sMwO9um+XOg36weidRcGR0Vq5PraS6Zc6K9qkwQR1OE2zyDDt/oimh1bZwHwcPSGlVsoe9pU+D7Xr6VeqRZBHJMxrVQgI39sj3V1mHtsUfIJTw+DYnlmgbIo/0HU241snTx0LkUeEciNkT6ymaV89/3B0/y4OAZ1mRHh+MfYc+Qhl0aLoGrkTL1SHpMap1Ibaq98W60TaiuPflkVItPXtUKVhvN+0xrjS6nb578KYH7O9Pcp7XHb1qS5970/ylFUupiF+TMtQ2kcm2sUMTyaKWcfGSrgApwF2JkJ19Hce+KnDh5y//Hdd5YNn30KNT47qX/lAutw2OUlE5809bd+njs584tTEwf0lB2+pS/nzPti/oNHCQ8KArjrF1EKlBhuPT8+VQoFEdFy/x55aTJlcd3V6/XFSmVxfePuYqXGyXCbZ1wJGd4YM5yy+fllQICeenrFc5Q9bVqT5px+jWGmZGk4DAgQMey4yoz+T1cXGQct4MPcdcUc4/Bn4lJVyD0DDUsjBo4apV9t+Gjkkj6TU57O+KHp0MtZL367qZA0k99lvvX1LNXKfkNkoQfGZiss/vvPkXyAsYXDIbY/RUi4EPzo4pIklX9xfQM6UBlCNPNXLtboJLqa1lyB+YZOfyN0jP3Wf/sAfGD60t7UYfO2rUnz59Kue8QHo1g9Yf5ol1c2EmgMgc0qdnWc+/y0dOFHZ8ZIyGEcXBzw8h1yVWA2upg4RBE6avhT/ZJeNaeG/bl4lHECy2PkoH7Vnpmj14+ckPqO7O55+rBLxgMu1SaJ+XcEyTBZJBAToid2C+FICdEb0Zdk+151Gh2q1IiZDLd5RqMh4UoAJSLdANlVs5+j6T20cU2aP8oPhh2MUpVhY0SXXF6aJMH4rJ9XMjq4Jfw4Xk6oheEKabCWy+KqypSh46AgLEVvMO6+mv3S2eLE/hjG4mgLi2TSlJGrkldPXJZwOdy4nzTahvrGLf2nJeJE6yHlhhWJeIO65Jz8/ZF0qd+Al1FDvUHKeLjNQwaHnddQVsFg8ekPbuOaNH+Ujxt1MCorMlBeyawmTcES4y+V89v0jIv+AsLXS+rGjokVgC6lvST+fLE+RdR3xk8IbXgaXSrBVRde8GcBXMHv+WLvuwRREcL1sgeI/nOz0f6idro2EIB74wK6BaojZQpcnE10nS/U6NwbbvOQyaov7JOu/8Cxmot0x7ZtTRpC+Mi3DkYt4t8F9ksYxaxGm1Y0L2u9UTWCF/O6CMyZ67gxBwqCCElE+vMZP6E573+qwNWGPbOH3dqVK8S5Mk6GrDdfwNpANPC2Rnt9eTgXdIsN5XWHrKDo7C/3D/ZT9N3r8D1bhXmyg7ZJ139lc9l7M+mmbrRpTRpSeDE6GHUKOwsLpuUyufI8Ux/lzUhmN9JCvgkbgz21XMYj7D2ntw4DeJwoIicnaUNGv9IxYv6uxdOX/sd4XFk8zuPlv00cJSnYZp/a8MWKIBE/bI1ULcRT/eLZoXf91Kr3TMtGyS6ZdZ994wYpe0ZqEc24bZvWpCGEjw0jhEfYl2ruv1Imlq/ePCYr9k500xE7BDkJXedmfjktmGfMewQcwPHPFnf/ax2QPjtrENHzvrxv8YiMMHKOHiQOiaKtlPG+XzwHw9hp5CA7J6lkSt2hNp/Ft0u8RmrVBVrwrhquOliRSR23bdPSJOj4MJj4FyG88OFKfPWiZAZXJtMtSZI2MbuTFvKm37qly+uJj+eL1Uvn99cax/LwssKsLaygkGC1lIPjRCsfkl4+PWVk2Ye3epVBIKigppL8aYiXc3HACZgnmZjevXtFsc5fIffXFVfVHmjxsKu7HBLNskq6fmWuAsudvG3zOspxbSr8sYKPwLxe70ahmNyT3GikOuD6ytfN02UXG5jdSQvR2s3DnxbKNYb0iW8AJ3fK2mNN7c3F7DnRCSPK6l4JgYBfZp8AvK6fnEu0GOFCDWfCjZO5X5PbLh2orTToFBKZ6RvgemKQh5yUjmtOur5VyYcT2I3vtVaWLcOaNOO//oODZjwVhe7wQwrB+U1daE6zx5xWf0XO7E5aRj1lht72jCfrhiv5EMM5Apm+ptkRvfHKutXGSemX7yC+GzyDbbbU6adVRLdu0TjV3Iraxk/utdn3zQsLhmZ2UUokIWn9Z278uNXK6573K7FKug6Bd8jRnFcoR7VprL7k2tXg755cFIX+w0b91ZNQwG6a8+ywzKfQtOZCln7UGSkPjth4f9ioTYMC1TjG5rDF+lpq3O1ZLYRQmL7BWsM3pDzQ1RDzzL8Ak7IVYSm9xs3beNgmZtH41TOzhqSHKqWS0IyKWc97f/WWKyHdmpOuS6BUVTWO+h5tKvyCF9EP2Umpgll/wIZDahXaxSBzWmn+0EY6XrnLY+piaDZ+ueXgrc+2kKlCx6qCCKcO46gMtfbD2j/2ZUGemOjYNe34taeOA3vFqiLYIHsZOrO7rrrcQJh6CV8RkVRcVVN/zMran6mvqdRrFQqpVl9eXe+9MP6NmCCpWdfvIgHkl9IsMtCmwl/rPf3JZOFTUa/24byJpH4HUYTrGZGR5ozoj4NbfiuuULnOvTx5bxc2ueiGut/ztvNfG2o1gKtLkjQNta4rDgJgSJheYDf4fOlYfU1VcVKEQqKQ+usM5dV1uy3plVeP1VeXk98AZYS+sqbe80X7Gg0yuXGU6ULWIJAgfTuLOobWtuvc3Xr/pd4fR4WjKapxqCC5AB1yHYrVbzC/kLTaIvXzGabxnl+YyCfEZ/kV205k3N8dh4oBfRWaSqOjf3YHoXxGCbl+BXUY3ISjhuDKgbrq4iStREJ+A2p3e7CA22COjOy8r9laDJ7SLdtOnUrfxgscIlR4cyeGFqbq0K5IYSNKdJmRUWbJ29Y/3vJ7cUqjlFmOv5FrG8jKuAAPrLSerni5WgJw3YLKALkxseZ5QvkoTA0g5njVKQv0DcFl8htAfjEUOgPxDXCSOO+ISVD1J0IL3+6NVVXNOjCfsr/NhZ85KwMkZy4RIyROXI2+dpmRMdWy+OXq7i2/F+fvYHDzhBs7eknJJSoCK61MxKYuEEqGvFulFRle/aFEA1iQBQCP41bvjaYhOHegtqpl4YB5mOYaevuu2Ww0qrufovuQb2x3t7nwzwcOx2DC7zjxCA+NRijLVUbG45bI7g035ku7ww1mgwb2vF3uT06Fiq5ucpgcbxMAACAASURBVJx+LOdzhcE1v9boRFoN8cXQQC5ktTTUTGkIli64381wwEY84AaalYNppLlhH+UczrYdq2lz4Qf88XoYEA/EL6KNyZLz6KyrjAxTuiVJSOtMfBtNk7HEkE9Ga1kQ4JHVZi+toTaEKxNlHbi2hBReTw74QKXnd23bEGQZMlISo9USkTapuLrugJNQ9m5WSAPaz5k4gM/laFIXPmuzs82FL2pY78/jPMF6HDWK+08i+pkuMjJM6ZYkVcxKjrvJZRHtqCVjfpkVziZns5tjPPv1ogCVYtxToyXGBYugGGq/8sZtmrFuCGQyhUTI5/JFps4gjc08xO6CLnEHSUqxAOyO2Idt9rW58HO393mIDeLlmQglLFaRH7yLjAyZ5cXXmpbfjGMGUBPV3ObCQwkcANixS8gYz+VqeWA3iSBLyAUcAHEMcFL6MJ045A43vnzxsbsGZET7Sc3RZZ4kOHPY7B3WtvwkR9sHY/E5OIvdp7vttMk2F/76QEmqDheICc0fywogXGNXGRnNpl3m2bNJy3mRlwbQrq/qxiOf/CVEr7NeJ4ngkWN8MAKDOEj5IL+Vq2iYGoLEUAmHRVZuE/rH9Z1hDAd8gkXi0Wwx5OLyCbaVO9tceMJWLzqmBgI28VlJZxW4dq5kTVYsn7rYtcfkT/HixRo25xB9PXbCpoZTffniQAhgkYKcRRCyeIUX38U5V49uXTguP9pPyCa+c1y+DEIBxPkPyIYPsp3IeRuEzxtUpsFxjHgVuZPoyiMXGRmBTTOO6x1ME/KAM1Kvj/O/10+MQY5ubTmOk00wRxTH5iTc6/o897l+5uhr25c/cs+UwQMMWYlxocFqpVjI47BwM2wOj8XBjOsjYoHhdkHS2yD83Of+eyAcgLQhv8zulbyaDKA4zchIaMoraPRwvjQNPWa7PqYFfDRQSTz5PD9cDCAnXMLBg/ILW+LdX/rqwEvrliy8b8LIAUWZKboIrZ9CIuCxLdKy2FyBWOGnDe4Sn5bTe9CYe2pWbHrtwJlm43UsjyMO4sOCuMpe9m7GbRD+n5H9x2uFYMqnRZfl28iVbZ1nZJjTLUmi3F0xwhXHGc/ocZ/vR4ihqVga3w9To0t5dOtLNik7tDSvR2LX0ECVzKgsiZWyEbqUzKIBI6fMWmJUllkrdalao6qq1WIsII0PpQyK3AbhiVs6bZgM2WWDftJ+KCGHD5xmZJjTLUmmM8vMZU5cS1dZYcaNw0XkmoUwM1SoLY2KiO0aHKiUifhcNs4yScsmOmMyRaC2q657RnH/MZMeXLxh2zvHvTGx7t/lUZJ+ZCja3w9Kfiumditui/AIha2YA18O/O6ugQNIWZ1mZMxrDrD8Qilp4RkH1d69Hg1PB2sBJg7E/Hro4ssnTFm4eNvznx5v9SycnRnidJOF7JuGA0nGBuoht0X4hnu5yWkYX33mrOpLo5bOMjK2WI2dKb1bZiyC5gPxMtcNnOc/S8CfRv8Uf+v6aK9wrFweUWu2BiskbAiFGS9Rj7otwi9anTuCD6DkNPL7muzKO83IOGqVFtV3Rsvvh8ruFqyg5yY7pMXrtCz/URlDM+zrsLQORsPeNJh3RCCGooGqD/p9Tjnwtghf0FgtC4AAG4Mqx5JdeeQsI+O6VXWSV6MdHtYCAlt7jdtLBs3h45GRH91CjW1S/LqhTicqtuoiXZbF8CWymV0X7F1COfY2CT9NFsDhYIonv9RcI7vyTjMyrEflJF70wjdHeO9atKwSVTZUShgtu+4NdhskSbZf5ehsriA2d92jrSb85wvmfkTZ6ET4xStzh/HxdKBhZch+STZmhzjJyLAWPmEroxtihMpRPWPv8KMu+OsX5YY2mlJhbdgtZPHZIjh8wJ/lH/T9gnKCx8JL/0HvcEvKOJQEXmfO3X3cpHQRB2dtlSonrTU2304yMpRWozgLClzeEFNWxXvtUnTUSBZfNAS0xdLJ9obdwsNs9d2swNgUSXIWzfICHgsPrhtDLBsoeWvOu3PLP8hTA9CrEucPYRmnJTjOyIi0+vQueS+9Xu7F1YcoHNfqzs8XVbXiOzRhb9gtnOTJlRxWbGAtos148Ibw2m8Quui8Jo09eTMz4yU9Hiz3Y2N/FoSQWxxnZOitO13+buTHOWV2Dy9diIbGSslGwqlrzandFqiG3cw1ZRh3ILg5pHwi/fKQngu//pngzwjdKIlRToV/ZOmtxtE61JgQgU34imOcauswI2OA9TK5QyY5OMpNGqSOC9p5yn614XKbOHV0ht1CQg+eBsJFuopP6LvAHgtfSvAGQlsoQ2xOhb85Lzt/yOScfM3FI2lHuPWnG51kZEy1rjX+YYjLO2LEZO85C3ZcK1a83hZOHb1htzAlQlzFYYFQ7f008+ZIvNWd+5vyjzoV3sLdz6DfInhB4/PPOs7IeNzmO0VXedx9rolaq+j4Nnn5+dZ36hwZdgs7ZKpHpdEYMKjeLaGfe3abYvUW/jfDYNAmcBs/H+g4I6M53ZIkva7lt9TMsDJvXIXKRb3mSOs7dQ4Nu4XT4oiR0VPvARATFv2H/pA2qknjhL9Lf+OkoQLHGRnN6ZYkKzKY3pITLguZLb3kLgtFVa3u1Dkz7GYa/FO79M1G8QIxnufomDaqSeOEhkKkAxcMiMzIoMYZSGTWf1zzRnp9KcPF1tzjTGzk163s1Dk37BZ6JMnnBzY0sopkmP9HB+jyAG57U09StWkG4Bs9dwcZGbZSaz1dZx6hc95xFOyoFtW2rlPnyrBbeCBAvFJ8Fm0Ee3gsPKDHANrqa+1A+P/NiQDgAeNL+owMmU3DNq6y5fdkJrcV1tA65Jf0das6dS4Nu4W9YtkiCdF578H7gBOPoQd33kdXj7KtatI4ZQ2E0LheGn1GRqDNSPaXgYyv64BvJV7PsGyolGxpTaeOgWG3cE6iHRlAZhZxch8T9oQTJ09rnTLiZpgVKnDAGowPA4yvaDMy4m1DzTLHpXeYkTrfwwtQ2Ckr/rj1nDpmht1Mo1YXn15BvNgNdm4SzAclIZU1M2mOa4WaNC8VGQlhHiJZA8QsMJ98RZuRUVBr82cu08XuHXBM4foYt7hWrHyj1Zw6pobdQl60Ypyx3cznoIusAwDDAyRl91CPa4WaNGbceeJ57GyIGRt7uoyM0bZh2o1MlklzQoyXJ9qvEVfuaC2njrFht/CIQviQwrhaD78HQpIiCLFhVbumU1fYbNuaNA5Yo5VPZ0Et+ZIuI2Oe7XzWBjHjC9Pxlr/rY9zgbJJmfys5dW4YdguHRNJ5poWPDoF6wio+pJOwKvQzD1LWNm7bmjSOWKOPyI6VwAXk60RqssgWuyHfSKY1rGgJ8epSifOE97eOU+eWYbdwQew31Lyk6QB2IyH8ujKO4H3eiq1PUQ5tB905QvjKRMWbSjZONvY0GRnW6ZYk0zyJt+700iiPkZORujdbw6lz17BbCAlPip5qeilOIX7Ifk/BWL3Ye7Oo003bg/DnxgwLUFzwT5AYG3tqRsZ1O2/sjCfp8BrvzcZprBItaw2nzm3DbqGvVt7bXFfpS0Delwz9BHE2q5xmOeU2rUlDz768URNYKbWPJQg58xFtRoZ9lNZp/WTnbIpq8an2HFDrN3vfqWuBYbewQiy6J9B86kgW+UKGkAjjxFSPaIUFDt2pSUNP1l9rVvKV4c+IK7saG3tqRoa98L1bPtVRyWD9XEZcL1c863WnrkWG3cIRgXia2DLjRBZn/IluqaEyDy14mXJ029akoeNKfzS1i0CAz/XPVcSRjT01I0Npt2En3UqUjFic1NIz7dghLa7xslPXUsNu5rJMWSGxpFmdhcZlEGSNFf4gQn7zELVwXxvXpKHhVtatHgPxCH7UB/ggFXc+sWWkfUZGpP2DJWphen2j3Dsr4l4yaDZ52alrsWG3EB2QHNA0B/Qu3Dg/T7bzoQeB5p76p6lzxdq4Jg0dy8aU7mexOdwQdj+lhgzjUDIy9Pb3HdvCj2h6ZsvOs2OVaIR3nToPDLuFYWpVakXTX/4mV0Y2/8CfYNmb5dlUT6SNa9LQ8orfWMG/CxU4S3xIqiQbe/uMjAH2owxzKCXKGXFD7I2H9Edd8ApvOnUeGXYLG0Siwc0jXJcxUzREtrluBru7NpVm8aA2rklDz9KRuuE6DR8HvfXBZGNvv0aGTbolyYWWhdvH92rRabbUSGZ70anz0LBbOCkUjVM0r6s+BzN9L2VXFGpWmmhuCbU1aeOaNA54VdO3bHK3gnz4Outl0rO3y8h4nJKTpW5JcvRVL2RYHtfqqr3n1Hls2M1cU0r7iq2+PiGhpt+y7QvZokeXbnpsG+WUtq1J45DaiZ99EFleAdhFfXPIxt42I2OPzv74gXe7cXELgytcH+OcxkpJjdecOqNh984k0ARFsnXxqRvYfNML2fyH5aJYUesVFfZYePTWPTNPvJaGg+GSb8jG3jYj4yxlacMD4e5c3MQFkae1XferDUO85NR5xbBbmCJVd5lq9fdj0JyyIHsuUqJksyoff5ZyTpvWpHHFbFYEPiTxTbKxt83IkFEOFbu/nEgvD2tcXCtWzPCOU+clw25hh0CYnW29ITrA/EJ2BbJwiFXIqV/59hCrt/Bauni8QKbaTTb2thkZ1MzaVLcfvB/FnmVYbpMX53rFqfOWYbdwWsgrC7T23hpxSy9IVg3FQCurXNFaTzwdbgv/4LTx6X4hicEBiGzsbTIyqCN2tdn2W1yR6dEyKhf1mjHecOq8aNjNNPgL+4ht1gbaCC02RBYKMV5OfuvZeDrcFf5KEZo9XBKgDBM8Qjb2NhkZgZSFg65SW3/nuC6J4IyFov5ecOq8atgt9BAnN0VqTaT4mX7/7wkOBsRz0epNy1rLq6fDXeFP3INy8sWpgnFcwQ2ysbfOyIinzuwPtC/254IkDzL1zsRGlHjs1HnZsFt4gK/W2K3WxzY5ejcKNwsAvDO9f/qjrdaPp8Nd4a/lnC8di5e8wkoHZWRjb/2I2qVbkowe49bVD3uQYVktGuyxU+dtw25hL5evs+ul7oamcMWuRxHOWj2s5q6a7TepJ7Yf4dGThQO3SHJL2Ivj4X/Ixt4qI2MUdVb8cffWKota5ebdNHHIL7aHh06d9w27hXNCbq79XIRs83d8xSvX4FvfTXBwZjsSHh2OWPP7q4Fy5VKc1TNQY52RMY+mfIjEnV75mwGuj6GloVLSxzOnrlUMu5lGLTdPYf85cM1a7787EZu+7EkHp7Yn4dGTg1+eFrKHK48A8duwO60yMuzTLUmylrlxZS3Vu2HETll6hCdOXSsZdgt53Hix/dUPQXNVhP+pWRETZD9STjLRroRHJ1etKjo2OQNCPGoe/LU5I8M+3ZJkbTfm16UWDWbEtWJFlidOXWsZdguPsBRSSk3DYsvi7i/GF4aXpetp8u1I2pfwBMuyR1aywoEoR6ptzsiwT7ckueHG6vU0RYMZsEbczQOnrvUMu4VDHH7IVMpWwQjzi0W8T8G9n/fPpI6Yk7Q74dH+hOldUAQoTOXOb87IoJsUH0a/nBMNtEWDXXE2SZXQYqeuNQ27hQtCdhw1jPUl/Nr8Kj1ODmBgzjrqRAWS9ic8ekyfHCeFgIzZN2Vk0Ak/ZTDTKzIoGkxhnjCppU5dKxt2CyFYaiC1fz5EZH5xVjQIAMD7OHks7dntUHi0L2X9HICBWLVfU0aGfbolyWmmc6GYFg224mSkNriFTl1rG3YLfbFoMc0q7uJy84uc6XII+Dx0xxDa09uj8Oix/lFqFga3YlMsGRmUdEsSObNyZG4VDTadUSWKaZlT1/qG3cIKqJLQ2Lqz8LjpxbeSzVALQkFuCX3qQrsUHj07eBp3FGA/AX81Z2T0oCspUESdCkiH20WDD6i1kpY4dW1h2C0cYfGUdHVVqgTmF93m8/ASuBPAEfQ92fYp/Nb1G7tVRIJAP605I2PAAzRHbYtjcq0bYkddWXqul0siW+DUtZFhN3NZjGtp84kU5oktx2X3QH1POJQLpNTJFCTtU/jvBnxRgdangGjufFNGBiXdkqSR0XxpN4sG75D6C9136trKsFuIBl1pV425DM1LQ8UvYXH2x7O+zYCxJcsG5A/92v7I9ik8WlVcGpIwJhj2wTcaY/LUdEuSrjTLcdvjXtHgSwap2m2nru0Mu4VhIJwSqTUyk2v6fVjdR6hG/iJ0AvC2KzagU9n2JqidCo/O7dm/54ubxZDPFZCtPDXdkmRWiesLuVU0eJVI6a5T15aG3cIGKKNEak1oDKbfXWqxrtORTIaQUMON91+OnrP/t9qr8CbOSiA+mH2KLt2S5LyTgiaWQ9woGvyjTihwz6lrW8Nu4SSbK6JEao3cwExVN94KiAsSXzMKX4TztizWnKUUJ/Fc+PfG6+P049+jbPeG8GsWCQHwI6dB0CfcqFz6bQXMiwbXiFTuOXVtbdjNXJPhSmqk1sijHNPvkAVwoh5dVhGf2n1wuKDixSfG2C8L6bHwa8Tjn9zy5AQxJdHWG8LPjv+JB9mcRvrQHdGOuyrWy7xo8HEtj++OU9f2ht1CAghwlHAY2t34a2eIOi5oP9rflRC+hvOgvLQykpLJ4rHw5ofkA0pehDeEn5mDsvwBFtznffqMub2RLi7AtGhwYyVX5IZTdzsMu4UpIIAmUmukETMt9xEwBb6mRmhFHiH8O0Eheb+WUpcB8Xx+vMlp/sO90iQMqZ1YkC2BQHA2359+zpTY+QPNtGjwfhVXxNipuz2G3cIOTEQXqTWynm38taWLIK9oOkKTxpAG8m4YXLiUeqzHwg8pfO/KrSuHCikye0P4o8Muf1odAcHolwPoe25Jm52ez6xo8LViNpuxU3ebDLuF01yOwOGoZIxp2Qd1P/yC5NrHfSR83PAyehOypUlFB+2P9Vj4v8YLAADCCX/Z7/CG8Kgu567Qyf/F8JeoRsrIYoOzsw8xWiVpq5itYejU3T7DbqZBhYscf5lx4zdydQx72OKMCznHhZvYb5U93zuW9UvPTwp+sDvWC925f08dO/UvdbNXhEfXvtg79tadgKPsS7v7itNyZEyKBl/UQzYzp+52GnYLPYDE8czPXbjxlzIO5nEGx3eNZOsgruAVpsB9Tyx7cbXdwe27H2/kiaRQDqxS/kC7U+PE2DIpGvwQB3alv7Itt9ewW3gAyJxUXE8x5pssiAYTjyoDUjUY1h/DVUIWBGVdH37NPkORgfBDm5jo+MCWlyZxzawX9wMWP2of3b7hjtKHEZOiwWd0QMDEqbvNht3CXoxHH6k1wSbX7GyU+7OKBBhkq2NieohYGBSVQxYnRW9fT5qB8PLHLYQ6PrDlpUlcc//H72qBYmkBXdrgkWCHp21xWTS4moUxcOpuu2G3cI7HFjppdA5i5E3OiIKyOlASHTo1LBLjhMN+MTII+N3j7XtFDIRvXj/EQX0werwn/IFR0z4NAN889zTdTsk1R6e5Khp8SAX8XDp17cGwm2kMxDn0kVoTOeQXvUEqxrkQ+zwkGZ1SKcTdsaw+8cIYtj493K4r3wFsPEJrNQWZIGErbaOsf8LBSS6KBjdUYixXTl37MOwW8iDPQaTWBJecLDQpCFTxoSBiiLI8NTAslAPw2Rmi5aBmd22v722O9lz47174ivh5k7IIvBeFR/uHNUAg+Z5u1ypHNWKdFw3eKQYRLiJ17cSwW3gE8JxODf8CayALKXLEaZDXS5G5+dLa/kIW4IIh6zn38uQx32y3DaozEt6RtiS7uV3Yd930bL1616zLgIAdSxemu+GgHJnTosHX+kC+c6eu3Rh2C4dwtqNIrYk+pLdTKYPhOJAVyQs2oGrRbxFsDpiABIH+eHTjtnU2hzMR3qG2JIlr0bm8in9bWXiEWAAawujseQitnXZaNHgNFzp16tqRYbdwgYcLHUVqTQgWI3SZj7MAUO5QjXo8ebKAHche2QPkINn78UCVHm87kslEeIfakvB/Q+ifvv3/9KQmDRO4bKiYrKHJsq6iy8pyVjT4bAJQO3Hq2pdht6DF2M7nj5zFbqBbvbgAF2M8LLh/JAZwHs6WTMb4/8j2FnA52cm21RyZCE/V1opwcoGCGwPyW/uJl8IgOHO2ilp+9mu6HA0nRYPnsZw5de3MsFsohSwXww5DNOiT7hgAkkgIICF/yIC7OWO+ymRzQRr/3s+eg4aCiOetj2civENtSe40epoNQ1pb+DQwlINfWCajLIqCZDRJdcMdFbE4GQbCHP7L7c6wW1gGMVdr9EkeaMjIhxCqh65YJU2Om/rgvfvulUvY/lownjPiSDacWb++1Nr6MRHeobYkN0yjMzd/sN/hZeHzWCUyfjJaLT5mvyd/IeVgR0WDGydiPEdOXTs07BaO4MBJpNbIZezqF2NwAENT0c37niE2XMg5h/43uGpyFOBxx+VwxNP8/2vTH2YivENtneJd4S+kSQKmxMHtaKvQPi6zJZFytIOiwQdkMJfeqWufht3MZSGUUgY/7ahSojMaCJ75zs+Qa4psfFJiyHux2nBLhLNGSRW4QYLWb7U6oR2UJmFCdWmwAL8mjhQ0oD1Cu6H5Rsp86XO0S9pd7w+V9E5dOzXsFrpgHJffScVd6BvCuB950HYFjBlJF5QACiKOsNcEns2xtoluCD+y7h+aIzwvTcKA7TUoLxeuzhuM9X7/ymHxdtu9Ufaz32mLBu/g47QDOu3WsFsYAjFnkVojN7DLKIXw6XTLbavPrHokXQ4gb8x7Qi2/32fWe9wQflIJ3TRzj0uTMGHy143qaJYsnisCBsP2E1LbINR0uzEEuqLBlzJgCM2/2o4Nu4UNEDiN1BqZJUUbAQCikl62hXd/Mkw7NAeseuchWZ7dfDO3mnqaVbM8L03ChAc+2Ng3li9NFvXl8PamfHNGvth67y8q26NpigavZHOpSRnt2rBbOMkCDBbx1Iz5iwuB/8h+70y23fFxbEIptmvnSlm43VzxdlCahAGf9xwyMAaDWj6PDyJ6J2w/r55uvVtpE9OiFg3+MQJmUpy6dm7YzVyTQI3rDPFG7NWuAMKwpDSUZ7frB8PP/KjcszKZ3SQ0BsI35244GAjztDSJK75+7fR7MlVfCGWSyHECVv/HEr69EmS9zkPp/daHU4oGz8Ll9k5duzfsFmIxnvNIrZFacYYWYOqen+bfKLLfd3QACx5AMqndN4KB8NqfLTgs1udhaRLnTB65fHBscERvDLCgJFkgAkEJyduvhQxqPuLVaKvD7YsGH1didouBdADDbmESxJms9BNa0hMA/35xd9VNpPED/TiTkVDjvvDcJhzmsBlotnlL+JfnILQpq2hKMAfgmBBXhEAgmhd36kaMVdslsXp4Q22KBjcOgkE2/2KHMOwWdkDIaDU//AgbgKxMXkxPulUQIvyUCI+N+85mY3upUOGYmR8hTK2QcITxYvDyJo0qmQcAOy7thcb0Hk1yxzeHJnba5GLtE7JtegAdw7BbOM0GjKqpbObqAMD6BzxMv9sgDXsZRkcNtllAhJnw97hYKro1hV+2GxH/VWpwEC8iqnt40DpBTDjRcekfcwoVNw3Qz28ei7MuGnwtG6ZbOXUdxrCbaVBAV1PETETLxAAGyJYOot37sU78mB+ckYfGfGK1lZnwU9W6RxyskGjES6VJaPlv1glcQEjvB5XJ0WH7+sYOCMUAgIJuL6AhlgH6S03p9dZFg5/hiJsnkHQgw24hFRMzW68XJx4FriCG4tGT3BozqatUg8H8YGSTW8+wqW94bagwf5NbxXy85tydGotjCzCAyWJ5UWm7DgQmsBIiAcB5/qdQ0wC9v2Vhq+aiwRdjMMsajx3LsFuYCdnMbvl1HoTgmWPKf/Npdr40H+V1UUlBfMV7y61Xw2Fu408mAP5YBl0LC17sxweBrHwJAEGsoBT9Q++U6vqFCAEI4YqfQZYB+iHmuEVz0eD7cT/Lv9axDLuFPRC6jNSaSNIAIB91R+RouuMf+PCmwo8vBQXFk3KtE5gYCn95fa5swqGfpsUyuxUSrwl/680u4NHkODbRUZ0TMCh116HAFHGujgt4PbBaZB6gPxhqPLSpaPDpAJY56NDRDLuFcxwGkVoj/8UxgGuTU9Sv0e19ctuzk0UcnqKPPNMmb4GZ8AMFfZ4nB7waKZOhHeMt4W+WzY7D5d9nZcRCoGaFJWU/tL90Q2mQkgPYEdyoK+YBeolxPG6GuWjwKCzR6NR1QMNuptEPZjE7cl8q4etGXvx5NP3E4d8zB3+YBlRxo+NsR1OYCb/Uksj0N7ObIfGW8PWPIUMgtuC7pFQhCwt4O3pK3D339stmF4RzIXxQKtpsGqBPr0NNRYP3CQRvoQ5q2C1kQj9ma3mc7aIFIFc3aPheBwecM6TmPH5PfP+Hba0dM+HfNf58jtGdWPCW8NM/uSFNBt2Hf5eZ2o0LAliD/aKHj6hN6B8XAgErtZtCv4McoF+RgcxFgxvyMXI5145p2C0sglxm7tTbuYSjKzWkOfmWXMzYkb5Yv81gm6PATHjV9H/Q7xXMOpUWvCX8k1vX3h8MSh9840xSph8GoLJfjW53b8OL0sQuCgjmpRh4VeLt6JrUXDT4abbi2w5r2C0cwjCGa7IbTvAAK3wh31ln+/zskqz+i+y6ZMyE/2+vhPUBE91b3tVbwl/OLH3nYRC6dwn6LnMV25+Qvmv3ngXT5KOTOdIgADgbn+BqxWuQ9kOyaPDVePzhjmvYLVzgAEZLeSD0b6qe6MLzcrSGd918D4Ze/bV44G5lVq959Zd6Zz+C4cuIdvvHO7kBfTAg6PKNJrs+KwITji7GQfQXD4m5+CP9kuYLr9TgUcs7sGG3oAH0MTgqV9givFLNGht4Z5cz7r0HM+GPxvR7NWIIfeaqI7zXj7+cuRMHKWQV4XP+X2Z1lQMgFApkEVqhOM6PS/Tyuoeny2CIMkUlx8LE6QyWOW3n9IQMa2U3VgslgzEMx/nalPC8A65PsIKZ8PL11c6dMQAAIABJREFUhAUdF+jWlb0YwLn8KA6M6++f80c/xJYmQABgn9gJ4WydKCIjY3y0UMKCAMMg7NCG3UItZFjvfJlU/0v2BkD04mUPT+N9UujWuzAT3nTQbicHUvFqlq0AGtNqCOHRyaz/bCMecwAxPhYXoQjMOhIdG8PiCgAQh3doy27mQ4zFyFTtCYk8jtC2CHwRDMV4HL/CJNfnWNEh5scjJAKQjDeSwqOzC6ZtDQXRGMQCprOHqtXTjzT2iA9KwAAACknC1E9cXat9c5nHKFJ7TKfaaXwRKJspToJ+ePwvTteBotBBhJfxADm0dK4pu6YQsLpiuJj1Qu+0lEMvSQ1FUBoMANZrZ2WESFtez3Qh0/ZHCLzL9UEXiuWW/DL2dFSJcXHQu+f/yyc+TgnJ+e7NwqN5APMXB8CxGf8mzalk3zseVvFXQkzOXkg8DdVJMqWh1j1ftJ3QHzqb12/ieqWw0vLNPg5O38p4DMDUsI9bw8a3BK8Knyfj8pGN8GgDBoOhUDMBDaytSMjHlAXJ6H6AVbMExnjdL7UGlSSpmlKYoZ2zFqpcNla10uLm5PnJPHRpIGIJ304saA2vviV4Ufjf5/vzEsCXtsKjEyLAxvlZr8b6F8u1IPTTnggZIPy0CIaYnaPr9eVaYUTl7o7j6Z/E2K4itZuVOutvc0gqQhmb4KNzImkXinFMRxD+98zXMqShpO2zER6hXoRVHyaPiK4IAVyt4X2iYxvKBQdPRcAezc38gSqd3L+4zq0cktvFNT50Ean9MDLY9sFmPYnQ81jM/fnvuvleHUH4x15CeUmjYBhFeBQGQILCj/+/hWAK/2dywyWZHOxAWwT48BtWh52o0Svl+hoPqkK3DRGQZplpK07r5WtttxwnOzulkrI73Ku0hTqG8Hd/gTJLh3LxRnvhb+UfgOy8fB4EWE6qabbgh6Jwwv9vHIdzFthe5EJdsUZCtPveuqlWYDTs72z31XJRtf22sRKEvsXeffJFt9+sIwi/YTVaoBL6E4+y/RNfeLGHnCUBGAg+aZlBslaRBB5C6MduUEb5NG7sroyQEO2+wzURbyvPQa2TvY3VwnLq5O/A3gj5JW1NyaZWInCBV4T/fMHcjygbvSf8vyX3RvPk80BvivAfZMdNA6AHhj2Q01Q3eEJCtnFAaa8ChJ2guRrZ2ZPqa9zIHmwbTmN8J44IGZ6l2Yy/iR7D7p/5yNqx7lZE9Vh46T/oHW5JGecV+x1e9OobR47Qce+HIorw6Esu7H7qMXDHM781b0se3g8YJ07XsLEe9Gsgna81BIh1VYe9doee0yDEHEdqTeFZKscxdIU9JgetnNRP5aYR81h4cB0VLCGaY0rFZm/244emHWFvYcHz9sLfg8vT1q2XcGw23tCsGAKMyXeXDJBdeQPRc313uwryxUCHxTaawrMUhmpQd/7v5UdYmj+yxzFYnN8Kbwiv/Qahi61Sk8ZC6VSkiFCBebbC7xZwnkK/bauHK22PPiN6ZxIwVSg8EgF4zkoPt5sg353A0ZrwVuFZCn5j3oSrUZg4lDO4VwPddArHeC78+meCP0PoLGVlUW8KP76oOpoXChKthb8Qj1UYQzNlbPvD94p/uReYB5GX8ID6JacXbw9Bvl0wmX6HdXiWCv6tVHvdoE7pxg18inYejWM8Fr6U4A2EtlCKv3pT+A1PHHqyCwaxsc1FZiZgIWb7jd1POf6RoIaHgcL0gV0rx1n0FtKK2xzkO4c7qI9nE56151YNDARPKcrRxWj18NfOuLWovNe6c39TEvK8KfzNiimr81gAW8gxz8PfwRdY0omn4jQn9M1Gy4HQ3G07rmPzaX1iO25bkK9RjNN2MuzCs/asiAzChZwXiFdv+0lHZVGXfnRGR+jHkxzdMfIJHIYIjXL/NxpvnmWC065p1/Vu9CTgWmz3ZrlEQNMLpuG2BPkS4Fs0WynhWVtuPS3HMSANNxQsb7g+AkSsvuXkYCreEr41a9KYKMp/F8pw0nWtNM+TMbIcoz36qnIT2gxxy3PeUCXyo8a9HNDWQb77AXVtTprwrB0r7wuHAOJYzxU1M8av5+yaxTAx14y3hG/NmjQmsuf9S/yjmT9v4Umtk2y4lDc2cUJ4FG2FmGUWLfoxSRKiplsvgp42DPLth9SR9Cv9xQ+4OC2vUQSiYyKw6DgRxusnXXvL4Na7dpSmHqEh/Yv5gHMfl2Wz7sMO6Mjn3Sa9hF7H4PtNG/b4BWqC3SoXbQ7yuT0A4hYXMJX9pptTRUPpFpO0omGlkANgUqSkYFVVVVBIr6jn2tqrd4i3ha9bVT6ZBWC4rTkUdXN4woxIsmAXtEq3rhGnK/RuxmrP1xW3bpBPzLb3JpdJ9Q4XXTdyfKQK46sruHyVICQNoZ965fyG0ElGq6Y00TFq0pDcHKXumgo2RtrM4PsYOPHBs4gOzkEcWEW0LhqUhXRjHS5ozSBfKrQbUHAUnjVzYUEUGw+4+yqaHcbnyEPDFfdNz/7qk8xZ9xh+dut9PRa+bWrSkOwUaXpDVRcbO610uAIbQWPIPIQO42Cu1bZ3QkKLJUy9PBtaJ8g3C9guI+M4PEtwo94ghFy9aR583k22YYO2O0+dfN81dP2jY26GIDwWnlq35Nw+IwMHuncnrnhncL+h/gCkWYfhfgRO28TzEsIzP8ICNhUpaiWF3eXujmWZ8XqQ711o00A7C88eGK7GMP+7muIReQiDkFvR7ekx9cxq49rief14St2S92YZSe/TgttxzIsBkUIx5IqgdW5ZSIDzkw6LviX8ew6wqVdxrVw6LTKYUlebKd4M8v2BW89AdhyePVUdxQK81Drr9xzzPhwjBLg8UXangW6RYRd4LHwb1aQ5ONhQ9jUU8qBY37zxCvjM8RlG6tTXybFbkGOz9Vhk8AOKJE9G5L0U5JPwrIR2EJ69Xt9HBjFFpX1ljov5QMVJBzAh6dkgt70WLwjfRjVp7n5U6pcKZytAAnimaWOCzOV548jBjzN80NV28ya5YYao2DPdTnoc5OuONU9rpw/PHqgMwgAnpoZuhvqL4NPSFxVRUNiNPcm9GewkHgvfRjVpivsNk+AQCxDdnYhb1mNphLTL/dgSX0n8+FEIQ2wb0YYq8YOVkmpP2+uLngT5FjR3NenCs19W69gASoodZVXNYaFfe6kDAJZl2OakzrcDOko/vvcd9TBY44fj6t+hxWLnCxiceF1FjtafFQGVXRDuTFLAVr2MbmlGN2lpkO9DaBlwoIZnf38kXQQBu8v91FXBmxggJn6UbgZqoXxcrnuBetRhatKgiffkKLlqzoj7Q/Z0x8yhNEhbXtqe0yLyWbogA2L7nth2edJrsSHuTUBxhPtBvr9x82Q3Svbs7mIVj8uS6uuct0exZFf2VyXw4z3waoDb7p3HwrdJTRqEdk395+yl7MWL0LXCWKHJYI/iuDjHzB4pOXv6ogLyKEOzNeKqzcokb4Vk3QvySUXGX3bZsyeqdWKZROBP8eWoKEqJH39AKIJr3vd322Z53p1ri5o0BEuyhmS+fmtW7uCs7neAp0hnBpvP8NRFWtK+X/EHbIr7dMGgepHwpr03BM84yJeD/Un+sg7PXqjVK9VBGrGO1pejwJ1P/EhjB0K2f3lO2z/xbVKThuSm0Zr8+xv6uwjHSoq+eJAuAYOe3gby59VAgB+h7HtLoztRKazyauoNgyDfIkg2DM3h2Rv1xSpxZJRK7tCXo4C9SbQX7P7++KcFb410+x47Rk0aW+ZFwKLverDdWI0p3FiP7EY4wGiWAawVl581yFZTd3iE8yDfx3CuVXj2QKVW0CU1URJRzSBPqOkNANEufAl+5mp6KyvcDyR7w7lr7Zo09uTdwQNiOXBjbavLMuMqEzciAaQZkr9aLlv7sU5jX8HScxwG+f7Fsyzh2VPVOqG2d0mIzJUvZ8+LZIuXyauA695sySftHa++VWvSUIh4eiSUQH22Gx/UcbHxa9IQDQDdvMSjkZEn6p0nuLUYSpDvr59vSZXXhwgqG67XF2tUvccZpEx8OXvuFxLfZPxuDIsa0ZKBI+8Ib6DZ1nrCd1mcngDBscnu6LRFYQw03YyHYDrd/pViw1WnKa0eYRXka5jYc7QEW8BW5/lp5Prpd+qY+nL2FIYidDeUQ25Cb/cGZE20/5o0VArnSOO1QDbgO9eHNjPVNIDbmIIB2uzM65Xihde97eVZc7Gu2F8QUTlq7e/TAI7LRRFDw8rc8eXsichHiB3IESxOODGgBad3ROFXzVsUR67VHe0qW94GfbnpdzYL0I8bnk7SHDyfL/e2l2fNje0VPDaPuHUYLgeQrXnXg2tJZqK3AD9QNTTxam8XeVp0eEf41qxJQ+XW4kB/jgwCKHen99oQYJ4xX8wCKfSHbFXoz38S7W9fo9irdF0bqy4TR71FrtIIYNgMt7681rD/cyYahIm37Sv4p/B2DMs6pPWEJ5MQ0nL9cTmUuPOxnZO8anpRzIHR9AGWxiphFXpVo/uSdq9XiC/niYLlKSq1CEAVTogPWGHjdjua2ekEWDAEAtWo+t2jXqCtku2Cjil84c28fTVAHMDHF7g+uIlDEnNwth8HBjkYUrlgUO1CtRJDK3l5xHvLMAjSsnBckgIE8sOjFRCSzz5LW15HRqiufXzyI0bLEf8CD/WDMk2ONjB7mhvlI5romMKvnrV03koM4k+GgiQ3wq2r/cxP1nAeVDrqA72pSTrbUOVsqqJHTOCwGtVA6g+E8cQz/ybRka8K4KvkGCDkx9WJwTl+XYYNZJBYUY8V4LBbcUsceiMdU/hbTxgilQGAw/u4EIrcGAyvsCRjjxJAkcMoWY2wvMFZ9psnNMiwsLxRSQADGRmQBfClhz/6h9Relj0kiFyUlVBf5NethPiC/nbA6QJm47FK0Oui4s+W3kjHFJ7kvblRwRzZlek8QTnzLlispSt3lxDyHMYBLhXL1pMB1VZYAX2s0DifXAWg/2uhUcRjLhmT9Tmx4avRfqoRW0v40Kg9ZAlV6tKyMY7/sQsSnA0m7Axrcf5YhxW+YW3lSbw3FoG2i0KCTjE965pqlfnVNCHGpg7ZWPg4MvIkej1U5+2SB+d5mLHPUHAXBDKVJoKDQ+Vp8wyqr0b5yfgvRT8hh1xyUpwqSMESGqbW0gs0Si0DHPF9fVo8rthRhT+XOyyvGydEC/LRcVl38SKm550SW9SuEWK4o8pNBCskxVdJL8+7efQZbFMcad3UozwoCAyGbAAkOU2Ru80iCfQPlLKLwkytPs5XKdicpCqq15+Jc2F66TL3R+UsdFThRx57b27fGOxlLViGrkQmhiUxDXu+KrMsar9AhGNOZlFeLxcuRg3VYoeL6LSAg2xo/rw3FWThkHdKrhsAALZjv3mo49tREzhQqrpvQGzU4Me1OGn0IU+aPCpJLowor7Najb9BgcE4A+vels/p7KjC56HDqX4CXKln4e8gVB5SKXuT4ZmztRbLuUjIhs7mFp9K0hxCF4vF7nQZnaPFipr/yI0BUj47khAXG5VlihzcKll8Hx+GZLI4fCwxRS8NMHb1iAMUfWpqDP4Cf0ONMVPs1xwFAMPqu3zT8lvpqMIX/Hvre1nmfLCRzxUQT8IC6ZPycoanFjbNSl4p4cJZzg6tVxAd+m+TVO4vHEnLUxC3ssl5jQrCuWPhhEHHZqWZ+uKX7wjkSoiNgVpWhFKx99G7SpOJ3SxjlI8dOv5AXXmERJpUlf+eDrDFw1Oe3tViS9RRhd88/kqDn24lFKmjsQDiEd4pXmvQMktxbwy71/KyTiIE45weS4byyEQZuqUS3aVBBKdZ/bl66qPJAEIBwIlH2j/zK9Mb9umlAUoh4AbkSLuho9Ih/bOIbwe/pLa8C5eUn5f41H/XDuWzMJAi14vCq3JbmkXQUYVHO0p6hq9XKUHO+QhIls/+Vlm1QrzS5Wkkl+RNT/AWsQQ4H9v6UU8uHbhM4mLmMhPGAoF1/+xWfXE8YcXD/fgxhLaTSk1b/xwNgSA9JqVb+JNx+cP2xKhyhUR7DxXTjzfuf+i+ngriDCjkrD2SJ8PVK07rr2S28GY6rPAEdVNy/mLxUdlI4xD7lWj96VBmPt4xcVMwfqtYCVzUhNjrn/QLaqyWeOrlnWdB+8Gsm13KCBm5HC6hraWkzGtcHCTJYgp355P9++nxo7qqoZCQm6uY/czweUSbcGBUAFmGi3D3FX66H4Y5ybx3RkcWHr2gLEgHtV3PpWPGUEu5/y9VMrplhCisVzR9QbYLtSDeRXi2RlzZgC4Vi5wtleiaDEit35azhQ1wDoZ3BTygM93FXrEA/l97Zx7QxPH+/5nd3NnNQQgJ9ykIyI0YznArCAqKN1oVxdYbsB6VT61aK7XWaq1abzyr9rK21tZaq7Wt2io91J8fq7XWT72/XlWKiDC/bBJCQjgSIKBsXn9AMtnd2c07uzPzPDPPM0TODM9VO6BWLY3yGzXFDlAdfPb4fwe/vWrp2jMo1h5gzCRflpixJP5xy87mmRYevSjvBTGF8msnpjrW13zhkb3CXFN2HFe3rn4v4QVdmxkW3VYK16t6+QppK9IUH4bQuD1eOs5zMGCwcVLVzEOxOsH7Hi8c9PB3jtd0A29HfaJYpUjpNtRD7crhJfkEDxyQzGVLsiGUMUMxTrLRMU3j2RY+eYPAHUTci7vNF6r9Gl+Sy8qVzqZ4t8IH6l5+SQRBu+Z6x8c8PVXNwz4XpxbHRHHEjML9qtileorbsjxFLAh8cC5lKPx5LA+wlz33qTaM2JWp8UEJkTtQ+QvjNn0lg0BS6C1hFwnlyRhkAIDzwPLLa0peX2d2xr1nWviahMchPpBxJ738HDNQXXLBNg+9Qb7dzH6ImpZRN4I/QoZCYbMTmxcLqBUva2xMCZXYAO8CvIGv+pSnGGOewLhCbxYAAid8j+qi+vgBP/J4ebreZn9HfnfvXeF3dwMVEtV9LwlkvLA72xOH8YEMCKFnUbeuM2N/MPN8nmnhUezjmCezwfVohD7DNNbLisCgynMOiuYtWleFdelfjpJxkN/s1M3ybKKksYQBzVLFh1nGhfnk6748bjJwBRxvVTPu5gn73UEVowA76c7Pz+tv+Udvv+FlE7PCT3jvGswUMcJTbx7OwhiMt6q3uAIoLb8bf8vcR/6zLXzp0Hn9oyB3uerl4tollLmyyyhf3Hz69cOCOs/Wr4JkyGncZVPLz77y7xtOEdIsIyHbyJ+yXax8MNWfHMZmYpDNghCDpC20PY9qmFj6vhj9CKXlCW98PnNYDToT46eQQwwkJn2DUFfG845PUHlSD2Ar9axKMHO97LMtPDowJkbOBHOpixiMndCUlRBfos+E45rdt0RWNz47JegDmU24bGrZLKbm5lxQmBEqUc11HEyrV3QpSPUrOiB4q1s3gg3ZhCfGx5gwMBIXVaNRUDLewBn/1vrS2ZOi5/+zZrJzAkc5Dzrb/4TQFzC1ZyJC0afxFCA9ZxREuhmeceHR3tQ+ckAmf656GcDR3lMHBEvQXYVLs4tgs/SiqpwlsyBugpqqpzN1u+93MS9UYgQmqOdbLyDmIHRXuNdvJXcFnycOGcBkE0AKuAcx6YNLgHPHYOMR3ReJUrspbdd9/ZzcJ+I5CZOkBghy9mPXl1G+TNXQ+0uLzTkd1BbCf5un8FfkfWtU3j7Cxz70XkmAAnfVg7FaKtcWXrQdoLqhyRXN7ew7qu71JfFQDDMlHOylIFtqLvx6iRmhEg9D3NB2s18aRM2w833hrmAVdyHcFBXdQwJkXrYsnLBx4pxngdcNJv2lFb5qFxcV3Wfy7E9y3HulxXSFI1Wl74DXbpDvuHaB0Ee8P8Hkk9HQauFXkXnLNy8fQxrNsG4X4R8nP+zuTUKbkKQvVGNedu3VVyp8y9FZubIZW1u57fq6N5fFuVjTLpta9toFUfbbYtN7eXKmq/7b20qJesLvVH80KU30HDMq1LOb/WTc2xnniAR9BGwoA6sNTMS5IWFsCDhsUeDsqJKYr8/0EagTmZD2aCEjhAR8n9D2b+PtNY+8Hxzrf9A+d3zMo6jHCiFwPh48/ZVzZ3FdDO3hdpdQda64mXAX58gf697csM3Fm3bZ6CgmqRU35bkmhkpcBbn6nc1iQrNe54DgNrLrmSBakKgYrOT5SeN4OE683686HwfgzrfaQ1e8O3HIxP4LeGwMcl3tFMh325/FEz7YwMBU3cwiWBY7lwltoypiypUmnUkdrQ+MoDY3oTsWzUnTODv7/Cea9IcYKTx2IPGb9zBdOKQV5F6EdgtfaHr3XcJbdW9uSUcym3HZ6DZVSigj3kWFKaESqzgCvYi7J5x9NW2EqoFHZTakYxFa9d7S4ZFOfBJzg0wGw4aDQ3D23zT1RhWJy8OeCy+ETCmTCfnQfn6EpiOyEbIuokpmYgqy586URM1N32PSedfRauEHJn17v+b+kSQjmdtHeFT20kjm9JnDcEBmHw+eHIWvnPSyJobYQcHrqi83yNM4Oo8+M5z1Ol33HXLZQNH4xvocdPGkRv5HTQiVOAzn677l8mzhBu1LX9WPsidPokTfJmcElsfOJXgsr6Ghw5hcgDF2oyMa33HpO++uQ9NZdgPkkgTAYEn652nX1W7H+IUFcczYf7fMftFuVLHZkwNbLfw/eTwAAH/MP/U/aCfhEfq/8H5zvdgsKtFor61sxq/7o0+ry686UDfNArLpeP9K/eA9DxxzeSDIxAVJrwuyqT7EhuZCJV7HHHW2m7c1+1CoGniEOJh91Zqhs4qcl9mxbVyZGMbgYNKp8mFHt0dq2vjZ3xVFJ2FJhyYL0sMJEOvu51Z7qAIoPTkCDk2fWZS507QTNqANhnOPfy/7vQEXUbsJjyKPvTwvKB59LgRMiEO3jQP9/lSXq7t46EzTfbxqV/3cGuVOOSLoYeJMNtXdqx44FDcdKjGYT2o/PuXhrPMHqxr4H6cqAWvkeL8nq7b18MU5DAIAGSScyhL37565TNur37pknfdubHNJ1xcjSwKdltm9MEHdKzldNDZgPJTvISWn+vVp0SSRZ30cT7E984s9XZVfLXYqHeAvZgDhieAY7febL6GGedm2Pzax922R/vT5Ss8sKZSbOqGpzNP5KNL08hqdAn8IumlW5FMGWl2pqoHfnXHSEbj9ukvgyFuXxbF1U0+vigtdK1qpt/fjngtJR7ggUfAkM0II+aJlq6k2/nDSsXNS9xTg7QfLtpiXaLCWZycnTROcWrjo4skFrylq0LX41FwxI/y/z2k/eZekOj0fCyY1sfdRQt9MX9mlrwu0MdkRs0GspG7ni42HSrTxEKt/FJSBtq5U1cAnlN8GXL6ABW3+eBwZJsIAFubss+yPxO399Xev2u5KMHdGv4hmOJK97bleabm5q8tcB5VWS+I/dodsh4gOFt7yOWmaZ+mgzzY7R41aBUCXyNqyH0WUSet2k328d2305+1UByQGQoHJ0TZU9/Ec6v+xRkIlLsWdqJ/EpSB7fYfuZFUDH18lgGxhj3Fr7Latkh/0wtz4Ij/3ZOWB+jlGlALRJUHVXtKxxC/JC8P3/j1FFnY5XcaGOEcKRuKlHSu8Me0vPCpbtPr2J37rnICAqYt3ct1RPS6aQW5rfL8xAfrvqoMV0RiveZdNLReD7NWSb7ZpIFRiFSveVfWvgGdgqqdG8CjZiZGgDK9GD8PeejukEp162f/GrZQahH4eqb/pzVlcLtN5Ur7wUMWWeTMWxniJLmQOSZ3AYbKkc/OFOMaQ9mjRSq9OJbyauSMCMRCkkNe269VKN6qjdEqmbHyCVfAQg7fRPXpBjgkum1p2iNWmPNRAqMRsvvRArYFWBzWCR5eE9sy4CN+t7yV9jtB7ae9vjFYN1BYP/nhFpP4g4V70+wwFzuH4qx5Kdz+elsChpt9hLAh5Qpvi93tFQAAXvfCm6aeqo/XCf7niZsWro439Gx0lPDoRBr1B7Boyu1boKTbUKFfVxzvR2C6V8iUG7+PC+kG2OQ44jSlP1cszDKJzczz0CKw10NZBjeDLRMsuwrgLV9a8qzY7nF+5Tm1K+mXZFoP5oqtLl7FPYIAltMEhZHBl0vhZu/rGXrm33nFMih2P9FL9DmZWx5hxprW0Wvg35Z7ehc/nc408Ih0mPBqOz+YCZXmaTe1Nu5avfs5vJo16oLVcJAznw6X5jcVY5mTwu6GUqOdsX9cPlfhPjKM3X2YUUIkawe8mdqB3wPRmj1t8ZJpfLLWWBvLFJNPGRszgEUyMx8U0S2xUAwHAfJzegpVUrc9QcfQm9h5CO/11JT+VqInpbf7ZtAUP5tizXQ5BoES7xUrtN3JCpE7fp+rjNTY3bR9p2JHv3XUGxjLJZVPLAbmveu7Ej77yWsP8lolYMuZU/yhUA7+EVA0De8G5zR71oznbFy7McZIzufYROWkDRyQH2RGEkC9wi8p6fv6OE/cTJ4tEfWObPYwxrRaedRfZqhql/+PqSi7uUtO7JUG4Wk91+q5h0fC7PADjUXWuYLOm9K67Un3bTRPsaGS/1xwNuwCD3Uowtmkum1q0pjykC5VYwu0OvH6rN5S8K/gCTbOluoEytlHkZyNqho/vYRv8nJcDYae6u33UYut/vhqfJfBOaMEU61YL7/AnmvUPQn9I6n/QQY/6XyagQdFA+p0LhitVLaljkOYer05zVVtljknSGunjZUQbvs91WY2xzfvxlmcLNfZhKlTi1fFRJIA4sNlouJGqgc92orqb1QJO88Ij9MPGkQOPo6TQb1QPd4Ys39A8XC5ev5N3a2P/RalpW9s5qfB4zRSMZWn1P+gg4b9YWOWZAyW9PmKxWUpEzXTRmsuKxGrTZlW2tJHwoT4TDd8/J38P45josqmFio1K/a/I5cs/j8agqi1mCA20mupf3SNI/dv7zBszRXjVL2TQ+NUeLsPYEGO5jna019c+OA8hUSVKDH74YNJys860rYZz/xhFXuog4a8nfz8Ni8eFAAAYC0lEQVQhAOLbRrzDEXOUqoKLfp6agBk7SM1zv5RseEUMlYDagEnyj3BhoJlBkJaSqeqvYoMzgwFjowVwAsnW898dEFxy1d4jwwdB04RX9Ru2zV7Zf7YtFkUGVp7Ld7TNVvUmajamxie4qj70PPIoeWP/R9VKs86z843j1wXbDmBhSQoU5ejGVRvB5hEac87Pognq/1f9fG81tCeVgNqAAtkBXGCqy6aWylxygerfMu8BIFGW4QJEt4S4Lo7SXeEGSe2DxXMR11ThVQ+q/p6vpkBmbhQ1t+Rcvr0ou3hKxfccallIUsm1wch5ZcckFbZ4Thoz2CA7kgRtBAcqxJ4pGuVvac059z0Vmvu3SNDgWigqAbUBL0u+Y4odzF2DTsVG/as7IYGoMFUOwK6bIlgbW983S6Rb0UuutzVdeFW/9IXf/Tnwo48E6h/Oz+GQFcAJkLxUgSYPQpGDYeAc43n7TfGs5KQxg08GJoshLynz+0NCp0KN8qjWnJPtornXj0oaDJU1zbNewTybMo7Q1uy1M9vE5NQcjCHv5iHnsXzQLQk3SN3fnyoldKOKMw5zPM0R/nH/vC5xTP79O4Fu/0No5ZS4oxhcPeKNPLQlFKUzXXOczRp8Pjs5aUznavKubGfQZW0eygsSl2qVrzXnvCI8qn5fmWbXUDjU6Ix6BW+JfubzRWaHHNnTg8d3WNQ320/EIAS/o1u2MnZXeY8EjKhzAczIyIswR3i0T0Fkf8mSJCaEE6vWiLtwmTxniLmIZ56X/RshzX/9kdKsM3x2ctKYzmZfm764bXqsqgWaQB7VKl9rzvmQ1Hbh1jcU20adgNqAd4SnJDzSdJeN9hTW/43FTXeS/RHvSHirOnNfs3wYaxQs/HTdJuFr0jPMEf67PjdTTse8iSWjoxECR88CFoPHIQDPaVm+8Aa5MPr39m/j2z0nTbOsdjqT6cwUKVM2kSU2f9UqrzXnnJNoky//7dFAOFR1AmoDVhEnpBzCDJcNxYX4/jA2PWsLio+JlZGPUNF+ThybRS7Uc6SJ7nfPN0f4cWcf9zgxJXAFFuTLx3mQKQ8QED4BELhxsG5Y92Po14HNH0OPZzEnTbO8P0KZbgOxU/cypzkWeN6tVV5rzrnvre3ioQKBca52dQJqA7YITriyCPPWTN3zDAN93cZ/inIyM1gJL6Kx5wPCp8DuG0t1W9wRI89XzRF+yLWal2f0kk6LhYDNEUAY7M2X2EZwVO9suWzbovEJ5vVEnsWcNM3yd8rt79/wx/F9v0yJyo3pfU+nvNacky3TfklHbIz7eOoE1AbsIH8MYvLNcdmgT5aUgoQe0tiadRwmJoUhQRFxC6plgJH0/2q3eEeBpNvMEX7NIoSe9CralH6RCwV2YRkfBPQJTHlPEYoDAI/G/XTKzNQaz2JOmubZEVMQHH/bHXt5dIX4U7dZesprzDnzhdqVbxVK43Co6gTUBnxGHIpmkub0mreunQj6XhkY2M1ZyOjNknebzI8PIuW4s2332talZzES7jNH+OpxmYWxWysH200RDBwiSRTY9O/efZAjK0cwxt2hItnsWNvPYmoSEygv+6H3E9QbJqBDosvi9+9x/eOUvY6rP1Kbc77UBchaYxwONcAomso+8kAGQ2iGy+ZSajAGCb6HcOQYpi3EMOErr5/M+fQ1/quc2vmWsrOV7G4eIxu0JDXC9TLKJliwoOj9f6KPB58+9bjm/Kmk3en/PZvxq6kx/uropMKr2BI9PsUfdkejI8rIM/vwOHQ9VmNlUptzqNAZGi4bhUPVJKA24DC5eyBuY4bLZicT48K/0ryj+stDIIv5fNBLaND1+1jWJK7GilctQDO4+xYeNM/qQvFoaKanpE+0dgbf5cT+cvt+yeaHrX8Wc9KYyKPT99BE6Fjh9vomQi4FkCH3147KVpODn1ChM7Qb5tcPh6pJQG3A9+SH4zEHM1w2HE4BDBYw+PyAESyCPUkxE62f9689pjgqVT849ngXkqy4WahvCwLO3zz793/rHu1/XrzYkqzInc9Wb8g0KCgjd3hxHJIBxLJjb2pKHyRJ9qtDZ2g4bFPvUalJQG3AMf7m2VgX0102uL8LwBjD/LgkU8C2dZmyGNUUxTvybNB99S9uWNCqEKdQBRpws8WX1jo6u/CoELKmET9ycDYVOJStqM1VR5lzqNAZGirqh0PVJKA24FfB+iWYl6kumwroP57hBQt8hXymUBH6Xd/fEFraXRwHXVNS02XPx/DIYSSMyfyhpdHKWk2nFx7NEmFkqhvAcAkG7aKl8gLNaI0y51ChM7QsIQzbdU0CagPOCNeUYv4mumwOgndFfDaA0KeLXMQTBa1H6IMJD9PeFjMe/S8ykXOYlLK5TjGcWNPC71qAzi88muUAAA4w+BpXCsjMkEhBkMY1V+YY9It8QO1Wl+qFQ3WfgupzUbT4M7ybaS6b13AU3GUo/I8M4xb3cXJhd4/6LPd//waHD+Pz7dlQDCGUTJhTJm19gNyWQgPhf/BTqKekYiyZAHpdi7n6hq8oW22eKyAWqNdVajAMh6pNQG3AJXHJQdxPZMoqm0E8ZLOZyWK7CyATBiTNTf85te+VmtLA/j1YkCeSsEkvmYeyV58rrb66lkID4V/6PiwVAhYLMkR+qZAbGpCl3JtvJy8oV5tzetvp+sSG4VC1CagNuG47+yTDW2CCyybApUKEsKxTyYyAiVKMnNHzrR1jp9agZa6Jd0SATS4ryPap+OdMh7XwtBC++Mi0pTNwyAAMccCluUw4EV3qXo6+ThQE7aDMOZGkLqWoYTjUbTbGPpwb0hkXWB5k8y4bm8QtQd+ANSgcD2C5YBwoWLp99aLI3srR4l7i11Z7BLtFDoxPy2jJOKyNoIHwP/b7ZtDoaDeIEeOStqAYKSS6+gb06jlYOaOLIOv8LQXBrlu9/AahFw61wMv4YLfsiq5y5IJmXTasGQMmxoFLF6DHYHuIY11ZAd1UKj9EaOWsJa9dijkdXYWetCBAZttBA+HRjhh/VleHgq39NvX3Trb9fiIfU42wU17Z3r3m79G2jrPe4cI+qvZbM6A+qx8OVdGAJfS+Q/49wl7QnMsG7nY7wmOed2DeiQOAKxYSSoVmNkfN3Gh3cWTv+i7AdocOwiP0+PCAvcOvKH+LvfV43YzE8iRbBsQwCPEuQ9Z9kSYI8IbOMbn9+2iCCuaLdaupdAmo9XngNLpCIhE37bL5Fdwlb0OGD7DBAezlPKkkEr2vW1r1GLUwxnxbQg/hVQ12rK8oNIWacvm6SJlRGtw3wsGVFGAQQJbUjoED9il0SBvuUC8c6lWygWBSlR4DKmWEtEmXzSrGGYdh0IuBAej4SqH/8q9+RlvWtekFtRa6CK/HuzOq0RSP6J42DL7YKSfOjUOtPAQgRTd36W6YLnOnLgG1PpVeWdXuPMemXDajyVlBDCblKg+b7OTq5/8Q3VB23NCtIWgofM3iiLD+RUwf1/k7hfO8v/jqqy/XrlRslWI2brq5DK/qQmXpElDrU+WdjELZXZtw2YR5BnfDbDHbWdPlEvf9NQkhyl5H2/gyWgkNhS/PGjY1ojsZRcRmMod0iTh9Nmb8OOmm2ViBmzC/tqNdFyprYHgDh6gOikcxzMjGXTZ2GfwxOHRx8PHs5jB6Ffp6XttfRiuhofBjFv70w3D/mKk4A8JtGWcTU86fOL7OwQMkVl3NJrO1pvi6cKi6BNT6VIcoUCYe3ajLhj2f7yGHmIjl4Tj6KwX62CIpyVsF7YQv7yP3suvK7irHxAQbQt54L0cnfzsnuTtBxb6+n8tXalv12nCo5ZIGM53EdkeD8J6NuWyw2f6YyPE4K7TqQsL1+CvxHWipaQTaCf/SB+4f/mIrh5Cj6tSJIr0hZLzt8vZ2QY4Yqq125flEkCZiYG041N8bnlWf5lc9Acts2GVzHfYfCqFj6r40+ws/JBLJTcXZ6yBoJ3xyla9fJsYF/SI/7TvST0J6CADECCkuFII+mi2qisVBGqkXEOo+Xl0CagPSfKtexrIadNnsYrr1hIBajr2MSOnnnjXTIpfSKmgnfNbtUA8Ol+HnLiy492RxQnScL5W0k+lTKOAydRutcPBUG/BPafp4dQmoDch0q3gby2rIZTNBRNoC1qe/oQufTmLHKNHEryxzMa2AdsLvlMeREFuYtloXA3HSMC4D2ArFgfhndZtt95RTix+04VDrElAbMMS1YhuW2YDLJtJV9RxhBo7y66cUyjCIDs1p46toPbQTvuhlJQD88XfX6ISvXMDFINaVVcg2GJh/7KEOiqkOh6qXgNqA4S7ln2Opxi4bBxkbMAa9FUlwKNtg8O6d7zS0d4fSJsL/9sp/jhsVPqXCJz45CQ/N+xrVCb/fHjA8Fk8TRwn4hv6yI0E2xdWacKh6CagNmCC/+w0eJ3i9XjGTyQBUIkgqTBkWfzwvpumg+R1Bq4UXPkIH2elZrE/qf/CUCt/vJppeOO60TvhLEZCZNS++i2+4WBBV385yRknZdKhwqHoJqA2YIrtdxoiyMXTZnIdsleRJbswsMrTkzWD/cKPVOh1Pq4UHFSixBKG1RolTn1LhD/S59iTHo0YrfFUezszWzrdwk7zoYrS52qbzq0xZtcam4QzlxZLrf7BCZAYum80QAxCShD82LjQp5ovojptZ1zhtIbzTfxG61UE5acznYL+k/8wofPh8l0sIlbDwvrppNl/AUN6rHxut/qRsOn9mS0/oJaA24BXJ1etcDxd9l80sAMEYFwZX9NnzfpIeeecb3rFjab3wazY6/4LQZWH9D55W4dVMtB/g1Wu6GEvXm121lcMWES9FGa9Gomw6c8nZ4Y0sQJ8vvHBf4Bik1zNMVzXurlwx1z7tWMzTZ7PT0Grhe6v4XPV0M0px+VQLnzMuIsAVJlzctE6l89/rSm/8uabEvRCcF/QsjmvA/l5VLPa1sxWVfLSioTjIb4t+r5BIUupcNsHqGLNYhpdf5FPYumtoq+HcQ6MW8KkWPh4FAsDgMfh8Jkky+XycwaamYzoBwMLZ/klDp6/4yjAL/b9ePBwDY3eOmtXA0VYIz1bKiAydy8YZQhzjcMD42KEWv5KWQrtxvIbUyzMBNcQm7BVynyvonB3BwAGU9VKoxmAQF8vtCCYDxzCcxbNx9g5KGjozu6BskxBgM+eENJTyabOgrNqDN7zWZcMFkE/iLObQ6Q0bfp4GOkVOGvNZLR6AAy7pRzozKaXV8b8hOcTO/S0CU5Uw8C7LlsTeq/59//KCnFh/Zxsehqt+JhAAkX/CSw0cbwt5EoWxx2tdNqqf1NzXAEPsSXZMIGdT6Ew5acwg6yOZF5fHduzX92x0dHWPSEDYh/5B9BPIxh0rYbLHy3HCkS20L9xGWeqrdr1SND/Ll/djWFqmanzOsmkoueQe4jCKZxZqXDYA4JP4UqmT+/Od/4435qkWPh6F+0owLrSPcBn6Vm76fhYDF6V49f58VMnlxZ7DBX5SDDJYGOSINzyp7LkgtJcHA5b+7SsMdWUDCYSiYuMO4F7iIMrGZ1EumyEASqEPX4CNIDr/HW/MUy18rzvJ/6Q4AMAhPoxEe2VjAz8caZPu+BOq3jhieH+EjjyXMZynum+ZGMA5dmmLQ3l2owcOi9sVlB4jw30cIeR2W1XfYfcluR8Nw2aT+zZIAReKMcxJNHtKZ77jn7qcNKZwKGlpjGyMgIe7/jXwBnozb0pOwqJ0rXNuyBvnvrLJeHM4NTWLr/AWCyEQdZv0xUL0p2JDiFxkB+IDXFi27vygenmtjpAfo4nYTFYIFwAM55C+HnvCctr/0kykM+akMYXTL+ZI8wLKa6IrI2sQ2j8+O6eoNoz9k9KxxRcLgxIjUECqEDC7L3Tts2nZ1tc/QOjKy0P4SWEczG6smz/HPt+XVOpnB0dHyffRHMxb1Q/ghC1zn7kyb/72BhZkPCVYICfNJwPUeKe2+uQsy76eC6PTC4etbPDD6j7ZfnliXwFfzMbmegf1WJ6qWf3SI9K/KxPIJJEjownHtcUewmy9zK6/Cjag54EXwNkORETGstO7Is0JatW+WCAnTeUdNeuWtvrkLMypWSOGTjvSyIdVheE5YxdvGbAcPVwWE/7Cau1s69EHAkcoulF9+w8Tt3iIii/ny0W5unl3pwRrD9hijFGubIX82vqJb9xth6toIZbLSbPT6OH/bFGd+ebJzdHXE1eVrUp8pCu9oHgnQDpAIiJUg33F4SNBgvzKC7k28nztrLyz5FhFFMAxktcl0uxg5+2K5XLSPOvCoydbC5c/QI/WFqx9pFd6fdELrvmKv1EXCDCAOUxT8rPvomPZYg/NEO+SIPAlPoASGVFa2EHnbRqWy0nzzAvfKGeiFgekjPYHPDc7FsBDuqun4u9WEr4rVEO8yxzfgC4AslyJluR/bD8sN47vvMKj628WTnglrJRN9AoczBdBJp/Z/VdUs1Npyw3agm4QUlcc4KF5so4+zSaxXE6aTiy8mnjkGyOAJOGgzHHFIXTKmfnHydRJqiHe+zjBFoG+hFGv56nCcjlpOrvwaddSbsV6ZHSdJwmRC6iJlcxpGwY4H1/SlXLwAV7MKPuOPsMmsVxOms4u/MnoOX7klECPMFFQWFiovwufrfbxMSCV75fhYid4es21FJbLSdPZhUc3Vs/3WPg7ehilflcZdS1zcqSUg7MdIfSVKELe+08Hn1/TWC4nTacXXsUPsRu3Jn2ueV0am7HKyd+Dy2LhgkyG7ytK42BpTxOWy0lDB+HRjQ1rdJMzf/XadO9mZE8p+j4n2+Gtj56CAEdNYbmcNLQQ3oDS9NIl7qkhQnm88KmdY6nDcjlp6Cc8urjhw/Jz64tHNDBP46nDcqlJaCj8s4RVeJpiuZw0VuGfaqy2eppiFZ6mWIWnKVbhaYpVeJpiFZ6mWIWnKVbhaYpVeJpiFZ6mWIWnKVbhaYpVeJpiFZ6mWIWnKVbhaYpVeJpiFZ6mWIWnKVbhaYpVeJpiFZ6mWIWnKZYT/ougZPNxENm0C5z2qYYUtE89hPnftE/T6exbIXyLKChrfpu2IL59qlm9rflt2oK2vxyr8K3CKrypWIVvEVbhTcUqfDNYhW8VVuFNxSp8i3j2hS/6pX3qSW6fatbtaJ962v5y2lv4BzXtU88/7VPNo8r2qaftL6e9hbfylGAVnqZYhacpVuFpilV4mmIVnqZYhacpVuFpSvsIvzSYMU7z6k8ulemiNwBAaPlq0CZvlvePFq+nikpgAKZYvB50JoGQF9VPedtC2kf4D/YM015BRoxa+DUVFY+a3KNNqvlUtufGT39avp6KiorbxLeWryckr/x314ZynLeA9nrUT9BcwceZC9XCb2yXakIsVU29elRs9miHekSHERrTRk+W9hX+ofcfGuGdnZMOWryaR3Chg3xShcXroUica4lq6tUzd0z5efd9bXPk9hV++itIfQV7T55dyP7N0tX8AWKuXw582QLV1LschP7C/7RENfXq+ckHgIltdOR2Ff6Md0XtN4VQuiUycBtUcxXsRmhduAWqMbqceQmWqKVePeWSBRWXI+e3zZHbVfhVPJmMYLlqSrIskcTJsBrbTywqvN7leJVaopZ69ZwHDxBaHt02R24f4asqnh9TUYX+vXbt2uyE6+jhtiv/t5Z13NLVoBdjb10JtsCDpX496FvCKPOuBeqpsit5fDV6fNscu32En00NdGeoX1LPrAexQl7IRxavBj0aI5BNscCwsX49KG9k21fSQD3HokjpsDZKWW+13NEUq/A0xSo8TbEKT1OswtMUq/A0xSo8TbEKT1OswtMUq/A0xSo8TbEKT1OswtMUq/A0xSo8TbEKT1OswtMUq/A0xSo8TbEKr4HttNiwIFU8qGPOpJ2wCq+B/T/tC91CxbeswtMBnfC6hYpW4TsnF8Qn0RXJN4v6qV5PnFInvG6holX4TsqaruWpRegq7y6qkp6wCk8jMrsFPEKo1xr0qS+yCk8j9gAqxsB7cWjQa1bhacQDjzyH2whViE7x/7IKTyNGD0BjB6j+jwmgljirhR83TLdQ0Sp8Z2W36nZ/4LkVoSNgA9IKn75Cb6GiVfhOzl/c+6q/jl2Woidd9VbWZrqO7bBTag9oL3z1lFEdfQodAt2Ff8j3u9zR59Ah0F142mIVnqZYhacpVuFpilV4mmIVnqZYhacpVuFpilV4mmIVnqZYhacpVuFpilV4mmIVnqZYhacpVuFpyv8HlgqNhDqE2NIAAAAASUVORK5CYII=",
null,
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raISQ4rYJuNJDCybweKnhgPD48xY8ZMnTqVdBBMchgN22wkh5H9+6DoSTp69OjFixeTkpJIB6EoTHKYCttsOgsj+3eh6Eni8/lHjx4NDAwUiUSks1AUJjnMg2020sHIvhUUPWG2trbe3t6TJk0iHeS/MMlhCGyz6QqM7N+Goidvz549paWl//73v0kH+R+Y5JCFbTZdh5F9CxQ9I2RkZCxbtoxp/y1ikkMKttnIEEb2FIqeIczMzCIiIhwdHUkHaQMmOTTDNhuZw8geRc8U69atq6urW7FiBekgbcMkhzbYZiMPCj6yR9EzyNmzZzdt2nTjxg3SQdqGSQ4NsM1GfhR5ZI+iZ5B+/fpt2LCB5gvWdxYmOfKDbTY0UMyRPYqeWebPn9+3b9/58+eTDtIBTHJkDttsaKOAI3sUPeP89ttv+/fvv3DhAukgHcAkR4awzYZmijayp6Pom5qaYmJioqKiTp06RVHUqlWrbG1tw8PDX716RcPqrKOlpSUUCj09PZuamkhn6RgmOV2HbTZEKNTIno6iX7x48bp1616/fh0WFhYZGXny5Ek/P7+//vprwYIFNKzORv7+/sOHD58+fTrpIJLCJKcrsM2GIEUZ2Yvlr0+fPnfu3BGLxUVFRRRFPXjwQCwWP3z4sE+fPp09VVRU1PTp02UfsS0TJkygZ6E21dTU6OjoHDt2jGAGKfzxxx/GxsbGxsZFRUWks7DDv/71L2NjY9IpFF15ebmrq+uuXbsIZggKCmruSXmg4xV9VVWVvr4+RVH9+vWjKEpXV5eiqN69e1dXV9OwOksJBIJjx47Nnj2bXX9KmOR0CrbZMATnR/Z0FL21tXVUVFR2dvZnn31mamq6ZcuWqqqqLVu2DB8+nIbV2Wv8+PEuLi5ubm6kg3QaJjmSwDYbRuH4yF5OPym87dq1a1ZWVjo6OqtXr7548WLPnj0pitLT07tw4UJnT6U4o5tmjY2Nffv2/fHHH0kHkRImOe/z/PnzHj16HD58mHQQaO2vv/4aM2bMuXPn6uvrjx49um3btuzsbBrWlevohk/DvyUWFhZv/3D64MGDR48eGRkZ8fl0rM5qPB4vLS1t/PjxkydPbv4Hkl2aJzkbNmwYOXKkg4PD4cOH8ZdOYZsNszXvsg8ICCgpKfnkk0/Mzc0TExPj4+NjYmJIR5MegX30ampqgwcPxhNeQlZWVmFhYfb29qSDSA+TnFawzYbhevXq5ejoaGxsXFJS4urqun379u7du+fk5JDOJT1iH5hKT09fvnx5OwckJiaOfMfBgwfLy8tpC8kQGzZsEIlEa9asIR1Eevh0VYvPP/8cV7NhuLq6uuzs7I8//vi3335r/pj6+PHjr169SjqX9Ii9rC4tLb106VI7B/j4+Lz7g+3ChQs5+D6JBLKysiwsLAICAgYOHEg6i/QwyTlw4EBcXFxxcTHpIPA/GhoaCgsL//zzzz///LOwsLCxsbGysvLFixfHjh0zMzOjKOrGjRsfffQR6ZjSI/aKPjg4OD09ndTqrGNoaLh8+XJmXrC+sxR2koNtNszR0NBw/fr1+Pj4zz77zMXFZdKkSc3XvZk7d25qampGRkZKSkpubm5JSUlpaenevXtzcnKcnZ1Jp5aeYr2eYrXo6OiEhISFCxdu3bqVdJauap7k5OXl+fv7r1279sSJEyYmJqRDyReuZkPWu6/Zzc3Nra2t586da2Zmpqys3Or4Pn36pKSk7Nix49ChQyNHjjx+/Dirf/qkKXpOTk5cXNz169crKys1NTWHDRs2e/bssWPH0rM6Z2RmZg4aNGj27NmWlpaks8iA4kxysM2Gfp1t9nfp6ekx9ouAOouO55VQKFy8eLGvr29AQIC2tvarV6+uXr3q5ua2YcOGsLAwGgJwhq6u7o4dO5ydncvKyng8jlx5dPHixfPnz581a1bv3r23bNkyZ84c0olkD9tsaND1ZucwJbFYLO81Pvjgg8OHD9va2r594/nz5318fEpLSzt1quY3Y3/++WeZBmybnZ1dZmYmDQt11tixY42MjPbt20c6iIw1T3IoiuLYJGfRokXHjh27c+cO6SBc875mt7a2ZmOzBwcHL1261NjYWB4np+MVvUgkan7n+m1mZmYikYiG1bknIyNDX18/IyPDycmJdBZZ4uQkp/lqNthmIxN4zS41Op5IHh4efn5+X3/99YgRIzQ1NSsrK/Pz81esWOHu7k7D6twjEAgSEhL8/PzKyspUVVVJx5ExLk1ymrfZnDt3DttspINmlxU6ij42NnbhwoUuLi4tF2JUV1f39/ffsmULDatzkpubm62traenJye3qHJjTw622UgBzS4ndBS9pqZmbGzszp077927V1VVpaGhYWRkpKKiQsPSHHbkyBF9ff3ExESubuRg9SQH22wkhGanB33PHBUVFTa+LmMsPp+flpbm6Ojo5OSko6NDOo68sHSSg20274NmJ4I1L5HgXaNGjfLx8XFxcWH+N4l3BesmOYsWLXr48CG22TRDszMBip7dYmNjBwwYsH37ds5/AS9bJjnYZoNmZyAmPlWgU06fPm1tbe3j49P8fY3cxvBJjmJus0GzMx+KnvVMTU2joqLs7Oxu3bpFOgsdGDvJUZxtNmh21kHRc8Hq1asPHz68ePHiDRs2kM5CE6ZNcri9zQbNznYoeo7IyckZPHjwrFmzOP9y8m3MmeRwbJsNmp1jUPQcoaent2HDBmdn5+ZLvSsOJkxyOLDNBs3ObSh67ggLC9uzZ09oaOiuXbtIZ6EbwUkOS7fZoNkVCoqeU06fPm1gYDB79uwxY8aQzkIA/ZMcFm2zQbMrMhQ9p2hpae3evdvDw+PJkyfM3GYub3ROchi+zQbNDi0UsQu4bfr06Xv27PHx8Tl69CjpLMTQMMlh4DYbNDu8D4qeg1JTU/v27Xvs2LHJkyeTzkKSXCc5TNhmg2YHCaHoOYjP5x85csTLy6u0tFRDQ4N0HJLkNMkhtc0GzQ7SQdFz0/jx493d3V1dXbOzs0lnIU+2kxw6t9mg2UEmUPSclZCQoK+vv2fPnsDAQNJZGEEmkxx5b7NBs4M8oOi57MSJE7a2tm5ubn369CGdhRG6OMmRxzYbNDvQAEXPZZaWlhERERMnTrx69SrpLAwi3SRHVtts0OxAPxQ9x61fv/7QoUOrV6/+6quvSGdhls5OcqTeZoNmB+JQ9NyXnZ1tbm4+Y8YMY2Nj0lmYRfJJTqe22aDZgWlQ9NxnYGDw9ddfOzo6su56LPRoZ5JTU1PTvXv3DrfZoNmB4VD0CmHRokX79u2Lioratm0b6SwM1WqS8+bNm7i4uJ49ez5+/PjWrVsXL158e5sNmh3YBUWvKLKysgwNDf39/UePHk06C0O1THImT55cWVmZl5fXu3dvY2PjQYMGqaurX79+Hc0OLIWiVxQ6Ojrff/+9p6dnWVkZj8cjHYe5Ro0aNWXKlKamplGjRjU1NWlrazc0NLi5uTk7OzfvuhkyZAj+AIFd8N+rAvnkk0/MzMxmzpxJOgjTKSkphYeH379//82bNwYGBmpqamPHjl25cuXMmTOHDh2KlgfWwX+yiuXkyZPp6emnTp0iHYTRvLy8Nm7cqKGhYWZmFhoaqq6uPnTo0KCgoClTpsTHx7969Yp0QIDOwehGsQgEgoSEBD8/v8ePH6uqqpKOw1DNO5TGjx9fXV29aNGixMREe3v7qKio8vLytLS04ODghoaGKVOmeHl5aWtrkw4L0DG8olc4rq6uEyZMcHd3Jx2E0UJCQn7//fdTp07xeDx7e/vmG3V1dWfNmpWYmBgTE0NRVHBwMF7jAyug6BVRUlJSfn5+XFwc6SBMZ2xs3NjY+PTp01a3o/GBXVD0iojH46WmpkZGRr548YJ0FqYbPnx4bGzs+34XjQ+sgKJXUNbW1jNmzHB2diYdhOn8/f0l+VJGND4wGYpecQmFwqdPn+Kzsu2bPXv27du3JT8ejQ8MhKJXaBkZGV999dXDhw9JB2EugUCgrq5+5cqVzt4RjQ/MgaJXaKampkuXLm3ZVQJtGjt2rFAolPruaHwgDkWv6L788ksej/fFF1+QDsJcISEhGRkZXT8PGh9IQdEDlZWVtWvXroKCAtJBGMrBweHZs2dNTU2yOiEaH2iGogdKT09v48aN2IHTjv79+ycnJ8v8tGh8oAeKHiiKokJDQwcMGBAUFEQ6CEO5urrGx8fL7/xofJArFD38x8mTJ5OSkjIzM0kHYaLIyMgLFy7QsBAaH+QBRQ//oaWlFR8f7+3tXVdXRzoL4xgaGtbX19P5QWI0PsgQih7+y8vLa/To0d7e3qSDMJGFhUU710KQHzQ+dB2KHv7H8ePHz507J483HtnO19eX7B8LGh+khqKH/8Hn85OTkwMDA6uqqkhnYZaQkJDCwkLSKSgKjQ+dh6KH1saNG+fp6eni4kI6CLMIBAKBQHDjxg3SQf4LjQ8SQtFDG+Lj4+/evfvDDz+QDsIsY8aM2bFjB+kUbUDjQ/tQ9NC2zMzMpUuXPnnyhHQQBgkKCjp58iTpFO1B40ObUPTQNjMzs4iICAcHB9JBGMTV1fXJkycyvBaC/KDx4W0oenivdevW1dbWrly5knQQBtHX109NTSWdohPQ+ECh6KF9mZmZmzZt6tQ3b3Cbs7Pznj17SKeQBhpfkdFR9Hl5eSUlJRRF1dbW/t///d+oUaNGjRq1cuXKN2/e0LA6dIWBgcH69etxwfoWkZGR58+fJ52iS9D4CoiOog8ICGj+7PiiRYtSUlJCQ0PDwsKOHj26ZMkSGlaHLgoPD9fV1Y2MjCQdhBFMTExqa2srKipIB5GBVo0fFBSExucqOoq+pKSkf//+FEUdOXLk119/DQ4ODgoKSktL+/nnn2lYHbouKysrPj7+4sWLpIMwwtChQ1k6vXmf5sZPSkpC43MVHUVvaGj4xx9/UBSlpKSkqqrafKOqqmpNTQ0Nq0PXaWlp7dy508PDgxUbTuTN29s7MTGRdAq5QONzFR1F/+WXX4aEhMTFxS1YsMDb2zslJSUlJWXq1Km+vr40rA4yMWPGDAsLC39/f9JByAsNDWXU52PlAY3PMXwa1vj000979uy5YsWKK1euiMXi3NxcXV3dwMDAVatW0bA6yEpaWtoHH3yQnp6u4FdH0NDQUFVVLSoqMjU1JZ1F7pobf9asWeXl5WlpaUFBQY2NjVOmTPHy8tLW1iadDiRFR9FTFOXp6enp6fnmzZuHDx92795dX1+fnnVBhgQCwZEjR6ZOnfrw4UM1NTXScUiysbHZuXPn1q1bSQehjySNX11dLRQKr1y5MnDgwPDwcD09PbKZoQWt++i7des2aNAgtDx72dnZOTk5eXh4kA5C2KeffnrixAnSKch431SnvLzc09NTV1d37dq1NjY2kydPxvUzmIPYB6bS09OXL19OanWQ2s8//3z9+vW4uDjSQUiaPHlyWVkZ6RSEtWp8Ly+v5j8TLS0tFxeXr776SigUks4I/0HT6OZdpaWlly5daueAxMTEb7/99t17WVhYyDMXdIDH46WmptrZ2Xl4ePTs2ZN0HGJ69+598uRJZ2dn0kHIa278V69ede/e/dWrV6NHj75169bQoUMPHz5MOhr8B7FX9MHBwenp6e0c4OPjc+kd/v7+urq6tIWENllbW8+aNcvJyYl0EJImTpz4448/kk7BICNGjMjPz583b16/fv0oijp79qylpSXpUPAfuNYNSOP7778vLy/fvHkz6SDEzJ8/Pycnh3QKBhk3blxtbe2nn36qoqKyevXqgwcPhoaGkg4F/0FT0efk5AQHB9vY2FhYWNjY2AQHB+NJwnbZ2dkrVqwoLi4mHYQMCwuL6urq6upq0kEYZPfu3SYmJtra2lZWVmlpaQKBgHQi+A86il4oFLq5uVEUFRAQEB0dHRAQoKSk5ObmhvdqWM3Q0HD58uUTJ04kHYQYMzOzn376iXQKZqmpqYmKinJ3d1dWViadBf6LjqJftWpVWlpabGxsRETEJ598EhERERMTc/LkyTVr1tCwOshPdGk0y+YAACAASURBVHS0qqrq559/TjoIGVOnTj106BDpFMxy7dq1YcOGkU4BrdFR9CKRyMzMrNWNZmZmIpGIhtVBrjIzM2NjY/Pz80kHISA0NPTatWukUzBLVVWVlpYW6RTQGh1F7+Hh4efnl5OTU1FRIRaLKyoqcnNzfXx83N3daVgd5EpPT2/z5s1OTk4KeL0zHR0dZWXlu3fvkg7CFM+ePevduzfpFNAGOoo+NjbWyMjIxcVFW1ubx+Npa2u7uLgMHDiw+XMWwHYhISHGxsaBgYGkgxAwevToXbt2kU7BFFevXh0xYgTpFNAGOopeU1MzNjZWJBIVFRVdvny5qKjo5cuXMTExmpqaNKwONDh9+nRKSsqZM2dIB6Hb7Nmz2fUVsnKFomcs+vbRq6iomJiYWFlZmZiYqKio0LYu0EBNTS0+Pt7X17euro50FlpNmzbtwYMHpFMwxdWrV4cPH046BbQBH5gC2fDw8BgzZszUqVNJB6EVj8fr1atXZmYm6SCMcO/ePUNDQ9IpoA0oepCZo0ePXrx4MSkpiXQQWjk6OuLdJoqi6urqVFVVlZSUSAeBNqDoQWb4fP7Ro0cDAwMVauNsZGRkdnY26RTk3bx5c+jQoaRTQNtQ9CBLtra23t7ekyZNIh2EPsOHD6+srKytrSUdhLD8/Hy8E8tYKHqQsT179pSWlv773/8mHYQ+gwcP3rdvH+kUhGHLDZOh6EH2MjIyli1bpjhfzTF58uSDBw+STkFYQUEBLn7AWCh6kD0zM7OIiAgHBwfSQWgyb968q1evkk5BWG1trYJ/kzCToehBLtatW1dfX79ixQrSQeigq6urpKSkyBvqy8rK+vbtSzoFvBeKHuTl7NmzmzZtunHjBukgdBg5cuTOnTtJpyAGA3qGQ9GDvPTr12/Dhg0KcsH6mTNn/vrrr6RTEIOiZzgUPcjR/Pnz+/btO2/ePNJB5M7Pz6+kpIR0CmJQ9AyHogf5+u233w4cOHDhwgXSQeSLz+fr6Ogo7CenSktLm78THJgJRQ/ypaWlJRQKPT09OX/BegcHh9jYWNIpCHjz5g322zAcih7kzt/ff/jw4T4+PqSDyNe8efPOnj1LOgUBBQUF5ubmpFNAe1D0QIf09PSsrKyUlBTSQeRo1KhRIpFI0S7UTOHqxGyAogc68Pn8I0eOzJ49u7q6mnQWORo0aJACfkQW78QyH4oeaDJ+/HgXFxdXV1fSQeTIy8srISGBdAq6Xb9+HdetZDgUPdDnwIEDhYWFe/bsIR1EXsLDw//66y/SKejW0NAgEAhIp4D2oOiBPjweLy0tLSoq6sWLF6SzyIWenp5YLH7y5AnpIPR58OBB//79SaeADqDogVZWVlZhYWH29vakg8iLlZWVQl0LAQN6Vmij6D/77LM///yT/iigIDZs2CASidasWUM6iFzMmDGD25uLWkHRs0IbRS8WiydNmmRubv7NN9/cv3+f/kzAeVlZWd9++21xcTHpILI3c+bMv//+m3QK+qDoWaGNot++ffujR482bNhw9epVc3Nze3v7vXv3VlRU0B8OuMrQ0HD58uWOjo6kg8ieqqqqlpbWxYsXSQehSVlZWZ8+fUingA60PaPn8/nu7u4///zzhQsXysvLAwMD+/btGxgYqMhX3AbZio6OVlNTW7hwIekgsjdhwoTdu3eTTkGH169fa2pqkk4BHWu76EUiUUxMzPjx48eOHTt69OicnJxbt25paWm5uLjQnA84LDMz88cff7xy5QrpIDIWGhp65swZ0inoUFBQYGFhQToFdIz/7k3Tpk1LT08fN27cvHnzJk+e3LJDdsuWLVpaWvTGAy7T1dXdsWOHs7NzWVkZj8edDWC2trbPnz9vaGjg89t4fnEJBvRs0caz65///OedO3dOnDjh5+f39ucgeDyeQm0QBhrMnDnT1NR09uzZpIPImJGRUWJiIukUcoeiZ4s2iv6LL77Q19dv82h1dXU55wGFk5GR8euvv2ZkZJAOIkvu7u779u0jnULubt26NWTIENIpoGPc+XkZWEogECQkJPj5+XHpuo8RERF5eXmkU8iXWCxubGxUUVEhHQQ6hqIH8tzc3MaOHevp6Uk6iMz069evsbHx6dOnpIPIUXFxsZGREekUIBEUPTBCUlLSpUuXuHTpx+HDh3P7C6cwoGcRFD0wAp/PP3HiRHh4uEgkIp1FNvz9/Y8ePUo6hRyh6FkERQ9MMWrUKF9fX858VmPOnDm3b98mnUKO8vPz8cVSbIGiBwaJiYl59OjR9u3bSQeRAVVVVXV1de59HKzF8+fPdXV1SacAiaDogVlOnz69bNmyhw8fkg4iA2PHjhUKhaRTyEVlZSU+PskiKHpgFlNT06ioKAcHB9JBZCAkJIRjnw9okZ+f/+GHH5JOAZJC0QPjrF69WiwWL168mHSQrnJwcHj27FlTUxPpILKHd2LZBUUPTJSTkyMUCgsKCkgH6ar+/fsnJyeTTiF7KHp2QdEDE+np6W3YsMHZ2Zl0kK5ydXWNj48nnUL2ioqKTExMSKcASaHogaHCwsL69esXGhpKOkiXREZGXrhwgXQKGWtqalJSUlJWViYdBCSFogfmOn369KFDh86dO0c6iPQMDQ3r6+tfvHhBOogs3blzx9jYmHQK6AQUPTCXlpZWTEyMh4dHQ0MD6SzSs7Cw4Ni1EDCgZx0UPTCaj4/PyJEjfXx8SAeRnq+vL8fej0XRsw6KHpguNTU1Jyfn2LFjpINIKSQkpLCwkHQKWcImetZB0QPT8fn85OTkTz/9tKqqinQWaQgEAoFAkJ+fTzqIzIhEIh0dHdIpoBNQ9MAC48aNc3d3d3V1JR1ESra2trt37yadQjZEIlHPnj1Jp4DOQdEDOyQkJNy+fXvPnj2kg0hjzpw5J0+eJJ1CNq5cuYKLVrIOih5Y48yZM1FRUWz8hnpXV9cnT55w41oIeCeWjVD0wBrm5ubz5893cnIiHUQa+vr6qamppFPIQH5+PoqedcgUvZGRERtflwFx69evr6ysXL16NekgnTZp0iSWzp1auXv37qBBg0ingM7h07DGu98ZVFZW5u/vr6qqmp6eTkMA4JLs7Gxzc/MZM2aw68OZ4eHhY8eOJZ2iqxobG/l8Po+HSQDL0FH02dnZ1tbWbm5uLbf8/vvvY8aM0dDQoGF14BgDA4Ovv/7a0dGxuLiYdJZOMDExqa2traioYPX3dRQWFuJaZmxEx7/MN27c0NHROXfu3PTp05csWbJkyRJ1dfWIiIglS5bQsDpwz6JFi7S1taOiokgH6Rxzc3O2T2/wTixL0VH0RkZGv/zyS2BgoIuLy8qVK2tra2lYFLjt7Nmze/fuvXjxIukgneDj45OYmEg6RZeg6FmKvlnb5MmTL1++XF1dbWlpWVlZSdu6wEk6Ojo7d+708PBg0Z7FkJCQGzdukE7RJdeuXRs2bBjpFNBptL6poq6u/u233yYnJ2/evFlbW5vOpYF7ZsyYYW5uHhAQQDqIpDQ0NFRVVW/dukU6iPSqqqpY/R6DwiLw7rm5uXlYWFj37t3pXxo4Jj09/eTJk6dOnSIdRFI2Nja7du0inUJKz5496927N+kUIA06dt20KT09PTc3d82aNe874OXLl3///XerG588edLY2CjnaMAaAoEgISHBz8/v8ePHqqqqpON0bM6cOdHR0Vu3biUdRBoY0LMXsaIvLS29dOlSOwf8+eef775zVVBQ8MEHH8gzF7CMq6vrhAkT3N3dWfG63svLa+bMmaRTSOnq1au4yg1LESv64ODg4ODgdg5wdHR0dHRsdePChQvLysrkmQvYJykp6YMPPoiLi5s9ezbpLB3r06dPenr6u58iZL6rV69OmzaNdAqQBj7hBqzH4/FSU1MXLFjAiq9mnThxIkt309+7d8/Q0JB0CpAGTUWfk5MTHBxsY2NjYWFhY2MTHByck5NDz9KgCKytrf39/Z2dnUkH6VhERAQb/+Ovr69XVVVVUlIiHQSkQUfRC4XC5usfBAQEREdHBwQEKCkpubm5CYVCGlYHBSEUCp8+fcr89znNzc1ramqqq6tJB+mcmzdvDh06lHQKkBIdM/pVq1alpaXZ2tq+fWNgYKCPj09YWBgNAUBBZGRkfPTRR1OnTmX4hGHIkCF79+4NDw8nHaQTsOWG1eh4RS8SiczMzFrdaGZmJhKJaFgdFIepqemXX345ceJE0kE6MHXq1EOHDpFO0Tkoelajo+g9PDz8/PxycnIqKirEYnFFRUVubq6Pj4+7uzsNq4NC+fLLL3k83qJFi0gHaU9oaGhBQQHpFJ1TUFCAix+wFx1FHxsba2Rk5OLioq2tzePxtLW1XVxcBg4cGBMTQ8PqoGiysrJ2797N5CbV0dFRVla+e/cu6SCdUFtbq6amRjoFSImOotfU1IyNjRWJREVFRZcvXy4qKnr58mVMTIympiYNq4Oi0dPT27hxI8N34IwePZpFmxHKysr69u1LOgVIj7599CoqKiYmJlZWViYmJioqKrStCwooNDR0wIABQUFBpIO81+zZs9PS0kinkBQG9GyHD0wBN2VkZCQmJmZmZpIO0rZp06Y9ePCAdApJoejZDkUP3KShobFv3z5vb++6ujrSWdrA4/F69erF2H+HWkHRsx2KHjjLy8vrn//8p7e3N+kgbXN0dGTLfoTS0tJ+/fqRTgHSQ9EDl6WkpJw7dy45OZl0kDZERkZmZ2eTTtGxN2/eYL8N26Hogcv4fH5ycnJgYGBVVRXpLK0NHz68srKS+V+hXFBQYG5uTjoFdAmKHjhu3LhxXl5ezLws8ODBg/ft20c6RQdwGXoOQNED98XFxd29e/eHH34gHaS1yZMnHzx4kHSKDuCdWA5A0YNCyMzMXLp0KdO+tWbevHlXr14lnaIDN27cwHUr2Q5FDwrBzMwsIiLCycmJdJD/oaurq6SkxPAN9fX19QKBgHQK6BIUPSiKdevW1dbWrly5knSQ/zFy5MidO3eSTvFeDx486N+/P+kU0FUoelAgmZmZmzZtun37Nukg/zVz5sxff/2VdIr3woCeG1D0oEAMDAzWr19vb29POsh/+fn5lZSUkE7xXih6bkDRg2IJDw/X1dWNjIwkHeQ/+Hy+jo4OYz85haLnBhQ9KJysrKz4+PgLFy6QDvIfDg4OsbGxpFO0raysrE+fPqRTQFeh6EHhaGlpCYVCT0/PpqYm0lkoiqLmzZt39uxZ0ina8Pr1a3xpBDeg6EER+fv7W1hY+Pv7kw5CURQ1atQokUjEwKtsFhQUWFhYkE4BMoCiBwWVlpaWkZGRnp5OOghFUdSgQYMY+BFZDOg5A0UPCkogEBw5csTf37+6upp0FsrLyyshIYF0itZQ9JyBogfFZWdn5+Tk5OHhQToIFR4e/tdff5FO0drNmzdNTU1JpwAZQNGDQvv555+vX78eFxdHNoaenp5YLH7y5AnZGG8Ti8VNTU2qqqqkg4AMoOhBofF4vNTU1MjIyBcvXpBNYmVlxahrIRQXFxsZGZFOAbKBogdFZ21tPWvWLEdHR7IxAgICUlJSyGZ4Gwb0XIKiB6C+//7758+fb968mWCGgICAv//+m2CAVlD0XIKiB6AoisrOzl6xYkVxcTGpAKqqqlpaWhcvXiQVoJX8/Hx8sRRnoOgBKIqiDA0Nly9fTvaC9RMmTNi9ezfBAG97/vy5rq4u6RQgGyh6gP+Ijo7u1q3b559/TirAvHnzzpw5Q2r1t1VWVmppaZFOATKDogf4r8zMzNjY2Pz8fCKrjxkz5sWLFw0NDURWf1t+fv6HH35IOgXIDIoe4L/09PQ2b97s5ORE6npnhoaGhw8fJrL02/BOLMeg6AH+R0hIyODBg+fMmUNkdXd3dyZcCwFFzzEoeoDWMjIyjh8/TmRcvmDBgry8PPrXbaWoqMjExIR0CpAZFD1Aa2pqavHx8b6+vvRfOlhfX7+xsfHp06c0r/u2pqYmJSUlZWVlghlAtlD0AG3w8PAYM2bM1KlT6V96xIgRZDdZ3rlzx9jYmGAAkDkUPUDbjh49evHixaSkJJrX9fPzO3bsGM2Lvg0Deu5B0QO0jc/nHz16NDAwUCQS0bnunDlz7ty5Q+eKraDouQdFD/Betra23t7ekyZNonNRVVVVdXX1K1eu0Lno27CJnntQ9ADt2bNnT2lp6fbt2+lcdNy4cQQvWSwSiXR0dEitDvKAogfoQEZGxrJly8rKymhbMTg4OCMjg7bl3iYSiXr27ElkaZAfFD1AB8zMzCIjIx0cHGhb0cHBoby8nMinc69cuYKLVnIPih6gY+vWrWtoaPj6669pW9HAwCA5OZm25Vrk5+fjnVjuQdEDSCQzM3Pz5s03btygZzlXV1ci32SLLTechKIHkEi/fv02bNgwceJEepaLiIgg8iUkd+/eHTRoEP3rglyh6AEkNX/+/L59+86bN4+GtQwNDevr62n+yvLGxkY+n8/joRa4Bn+jAJ3w22+/HThw4MKFCzSsZWFhERsbS8NCLQoLC3EtM05C0QN0gpaWllAo9PT0pGFLjK+vL83vx2JAz1UoeoDO8ff3HzFihI+Pj7wXCgkJuXXrlrxXeRuKnqtQ9ACdduLEiaysrJSUFLmuIhAIunfvTuf3Gl67dm3YsGG0LQe0QdEDdBqfzz9y5Mjs2bOrq6vlupCtrS2dlyyuqqrCd4JzEooeQBrjx493cXFxdXWV6ypz5sw5efKkXJdo8ezZs969e9OzFtAMRQ8gpQMHDhQWFu7Zs0d+S7i6uj558oSeayFcvXoVFz/gKpqK/s6dO4cPH75582bLLY2Njdu2baNndQB54PF4aWlpUVFR5eXl8ltFX18/NTVVfudvgXdiOYyOok9JSbGwsFi2bNmIESMiIiIaGxspiqqvr1+4cCENqwPIj5WVVVhYmKOjo/yWmDRpklx/aGiBoucwOor+//7v/7777rvbt2+XlJRcv37d39+/vr6ehnUBaLBhwwaRSLRmzRo5nT88PPz8+fNyOvnb7t27Z2hoSMNCQD86iv727dvNX7Ksr6+fnp5eU1Pj7e395s0bGpYGoEFWVta333579+5deZzcxMSktra2oqJCHidvUV9fr6qqqqSkJNdVgBQ6ir5v3773799v/v/dunU7cuSIkpLSlClTaFgagAaGhoZfffWV/K53Zm5uLu/pzc2bN4cOHSrXJYAgOop+0qRJb19wVVVVNSkpCRu5gEsWL16spqYmp7edfHx8EhMT5XHmFhjQcxsdRb9169a1a9e+fQufzz9w4EBxcTENqwPQIzMz88cff5THl3qHhITI+zr4KHpuo6PoVVVVNTU1W92orKxsZGREw+oA9NDV1d2xY4ezs7PMt71raGioqqrK9bo3BQUFuPgBh/FJLZyenp6bm9vOXoXr16///vvvrW68du2ampqanKMBSGnmzJm7du2aPXv2vn37ZHtmGxubXbt2bd26VbanbVFbW4tnFocR+2RsaWnppUuXSK0OICcZGRm//vprRkaGbE87Z86cEydOyPacLcrKyvr27SunkwMTEHtFHxwcHBwc3M4Bw4YNe/dnyZs3b5aVlckzF0CXCASChIQEPz+/srIyVVVVWZ3Wy8tr5syZsjpbKxjQcx6udQMgY25ubmPHjvX09JTtafv06ZOeni7bczZD0XMeTUWfk5MTHBxsY2NjYWFhY2MTHByck5NDz9IA9EtKSrp06VJCQoIMzzlx4kQ57aZH0XMeHUUvFArd3NwoigoICIiOjg4ICFBSUnJzcxMKhTSsDkA/Pp9/4sSJ8PBwkUgkq3NGRETI6eVRaWlpv3795HFmYAg6ZvSrVq1KS0uztbV9+8bAwEAfH5+wsDAaAgDQb9SoUb6+vs7OzhcvXpTJCc3NzWtqaqqrq2W7PebNmzfdu3eX4QmBgeh4RS8SiczMzFrdaGZmJsMXOwAMFBMTU1ZWtn37dlmdcMiQIXv37pXV2ZoVFBSYm5vL9pzANHQUvYeHh5+fX05OTkVFhVgsrqioyM3N9fHxcXd3p2F1AIJOnz69bNmyhw8fyuRsU6dOPXTokExO1QIDekVAR9HHxsYaGRm5uLhoa2vzeDxtbW0XF5eBAwfGxMTQsDoAQaamplFRUfb29jI5W2hoaEFBgUxO1QJFrwjoKHpNTc3Y2FiRSFRUVHT58uWioqKXL1/GxMS8e10EAO5ZvXo1RVGLFy/u+ql0dHT4fL5sr4d848YNXLeS8+jbR6+iomJiYmJlZWViYqKiokLbugDE5eTkCIVCmbwYHz16tGy3q9XX1wsEAhmeEBgIH5gCkDs9Pb0NGzY4Ozt3/VSzZs1KS0vr+nmaPXjwoH///rI6GzAWih6ADmFhYf379w8JCenieaZNm/bgwQOZRKIwoFcYKHoAmmRkZCQmJp47d64rJ+HxeLq6upmZmTKJhKJXECh6AJpoaWnFxMR4eHg0NDR05TxOTk67d++WSSQUvYJA0QPQx8fHZ+TIkT4+Pl05SXh4eHZ2tkzylJWV9enTRyanAiZD0QPQKjU1NScnJzk5WeozDB8+vLKysrq6uotJXr9+jS3OCgJFD0ArPp+fnJwcGBhYVVUl9UlMTU3379/fxSQFBQUWFhZdPAmwAooegG7jxo1zd3d3dXWV+gyTJ08+cOBAF2NgQK84UPQABCQkJNy+fTs2Nla6u4eFheXn53cxA4pecaDoAcg4c+bMwoULnzx5IsV9dXV1lZSUurih/ubNm6ampl05A7AFih6ADHNz8/DwcCcnJ+nuPnLkyJ07d0q9ulgsbmpqkuG32gKToegBiFm/fn1VVVXzVc86a9asWb/++qvUSxcXFxsZGUl9d2AXFD0ASVlZWRs2bJDigpS+vr4lJSVSr4sBvUJB0QOQZGBg8PXXXzs6Onb2jnw+X0dHR+pPTuXn56PoFQeKHoCwRYsWaWtrL1iwoLN3dHBwkHrfztWrV4cPHy7dfYF1UPQA5J09ezYuLq6zXyMeHh4u9dXNnj9/rqurK919gXVQ9ADk6ejo7Ny508PDo6mpSfJ7WVtbv3r1qq6urrPLVVZWamlpdfZewF4oegBGmDFjhrm5eUBAQKfuNWjQICmuhZCfn//hhx929l7AXih6AKZIT08/efLkqVOnJL+Ll5eXFNdCwJYbRYOiB2AKgUCQkJDg5+cn+TQmPDz8r7/+6uxCKHpFg6IHYBBXV9cJEya4ublJeLyenp5YLO7sdRSKiopMTEw6nw7YCkUPwCxJSUnXrl2Li4uT8HgrK6sdO3ZIfv6mpiYlJSVlZWWp0gEroegBmIXH46Wmpi5YsODFixeSHB8QEJCSkiL5+e/cuWNsbCxtOmAlFD0A41hbW/v7+zs7O0tycEBAQHFxseQnx4BeAaHoAZhIKBQ+ffp069atHR6pqqqqpaUl+Yet8JlYBYSiB2CojIyMr776SpJX6xMmTNi9e7eEp8UmegWEogdgKFNT02XLlkkywJk3b96ZM2ckPK1IJOrRo0fXogHLoOgBmGvp0qXKysqLFi1q/7AxY8a8ePGioaGhwxOKRKKePXvKKB2wBooegNGysrJ2797d4TfEGhoaHj58uMOzYUCvmFD0AIymp6e3cePGSZMmtX+Yu7t7QkJCh2fDlhvFhKIHYLrQ0NABAwYEBQW1c8yCBQvy8vI6PBWKXjGh6AFYICMjIykpqZ2rz+vr6zc2Nj59+rT989y9e3fQoEGyTgdMh6IHYAENDY2EhARvb+92rnc2YsSI9jdZNjY28vl8Hg/PeoWDv3IAdvDw8PjnP//p7e39vgP8/PyOHTvWzhkKCwtxLTPFhKIHYI2UlJRz584lJye3+btz5sy5c+dOO3fHgF5hoegBWIPP5ycnJwcGBlZVVb37u6qqqurq6leuXHnf3VH0CgtFD8Am48aN8/Lyet/HZceNG7dz58733ffatWvDhg2TWzRgLhQ9AMvExcXdv3//hx9+ePe3goODMzIy3nfHqqoqfCe4YkLRA7BPRkbG0qVLy8rKWt3u4OBQXl7e1NT07l2ePXvWu3dvWtIB46DoAdjHzMwsIiLC0dHx3d8yMDBo891aXPxAkaHoAVhp3bp1b968WblyZavbXV1d2/waQrwTq8hQ9ABslZmZuWnTptu3b799Y0RERJtfQoKiV2QoegC2MjAwWL9+vb29/ds3Ghoa1tfXv/t9syUlJYaGhjSmAwZB0QOwWHh4eO/evSMiIt6+8cMPP4yNjX37lvr6elVVVSUlJXrTAVOg6AHY7ezZs/v27btw4ULLLdOnT2/1fuzNmzfNzMxojwZMgaIHYDctLS2hUOjp6dmyqzIoKKiwsPDtYzCgV3AoegDW8/f3t7Cw8Pf3b/6lQCAQCARvfykVil7BoegBuCAtLS0jIyM9Pb35l7a2tm9fsrigoAAXP1BkKHoALhAIBEeOHPH396+urqYoKigo6OTJky2/W1tbq6amRi4dEEZT0efk5AQHB9vY2FhYWNjY2AQHB+fk5NCzNICCsLOzc3Jy8vDwoCjKxcXl6dOnzVP7srKyvn37kk4HJNFR9EKh0M3NjaKogICA6OjogIAAJSUlNzc3oVBIw+oAiuPnn3++fv363r17KYrq27fvL7/8QmFADxTFp2GNVatWpaWl2dravn1jYGCgj49PWFgYDQEAFASPxztx4sT48eO9vLwmTZr0008/eXl5oeiBjlf0IpHo3T28ZmZmIpGIhtUBFIqVldWsWbMcHR3Dw8PPnz9P4RU90FP0Hh4efn5+OTk5FRUVYrG4oqIiNzfXx8fH3d2dhtUBFM3333//4sWL48eP19bWVlRUlJaW9uvXj3QoIImOoo+NjTUyMnJxcdHW1ubxeNra2i4uLgMHDoyJiaFhdencvXRJ+/nzx3//TToIgDSysrJWrFhhYGCwZMkSsVhMOg4QRkfRa2pqxsbGikSioqKiy5cvFxUVvXz5MiYmRlNTk4bVqMVD0AAACVNJREFUO0vc1PTDuHE3pk8Pev06z8kpLjiYdCKATjM0NPTy8rpx48bBgwdfvHjh5eXVvO0SFBN9++hVVFRMTEysrKxMTExUVFRoW7ezDi9ePODhw5Zf9szM/CstjWAeACmIRKL79+8PGTKkoqJi0aJFs2bNWrt2LelQQAwdu27alJ6enpubu2bNmvcdcPr06cTExFY3nj9/Xt7TxmcXLrS6luver74SpqTIdVEA2Xr06FF1dfXw4cNv3br1wQcfODo6tvOl4cB5xIq+tLT00qVL7RxgbW3do0ePVjcaGBh069ZNnrkoZU1N6n+/itPso49Gz50r10UBZOv27dvHjh374osvAgMDHRwcKioqNDQ0SIcCYogVfXBwcHC74+8ePXpYW1u3uvHu3bvl5eXyzEX9MzKyNDKy5ZcPVVWnr1jRC5sWgFUsLS337NkjEokmTpxYWVk5f/789p9uwG241k1rVq6uOitWlGhqlgoEJXp6dj/+iJYH1lFWVj548ODx48cnTJjg6+vr7++P3cyKjKZX9Dk5OXFxcdevX6+srNTU1Bw2bNjs2bPHjh1Lz+qdNfaTT8Z+8gnpFABd0qtXr++++450CmAEXOsGAIDjcK0bAACOw7VuAAA4Dte6AQDgOFzrBgCA4+iY0Tdf62bnzp337t2rqqrS0NAwMjJi8lUQAAC4hL4PTDVf64a25QAAoBk+MAUAwHEoegAAjiN2rRvpaGtrr1u37ujRozSsdf78eXlfQI02TU1NdXV1AoGAdBDZqK+vpyiKM2/z1NbWqqqq8ngcedVVXV2tpqZGOoXMNDU1jRw5koaFHjx40L17dzmdXAnfPvM+dnZ2mZmZpFPIxrVr12JiYrZv3046iGz89NNPFEV9+umnhHPIyIIFC0JCQj788EPSQWSDS08ciisPhyMvIgAA4H1Q9AAAHIeiBwDgOBQ9AADHoegBADiOZdsr6cTnc+cPh8fjcWb3HkVRysrKpCPIEsf+drj0xKG48nCwvfK9mr8Mi3QK2RCLxa9fv+bM10PX1dVRFKWqqko6iGxUVVWpq6srKSmRDiIbXHriUFx5OCh6AACO484PjAAA0CYUPQAAx6HoAQA4DkUPAMBxKHoAAI5D0QMAcByKHgCA4xS96CsrK/38/NTV1fv37y8UCqU+hiE6jFpXVxcREWFsbKympjZixIjjx4/TH1Jykv/J37t3T01NzcXFhbZsUpDw4cTHxw8ZMqRbt25DhgzJy8ujM2GnSPJwbty4YW9vr6mpqa+vv2jRoqamJppDSui7776zsrJSUVEJCwt73zEs6oE2iBVbcHCwnZ3d06dPs7OzNTQ0srOzpTuGITqMWlFRERERkZeX9+TJE6FQ2K1bt9u3bxOJKgnJ/+Td3d1tbW2dnZ3pjNdZkjycX375pU+fPsePH3/y5EleXl5xcTHtMSUlycOxsrIKCgp6/fp1UVGRoaHh7t276c8piaSkpOPHjwcEBISGhr7vGBb1wLsUuujr6urU1dWzsrKafxkUFBQUFCTFMQwhRVQTE5NDhw7JP5o0JH84R48e9fDw+Oabb5hc9BI+HCsrq71799KaTCoSPhwdHZ2WY4KDgz/77DP6InZeeHj4+4qeRT3QJoUe3dy7d+/169eWlpbNv7S0tLx+/boUxzBEZ6M+fvz43r17jP0GOwkfzuvXr6Ojo7dt20Zvuk6T5OG8efPmypUrjx8/7tevn76+/oIFC2pra2lPKhEJ/3YWLly4b9++6urqO3funDlzhuGztXawqAfapNBFX1VVRVFUyxWLtLW1KysrpTiGIToV9c2bN/7+/nPnzh06dChN+TpJwoezatWqGTNmDBo0iNZwnSfJw3n48KFYLE5NTb18+fIff/yRlZX1zTff0B1UMhL+7bi6uubk5Kirq5uYmLi5ubG36FnUA21S6KJvvppjy1/Yq1ev3r1MnSTHMITkUevr6319fXv37v3dd9/Rl6+TJHk4N27cOHbsWHR0NN3hOk+Sh9O9e3eKohYtWtSnTx8DA4MFCxakpaXRnFNCkjyc6upqFxeXWbNm1dTU3L9//88//1yzZg3dQWWERT3QJoUueiMjIzU1tfz8/OZfXr16ddiwYVIcwxASRm1oaPDz8xOLxfv372fyhd0leTjZ2dmlpaVGRkZ9+/Zdu3ZtZmamkZER3UElI8nD0dfX19XVZcX1iiV5OI8ePXr+/PmCBQsEAoGBgcGMGTPS09NpTyobLOqBtpF+k4CwoKAgJyenFy9enD9/XktLq+Wd9JiYmBMnTrR/DAN1+HAaGhqmT59uZ2cnEolqampqamoaGhqIRm5Phw+nurq67P9btmyZnZ3d48ePiUZujyT/sX3xxRdjx4599uzZw4cPLS0tV6xYQS5vBzp8OPX19Xp6euvXr6+rq3v06NHHH388f/58opHfq76+vqamJiwsLDg4uKampr6+vvl2lvbAuxS96CsqKnx9fdXU1PT19Xfu3Nlyu7Oz87Jly9o/hoE6fDjFxcWt/qXfunUrubwdkORvpwXDd92IJXs4tbW1wcHBWlpaffr0+eyzz2prawmF7ZgkD+fChQtjxozR1NTs3bt3QEDAy5cvCYXtwLJly95+UkRHRzffztIeeBe+eAQAgOMUekYPAKAIUPQAAByHogcA4DgUPQAAx6HoAQA4DkUPAMBxKHoAAI5D0QMAcByKHgCA41D0AAAch6IHAOA4FD0AAMeh6AEAOA5FDwDAcSh6AACOQ9EDAHAcih4AgONQ9AAAHIeiBwDgOBQ9AADHoegBADgORQ/Q2t27d3v27Hn58mWKoh49eqSrq3v27FnSoQCkpyQWi0lnAGCcmJiYLVu2/Pnnn1OmTPnwww83bdpEOhGA9FD0AG3z9PQsLi5WUlLKy8vr1q0b6TgA0sPoBqBtISEhBQUFkZGRaHlgO7yiB2hDVVXViBEj7OzsTpw4ce3atZ49e5JOBCA9FD1AG4KCgiorKw8fPjx37lyRSHT48GHSiQCkh9ENQGspKSnp6elCoZCiqC1btly+fHn//v2kQwFID6/oAQA4Dq/oAQA4DkUPAMBxKHoAAI5D0QMAcByKHgCA41D0AAAch6IHAOA4FD0AAMeh6AEAOA5FDwDAcSh6AACOQ9EDAHAcih4AgONQ9AAAHIeiBwDgOBQ9AADHoegBADgORQ8AwHH/D/aO05h7FO77AAAAAElFTkSuQmCC",
null,
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",
null
]
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https://it.mathworks.com/matlabcentral/cody/problems/2605-find-out-value-of-polynomial-at-different-value/solutions/505529 | [
"Cody\n\n# Problem 2605. Find out value of polynomial at different value.\n\nSolution 505529\n\nSubmitted on 26 Sep 2014\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%% x = [1 8]; n=0; y_correct = 8; assert(isequal(your_fcn_name(x, n),y_correct))\n\n2 Fail\n%% x = [1 0]; n=0; y_correct = 0; assert(isequal(your_fcn_name(x, n),y_correct))\n\nError: Assertion failed.\n\n3 Fail\n%% x = [1 0 5]; n=1; y_correct = 6; assert(isequal(your_fcn_name(x, n),y_correct))\n\nError: Assertion failed."
]
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https://syairtogel.co/what-does-base-ten-mean-in-math.php | [
"# What does base ten mean in math",
null,
"What is the Base-10 Number System?\n\nJan 24, · Simply put, base is the way we assign place value to numerals. It is sometimes called the decimal system because a digit's value in a number is determined by where it lies in relation to the decimal point. The Powers of In math, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are base ten numerals. We can only count to nine without the need for two numerals or digits. All numbers in the number system are made by combining these 10 numerals or digits. Here, for instance, the number is formed using the base 10 numerals.\n\nKindergarten Work with numbers to gain foundations for place value. Grade 1 Extend the counting sequence. Xoes this range, read and write numerals and represent a number of objects with a written numeral. Understand place value. Understand the following as special cases: CCSS. Use place value understanding and properties of operations to add and subtract. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes what is the easiest student credit card to get is necessary to compose a ten.\n\nGrade 2 Understand place value. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, odes and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.\n\nGrade 4 Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Grade 5 Understand the place value system. Use whole-number exponents to denote powers of Perform operations with multi-digit whole numbers and with decimals to hundredths. Understand the following as special cases:. Kindergarten-Grade Mathematics Appendix A.\n\nKindergarten\n\nIllustrated definition of Base Ten System: Another name for the decimal number system that we use every day. If you notice, there is no one digit for the number ten- we need to use two digits, the 1 and the 0. We can only count to nine without the need for two digits. Therefore, we use base ten in order. 17 rows · Mar 31, · From Simple English Wikipedia, the free encyclopedia In mathematics, a .\n\nIn order to give you the best experience, we use cookies and similar technologies for performance, analytics, personalisation, advertising, and to help our site function.\n\nWant to know more? Read our Cookie Policy. You can change your preferences any time in your Privacy Settings. Parents, Sign Up for Free. Let's learn! What are base ten numerals? We can only count to nine without the need for two numerals or digits. All numbers in the number system are made by combining these 10 numerals or digits.\n\nInstead of handing out place value worksheets to your child, ask them to use base ten blocks to show the place value of each base ten numeral in a number. This will help them to not only help them to understand how base ten numerals form big numbers, but also their place value. Base ten numbers , Place value. All Rights Reserved. I want to use SplashLearn as a Teacher Parent Already Signed up? Sign Up for SplashLearn. For Parents. For Teachers. I Accept Update Privacy Settings. Fun Facts Base ten numerals form the basis for our counting system and thus, our monetary system.\n\n1.",
null,
"Zolokasa:"
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null,
"https://ecdn.teacherspayteachers.com/thumbitem/Base-Ten-Math-Strategies-4866633-1568475609/original-4866633-4.jpg",
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"https://syairtogel.co/img/1.jpg",
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https://www.instructables.com/id/Counting-ICs-with-an-Arduino/ | [
"Learn Counter ICs Using an Arduino\n\n48,450\n\n61\n\n18\n\nHave you ever needed to count something? Sure, we all need to count change, count blessings, and occasionally count cards, but that's not really the kind of counting I'm talking about. In this Instructable, I will elucidate how Counting ICs operate, and show how to connect one to a microcontroller so you can see exactly how it works in a controlled way.\n\nTeacher Notes\n\nTeachers! Did you use this instructable in your classroom?\nAdd a Teacher Note to share how you incorporated it into your lesson.\n\nStep 1: Why Use Counting ICs?\n\nYes, yes, why not just use the microcontroller? Arduinos are pretty good at counting things. But what if you want a cheap hardware solution that operates with events as fast as 30MHz? That's what counting chips are for.\n\nMy work in the atom optics lab at my university has taken me through some real twists and turns. I've learned more in my two years as an intern there than I have in most of college, and it's way more rewarding than turning in homework. If you ever have the chance to work in a university laboratory, take it, no matter what. You'll never regret it. One of the things I've had to learn pretty thoroughly is electronics, since one of my duties is troubleshooting electronics and occasionally building additions and hacks to them. My most recent project brought me face to face with digital counting ICs.\n\nThe project involved using a Michelson Interferometer to compare the relative wavelengths of two lasers by counting the number of fringes of each beam when a retro-reflector cart was translated across the beam paths, thus changing the path lengths of both beams by identical amounts. Light has such a short wavelength that moving the cart even as slowly as a few centimeters per second produces fringe patterns at around 150kHz. The interferometer operation simplifies down to the relation:\n\nλ21(N2/N1)\n\nwhere λ is the wavelength of a laser, and N is the number of fringes produced by translating the cart a certain distance. So if we know one laser pretty well, we can find the wavelength of the second laser by counting their fringes. For light being measured by translating the cart over 1 meter, N is going to be around 40 million. Try counting that by hand. No, we need high speed event counting methods.\n\nAnother use would be in something like a Geiger counter. If you need to know how much radiation you've been exposed to, you can hook up a traditional Geiger counter to a counter IC and count the number of radiation events, then use the appropriate math to convert the radiation count to rads.\n\nStep 2: Basics of Counter ICs\n\nThe basis for digital electronics is that we only care if a signal is HIGH or LOW. Analog is concerned with everything in between, but digital only concerns itself with those two states. Typically, digital electronics use +5V for HIGH and 0V for LOW.\n\nCounter ICs are a complex configuration of NOR gates. NOR gates are a special combination of (at least) four MOSFETS. NOR gates have two inputs and one output. The inputs and output can be either HIGH or LOW. The output state depends on the input states in the following way:\n\nSource: Wikipedia\nINPUT OUTPUT\nA B A NOR B\n0 0 1\n0 1 0\n1 0 0\n1 1 0\n\nSo the output is only HIGH when both inputs are LOW. This is the most basic part of a counter. Each of these NOR gates are paired in a configuration called a \"flip-flop\". Flip-flops have two inputs (S and R) and two outputs (Q and Q*), and have only two stable states:\n\nSR latch operation\nS R Action\n0 0 No Change\n0 1 Q = 0\n1 0 Q = 1\n1 1 Restricted combination\n\nThe two output states can be chosen between by setting either S or R HIGH. When both inputs are LOW, the flip-flop stores its output state according to whatever input it last received. If we string one of the outputs of one flip-flop to the input of the next flip flop, along with some other necessary connections, then each flip-flop down the line depends on the previous states of the flip-flops before it. The previous states depend on the number of triggering events that the system has received. The first output changes state with each external triggering event, called a clock pulse. The second flip-flop changes state every two clock pulses. The third flip-flop changes state every four clock pulses, and so on, with the number of clock pulses required to change state doubling for each subsequent flip-flop.\n\nBut what happened to the other flip-flop output? There were two for each one. In fact, each extra output represents one bit of information. If we were to test the voltages of these outputs after sending the counter a certain number of clock pulses, we would see:\nClock Pulse Output\n0 LLL\n1 LLH\n2 LHL\n3 LHH\n4 HLL\n5 HLH\n6 HHL\n7 HHH\n\nWhich is binary code! With this configuration, we can only count 8 different states, but by adding another flip-flop, we could count to 16. With two more, we could count to 32, and so on! The table shows a three bit counter. If we had an 8 bit counter, it could count up to 256, and would be able to store one byte of information! If we string two 8 bit counters together, we can count up to 256*256=65536! Depending on how many events you need to count, you can just string a bunch of counters together and reach the appropriate counting limit. Counters in this configuration are called \"ripple counters\", since the state of the previous flip-flop ripples along to the next flip-flop. There are many other types of digital counters, but this is the easiest to understand.\n\nStep 3: Get a Counter IC\n\nAs I said, there are many different types of counter ICs available, but the simplest ones are ripple counters. Your first counter should be one that has continuous outputs. The first counter I ever had to learn was the obscenely complex 82C54 with 24 pins and 6 bytes of highly controlled storage and required the use of a microcontroller. It had outputs that could only be read when it received a command from the microcontroller, and you don't want that. Maybe later, but not right now. It took me weeks to figure out how to use it. The counting pins should be dedicated and continuously readable by even a voltmeter as the counter does its job. The chip I use in this Instructable is a 74LS161, which is a 4 bit, presettable binary counter. The datasheet available on Mouser is pretty useless. I used this datasheet.\n\nThe 74LS161 has 16 pins. Two for power, four for operation control, four for count input, four for count output, one for the clock pulse, and one for the \"carry output\". I will be using the pinout names from the datasheet linked above (from alldatasheet) from now on.\n\nTo get the feel for basic counting operation, we just want to tell the chip to count and introduce a steady, slow clock pulse. Place the chip in your breadboard and make the following connections:\nPins 1,7,9,10,16 to +5V.\nPin 8 to ground.\nPin 2 to ground through a 470ohm (or similar) resistor.\n\nPins 8 and 16 are to power the chip. Pin 1 is the master reset (*R), and resets the count when the signal goes LOW, so we want to keep it HIGH. Pins 7 and 10 (CEP and CET) enable counting when set HIGH. They control subtly different operations, but we don't need to worry about that. Pin 9 (PE) allows you to write to the counter when set LOW, but we just want to count, so set it HIGH. We'll talk about writing later.\n\nThe chip is now set to count! whenever the chip detects a \"leading edge\" on pin 2 (CP, the clock input), it will advance the count by one. A leading edge is the moment when CP detects the signal as HIGH. This is so the count advances right when CP goes HIGH even if CP is held HIGH for a long time.\n\nBefore we go on to using the Arduino, test out the chip manually. Use a voltmeter to test the voltages of pins 11-14. These pins are named Q0, Q1, Q2, and Q3. Q0 (pin 14) is the \"least significant bit\", meaning it changes state with each clock pulse. Q3 is the \"most significant bit\" meaning it represents the highest order of magnitude for the chip. In this case, if Q3 is HIGH, it means that the chip is storing a number greater than or equal to 8. If you just turned the chip on, then they should all be near zero, but they might not be. Just remember the state that you measured. Now use a wire to connect CP to +5V briefly. This is a very long clock pulse. If there wasn't any noise while you connected the wire, the count should have advanced by one. Measure the output pins again and compare the new state to the old state.\n\nWhen you read the pins, you can represent the states with a binary number in the following format: Q3,Q2,Q1,Q0. So if the count is one, Q3=0,Q2=0,Q1=0,Q0=1. If the count is 7 (0111 in binary), then Q3=0,Q2=1,Q1=1,Q0=1. To represent the count as a decimal number, use this formula: count = Q0 + 2*Q1 + 4*Q2 + 8*Q3. In all likelihood, there was some noise when you temporarily placed the wire on CP, and the count will be completely different since the chip can respond to signals as fast as 35MHz. But that's ok, we just wanted to see that the counting pins were working. Now it's time for some better control.\n\nStep 4: Reading Bits\n\nThe goal in this step is to get the Counter to reliably process individual clock pulses, then have the Arduino read the Counter and display the count.\n\nFirst we need to make the proper connections between the IC and the Arduino. This is all digital, and the Arduino only has 12 available pins for this sort of thing (pins 0 and 1 are reserved for serial communication). Use the attached image to make your connections. Pin 13 is used for the clock pulse so the Arduino LED blinks whenever a pulse is sent. Once you've made your connections, burn the script attached below to the Arduino, the code is annotated. Once the Arduino is blinking away, open the Serial Monitor and you should see it counting from 0 to 15 over and over again!\n\nStep 5: Upgrading the Counting Limit\n\nSo, you can count to 15. Good for you. Can you tie your shoelaces too? Let's expand this little venture and count to a higher number. You bought a spare IC right? You know, that one that costs 88 cents?\n\nPin 15 of the IC is called the Terminal Count, or TC pin. It goes HIGH when the count reaches 15. This is a rather bad design. What this pin is designed to do is carry the value of 16 on to the next counter in the sequence. But if it were designed well, it would simply pulse on the transition between 15 and 0. As it is, the first counter counts to 15, sends the 15 forward to the next chip (which is really representing a 16 on the second chip), and retains the 15 on the first chip for one clock pulse.\n\nCount TC Q0 Q1 Q2 Q3\n14 L L H H H\n15 H H H H H\n0 L L L L L\n\nThis means that when we read off the values from the chips, every 16 clock pulses we will see an erroneous count that is 15 higher than it should be. The number of counts is still ok, but the value that is read from the output pins is wrong every 16 counts. This could be fixed in software, but it's not important here. It's just important to see the limitations of the technology we have at our disposal.\n\nWire up the chips according to the schematic below. Then burn the attached code and open up the serial monitor. The number should count from 0 to 254, with erroneous numbers displaying every 16 numbers or so.\n\nStep 6: Writing Bits\n\nNow that we've got a little bit of control over this chip, let's try writing initial counts. Why would we want to do that? The counter that I used in the lab was a variety that counted down from a specified number, unlike the IC in this Instructable which counts up. If you ever have one of these, then setting a starting count is just like setting a timer. In fact, the counter you have can do the same thing, it just requires an additional subtraction.\n\nSince the arduino only has 12 available pins, we can't do read/write operations on the one byte configuration. We'll have to simplify it down to 4 read/write bits. We want to find an initial count based on the time we want to pass, the period of the clock pulse, and the fact that the counter counts up to 15, and then activates the Terminal Count pin.\n\nLet's say we want 4 seconds to pass, and t=0 is when we want the timer to go off. The period of the clock pulse is around 0.5 second. If a count of 15 represents t=-0 seconds (we're using TC as the activation pin for whatever it is we're doing), then 14 is t=-0.5 seconds, 13 is t=-1.0 seconds, and so on. In general, t=-(15 - count)*T, where T is the period of the clock pulse, and f=1/T for frequency of the clock pulse.\n\nSo to count down from 4 seconds before t=0:\n-4=-(15 - count)*0.5 ⇒ count = 7 ⇒ count = 0111 in binary. This is the initial count we want to use to have TC go HIGH every 4 seconds.\n\nPin 9 of the IC is PE, or Parallel Enable. This pin allows you to write bits to the counter when it is held LOW. The bits present on pins 3 through 6 (P0-P3), are then loaded on the next clock pulse. So the order in which you should load bits is:\n\nHold P0-P3 at the desired number. Set PE LOW. Send clock pulse. Set PE HIGH. The bits are now loaded and the next clock pulse will advance the loaded count by one.\n\nWire up the Arduino and IC according to the schematic below, burn the attached script, and pull up the serial monitor. You should see the counter counting up from 7 over and over.\n\nStep 7: Count All the Things!\n\nNow that you know how to count electronically, you can stop using those pesky fingers! Right? Hmm, maybe not, but if you ever need to count a lot of something very quickly, you now have to tools to do so. Just pick an IC that will do the job and let it do what you're either too lazy or too human to do yourself.",
null,
"Participated in the\nArduino Challenge\n\n18 Discussions\n\nAny suggestions about interferometry and fringe patterns? I am trying to use an interferometer to find the density of a protein sample. I was planning on using a Mach-Zehner Interferometer and taking an image of the fringes. It is my understanding that I would need to record the space between the fringes. Is this correct? The idea behind it is that the density relates to index of refraction, and when one beam goes through the sample it will be phase shifted from the original beam, and when that beam and the original beam interfere it will create horizontal fringes (which it does).\n\n4 replies\n\nThat sounds about right. Interferometry typically boils down to either a change in path length or a change in index of refraction. I haven't worked with Mach-Zehner (Zehnder?) setups, but from the schematic it looks useful in terms of being able to use a reference on one path to look for deviations from that reference in the other path. I'm not sure why there would be horizontal lines in the interferogram unless some angle is out of perfect alignment. If your sample is perfectly aligned and occupies a container identical to the reference, and the container is a perfect rectangular prism, I would think that no horizontal fringes would occur. As you added more protein concentration to the sample container, the entire interferogram would oscillate in brightness.\n\nA closer look at the wiki seems to indicate that the interferometer is usually deliberately misaligned to produce fringes. If that's the case it will take some geometry to figure out what the expected path length difference should be. What is the shape of the container, what kind of index of refractions are you working with, and what is your light source?\n\nSorry, I forgot to mention: Our protein undergoes a liquid-liquid phase separation at different temperatures and concentrations. So because of that we have a horizontal concentration gradient, and therefore a horizontal index of refraction gradient. That is what causes the horizontal fringes. So we are trying to measure the density gradient with the horizontal fringes, basically. It is a pretty neat idea.\n\nThat is a neat idea. There are a few conversions you'll need. Getting the index of refraction gradient shouldn't be too hard. That's geometric calculations and counting fringes produced by the interferometer, as you said earlier. More difficult will be converting the index gradient to a concentration gradient. Do you already have the data that would allow that conversion?\n\nI just did a rough calculation and it looks like your index of refraction gradient will be roughly dn/dx = L/(t*a), where L is the wavelength of light in vacuum, t is the thickness of the sample container, and a is the distance between each horizontal fringe in your interferometer. I assumed the index gradient is constant, the incoming light is perpendicular to the container, and the container thickness doesn't vary much. Definitely do check that figure."
]
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"https://cdn.instructables.com/F6Z/YNYX/HCJOD12S/F6ZYNYXHCJOD12S.LARGE.jpg",
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https://ai.stackexchange.com/questions/37942/consider-the-following-axioms | [
"# Consider the following axioms- [closed]\n\nI'm studying Artificial Intelligence and I have a question about first order logic and resolution. But I couldn't find any answer why.\n\nI tried using Google to get the answer but nothing was found.",
null,
"For first part it's extremely straightforward to encode each axiom into FOL wff's as knowledge base:\n\n1. $$\\forall x (c(x) \\to l(x, S)$$\n2. $$\\forall x (l(x, S) \\to \\forall y (d(y) \\to l(x, y)))$$\n3. $$d(R) ∧ r(R)$$\n4. $$\\forall x (r(x) → w(x) ∨ n(x))$$\n5. $$¬ ∃ x (d(x) ∧ n(x))$$\n6. $$∀ x (w(x) → ¬ l(G, x))$$\n7. $$¬ c(G)$$ (to be proved)\n\nwhere $$c$$:=child, $$l$$=loves, $$d$$:=reindeer, $$r$$:=rednose, $$w$$:=weird, $$n$$:=clown, $$S$$:=Santa, $$R$$:=Rudolph, $$G$$:=Scrooge, respectively, in the meta language.\n\nThen convert them to definite, unit and goal clauses via Skolemization:\n\n1. $$\\lnot c(x) \\lor l(x, S)$$\n2. $$\\lnot l(x, S) \\lor \\lnot d(y) \\lor l(x, y)$$\n3. $$d(R)$$\n4. $$r(R)$$\n5. $$\\lnot r(x) \\lor w(x) \\lor n(x)$$\n6. $$\\lnot d(x) \\lor \\lnot n(x)$$\n7. $$\\lnot w(x) \\lor \\lnot l(G, x)$$\n8. $$c(G)$$ (goal clause)\n\nFrom here we can further resolve clauses:\n\n1. [3, 6:] $$\\lnot n(R)$$\n2. [4, 5:] $$w(R) \\lor n(R)$$\n3. [9, 10:] $$w(R)$$\n4. [7, 11:] $$\\lnot l(G, R)$$\n5. [2, 3:] $$\\lnot l(x, S) \\lor l(x, R)$$\n6. [12, 13:] $$\\lnot l(G, S)$$\n7. [1, 14:] $$\\lnot c(G)$$\n8. [15, 8:] $$\\bot$$ Q.E.D.\n\nFinally note that not any arbitrary contradictory set of clauses can be derived by resolution inference rule such as the simple case where $$p \\lor q$$ cannot be derived from $$\\Gamma = \\{p\\}$$ by resolution, though the classical FOL is semantically complete per Gödel's completeness theorem and thus the formal system with all inference rules of FOL containing the axiom set $$\\Gamma$$ is strongly and refutation complete (but not necessarily negation complete due to the renowned Gödel's incompleteness theorems)."
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"https://i.stack.imgur.com/hyhXI.jpg",
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https://softmath.com/math-com-calculator/distance-of-points/factor-to-find-the-lcd.html | [
"English | Español\n\n# Try our Free Online Math Solver!",
null,
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transform ti-89\n• negatives and positive integer self quiz\n• factor tree work sheet printable\n• nth term solver\n• solve using elimination method calculator\n• ordered pair powerpoint\n• trigonometry poems\n• solve equations by ti-84\n• solving rational equations solver\n• sum of ordered integers\n• basic formula in mathematics\n• compound inequalities calculator\n• how will integrated 2 help in real life\n• algebra calculator\n• how to type in limits on my calculator\n• free online math solver\n• addition and subtracting equations worksheets\n• Holt geometry page 59 lesson 4-8\n• free online boolean algebra simplifier\n• laplace inverse calculator\n• free factor tree worksheets\n• cheap math yr 6 papers\n• finding the absolute value of a fraction using formula\n• coordinate pictures\n• how to solve verbal proportions\n• equations for ks2\n• Box method of distributive\n• free factor quadratic expressions online calculator\n• worksheet on expressions\n• sample inequality leson plan\n• introductory lesson for 6th grade on algebraic expressions\n• cheat on equations by adding and subtracting\n• algebra 2 chapter 1 resource book\n• free down load math problem solver\n• a compilation of hints that will help any of us remember the rules of algebraic operations.\n• why is it important to simplify radical expressions before adding or subtracting\n• adding and subtracting with equations calculator\n• worksheets of simplifications"
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null,
"https://softmath.com/images/video-pages/solver-top.png",
null
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.76346755,"math_prob":0.9928341,"size":67759,"snap":"2020-34-2020-40","text_gpt3_token_len":15167,"char_repetition_ratio":0.23800458,"word_repetition_ratio":0.017108168,"special_character_ratio":0.2013607,"punctuation_ratio":0.008416056,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999796,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-09T12:19:33Z\",\"WARC-Record-ID\":\"<urn:uuid:880d12f6-3b1f-44ac-a14e-e23f0f7bbf98>\",\"Content-Length\":\"225694\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9c20b2c3-e81d-4dae-93ce-7482494fa01d>\",\"WARC-Concurrent-To\":\"<urn:uuid:51763c53-c42b-4dcf-a8b0-d51a87e8279e>\",\"WARC-IP-Address\":\"52.43.142.96\",\"WARC-Target-URI\":\"https://softmath.com/math-com-calculator/distance-of-points/factor-to-find-the-lcd.html\",\"WARC-Payload-Digest\":\"sha1:XMUIR6QHKKJVWHGWT76ABBJ3JOI7SDRT\",\"WARC-Block-Digest\":\"sha1:ZUSVCMIJBXIAQ5EN22M5JN5QLAKL7XFM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738552.17_warc_CC-MAIN-20200809102845-20200809132845-00248.warc.gz\"}"} |
https://www.technocrazed.com/8-10-bridge-circuits | [
"# 8.10 Bridge Circuits\n\nChapter 8: DC METERING CIRCUITS\n\nNo text on electrical metering could be called complete without a section on bridge circuits. These ingenious circuits make use of a null-balance meter to compare two voltages, just like the laboratory balance scale compares two weights and indicates when they’re equal. Unlike the “potentiometer” circuit used to simply measure an unknown voltage, bridge circuits can be used to measure all kinds of electrical values, not the least of which being resistance.\n\n### Wheatstone Bridge\n\nThe standard bridge circuit, often called a Wheatstone bridge, looks something like this:\n\nWhen the voltage between point 1 and the negative side of the battery is equal to the voltage between point 2 and the negative side of the battery, the null detector will indicate zero and the bridge is said to be “balanced.” The bridge’s state of balance is solely dependent on the ratios of Ra/Rb and R1/R2, and is quite independent of the supply voltage (battery). To measure resistance with a Wheatstone bridge, an unknown resistance is connected in the place of Ra or Rb, while the other three resistors are precision devices of known value. Either of the other three resistors can be replaced or adjusted until the bridge is balanced, and when balance has been reached the unknown resistor value can be determined from the ratios of the known resistances.\n\nA requirement for this to be a measurement system is to have a set of variable resistors available whose resistances are precisely known, to serve as reference standards. For example, if we connect a bridge circuit to measure an unknown resistance Rx, we will have to know the exact values of the other three resistors at balance to determine the value of Rx:\n\nEach of the four resistances in a bridge circuit are referred to as arms. The resistor in series with the unknown resistance Rx (this would be Ra in the above schematic) is commonly called the rheostat of the bridge, while the other two resistors are called the ratio arms of the bridge.\n\nAccurate and stable resistance standards, thankfully, are not that difficult to construct. In fact, they were some of the first electrical “standard” devices made for scientific purposes. Here is a photograph of an antique resistance standard unit:\n\nThis resistance standard shown here is variable in discrete steps: the amount of resistance between the connection terminals could be varied with the number and pattern of removable copper plugs inserted into sockets.\n\nWheatstone bridges are considered a superior means of resistance measurement to the series battery-movement-resistor meter circuit discussed in the last section. Unlike that circuit, with all its nonlinearities (nonlinear scale) and associated inaccuracies, the bridge circuit is linear (the mathematics describing its operation are based on simple ratios and proportions) and quite accurate.\n\nGiven standard resistances of sufficient precision and a null detector device of sufficient sensitivity, resistance measurement accuracies of at least +/- 0.05% are attainable with a Wheatstone bridge. It is the preferred method of resistance measurement in calibration laboratories due to its high accuracy.\n\nThere are many variations of the basic Wheatstone bridge circuit. Most DC bridges are used to measure resistance, while bridges powered by alternating current (AC) may be used to measure different electrical quantities like inductance, capacitance, and frequency.\n\n### Kelvin Double Bridge\n\nAn interesting variation of the Wheatstone bridge is the Kelvin Double bridge, used for measuring very low resistances (typically less than 1/10 of an ohm). Its schematic diagram is as such:\n\nThe low-value resistors are represented by thick-line symbols, and the wires connecting them to the voltage source (carrying high current) are likewise drawn thickly in the schematic. This oddly-configured bridge is perhaps best understood by beginning with a standard Wheatstone bridge set up for measuring low resistance, and evolving it step-by-step into its final form in an effort to overcome certain problems encountered in the standard Wheatstone configuration. If we were to use a standard Wheatstone bridge to measure low resistance, it would look something like this:\n\nWhen the null detector indicates zero voltage, we know that the bridge is balanced and that the ratios Ra/Rx and RM/RN are mathematically equal to each other. Knowing the values of Ra, RM, and RN therefore provides us with the necessary data to solve for Rx . . . almost.\n\nWe have a problem, in that the connections and connecting wires between Ra and Rx possess resistance as well, and this stray resistance may be substantial compared to the low resistances of Ra and Rx. These stray resistances will drop substantial voltage, given the high current through them, and thus will affect the null detector’s indication and thus the balance of the bridge:\n\nSince we don’t want to measure these stray wire and connection resistances, but only measure Rx, we must find some way to connect the null detector so that it won’t be influenced by voltage dropped across them. If we connect the null detector and RM/RN ratio arms directly across the ends of Ra and Rx, this gets us closer to a practical solution:\n\nNow the top two Ewire voltage drops are of no effect to the null detector and do not influence the accuracy of Rx‘s resistance measurement. However, the two remaining Ewire voltage drops will cause problems, as the wire connecting the lower end of Ra with the top end of Rx is now shunting across those two voltage drops, and will conduct substantial current, introducing stray voltage drops along its own length as well.\n\nKnowing that the left side of the null detector must connect to the two near ends of Ra and Rx in order to avoid introducing those Ewire voltage drops into the null detector’s loop, and that any direct wire connecting those ends of Ra and Rx will itself carry substantial current and create more stray voltage drops, the only way out of this predicament is to make the connecting path between the lower end of Ra and the upper end of Rx substantially resistive:\n\nWe can manage the stray voltage drops between Ra and Rx by sizing the two new resistors so that their ratio from upper to lower is the same ratio as the two ratio arms on the other side of the null detector. This is why these resistors were labeled Rm and Rn in the original Kelvin Double bridge schematic: to signify their proportionality with RM and RN.\n\nWith ratio Rm/Rn set equal to ratio RM/RN, rheostat arm resistor Ra is adjusted until the null detector indicates balance, and then we can say that Ra/Rx is equal to RM/RN, or simply find Rx by the following equation:\n\nThe actual balance equation of the Kelvin Double bridge is as follows (Rwire is the resistance of the thick, connecting wire between the low-resistance standard Ra and the test resistance Rx):\n\nSo long as the ratio between RM and RN is equal to the ratio between Rm and Rn, the balance equation is no more complex than that of a regular Wheatstone bridge, with Rx/Ra equal to RN/RM, because the last term in the equation will be zero, canceling the effects of all resistances except Rx, Ra, RM, and RN.\n\nIn many Kelvin Double bridge circuits, RM=Rm and RN=Rn. However, the lower the resistances of Rm and Rn, the more sensitive the null detector will be, because there is less resistance in series with it. Increased detector sensitivity is good, because it allows smaller imbalances to be detected, and thus a finer degree of bridge balance to be attained. Therefore, some high-precision Kelvin Double bridges use Rm and Rn values as low as 1/100 of their ratio arm counterparts (RM and RN, respectively). Unfortunately, though, the lower the values of Rm and Rn, the more current they will carry, which will increase the effect of any junction resistances present where Rm and Rn connect to the ends of Ra and Rx. As you can see, high instrument accuracy demands that all error-producing factors be taken into account, and often the best that can be achieved is a compromise minimizing two or more different kinds of errors.\n\nREVIEW:\n\n• Bridge circuits rely on sensitive null-voltage meters to compare two voltages for equality.\n• Wheatstone bridge can be used to measure resistance by comparing the unknown resistor against precision resistors of known value, much like a laboratory scale measures an unknown weight by comparing it against known standard weights.\n• Kelvin Double bridge is a variant of the Wheatstone bridge used for measuring very low resistances. Its additional complexity over the basic Wheatstone design is necessary for avoiding errors otherwise incurred by stray resistances along the current path between the low-resistance standard and the resistance being measured.\n\nBack to Book’s Main Index"
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https://www.tutebox.com/3352/maths/a-quick-guide-to-least-squares-regression-method-2/ | [
"# A Quick Guide to Least Squares Regression Method\n\nCarl Friedrich Gauss’s method of least squares is a standard approach for sets of equations in which there are more equations than unknowns. Least squares problems fall into two main categories. Linear also know as ordinary least squares and non-linear least squares. The linear least-squares problem pops up in statistical regression analysis and it has a closed-form solution while the non-linear problem has no closed-form solution. Thus the core calculation is similar in both cases.\n\nIn a least squares calculation with unit weights, or in linear regression, the variance on the jth parameter, denoted",
null,
"is usually estimated with",
null,
"Weighted least squares\n\nWhen that the errors are uncorrelated with each other and with the independent variables and have equal variance,",
null,
"is a best linear unbiased estimator (BLUE). If, however, the measurements are uncorrelated but have different uncertainties, a modified approach might be adopted. When a weighted sum of squared residuals is minimized,",
null,
"is BLUE if each weight is equal to the reciprocal of the variance of the measurement.",
null,
"The gradient equations for this sum of squares are",
null,
"Which, in a linear least squares system give the modified normal equations",
null,
"When the observational errors are uncorrelated and the weight matrix, W, is diagonal, these may be written as",
null,
"Where",
null,
"For non-linear least squares systems a similar argument shows that the normal equations should be modified as follows.",
null,
"• Least-squares regression is a method for finding a line that summarizes the relationship between the two variables.\n• Regression Line: A straight line that describes how a response variable y changes as an explanatory variable x changes.\n• A residual is a difference between an observed y and a predicted y.\n\nImportant facts about the least squares regression line.\n\n• The point (x,y) is on the line, where x is the mean of the x values, and y is the mean of the y values.\n• Its form is y(hat) = a + bx. (Note that b is slope and a is the y-intercept.)\n• a = y – bx.\n• The slope b is the approximate change in y when x increases by 1.\n• The y-intercept is the predicted value of y when x = 0\n\nr2 in regression: The coefficient of determination, r2 is the fraction of the variation in the values of y that is explained the least squares regression of y on x.\n\nCalculation of r2 for a simple example:\n\nr2 = (SSM-SSE)/SSM, where\n\nSSM = sum(y-y)2 (Sum of squares about the mean y)\n\nSSM = sum(y-y(hat))2 (Sum of squares of residuals)\n\nCalculating the regression slope and intercept\n\nThe terms in the table are used to derive the straight line formula for regression: y = bx + a, also called the regression equation. The slope or b is calculated from the Y’s associated with particular X’s in the data. The slope coefficient (by/x) equals",
null,
"THINGS TO NOTE:\n\n· Sum of deviations from mean = 0.\n\n· Sum of residuals = 0.\n\n· r2 > 0 does not mean r > 0. If x and y are negatively associated, then r < 0.\n\n## One thought on “A Quick Guide to Least Squares Regression Method”\n\n1.",
null,
"regression melbourne says:\n\nHello, Neat post. There’s an issue along with your web site in web explorer, would check this? IE still is the market leader and a large component to other people will miss your magnificent writing because of this problem."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.9150112,"math_prob":0.9978348,"size":2589,"snap":"2019-51-2020-05","text_gpt3_token_len":553,"char_repetition_ratio":0.14429401,"word_repetition_ratio":0.0,"special_character_ratio":0.20664349,"punctuation_ratio":0.08865979,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999892,"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,3,null,3,null,6,null,6,null,3,null,3,null,3,null,3,null,3,null,3,null,3,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-24T16:52:01Z\",\"WARC-Record-ID\":\"<urn:uuid:81b38459-9e1f-4a7b-aa3d-123b412703f0>\",\"Content-Length\":\"68775\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d7fd088f-f6ef-4f7b-9d92-d559d7cae968>\",\"WARC-Concurrent-To\":\"<urn:uuid:ffb19300-0f5a-45a7-a9ab-7a28d94c40e4>\",\"WARC-IP-Address\":\"104.27.180.171\",\"WARC-Target-URI\":\"https://www.tutebox.com/3352/maths/a-quick-guide-to-least-squares-regression-method-2/\",\"WARC-Payload-Digest\":\"sha1:QH4DKB5E47PNRFWFBOI7YUIBAJHVFMSC\",\"WARC-Block-Digest\":\"sha1:2TYPXDYU6UU364CMXDGNHBHDX2O5OTEK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250624328.55_warc_CC-MAIN-20200124161014-20200124190014-00273.warc.gz\"}"} |
http://www.numbersaplenty.com/716787884 | [
"Search a number\nBaseRepresentation\nbin101010101110010…\n…101000010101100\n31211221202121010102\n4222232111002230\n52431444203014\n6155043130232\n723522411411\noct5256250254\n91757677112\n10716787884\n1133867638a\n12180073978\n13b5669757\n146b2a8108\n1542ddb8de\nhex2ab950ac\n\n716787884 has 12 divisors (see below), whose sum is σ = 1272046608. Its totient is φ = 353346000.\n\nThe previous prime is 716787857. The next prime is 716787913. The reversal of 716787884 is 488787617.\n\nIt is a happy number.\n\nIt is an unprimeable number.\n\nIt is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1261667 + ... + 1262234.\n\nIt is an arithmetic number, because the mean of its divisors is an integer number (106003884).\n\nAlmost surely, 2716787884 is an apocalyptic number.\n\nIt is an amenable number.\n\n716787884 is a deficient number, since it is larger than the sum of its proper divisors (555258724).\n\n716787884 is a wasteful number, since it uses less digits than its factorization.\n\n716787884 is an evil number, because the sum of its binary digits is even.\n\nThe sum of its prime factors is 2523976 (or 2523974 counting only the distinct ones).\n\nThe product of its digits is 4214784, while the sum is 56.\n\nThe square root of 716787884 is about 26772.8945764181. The cubic root of 716787884 is about 894.9461112129.\n\nThe spelling of 716787884 in words is \"seven hundred sixteen million, seven hundred eighty-seven thousand, eight hundred eighty-four\"."
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| {"ft_lang_label":"__label__en","ft_lang_prob":0.80720985,"math_prob":0.95797783,"size":1589,"snap":"2020-10-2020-16","text_gpt3_token_len":480,"char_repetition_ratio":0.1533123,"word_repetition_ratio":0.008,"special_character_ratio":0.47577092,"punctuation_ratio":0.13793103,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9914228,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-23T10:55:51Z\",\"WARC-Record-ID\":\"<urn:uuid:7ab844df-fb6b-44c8-9bcc-6f6c4c513401>\",\"Content-Length\":\"8441\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c5e72aff-c5a1-4929-ba3e-a14f54790e78>\",\"WARC-Concurrent-To\":\"<urn:uuid:754bb268-a707-443d-9a6b-1928c10b5611>\",\"WARC-IP-Address\":\"62.149.142.170\",\"WARC-Target-URI\":\"http://www.numbersaplenty.com/716787884\",\"WARC-Payload-Digest\":\"sha1:6SHSI3FQ5MI4GNWXCGYL32B6AV2W7KM4\",\"WARC-Block-Digest\":\"sha1:KB4APOEVY62PTZVVNWWIPFF4ZYJ2UYRU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145767.72_warc_CC-MAIN-20200223093317-20200223123317-00455.warc.gz\"}"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-2-solving-equations-2-1-solving-one-step-equations-practice-and-problem-solving-exercises-page-86/65 | [
"## Algebra 1: Common Core (15th Edition)\n\nPublished by Prentice Hall\n\n# Chapter 2 - Solving Equations - 2-1 Solving One-Step Equations - Practice and Problem-Solving Exercises - Page 86: 65\n\n#### Answer\n\n$p=2.5$\n\n#### Work Step by Step\n\nIn order to solve this algebraic expression, we must isolate the variable. A variable is the letter in the problem (for instance, in the equation x+2=10, x is the variable). Because addition and subtraction are inverse operations (they cancel each other out), we know we must add when a number is being subtracted from the variable and subtract when a number is being added to the variable. In the equation $4.25=1.75+p$ we must get rid of the 1.75, which is on the same side as p, in order to solve. Thus, we subtract 1.75 on both sides of the equation to find that p=2.5. We plug 2.5 in for p and confirm that our answer is, indeed, correct.\n\nAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback."
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null
]
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