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http://www.kirknorth.com/2013/08/
[ "## Friday, August 2, 2013\n\n### Introduction\n\nI have been using the Steiner et. al (1995) algorithm for echo classification for some time now. It has its drawbacks, like any algorithm. For example, there are many free parameters that are region dependent, like the automatic convection parameter and the peakedness parameter ($$\\Delta Z$$). These parameters, as one might suspect, would have entirely different values for convection near Darwin, Australia than convection near Oklahoma City, Oklahoma.\n\nThis algorithm was designed and tuned for radar data collected in Darwin, Australia during February 1988. Therefore, if I want to apply this algorithm to data collected at ARM's Southern Great Plains (SGP) site near Lamont, Oklahoma, I need to first check the results using the default parameters suggested by Steiner et al. (1995), and then tune these parameters accordingly if need be.\n\nIt should be noted that this algorithm is applied to gridded reflectivity data at a height chosen to be below the melting layer. In the case of Steiner et al. (1995), they used grids 240 x 240 km in $$x$$ and $$y$$, with 2 km resolution in each dimension. Here I will be using 100 x 100 km grids in $$x$$ and $$y$$, with 500 m resolution in each dimension.\n\n### Methodology\n\nThe algorithm is based on three criteria: intensity, peakedness, and surrounding area. The intensity criterion is a simple threshold, where any grid point with a reflectivity of at least 40 dBZ is automatically convective. The peakedness criterion ($$\\Delta Z$$) checks the difference between the grid point and the average reflectivity taken over the surrounding background ($$Z_{bg}$$). If this difference is greater than a certain value, then the grid point is labelled convective. Finally, any grid points within an intensity-dependent radius ($$R_{sa}$$) from those already labelled as convective by either the intensity or the peakedness criteria are also labelled convective.\n\nThe default parameters defined in Steiner et al. (1995) are as follows:\n\n1. Automatically convective: 40 dBZ.\n2. Background radius: 11 km.\n3.  $$\\Delta Z$$ = $$\\begin{cases} 10, & \\mbox{if } Z_{bg} \\lt 0 \\newline 10 - \\frac{Z_{bg}^2}{180}, & \\mbox{if } 0 \\le Z_{bg} \\lt 42.43 \\newline 0, & \\mbox{if } Z_{bg} \\ge 42.43 \\end{cases}$$\n4. There are three different relations for $$R_{sa}$$, the small, medium, and large relations, but each has 1 km and 5 km as the smallest and largest radii, respectively.\n\n### Results\n\nSo let's first check how the algorithm, with its default parameters, classifies a squall line event during May 20th, 2011. Near 1033 UTC the squall line, with an axis slightly offset from a north-south direction, was located approximately in the middle of the analysis domain, as it moved through in a west-east direction. There was a leading anvil region to the east and a trailing stratiform region to the west. The results are shown in Fig. 1.", null, "Fig. 1. C-SAPR reflectivity and corresponding echo classification at 1033 UTC on May 20th, 2011. The working level (or separation altitude) was a constant 1.5 km. The medium $$R_{sa}$$ relation was used for this classification.\n\nThe algorithm does a decent job at classifying the convective squall line feature, however it does miss its leading edge to the east. The trailing stratiform region to the west is another story though. The algorithm is severely affected by brightband contamination here, and a large swath of this region is labelled convective.\n\nOne obvious reason for some of the poor classification in the trailing stratiform region is due to the intensity criterion, which was set to 40 dBZ. This value is too weak for convection observed in Oklahoma, which consistently produces reflectivities of 55+ dBZ. Therefore, my first change will be to up this value to 45 dBZ. Another, albeit less obvious reason for the poor classification in the stratiform region is due to the peakedness criterion. Examining the peakedness relation, which varies depending on the intensity of the background reflectivity $$Z_{bg}$$, I see that it does not require a sharp enough gradient between the grid point and $$Z_{bg}$$, and as a result, the brightband contamination, which has a high intensity but at the same time is spatially smooth, gets labelled convective. Therefore, I will use a new relation for $$\\Delta Z$$:\n\n$$\\Delta Z = \\begin{cases} 14, & \\mbox{if } Z_{bg} \\lt 0 \\newline 14 - \\frac{Z_{bg}^2}{180}, & \\mbox{if } 0 \\le Z_{bg} \\lt 42.43 \\newline 4, & \\mbox{if } Z_{bg} \\ge 42.43 \\end{cases}$$\n\nBasically I have shifted the $$\\Delta Z$$ curve up by 4 dBZ, or, in other words, a sharper gradient between the grid point and the background reflectivity is required. The results of these two changes are shown in Fig. 2.", null, "Fig. 2. Same as Fig. 1 but tuning the intensity criterion and the peakedness criterion.\n\n#### References\n\nSteiner, M., and R. A. Houze Jr., and S. E. Yuter, 1995: Climatological Characterization of Three-Dimensional Storm Structure from Operational Radar and Rain Gauge Data. J. Appl. Meteor.34, 1978-2007" ]
[ null, "http://2.bp.blogspot.com/-H5afOuKFjqE/UfwZhBTB9qI/AAAAAAAAAJw/LoTXLgozQoQ/s640/echo_class_before.png", null, "http://2.bp.blogspot.com/-vLZ__nZ01gU/UfwqwSH5L6I/AAAAAAAAAKA/wsemoKaF0U8/s640/echo_class_after1.png", null ]
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https://xl-mhg.readthedocs.io/en/develop/examples.html
[ "# Examples¶\n\nThe following examples illustrate how to conduct XL-mHG tests and visualize the results using the Python API. For details on each method, including all optional parameters, see the API reference.\n\n## Conducting a test using the simple test function¶\n\nThis example demonstrates the use of the simple test function, `xlmhg_test()`, for conducting an XL-mHG test.\n\nScript:\n\n```import numpy as np\nimport xlmhg\n\nv = np.uint8([1,0,1,1,0,1] + *12 + [1,0])\nX = 3\nL = 10\nstat, cutoff, pval = xlmhg.xlmhg_test(v, X=X, L=L)\n\nprint('Test statistic: %.3f' % stat)\nprint('Cutoff: %d' % cutoff)\nprint('P-value: %.3f' % pval)\n```\n\nOutput:\n\n```Test statistic: 0.014\nCutoff: 6\nP-value: 0.024\n```\n\n## Conducting a test using the advanced test function¶\n\nThis example demonstrates the use of the advanced test function, `get_xlmhg_test_result()`, for conducting an XL-mHG test.\n\nScript:\n\n```import numpy as np\nimport xlmhg\n\nv = np.uint8([1,0,1,1,0,1] + *12 + [1,0])\nX = 3\nL = 10\n\nN = v.size\nindices = np.uint16(np.nonzero(v))\n\nresult = xlmhg.get_xlmhg_test_result(N, indices, X=X, L=L)\n\nprint('Result:', str(result))\nprint('Test statistic: %.3f' % result.stat)\nprint('Cutoff: %d' % result.cutoff)\nprint('P-value: %.3f' % result.pval)\n```\n\nOutput:\n\n```Result: <mHGResult object (N=20, K=5, X=3, L=10, pval=2.4e-02)>\nTest statistic: 0.014\nCutoff: 6\nP-value: 0.024\n```\n\n## Visualizing a test result¶\n\nThis example demonstrates how to visualize an XL-mHG test result using the `get_result_figure()` function and plotly.\n\nScript:\n\n```import numpy as np\nimport xlmhg\nfrom plotly.offline import plot\n\nv = np.uint8([1,0,1,1,0,1] + *12 + [1,0])\nX = 3\nL = 10\n\nN = v.size\nindices = np.uint16(np.nonzero(v))\n\nresult = xlmhg.get_xlmhg_test_result(N, indices, X=X, L=L)\n\nfig = xlmhg.get_result_figure(result)\n\nplot(fig, filename='test_figure.html')\n```\n\nThis produces an html file (`test_figure.html`) that contains an interactive figure. Open the file in a browser (if it doesn’t open automatically) and click on the camera symbol (the left-most symbol on top of the figure) to download it as a PNG image. The image looks as follows:", null, "" ]
[ null, "https://xl-mhg.readthedocs.io/en/develop/_images/test_figure.png", null ]
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http://xstrader.net/%E6%89%93%E9%80%A0%E8%87%AA%E5%B7%B1%E7%9A%84%E5%A4%A7%E7%9B%A4%E5%A4%9A%E7%A9%BA%E5%87%BD%E6%95%B8/
[ "# 打造自己的大盤多空函數\n\nBy | 2017-04-14\n\n```input: Periods(10,\"計算期數\");\ninput: Ratio(7,\"近期波動幅度%上限\");\nsettotalbar(300);\nsetbarback(50);\nif GetSymbolField(\"tse.tw\",\"收盤價\")\n>average(GetSymbolField(\"tse.tw\",\"收盤價\"),10)\nand average(GetSymbolField(\"tse.tw\",\"收盤價\"),5)\n>average(GetSymbolField(\"tse.tw\",\"收盤價\"),20)\nthen begin\ncondition1 = false;\nif (highest(high,Periods-1) - lowest(low,Periods-1))/close\n<= ratio*0.01\nthen condition1=true//近期波動在7%以內\nelse return;\nif condition1\nand high = highest(high, Periods)\n//最高價創波段新高\nand lowest(low,periods+20)*1.1<lowest(low,periods)\nthen ret=1;\nend;```\n\n```if GetSymbolField(\"tse.tw\",\"收盤價\")\n>average(GetSymbolField(\"tse.tw\",\"收盤價\"),10)\nand average(GetSymbolField(\"tse.tw\",\"收盤價\"),5)\n>average(GetSymbolField(\"tse.tw\",\"收盤價\"),20)\nthen begin```\n\n```input:length1(numeric);\ninput:lowlimit(numeric);\n\nif countif(GetSymbolField(\"tse.tw\",\"外資買賣超金額\",\"D\")>0,length1)\n>= lowlimit\nthen value1=1\nelse\nvalue1=0;\ntselsindex=value1;```\n\n=0　，例如tselsindex(10,7)=1就代表過去十天至少有七天外資是買超的。" ]
[ null ]
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https://www.w3resource.com/python-exercises/basic/python-basic-1-exercise-72.php
[ " Python: Check whether a given integer is a palindrome or not - w3resource\n\n# Python: Check whether a given integer is a palindrome or not\n\n## Python Basic - 1: Exercise-72 with Solution\n\nWrite a Python program to check whether a given integer is a palindrome or not.\nNote: An integer is a palindrome when it reads the same backward as forward. Negative numbers are not palindromic.\n\nSample Solution:\n\nPython Code:\n\n``````def is_Palindrome(n):\nreturn str(n) == str(n)[::-1]\nprint(is_Palindrome(100))\nprint(is_Palindrome(252))\nprint(is_Palindrome(-838))\n``````\n\nSample Output:\n\n```False\nTrue\nFalse\n```\n\nPictorial Presentation:", null, "", null, "Flowchart:", null, "Python Code Editor:\n\nHave another way to solve this solution? Contribute your code (and comments) through Disqus.\n\nWhat is the difficulty level of this exercise?\n\nTest your Programming skills with w3resource's quiz.\n\n" ]
[ null, "https://www.w3resource.com/w3r_images/python-basic-1-image-exercise-72-a.svg", null, "https://www.w3resource.com/w3r_images/python-basic-1-image-exercise-72-b.svg", null, "https://www.w3resource.com/w3r_images/python-basic-1-exercise-flowchart-72.png", null ]
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https://fpgatutorial.com/how-to-write-a-basic-verilog-testbench/
[ "# How to Write a Basic Verilog Testbench\n\nBy John\nAugust 16, 2020\n\nIn this post we look at how we use Verilog to write a basic testbench. We start by looking at the architecture of a Verilog testbench before considering some key concepts in verilog testbench design. This includes modelling time in verilog, the initial block, verilog-initial-block and the verilog system tasks. Finally, we go through a complete verilog testbench example.\n\nWhen using verilog to design digital circuits, we normally also create a testbench to stimulate the code and ensure that it functions as expected.\n\nWe can write our testbench using a variety of languages, with VHDL, Verilog and System Verilog being the most popular.\n\nSystem Verilog is widely adopted in industry and is probably the most common language to use. If you are hoping to design FPGAs professionally, then it will be important to learn this skill at some point.\n\nAs it is better to focus on one language as a time, this blog post introduces the basic principles of testbench design in verilog. This allows us to test designs while working through the verilog tutorials on this site.\n\n## Architecture of a Basic Testbench\n\nTestbenches consist of non-synthesizable verilog code which generates inputs to the design and checks that the outputs are correct.\n\nThe diagram below shows the typical architecture of a simple testbench.\n\nThe stimulus block generates the inputs to our FPGA design and the output checker tests the outputs to ensure they have the correct values.\n\nThe stimulus and output checker will be in separate files for larger designs. It is also possible to include all of these different elements in a single file.\n\nThe main purpose of this post is to introduce the skills which will allow us to test our solutions to the exercises on this site.\n\nTherefore, we don't discuss the output checking block as it adds unnecessary complexity.\n\nInstead, we can use a simulation tool which allows for waveforms to be viewed directly. The freely available software packages from Xilinx (Vivado) and Intel (Quartus) both offer this capability.\n\nAlternatively, open source tools such as icarus verilog can be used in conjunction with GTKWave to run verilog simulations.\n\nWe can also make use of EDA playground which is a free online verilog simulation tool.\n\nIn this case, we would need to use system tasks to monitor the outputs of our design. This gives us a textual output which we can use to check the state of our signals at given times in our simulation.\n\n## Instantiating the DUT\n\nThe first step in writing a testbench is creating a verilog module which acts as the top level of the test.\n\nUnlike the verilog modules we have discussed so far, we want to create a module which has no inputs or outputs in this case. This is because we want the testbench module to be totally self contained.\n\nThe code snippet below shows the syntax for an empty module which we can use as our testbench.\n\n```module <module_name> ();\n\n// Our testbench code goes here\n\nendmodule : <module_name>\n```\n\nAfter we have created a testbench module, we must then instantiate the design which we are testing. This allows us to connect signals to the design in order to stimulate the code.\n\nWe have already discussed how we instantiate modules in the previous post on verilog modules. However, the code snippet below shows how this is done using named instantiation.\n\n```<module_name> # (\n// If the module uses parameters they are connected here\n.<parameter_name> (<parameter_value>)\n)\n<instance_name> (\n// Connection to the module ports\n.<port_name> (<signal_name>),\n.<port_name> (signal_name>)\n);\n```\n\nOnce we have done this, we are ready to start writing our stimulus to the FPGA. This includes generating the clock and reset, as well creating test data to send to the FPGA.\n\nIn order to this we need to use some verilog constructs which we have not yet encountered - initial blocks, forever loops and time consuming statements.\n\nWe will look at these in more detail before we go through a complete verilog testbench example.\n\n## Modelling Time in Verilog\n\nOne of the key differences between testbench code and design code is that we don't need to synthesize the testbench.\n\nAs a result of this, we can use special constructs which consume time. In fact, this is crucial for creating test stimulus.\n\nWe have a construct available to us in Verilog which enables us to model delays. In verilog, we use the # character followed by a number of time units to model delays.\n\nAs an example, the verilog code below shows an example of using the delay operator to wait for 10 time units.\n\n```#10\n```\n\nOne important thing to note here is that there is no semi-colon at the end of the code. When we write code to model a delay in Verilog, this would actually result in compilation errors.\n\nIt is also common to write the delay in the same line of code as the assignment. This effectively acts as a scheduler, meaning that the change in signal is scheduled to take place after the delay time.\n\nThe code snippet below shows an example of this type of code.\n\n```// A is set to 1 after 10 time units\n#10 a = 1'b1;\n```\n\n### Timescale Compiler Directive\n\nSo far, we have talked about delays which are ten units of time. This is fairly meaningless until we actually define what time units we should use.\n\nIn order to specify the time units that we use during simulation, we use a verilog compiler directive which specifies the time unit and resolution. We only need to do this once in our testbench and it should be done outside of a module.\n\nThe code snippet below shows the compiler directive we use to specify the time units in verilog.\n\n````timescale <unit_time> / <resolution>\n```\n\nWe use the <unit_time> field to specify the main time unit of our testbench and the <resolution> field to define the resolution of the time units in our simulation.\n\nThe <resolution> field is important as we can use non-integer numbers to specify the delay in our verilog code. For example, if we want to have a delay of 10.5ns, we could simply write #10.5 as the delay.\n\nTherefore, the <resolution> field in the compiler directive determines the smallest time step we can actually model in our Verilog code.\n\nBoth of the fields in this compiler directive take a time type such as 1ps or 1ns.\n\nIn the post on always blocks in verilog, we saw how we can use procedural blocks to execute code sequentially.\n\nAnother type of procedural block which we can use in verilog is known as the initial block.\n\nAny code which we write inside an initial block is executed once, and only once, at the beginning of a simulation.\n\nThe verilog code below shows the syntax we use for an initial block.\n\n```initial begin\n// Our code goes here\nend\n```\n\nUnlike the always block, verilog code written within initial block is not synthesizable. As a result of this, we use them almost exclusively for simulation purposes.\n\nHowever, we can also use initial blocks in our verilog RTL to initialise signals.\n\nWhen we write stimulus code in our verilog testbench we almost always use the initial block.\n\nTo give a better understanding of how we use the initial block to write stimulus in verilog, let's consider a basic example.\n\nFor this example imagine that we want to test a basic two input and gate.\n\nTo do this, we would need code which generates each of the four possible input combinations.\n\nIn addition, we would also need to use the delay operator in order to wait for some time between generating the inputs.\n\nThis is important as it allows time for the signals to propagate through our design.\n\nThe verilog code below shows the method we would use to write this test within an initial block.\n\n```initial begin\n// Generate each input to an AND gate\n// Waiting 10 time units between each\nand_in = 2b'00;\n#10\nand_in = 2b'01;\n#10\nand_in = 2b'10;\n#10\nand_in = 2b'11;\nend\n```\n\n## Verilog forever loop\n\nAlthough we haven't yet discussed loops, they can be used to perform important functions in Verilog. In fact, we will discuss verilog loops in detail in a later post in this series\n\nHowever, there is one important type of loop which we can use in a verilog testbench - the forever loop.\n\nWhen we use this construct we are actually creating an infinite loop. This means we create a section of code which runs contimnuously during our simulation.\n\nThe verilog code below shows the syntax we use to write forever loops.\n\n```forever begin\n// our code goes here\nend\n```\n\nWhen writing code in other programming languages, we would likely consider an infinite loop as a serious bug which should be avoided.\n\nHowever, we must remember that verilog is not like other programming languages. When we write verilog code we are describing hardware and not writing software.\n\nTherefore, we have at least one case where we can use an infinite loop - to generate a clock signal in our verilog testbench.\n\nTo do this, we need a way of continually inverting the signal at regular intervals. The forever loop provides us with an easy method to implement this.\n\nThe verilog code below shows how we can use the forever loop to generate a clock in our testbench. It is important to note that any loops we write must be contained with in a procedural block or generate block.\n\n``` initial begin\nclk = 1'b0;\nforever begin\n#1 clk = ~clk;\nend\nend\n```\n\nWhen we write testbenches in verilog, we have some inbuilt tasks and functions which we can use to help us.\n\nCollectively, these are known as system tasks or system functions and we can identify them easily as they always begin wtih a dollar symbol.\n\nThere are actually several of these tasks available. However, we will only look at three of the most commonly used verilog system tasks - \\$display, \\$monitor and \\$time.\n\n### \\$display\n\nThe \\$display function is one of the most commonly used system tasks in verilog. We use this to output a message which is displayed on the console during simulation.\n\nWe use the \\$display macro in a very similar way to the printf function in C.\n\nThis means we can easily create text statements in our testbench and use them to display information about the status of our simulation.\n\nWe can also use a special character (%) in the string to display signals in our design. When we do this we must also include a format letter which tells the task what format to display the variable in.\n\nThe most commonly used format codes are b (binary), d (decimal) and h (hex). We can also include a number in front of this format code to determine the number of digits to display.\n\nThe verilog code below shows the general syntax for the \\$display system task. This code snippet also includes an example use case.\n\n```// General syntax\n\\$display(<string_to_display>, <variables_to_display);\n\n// Example - display value of x as a binary, hex and decimal number\n\\$display(\"x (bin) = %b, x (hex) = %h, x (decimal) = %d\", x, x, x);\n```\n\nThe full list of different formats we can use with the \\$display system task are shown in the table below.\n\nFormat CodeDescription\n%b or %BDisplay as binary\n%d or %DDisplay as decimal\n%h or %HDisplay as hexidecimal\n%o or %ODisplay as octal format\n%c or %CDisplay as ASCII character\n%m or %MDisplay the hierarchical name of our module\n%s or %SDisplay as a string\n%t or %TDisplay as time\n\n### \\$monitor\n\nThe \\$monitor function is very similar to the \\$display function, except that it has slightly more intelligent behaviour.\n\nWe use this function to monitor the value of signals in our testbench and display a message whenever one of these signals changes state.\n\nAll system tasks are actually ignored by the synthesizer so we could even include \\$monitor statements in our verilog RTL code, although this is not common.\n\nThe general syntax for this system task is shown in the code snippet below. This code snippet also includes an example use case.\n\n```// General syntax\n\\$monitor(<message_to_display>, <variables_to_display>);\n\n// Example - monitor the values of the in_a and in_b signals\n\\$monitor(\"in_a=%b, in_b=%b\\n\", in_a, in_b);\n```\n\n### \\$time\n\nThe final system task which we commonly use in testbenches is the \\$time function. We use this system task to get the current simulation time.\n\nIn our verilog testbenches, we commonly use the \\$time function together with either the \\$display or \\$monitor tasks to display the time in our messages.\n\nThe verilog code below shows how we use the \\$time and \\$display tasks together to create a message.\n\n```\\$display(\"Current simulation time = %t\", \\$time);\n```\n\n## Verilog Testbench Example\n\nNow that we have discussed the most important topics for testbench design, let's consider a compete example.\n\nWe will use a very simple circuit for this and build a testbench which generates every possible input combination.\n\nThe circuit shown below is the one we will use for this example. This consists of a simple two input and gate as well as a flip flip.\n\n### 1. Create a Testbench Module\n\nThe first thing we do in the testbench is declare an empty module to write our testbench code in.\n\nThe code snippet below shows the declaration of the module for this testbench.\n\nNote that it is good practise to keep the name of the design being tested and the testbench similar. Normally this is done by simply appending _tb or _test to the end of the design name.\n\n```module example_tb ();\n\n// Our testbench code goes here\n\nendmodule : example_tb\n```\n\n### 2. Instantiate the DUT\n\nNow that we have a blank testbench module to work with, we need to instantiate the design we are going to test.\n\nAs named instantiation is generally easy to maintain than positional instantiation, as well as being easier to understand, this is the method we use.\n\nThe code snippet below shows how we would instantiate the DUT, assuming that the signals clk, in_1, in_b and out_q are declared previously.\n\n```example_design dut (\n.clock (clk),\n.reset (reset),\n.a (in_a),\n.b (in_b),\n.q (out_q)\n);\n```\n\n### 3. Generate the Clock and Reset\n\nThe next thing we do is generate a clock and reset signal in our verilog testbench.\n\nIn both cases, we can write the code for this within an initial block. We then use the verilog delay operator to schedule the changes of state.\n\nIn the case of the clock signal, we use the forever keyword to continually run the clock signal during our tests.\n\nUsing this construct, we schedule an inversion every 1 ns, giving a clock frequency of 1GHz.\n\nThis frequency is chosen purely to give a fast simulation time. In reality, 1GHz clock rates in FPGAs are not achievable and the testbench clock frequency should match the frequency of the hardware clock.\n\nThe verilog code below shows how the clock and the reset signals are generated in our testbench.\n\n```// generate the clock\ninitial begin\nclk = 1'b0;\nforever #1 clk = ~clk;\nend\n\n// Generate the reset\ninitial begin\nreset = 1'b1;\n#10\nreset = 1'b0;\nend\n```\n\n### 4. Write the Stimulus\n\nThe final part of the testbench that we need to write is the test stimulus.\n\nIn order to test the circuit we need to generate each of the four possible input combinations in turn. We then need to wait for a short time while the signals propagate through our code block.\n\nTo do this, we assign the inputs a value and then use the verilog delay operator to allow for propagation through the FPGA.\n\nWe also want to monitor the values of the inputs and outputs, which we can do with the \\$monitor verilog system task.\n\nThe code snippet below shows the code for this.\n\n```initial begin\n// Use the monitor task to display the FPGA IO\n\\$monitor(\"time=%3d, in_a=%b, in_b=%b, q=%2b \\n\",\n\\$time, in_a, in_b, q);\n\n// Generate each input with a 20 ns delay between them\nin_a = 1'b0;\nin_b = 1'b0;\n#20\nin_a = 1'b1;\n#20\nin_a = 1'b0;\nin_b = 1'b1;\n#20\nin_a = 1'b1;\nend\n```\n\n### Full Example Code\n\nThe verilog code below shows the testbench example in its entirety.\n\n````timescale 1ns / 1ps\n\nmodule example_tb ();\n// Clock and reset signals\nreg clk;\nreg reset;\n\nreg in_a;\nreg in_b;\nwire out_q;\n\n// DUT instantiation\nexample_design dut (\n.clock (clk),\n.reset (reset),\n.a (in_a),\n.b (in_b),\n.q (out_q)\n);\n\n// generate the clock\ninitial begin\nclk = 1'b0;\nforever #1 clk = ~clk;\nend\n\n// Generate the reset\ninitial begin\nreset = 1'b1;\n#10\nreset = 1'b0;\nend\n\n// Test stimulus\ninitial begin\n// Use the monitor task to display the FPGA IO\n\\$monitor(\"time=%3d, in_a=%b, in_b=%b, q=%2b \\n\",\n\\$time, in_a, in_b, q);\n\n// Generate each input with a 20 ns delay between them\nin_a = 1'b0;\nin_b = 1'b0;\n#20\nin_a = 1'b1;\n#20\nin_a = 1'b0;\nin_b = 1'b1;\n#20\nin_a = 1'b1;\nend\n\nendmodule : example_tb\n```\n\n## Exercises\n\nWhen using a basic testbench architecture which block generates inputs to the DUT?\n\nThe stimulus block is used to generate inputs to the DUT.\n\nWrite an empty verilog module which can be used as a verilog testbench.\n\n```module example_tb ();\n\n// Our test bench code goes here\n\nendmodule : example_tb\n```\n\nWhy is named instantiation generally preferable to positional instantiation.\n\nIt is easier to maintain our code as the module connections are explicitly given.\n\nWhat is the difference between the \\$display and \\$monitor verilog system tasks.\n\nThe \\$display task runs once whenever it is called. The \\$monitor task monitors a number of signals and displays a message whenever one of them changes state,\n\nWrite some verilog code which generates stimulus for a 3 input AND gate with a delay of 10 ns each time the inputs change state.\n\n````timescale 1ns / 1ps\n\nintial begin\nand_in = 3'b000;\n#10\nand_in = 3'b001;\n#10\nand_in = 3'b010;\n#10\nand_in = 3'b011;\n#10\nand_in = 3'b100;\n#10\nand_in = 3'b101;\n#10\nand_in = 3'b110;\n#10\nend\n```\n\nEnjoyed this post? Why not share it with others.\n\nFollow us on social media for all of the latest news.\n\n### Subscribe\n\nDesigned in partnership with ceotutorial.com", null, "Why not join our mailing list and be the first to hear about our latest FPGA tutorials\n\nClose", null, "", null, "", null, "" ]
[ null, "https://fpgatutorial.com/how-to-write-a-basic-verilog-testbench/", null, "https://fpgatutorial.com/how-to-write-a-basic-verilog-testbench/", null, "https://fpgatutorial.com/how-to-write-a-basic-verilog-testbench/", null, "https://fpgatutorial.com/how-to-write-a-basic-verilog-testbench/", null ]
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https://www.booktopia.com.au/greek-mathematical-works-from-thales-to-euclid-v-1-i-thomas/book/9780674993693.html
[ "", null, "+612 9045 4394", null, "", null, "CHECKOUT", null, "", null, "", null, "", null, "# Greek Mathematical Works: From Thales to Euclid v. 1\n\n### Selections\n\nBy: I. Thomas (Translator)\n\nHardcover Published: 1st July 1989\nISBN: 9780674993693\nNumber Of Pages: 576\n\nShare This Book:\n\n### Hardcover\n\nRRP \\$66.00\n\\$51.75\n22%\nOFF\nShips in 7 to 10 business days\n\nEarn 104 Qantas Points\non this Book\n\nThe wonderful achievement of Greek mathematics is here illustrated in two volumes of selected mathematical works. Volume I contains: The divisions of mathematics; mathematics in Greek education; calculation; arithmetical notation and operations, including square root and cube root; Pythagorean arithmetic, including properties of numbers; square root of 2; proportion and means; algebraic equations; Proclus; Thales; Pythagorean geometry; Democritus; Hippocrates of Chios; duplicating the cube and squaring the circle; trisecting angles; Theaetetus; Plato; Eudoxus of Cnidus (pyramid, cone, etc.); Aristotle (the infinite, the lever); Euclid.\n\nVolume II (\"Loeb Classical Library no. 362\") contains: Aristarchus (distances of sun and moon); Archimedes (cylinder, sphere, cubic equations; conoids; spheroids; spiral; expression of large numbers; mechanics; hydrostatics); Eratosthenes (measurement of the earth); Apollonius (conic sections and other works); later development of geometry; trigonometry (including Ptolemy's table of sines); mensuration: Heron of Alexandria; algebra: Diophantus (determinate and indeterminate equations); the revival of geometry: Pappus.\n\n Introductory Mathematics and its divisions Origin of the name The Pythagorean quadrivium Plato's scheme Logistic Later classification Mathematics in Greek Education Practical calculation Enumeration by fingers The abacus Arithmetical Notation And The Chief Arithmetical Operations English notes and examples Division Extraction of the square root Extraction of the cube root Pythagorean Arithmetic First principles Classification of numbers Perfect numbers Figured numbers General Triangular numbers Oblong and square numbers Polygonal numbers Gnomons of polygonal numbers Some properties of numbers The \" sieve \" of Eratosthenes Divisibility of squares A theorem about cube numbers A property of the pythmen Irrationality of the square root of 2 The theory of proportion and means Arithmetic, geometric and harmonic means Seven other means Pappus's equations between means Plato on means between two squares or two cubes A theorem of Archytas Algebraic equations Side and diameter-numbers The \" bloom \" of Thymaridas Proclus's Summary Thales Pythagorean Geometry General Sum of the angles of a triangle \" Pythagoras's theorem \" The application of areas The irrational The five regular solids Democritus Hippocrates Of Chios General Quadrature of lunes Two mean proportionals Special Problems Duplication of the Cube General Solutions given by Eutocius \" Plato \" Heron Diocles Menaechmus : solution by conies Archytas : solution in three dimensions Eratosthenes Nicomedes : the Conchoid 2. Squaring of the Circle General Approximation by polygons Antiphon Bryson Archimedes Solutions by higher curves General The Quadratrix 3. Trisection of an Angle Types of geometrical problems Solution by means of a verging Direct solutions by means of conies Zeno Of Elea Theaetetus General The five regular solids The irrational Plato General Philosophy of mathematics The diorismos in the Meno The nuptial number Generation of numbers Eudoxus of Cnidos Theory of proportion Volume of pyramid and cone Theory of concentric spheres Aristotle#151 Table of Contents provided by Publisher. All Rights Reserved.\n\nISBN: 9780674993693\nISBN-10: 0674993691\nSeries: Loeb Classical Library : Book 1\nAudience: Professional\nFormat: Hardcover\nLanguage: English\nNumber Of Pages: 576\nPublished: 1st July 1989\nPublisher: HARVARD UNIV PR\nCountry of Publication: US\nDimensions (cm): 17.15 x 12.07  x 2.54\nWeight (kg): 0.36\nEdition Number: 335\n\nEarn 104 Qantas Points\non this Book" ]
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https://sicstus.sics.se/sicstus/docs/4.7.0/html/sicstus/ref_002dsem_002dctr_002dite.html
[ "Next: , Previous: , Up: ref-sem-ctr   [Contents][Index]\n\n#### 4.2.3.3 If-Then-Else\n\nAs an alternative to the use of cuts, and as an extension to the disjunction syntax, Prolog provides the construct:\n\n```(If -> Then ; Else)\n```\n\nThis is the same as the if-then-else construct in other programming languages. Procedurally, it calls the If goal, committing to it if it succeeds, then calling the Then goal, otherwise calling the Else goal. Then and Else, but not If, can produce more solutions on backtracking.\n\nCuts inside of If do not make much sense and are not recommended. If you do use them, then their scope is limited to If itself.\n\nThe if-then-else construct is often used in a multiple-branch version:\n\n```( If_1 -> Then_1\n; If_2 -> Then_2\n…\n; /* otherwise -> */\nWhenAllElseFails\n)\n```\n\nIn contexts other than as the first argument of `;/2`, the following two goals are equivalent:\n\n```(If -> Then)\n\n(If -> Then ; fail)\n```\n\nThat is, the ‘->’ operator has nothing to do with, and should not be confused with, logical implication.\n\n`once/1` is a control construct that provides a “local cut”. That is, the following three goals are equivalent:\n\n```once(If)\n\n(If -> true)\n\n(If -> true ; fail)\n```\n\nFinally, there is another version of if-then-else of the form:\n\n```if(If,Then,Else)\n```\n\nwhich differs from `(If -> Then ; Else)` in that `if/3` explores all solutions to If. This feature is also known as a “soft cut”. There is a small time penalty for this—if If is known to have only one solution of interest, the form `(If -> Then ; Else)` should be preferred.\n\nSend feedback on this subject." ]
[ null ]
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https://m.moam.info/an-introduction-to-trajectory-matthewpeterkelly_6479d930097c476a028bc0a7.html?utm_source=slidelegend
[ "## AN INTRODUCTION TO TRAJECTORY ... - MatthewPeterKelly\n\nThis paper is an introductory tutorial for numerical trajectory optimization with a focus on direct collocation ..... Fi\n\nAN INTRODUCTION TO TRAJECTORY OPTIMIZATION: HOW TO DO YOUR OWN DIRECT COLLOCATION ∗ MATTHEW KELLY\n\nAbstract. This paper is an introductory tutorial for numerical trajectory optimization with a focus on direct collocation methods. These methods are relatively simple to understand and effectively solve a wide variety of trajectory optimization problems. Throughout the paper we illustrate each new set of concepts by working through a sequence of four example problems. We start by using trapezoidal collocation to solve a simple one-dimensional toy-problem and work up to using Hermite–Simpson collocation to compute the optimal gait for a bipedal walking robot. Along the way, we cover basic debugging strategies and guidelines for posing well-behaved optimization problems. The paper concludes with a short overview of other methods for trajectory optimization. We also provide an electronic supplement that contains well-documented Matlab code for all examples and methods presented in this paper. Our primary goal is to provide the reader with the resources necessary to understand and successfully implement their own direct collocation methods.\n\n1. Introduction. What is trajectory optimization? Let’s start with an example: imagine a satellite moving between two planets. We would use the term trajectory to describe the path the the satellite takes between the two planets. Usually, this path would include both state (e.g. position and velocity) and control (e.g. thrust) as functions of time. The term trajectory optimization refers to a set of methods that are used to find the best choice of trajectory, typically by selecting the inputs to the system, known as controls, as functions of time. 1.1. Overview. Why read this paper? Our contribution is to provide a tutorial that covers all of the basics required to understand and implement direct collocation methods, while still being accessible to broad audience. Where possible, we teach through examples, both in this paper and in the electronic supplement. This tutorial starts with a brief introduction to the basics of trajectory optimization (§1), and then it moves on to solve a simple example problem using trapezoidal collocation (§2). The next sections cover the general implementation details for trapezoidal collocation (§3) and Hermite–Simpson collocation (§4), followed by a section about practical implementation details and debugging (§5). Next there are three example problems: cart-pole swing-up (§6), five-link bipedal walking (§7), and minimum-work block-move (§8). The paper concludes with an overview of related optimization topics and a summary of commonly used software packages (§9). This paper comes with a two-part electronic supplement, which is described in detail in the appendix §A. The first part is a general purpose trajectory optimization library, written in Matlab, that implements both trapezoidal direct collocation, Hermite–Simpson direct collocation, direct multiple shooting (4th -order Runge–Kutta), and global orthogonal collocation (Chebyshev Lobatto). The second part of the supplement is a set of all example problems from this paper implemented in Matlab and solved with the afore-mentioned trajectory optimization library. The code in the supplement is well-documented and designed to be read in a tutorial fashion. 1.2. Notation. For reference, these are the main symbols we will use throughout the tutorial and will be described in detail later. tk N\n\ntime at knot point k number of trajectory (spline) segments\n\nhk = tk+1 − tk xk = x(tk )\n\nduration of spline segment k state at knot point k\n\nuk = u(tk ) \u0001 wk = w tk , xk , uk \u0001 fk = f tk , xk , uk q˙ =\n\nd dt q\n\nq¨ =\n\ncontrol at knot point k integrand of objective function at knot point k system dynamics at knot point k 2\n\nd dt2 q\n\nfirst and second time-derivatives of q\n\n∗ This\n\nwork was supported by the National Science Foundation University, Ithaca, NY. ([email protected]). Questions, comments, or corrections to this document may be directed to that email address. † Cornell\n\n1\n\nforce\n\nStart\n\nFinish\n\ntime = 0 position = 0 velocity = 0\n\ntime = 1 position = 1 velocity = 0\n\nno friction\n\nFig. 1. Illustration of the boundary conditions for the simple block move example.\n\nposition\n\n1\n\nposition\n\n1 a few feasible trajectories 0\n\n0\n\n0\n\n1\n\ntime\n\nthe optimal trajectory\n\nminimizing the integral of force-squared time\n\n0\n\n1\n\nFig. 2. Comparison of feasible (left) and optimal (right) trajectories for the simple block move example.\n\nIn some cases we will use the subscript k + 12 to indicate the mid-point of spline segment k. For example, uk gives the control at the beginning of segment k, and uk+ 12 gives the control at the mid-point of segment k. 1.3. A simple example. We will start by looking at a simple example: how to move a small block between two points, starting and finishing at rest, in a fixed amount of time. First, we will need to write down the dynamics, which describe how the system moves. In this case, we will model the block as a point-mass that travels in one dimension, and the control (input) to the system is simply the force applied to the block. Here we use x for position, ν for velocity, and u for control (force). x˙ = ν\n\nν˙ = u\n\nsystem dynamics\n\nIn this case, we would like the block to move one unit of distance in one unit of time, and it should be stationary at both start and finish. These requirements are illustrated in Figure 1 and are known as boundary conditions. x(0) = 0 ν(0) = 0\n\nx(1) = 1 ν(1) = 0\n\nboundary conditions\n\nA solution to a trajectory optimization problem is said to be feasible if it satisfies all of the problem requirements, known as constraints. In general, there are many types of constraints. For the simple blockmoving problem we have only two types of constraints: the system dynamics and the boundary conditions. Figure 2 shows several feasible trajectories. The set of controls that produce feasible trajectories are known as admissible controls. Trajectory optimization is concerned with finding the best of the feasible trajectories, which is known as the optimal trajectory, also shown in Figure 2. We use an objective function to mathematically describe what we mean by the ‘best’ trajectory. Later in this tutorial we will solve this block moving problem with two commonly used objective functions: minimal force squared (§2) and minimal absolute work (§8). min\n\nu(t), x(t), ν(t)\n\nmin\n\nu(t), x(t), ν(t)\n\nZ\n\n0\n\nZ\n\n1\n\nu2 (τ ) dτ\n\nminimum force-squared\n\n0\n\n1\n\nu(τ ) ν(τ ) dτ\n\nminimum absolute work\n\n1.4. The trajectory optimization problem. There are many ways to formulate trajectory optimization problems [5, 45, 51]. Here we will restrict our focus to single-phase continuous-time trajectory optimization problems: ones where the system dynamics are continuous throughout the entire trajectory. A more general framework is described in and briefly discussed in Section §9.9. 2\n\nIn general, an objective function can include two terms: a boundary objective J(·) and a path integral along the entire trajectory, with the integrand w(·). A problem with both terms is said to be in Bolza form. A problem with only the integral term is said to be in Lagrange form, and a problem with only a boundary term is said to be in Mayer form. The examples in this paper are all in Lagrange form. Z tF \u0001 \u0001 (1.1) min J t0 , tF , x(t0 ), x(tF ) + w τ, x(τ ), u(τ ) dτ t0 ,tF ,x(t),u(t) | {z } t | 0 {z } Mayer Term Lagrange Term\n\nIn optimization, we use the term decision variable to describe the variables that the optimization solver is adjusting to minimize the objective function. For the simple block moving problem the decision variables are the initial and final time (t0 , tF ), as well as the state and control trajectories, x(t) and u(t) respectively. The optimization is subject to a variety of limits and constraints, detailed in the following equations (1.2-1.9). The first, and perhaps most important of these constraints is the system dynamics, which are typically non-linear and describe how the system changes in time. \u0001 ˙ (1.2) x(t) = f t, x(t), u(t) system dynamics Next is the path constraint, which enforces restrictions along the trajectory. A path constraint could be used, for example, to keep the foot of a walking robot above the ground during a step. \u0001 (1.3) h t, x(t), u(t) ≤ 0 path constraint\n\nAnother important type of constraint is a non-linear boundary constraint, which puts restrictions on the initial and final state of the system. Such a constraint would be used, for example, to ensure that the gait of a walking robot is periodic. \u0001 (1.4) g t0 , tF , x(t0 ), x(tF ) ≤ 0 boundary constraint Often there are constant limits on the state or control. For example, a robot arm might have limits on the angle, angular rate, and torque that could be applied throughout the entire trajectory. (1.5)\n\nxlow ≤ x(t) ≤ xupp\n\npath bound on state\n\n(1.6)\n\nulow ≤ u(t) ≤ uupp\n\npath bound on control\n\nFinally, it is often important to include specific limits on the initial and final time and state. These might be used to ensure that the solution to a path planning problem reaches the goal within some desired time window, or that it reaches some goal region in state space. (1.7)\n\ntlow ≤ t0 < tF ≤ tupp\n\nbounds on initial and final time\n\n(1.8)\n\nx0,low ≤ x(t0 ) ≤ x0,upp\n\nbound on initial state\n\n(1.9)\n\nxF,low ≤ x(tF ) ≤ xF,upp\n\nbound on final state\n\n1.5. Direct collocation method. Most methods for solving trajectory optimization problems can be classified as either direct or indirect. In this tutorial we will focus on direct methods, although we do provide a brief overview of indirect methods in Section §9.4. The key feature of a direct method is that is discretizes the trajectory optimization problem itself, typically converting the original trajectory optimization problem into a non-linear program (see §1.6). This conversion process is known as transcription and it is why some people refer to direct collocation methods as direct transcription methods. In general, direct transcription methods are able to discretize a continuous trajectory optimization problem by approximating all of the continuous functions in the problem statement as polynomial splines. A spline is a function that is made up of a sequence of polynomials segments. Polynomials are used because they have two important properties: they can be represented by a small (finite) set of coefficients, and it is easy to compute integrals and derivatives of polynomials in terms of these coefficients. Throughout this tutorial we will be studying two direct collocation methods in detail: trapezoidal collocation (§3) and Hermite–Simpson collocation (§4). We will also briefly cover a few other direct collocation techniques: direct single shooting (§9.5), direct multiple shooting (§9.6), and orthogonal collocation (§9.7). 3\n\n1.6. Non-linear programming. Most direct collocation methods transcribe a continuous-time trajectory optimization problem into a non-linear program. A non-linear program is a special name given to a constrained parameter optimization problem that has non-linear terms in either its objective or constraint function. A typical formulation for a non-linear program is given below. (1.10)\n\nmin J(z)\n\nsubject to:\n\nz\n\nf (z) = 0 g(z) ≤ 0 zlow ≤ z ≤ zupp In this tutorial we will not spend time examining the details of how to solve a non-linear program (see , , ), and instead will focus on the practical details of how to properly use a non-linear programming solver, such as those listed in Section §9.12. In some cases, a direct collocation method might produce either a linear or quadratic program instead of a non-linear program. This happens when the constraints (including system dynamics) are linear and the objective function is linear (linear program) or quadratic (quadratic program). Both linear and quadratic programs are much easier to solve than non-linear programs, making them desirable for real-time applications, especially in robotics. 2. Block move example (minimum-force objective). In this section we continue with the simple example presented in the introduction: computing the optimal trajectory to move a block between two points. 2.1. Block move example: problem statement. We will model the block as a unit point mass that slides without friction in one dimension. The state of the block is its position x and velocity ν, and the control is the force u applied to the block. (2.1)\n\nx˙ = ν\n\nν˙ = u\n\nNext, we need to write the boundary constraints which describe the initial and final state of the block. Here we constrain the block to move from x = 0 at time t = 0 to x = 1 at time t = 1. Both the initial and final velocity are constrained to be zero. (2.2)\n\nx(0) = 0 ν(0) = 0\n\nx(1) = 1 ν(1) = 0\n\nA trajectory that satisfies the system dynamics and the boundary conditions is said to be feasible, and the corresponding controls are said to be admissible. A trajectory is optimal if it minimizes an objective function. In general, we are interested in finding solution trajectories that are both feasible and optimal. Here we will use a common objective function: the integral of control effort squared. This cost function is desirable because it tends to produce smooth solution trajectories that are easily computed. (2.3)\n\nmin\n\nu(t), x(t), ν(t)\n\nZ\n\n1\n\nu2 (τ ) dτ\n\n0\n\n2.2. Block move example: analytic solution. The solution to the simple block moving trajectory optimization problem (2.1-2.3) is given below, with a full derivation shown in Appendix B. (2.4)\n\nx∗ (t) = 3t2 − 2t3\n\nu∗ (t) = 6 − 12t\n\nThe analytic solution is found using principles from calculus of variations. These methods convert the original optimization problem into a system of differential equations, which (in this special case) happen to have an analytic solution. It is worth noting that indirect methods for solving trajectory optimization work by using a similar principle: they analytically construct the necessary and sufficient conditions for optimality, and then solve then numerically. Indirect methods are briefly covered in Section 9.4. 4\n\n2.3. Block move example: trapezoidal collocation. Now let’s look at how to compute the optimal block-moving trajectory using trapezoidal collocation. We will need to convert the original continuous-time problem statement into a non-linear program. First, we need to discretize the trajectory, which gives us a finite set of decision variables. This is done by representing the continuous position x(t) and velocity v(t) by their values at specific points in time, known as collocation points. t → t0 . . . t k . . . t N x → x0 . . . xk . . . xN ν → ν0 . . . νk . . . νN Next, we need to convert the continuous system dynamics into a set of constraints that we can apply to the state and control at the collocation points. This is where the trapezoid quadrature (also known as the trapezoid rule) is used. The key idea is that the change in state between two collocation points is equal to the integral of the system dynamics. That integral is then approximated using trapezoidal quadrature, as shown below, where hk ≡ (tk+1 − tk ). Z\n\ntk+1\n\nx˙ = ν Z x˙ dt =\n\ntk+1\n\nν dt\n\ntk\n\ntk\n\nxk+1 − xk ≈ 12 (hk )(νk+1 + νk ) Simplifying and then applying this to the velocity equation as well, we arrive at a set of equations that allow us to approximate the dynamics between each pair of collocation points. These constraints are known as collocation constraints. These equations are enforced on every segment: k = 0 . . . (N − 1) of the trajectory. \u0001 (2.5) xk+1 − xk = 21 (hk ) νk+1 + νk \u0001 (2.6) νk+1 − νk = 21 (hk ) uk+1 + uk The boundary conditions are straight-forward to handle: we simply apply them to the state at the initial and final collocation points. x0 = 0 ν0 = 0\n\n(2.7)\n\nxN = 1 νN = 0\n\nFinally, we approximate the objective function using trapezoid quadrature, converting it into a summation over the control effort at each collocation point: Z tN N −1 X \u0001 2 2 1 u2 (τ ) dτ ≈ min (2.8) min 2 (hk ) uk + uk+1 u(t)\n\nu0 ..uN\n\nt0\n\nk=0\n\n2.4. Initialization. Most non-linear programming solvers require an initial guess. For easy problems, such as this one, a huge range of initial guesses will yield correct results from the non-linear programming solver. However, on difficult problems a poor initial guess can cause the solver to get “stuck” on a bad solution or fail to converge entirely. Section §5.1 provides a detailed overview of methods for constructing an initial guess. For the block-moving example, we will simply assume that the position of the block (x) transitions linearly between the initial and final position. We then differentiate this initial position trajectory to compute the velocity (ν) and force (u) trajectories. Note that this choice of initial trajectory satisfies the system dynamics and position boundary condition, but it violates the velocity boundary condition. (2.9) (2.10) (2.11)\n\nxinit (t) ν\n\ninit\n\nu\n\ninit\n\n=\n\nt\n\n(t)\n\n=\n\n(t)\n\n=\n\nd init (t) dt x init d (t) dt ν\n\n=\n\n1\n\n=\n\n0\n\nOnce we have an initial trajectory, we can evaluate it at each collocation point to obtain values to pass to the non-linear programming solver. (2.12)\n\nxinit = tk , k\n\nνkinit = 1, 5\n\nuinit =0 k\n\n2.5. Block move example: non-linear program. We have used trapezoidal direct collocation to transcribe the continuous-time trajectory optimization problem into a non-linear program (constrained parameter optimization problem) (2.5)-(2.8). Now, we just need to solve it! Section §9.12 provides a brief overview of software packages that solve this type of optimization problem. In general, after performing direct transcription, a trajectory optimization problem is converted into a non-linear programming problem. It turns out that, for this simple example, we actually get a quadratic program. This is because the constraints (2.5)-(2.7) are both linear, and the objective function (2.8) is quadratic. Solving a quadratic program is usually much easier than solving a non-linear program. 2.6. Block move example: interpolation. Let’s assume that you’ve solved the non-linear program: you have a set of positions xk , velocities, νk , and controls uk that satisfy the dynamics and boundary constraints and that minimize the objective function. All that remains is to construct a spline (piece-wise polynomial function) that interpolates the solution trajectory between the collocation points. For trapezoidal collocation, it turns out that you use a linear spline for the control and a quadratic spline for the state. Section §3.4 provides a more detailed discussion and derivation of these interpolation splines. 3. Trapezoidal collocation method. Now that we’ve seen how to apply trapezoidal collocation to a simple example, we’ll take a deeper look at using trapezoidal collocation to solve a generic trajectory optimization problem. Trapezoidal collocation works by converting a continuous-time trajectory optimization problem into a non-linear program. This is done by using trapezoidal quadrature, also know as the trapezoid rule for integration, to convert each continuous aspect of the problem into a discrete approximation. In this section we will go through how this transformation is done for each aspect of a trajectory optimization problem. 3.1. Trapezoidal collocation: integrals. There are often integral expressions in trajectory optimization. Usually they are found in the objective function, but in the constraints as well. R occasionally they are P Our goal here is to approximate the continuous integral w(·) dt as a summation ck wk . The key concept here is that the summation only requires the value of the integrand w(tk ) = wk at the collocation points tk along the trajectory. This approximation is done by applying the trapezoid rule for integration between each collocation point, which yields the equation below, where hk = tk+1 − tk . (3.1)\n\nZ\n\ntF\n\nt0\n\n\u0001 w τ, x(τ ), u(τ ) dτ\n\nN −1 X\n\n1 2 hk\n\n· wk + wk+1\n\nk=0\n\n\u0001\n\n3.2. Trapezoidal collocation: system dynamics. One of the key features of a direct collocation method is that it represents the system dynamics as a set of constraints, known as collocation constraints. For trapezoidal collocation, the collocation constraints are constructed by writing the dynamics in integral form and then approximating that integral using trapezoidal quadrature . Z\n\ntk+1\n\ntk\n\nx˙ = f Z x˙ dt =\n\ntk+1\n\nf dt\n\ntk\n\nxk+1 − xk ≈\n\n1 2\n\nhk · (fk+1 + fk )\n\nThis approximation is then applied between every pair of collocation points: \u0001 (3.2) xk+1 − xk = 12 hk · fk+1 + fk k ∈ 0 . . . (N − 1)\n\nNote that xk is a decision variable in the non-linear program, while fk = f (tk , xk , uk ) is the result of evaluating the system dynamics at each collocation point. 3.3. Trapezoidal collocation: constraints. In addition to the collocation constraints, which enforce the system dynamics, you might also have limits on the state and control, path constraints, and boundary constraints. These constraints are all handled by enforcing them at specific collocation points. For example, simple limits on state and control are approximated: (3.3)\n\nx" ]
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https://www.enotes.com/homework-help/blocks-wirh-masses-3-kg-4-kg-6-kg-lined-up-row-347856?en_action=hh-question_click&en_label=hh-sidebar&en_category=internal_campaign
[ "# How much force does the 4 kg block exert on the 6.0 kg block and how much force does the 4 kg block exert on the 3 kg block in the following case:   Blocks with a mass of 3 kg, 4 kg, and 6 kg are lined up in a row on a frictionless table. All three are pushed by a force of 18 N force applied to the 3 kg block\n\nTushar Chandra", null, "| Certified Educator\n\ncalendarEducator since 2010\n\nstarTop subjects are Math, Science, and Business\n\nThree blocks of mass 3 kg, 4 kg and 6 kg are line up in a row on a table and a force of 18 N is applied to the block with a mass of 3 kg.\n\nThe total mass of the three blocks is 3+4+6 = 13 kg. When a...\n\n(The entire section contains 120 words.)" ]
[ null, "https://static.enotescdn.net/images/core/educator-indicator_thumb.png", null ]
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https://www.mathworks.com/matlabcentral/cody/problems/10-determine-whether-a-vector-is-monotonically-increasing/solutions/951316
[ "Cody\n\n# Problem 10. Determine whether a vector is monotonically increasing\n\nSolution 951316\n\nSubmitted on 1 Sep 2016 by Martin Martínez\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nx = [0 1 2 3 4]; assert(isequal(mono_increase(x),true));\n\n2   Pass\nx = ; assert(isequal(mono_increase(x),true));\n\n3   Pass\nx = [0 0 0 0 0]; assert(isequal(mono_increase(x),false));\n\n4   Pass\nx = [0 1 2 3 -4]; assert(isequal(mono_increase(x),false));\n\n5   Pass\nx = [-3 -4 2 3 4]; assert(isequal(mono_increase(x),false));\n\n6   Pass\nx = 1:.1:10; assert(isequal(mono_increase(x),true));\n\n7   Pass\nx = cumsum(rand(1,100)); x(5) = -1; assert(isequal(mono_increase(x),false));\n\n8   Pass\nx = cumsum(rand(1,50)); assert(isequal(mono_increase(x),true));\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]
[ null ]
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https://workmyexam.com/what-is-a-differential-equation-class/
[ "# What is a Differential Equation Class?\n\nDifferential Equation Class is regarded as the relationship between derivatives of a function of time and its variables. If you need for best online differential calculus class, you must hire experts online. For reliable services, pay somebody to take your online differential calculus class for you. Differential equations are used in calculus classes and physics.\n\nDifferential Equation Class consists of different terms like integral, derivative, integral-derivative and many more such terms. The different term in differential equations include: partial derivatives, integration, derivative-derivative, inverse integral, etc. It is very important to understand the difference between all the different types of differential equations and also to know what the difference between these types is.\n\nDifferential equations are not the same with linear equations. For linear equations, it is a linear algebra or algebraic equations. It also depends on the functions used in the calculation.\n\nDifferentials are used to solve certain problems. Differential equations are also used to describe processes. Differential equations are also useful in engineering, chemistry and physics. Differential equations also help us to find out about the relationship between different quantities. Differential equations are also used to compute the differentials.\n\nDifferentials are solved by solving a linear equation. This is usually done by multiplying the first number by the second number. These are the various problems which can be solved through differentials. Differential equations are used to solve some numerical problems. In calculus class, a student has to solve the problems of differentials before he gets to solve other problems.\n\nDifferentials have their own set of equations. There are different kinds of equations, but here, the most commonly used equations are the following:\n\nThe first number is the time, the second number is the time to the next step of time of function. The third number is the time required for the function to return to zero. The fourth number is the time required for the function to reach to point where it can be added again.\n\nDifferentials and their equations are very useful. If you want to master calculus, the use differentials. Calculus is not easy, but calculus equations can be solved using differentials.\n\nDifferentials give us an easy way to find the solutions of many problems. Differentials are also useful to find out the relationships between numbers. Differentials are useful for calculating and comparing different functions.\n\nThe third type of equations, which is used in calculus is the integral equations. In this type of equations, a positive and a negative number are given together. The derivative of any number can be found by solving the equation, thus giving the value of that number.\n\nIntegral equations are very useful in solving more complicated problems. Integral equations can be solved through calculus as well. Calculus gives us many useful techniques to solve differential equations.\n\nA student can choose any type of differential equation. Differentials can be solved using different methods. Differential equations can be solved by solving through a line, a curve, a spline, a parabola, etc. Differential equations can also be solved using quadratic equations and polynomial equations.\n\nDifferentials are necessary for many applications. Differential equations are useful for solving a wide range of problems.\n\nDifferentials are used in various ways. Differentials are used in the construction of many mechanical systems and are useful for many purposes.\n\nDifferentials can be used to determine the rate and velocity of different bodies in a fluid. Differentials can be used to determine the rate and velocity of moving objects, such as balls, waves, and particles in a fluid.\n\nDifferentials can also be used to analyze a fluid in terms of its temperature and pressure. Differentials can also be used to study the effects of heat, and pressure on different bodies in a fluid. Differentials can also be used to study the effects of velocity and gravity on the surface of a fluid.\n\nDifferentials can also be used to study the flow of a fluid, and the characteristics of that fluid. Differentials can also be used to model a fluid and their behavior.\n\n### Related posts:\n\nWhat is a Differential Equation Class?\nScroll to top" ]
[ null ]
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https://riptutorial.com/tensorflow/example/30756/padding-and-strides--the-most-general-case-
[ "# tensorflow Math behind 2D convolution with advanced examples in TF Padding and strides (the most general case)\n\n## Example\n\nNow we will apply a strided convolution to our previously described padded example and calculate the convolution where `p = 1, s = 2`", null, "Previously when we used `strides = 1`, our slided window moved by 1 position, with `strides = s` it moves by `s` positions (you need to calculate `s^2` elements less. But in our case we can take a shortcut and do not perform any computations at all. Because we already computed the values for `s = 1`, in our case we can just grab each second element.\n\nSo if the solution is case of `s = 1` was", null, "in case of `s = 2` it will be:", null, "Check the positions of values 14, 2, 12, 6 in the previous matrix. The only change we need to perform in our code is to change the strides from 1 to 2 for width and height dimension (2-nd, 3-rd).\n\n``````res = tf.squeeze(tf.nn.conv2d(image, kernel, [1, 2, 2, 1], \"SAME\"))\nwith tf.Session() as sess:\nprint sess.run(res)\n``````\n\nBy the way, there is nothing that stops us from using different strides for different dimensions.", null, "PDF - Download tensorflow for free" ]
[ null, "https://i.stack.imgur.com/68ZsM.png", null, "https://i.stack.imgur.com/rRse4.png", null, "https://i.stack.imgur.com/0Ydz6.png", null, "https://riptutorial.com/Images/icon-pdf-2.png", null ]
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https://engineeringtutorial.com/basic-electronics-questions-answers/
[ "Oops! It appears that you have disabled your Javascript. In order for you to see this page as it is meant to appear, we ask that you please re-enable your Javascript!\n\n### Basic Electronics Questions & Answers\n\n1) What is an Electric Potential?\n\nThe potential of a particular point, is defined as the work done to move a positive charge particle to move to that point in opposite to electric field. It may be an external energy applied to move that positive charge or may be internal potential energy of the positive charge.\n\n2) What is Potential Difference?\n\nThe differential in potentials at two points in an electric field is called as potential difference between two points. It is measure in Volts i.e. VAB is called the potential difference between points A & B. If the VAB is positive then it illustrates that the potential at point A is high compared to potential at point B. In this case there will be chance of movement of charged particle from A to B against to electrical field between the points.\n\nVAB = VA – VB\n\n3) What is a Transit time of an Electron?\n\nThe time taken by an electron to travel from one electrode to the other electrode is called electron transit time. It is denoted as ‘τ’.", null, "Where  V = Potential applied to electron\n\nd= Distance between electrodes\n\ne = Electron charge\n\nm = mass of an electron\n\nNote: The  transit time of an electron decreases with the increase in potential (V).\n\n4) What is an Electron Volt(eV)?\n\nOne Electron volt is the energy gained by the electron when it falls from one point to another point which has a potential difference of 1 volt. I.e. under potential difference of one volt, the electron moves from higher potential to lower potential, during this free fall in the electron field it gains an electron volt energy.\n\nIn other case it the energy required to move an electron in the potential difference of one volt. This is against to the electric field.\n\n1 electron volt  = 1.60217657 × 10-19 joules\n\n5) What is an Electric Field intensity(ε)?\n\nThe force experienced by an electric charge particle at a point by an electric field is called as Electric field intensity. It is denoted as ε and its unit is V/m(Volts/meter).", null, "6) What is an Ionization Potential?\n\nThe energy required to detach an loosely coupled electron from the influence of parent nucleus is called ionization potential.\n\n7) What is an electron spin?\n\nThe electron generally orbits around the parent nucleus and in addition to this it also rotates around itself like an earth. This intrinsic angular momentum property of en electron is called electron spin. There are only two direction of spins when it is subjected to a magnetic field i.e. either parallel or anti-parallel to the field.\n\n8) What is N type Semiconductor?\n\nWhen extra valance electrons are introduced in a pure semi-conductor material (silicon) by putting or injecting dopants or impurities, an N-type material is produced. The dopants are used to create an N-Type material are Group-V elements in the materials table.", null, "N-type semiconductor bond diagram\n\nGroup V elements: Arsenic, antimony, phosphorus.\n\nIn N-type semiconductor electrons are majority carriers and holes are minority carriers.\n\n9) What is P- Type Semiconductor?\n\nWhen a dopant from Group III elements from the elements table is introduced in to pure semiconductor, produces a P-Type semiconductor. The Group III elements have only 3 valance electrons in its outer orbit which there combines with four valance electrons semiconductor material (silicon). This results in missing of electron which creates a hole (P+) , or positive charge that can freely move around in the material.", null, "P-type semiconductor bond diagram\n\nGroup III elements: aluminum, boron, and gallium.\n\nIn P-Type semiconductor, holes are the majority carriers and electrons are the minority carriers.\n\n10) What are passive and active components?\n\nPassive components: The components which are passive in nature i.e. which can attenuate the input applied signal to a desired level. These are energy consumers and cannot boost the input signal. Resistors, capacitors and inductors are the examples of passive components.\n\nActive components: The components which plays an active role in the electronic circuit i.e. which can add energy to the input signal are called active components. These can amplify the signal to the desired level. Transistors, operational amplifiers are the examples of active components.\n\nWhat are conductors,insulators and semiconductors?\n\nConductors: The materials which permits the flow of charge carriers with higher conductivity are called conductors. In conductor, the valance band and conduction band overlaps with out any energy gap(EG). The conductivity of a conductor is normally  greater than 103. The examples of conductors are gold, silver, copper etc.\n\nInsulators: The materials which blocks the flow of electrons or which offers higher resistivity to the flow of electrons are called insulators. The energy  gap between valency and conduction bad in the insulators is greater than 1eV. The conductivity of insulator is less than 10-7 and the examples of insulators are rubber, glass, Teflon, mica etc.\n\nSemiconductors: The materials which are partially conductive and whose conductivity can be controlled are called semiconductors. These are most useful materials in electronic circuits. The energy gap Eg between valency and conduction bad of semiconductors are almost equal to 1eV. Silicon and Germanium are the best examples of semiconductors.\n\n#### What are the advantages of silicon over germanium?\n\nAdvantages:\n\n• Easily available in nature.\n• Cost is low compared to germanium\n• Higher temperature operating ranges compared to germanium.\n• Wider band gap than germinum\n• Less noisy compared to germanium\n• The material properties are accurately controlled\n\n#### What are the advantages and disadvantages of semiconductor over other devices?\n\nAdvantages:\n\n• These are smaller in size\n• Long life compared to vacuum tubes.\n• Operated on low DC power\n• Accuracy is high compared to vacuum tubes\n• Noise is less\n• Warm up is not needed in semiconductors.\n\nDisadvantages:\n\n• Cannot withstand for high power.\n• Frequency range of operation is low.\n• produces less output power.\n• Accuracy changes with the temperature.\n• Low ambient temperature.\n\n#### What is a mobility of a charge carrier?\n\nThe mobility of a charge carrier is the velocity per unit electri field. It is enoted as μ and its units are m2/v-sec.", null, "Note: As the temperature increases the mobility of charge carrier decreases because of the random motion of charge carriers.\n\n#### What is mass action law and law of electrical neutrality?\n\nMass Action law:  It states that in an intrinsic semiconductor the product of free electrons ‘n’ and free holes ‘p’ is constant. I.e.\n\nnp = ni2\n\nLaw of electrical neutrality: It states that when no voltage is applied to semiconductor, the magnitude of positive charge density must equals that of negative charge density.\n\nTotal positive charge density              = ND+p\n\nTotal negitive charge density              = NA+p\n\ni.e.\n\nND + P=NA + n\n\nWhere ND and NA are donor and acceptor densities.\n\nWhat is an Electric Potential?\n\nElectric potential of a system of charged particles at a point P is defined as work done in moving those charges from reference point to point P divided by total charge of system of particles. The reference point is generally taken to be infinity or some large chunk of neutral body such as earth.\n\n(Or)\n\nElectric potential at a point P is defined as the work done in moving unit coulomb charge from infinity point free of electric fields to point P. Electric potential is measured in terms of volts. It is also called absolute potential and is denoted by V. It is a scalar quantity. Electric potential of a point varies with the choice of reference point w.r.t which potential is measured.\n\nElectric potential Va = W/Σq\n\nWhat is Potential Difference?\n\nPotential difference between two points A and B is defined as work done in moving one coulomb charge from point A to B. Alternatively it is understood to be difference of absolute potential of point A and B. It is denoted by VAB. If VAand VB are the electric potentials at points A and B with respect to common reference point (mostly this is taken to be ground i.e. ground is assumed to be at zero potential) then the potential difference between points A and B is given by\n\nVAB = VA – VB\n\nPotential difference between points is invariant w.r.t the choice of reference point.\n\nWhat is a Transit time of an Electron between two electrodes?\n\nIt is the time taken for an electrode to travel from one electrode to another. Electron since a negatively charge particle travels from low potential to high potential in the direction opposite the electric field direction. Assume a uniform electric field E between two electrodes with spacing between them equal to dthen the transit time of electron is given by\n\nT = (", null, ")\n\nwhere m and q are mass and charge of electron.\n\nWhat is an Electron Volt eV?\n\nIt is the defined as the work done in moving an electron through a potential difference of one volt. Typically all the energies involving electron are specified in electron volts for simplicity and ease in analyzing. One electron volt is equal to 1.6*10-19 joules. It can be deduced as follows, the work done in moving a charged particle with charge q from point A to point B whose potentials w.r.t. ground are VA and VB is given by\n\nW = q*( VA – VB), with q=1.6*10-19 coulomb and VA – VB = 1 volt this reduces to 1.6*10-19 J which by definition is electron volt.\n\nWhat is Electric Field intensity (ε)?\n\nElectric field intensity at a point p in space is defined as the force acting on a unit charge particle with the assumption that the unit charge should not disturb the electric field itself but normally that is the case as one coulomb of charge includes 6.25*1018 charged particles with each particle carrying electronic charge i.e. 1.6*10-19 coulombs.\n\nSo the test charge used to measure the field should be as small as possible (Note: the smallest charge stable charge in nature is of electron’s).Hence theoretically electric field is defined as force acting on a test charge divided by the test charge itself as the charge tends to zero.\n\nE = F/q as q–>0 C\n\nIt is a vector quantity and always starts from positive charge and ends on negative charge.\n\nWhat is an Ionization Potential?\n\nThe minimum amount of energy required to remove an electron from an isolated atom or molecule is termed as Ionization potential. It is specified in units of electron volts. Example for Hydrogen atom the ionization potential is 13.6 eV.\n\nWhat is an electron spin?\n\nAn electron in an atom while revolving around the nuclei of atom rotates around itself. The spin of electron is assigned a quantum number known as spin quantum number which can take values of +1/2 and -1/2 for clockwise and anticlockwise rotation.\n\nWhat is an extrinsic semiconductor?\n\nIntrinsic semiconductor like pure silicon and germanium are characterized by high resistivity because of low free carrier charge density e.t.c. Hence in order to increase conductivity trivalent and pentavalent impurities are added. The added impurities are called dopants and the process is termed as doping. The resulting semiconductor after doping is called extrinsic semiconductor.\n\nWhat is N type Semiconductor?\n\nIf the dopant added to an intrinsic semiconductor is a pentavalent impurity such as phosphorous, Arsenic, Antimony the resulting semiconductor is termed as N-type conductor. The added impurity atoms will displace some of silicon atoms in the crystal lattice. Four of the valence electrons of dopant will occupy covalent bonds with silicon; fifth electron will be nominally free and can be used as carrier of current. The energy required to detach this fifth electron is of the order of 0.01eV for Germanium and 0.05eV for Silicon.\n\nThis can be understood alternatively as follows, due to replacement of some of the silicon atoms with pentavalent atoms from the crystal the energy band structure of the crystal lattice gets altered. The consequence of this alteration is the introduction of new allowable energy levels in the band structure in the forbidden gap close to conduction band. The energy required to excite the electrons occupying this new energy level to conduction band is of the order of 0.01 eV for Germanium and 0.05 for Silicon.\n\nWhat is P- Type Semiconductor?\n\nIf the dopant added to an intrinsic semiconductor is a trivalent impurity such as Boron, Indium, Gallium the resulting semiconductor is termed as P-type conductor. The added impurity atoms will displace some of silicon atoms in the crystal lattice. Three of the valence electrons of dopant will occupy covalent bonds with silicon; vacancy in the fourth bond constitutes a hole which effectively acts as positive charge carrier and can accept an electron.\n\nDue to replacement of some of the silicon atoms with trivalent atoms from the crystal the energy band structure of the crystal lattice gets altered. The consequence of this alteration is the introduction of new allowable energy levels in the band structure in the forbidden gap close to valence band. The energy required to excite the electrons from valence band to this new energy level is of the order of 0.01 eV for Ge and 0.05 for Si generating holes in valence band.\n\nWhat are passive and active elements?\n\nActive component is one which is capable of delivering energy independently. Examples are voltage and current sources, transistors, Opamp e.t.c. If the element is not capable of delivering energy then it is termed as Passive element.\n\nBohr’s model?\n\nBohr’s model is one of the proposed model of atom and was able to explain the emission and absorption spectra of hydrogen and single electron ions such as He2+. Some of the main postulates of Bohr’s atomic model are:\n\na) Electrons revolve around the nucleus of atom much like planets revolve around the sun in only definite circular paths called as orbits. Each orbit corresponds to a definite energy. The energy values are quantized and are allowed to posses only certain values.\n\nb) As long as the electron is in this path it will not absorb or emit radiation and the atom will be stable. Hence these are called stationary orbits.When an electron drops from higher energy orbit to lower energy orbit, the difference in the energy of those orbits will be emitted as radiation.", null, "where hxv is the energy of emitted photons.\n\nWhat is a conductor?\n\nConductor is a material which offers less resistance (ideally zero) for current flow. In conductors even a small applied field generates large currents. Most of the metals are conductors due to presence of loosely bound valence electrons. Conductance is a material property which quantifies how good the material fits as a conductor. It is measured in units of Siemens/metre. Ideally the conductance should be infinity for a perfect conductor (such is the case of super conductor). Silver is the best known conductor with conductance value of 6.30×107 S/m at 20 Deg C succeeded by copper 5.96×107 S/m which is widely used conductor due to its less cost compared to silver.\n\nWhat is the effect of Temperature on Metals ?\n\nIn metals the valence electrons are almost unbound and are available as carriers of current at room temperatures. An increase in the temperature increases the vibrations of crystal lattice. The increased lattice vibrations in turn increase the collisions between conducting electrons and crystal lattice .The result is the decrease in mobility and hence in conductivity.\n\nWhat is the effect of Temperature on Semiconductors resistance?\n\nANS:  As the temperature the density of electron and hole pairs increases which varies as T^3 *exp(-Ego/KT). Also mobility decreases with increasing temperature which varies as T^-m where m is from 1.5 to 3 due to increased collisions of electrons with positively charged lattice ions. On a whole the effect of former dominates the latter and hence the conductivity increases..\n\nWhat is Mobility?\n\nThe ratio of drift velocity of electron to the applied electric field is a constant for wide range of electric fields at constant temperature. The constant of proportionality is termed as Mobility denoted by µ.the units of mobility are m^2/sec/volt.\n\nMobility µ = Vd/E where Vd is drift velocity of electron and E is the applied electric field.\n\nWhat is Hall Effect?\n\nIf a specimen carrying a current is placed in transverse magnetic field an electric filed is induced in a direction perpendicular to both electric current and magnetic field. This phenomenon is known as Hall Effect. Let us consider a semiconductor bar of breadth ‘l’ in the in the direction of magnetic field and width ‘d’ carrying a uniform current ‘I’ travelling in X direction and placed in uniform magnetic field ‘B’ in Y direction. Assume the semiconductor current is composed of flow of charge carrier each carrying an electric charge ‘Q’, the Lorentz force on each charge carrier is Fl = Bo*Q*Vo where Vo is velocity of charge carrier and is given by Vo = I/ (l*d*Φ), Φ is charge concentration (or) charge density, the force due to electric field produced by displaced charge is Fe= E*Q. At equilibrium these two forces balances each other\n\nBo*Q*Vo = E*Q\n\nElectric field produced by displaced charges is equal to E = VH/d, where VH is hall voltage. Hence   VH = (Bo* I)/ (l*Φ), VH = (Bo*I*RH)/ l where RH is hall coefficient given by RH = (1/ Φ).\n\nWhat are the Applications of Hall Effect?\n\n1. Hall Effect is used in measuring magnetic fields (The hall voltage induced in a material is proportional to magnetic field provided the current, carrier density, breadths are kept constant).\n\n2. It is also used in Hall Effect multipliers which provide output proportional to the product of two signals. If the current is made proportional to one of the inputs and if B is linearly related to the second signal, then induced Hall voltage is proportional to the two inputs.\n\nWhy hole mobility is less compared to electron?\n\nANS: Mobility of charge carrier is inversely proportional to the mass of charge carrier. As the hole is having higher effective mass compared to electron for this reason hole mobility is less compared to electron mobility.\n\nRelation between intrinsic carrier concentration with temperature and band gap?\n\nIntrinsic concentration in a semiconductor is given by\n\nWhere ni is intrinsic concentration, A is a constant independent of temperature, T is absolute temperature in Kelvin, Ego is band gap at zero degree Kelvin, K is Boltzmann constant.\n\nWhat is mass action law?\n\nMass action law states that at equilibrium temperature the product of concentrations of free holes and electrons is equal to the square of intrinsic concentration at that temperature.\n\nNo*Po = Ni²,\n\nwhere No is concentration of electrons in doped semiconductor’s conduction band, Po is concentration of holes in valence band, Ni is intrinsic carrier concentration.\n\nExplain Electrical neutrality based on law of conservation of charge?\n\nLaw of conservation of charge states that electric charge can be neither created nor destroyed, total charge is always conserved. Accordingly in an N-type semiconductor the free electron density will increase due to excess charge carriers donated to the conduction band by dopant. After donating the excess electron the dopant atoms will be positively charged (similarly after accepting an electron from valence band acceptor impurity will be negatively charged). Obviously the positive charge of dopant atom exactly balances the excess electron charge by donor which is negative. This is termed as electric neutrality.\n\nWhat are the types of photo excitation?\n\nThere can be two types of photo excitations they are a) intrinsic excitations b) Extrinsic excitations\n\nIntrinsic excitations occur when an electron in valence band is excited by a high energy photon to conduction band. Alternatively a photon may excite an electron in donor level to conduction band or a valence band electron may go into acceptor state. Such excitations are termed as extrinsic excitations.\n\nWhat is ohms law?\n\nANS: Ohm’s law states that in a conductor current density is directly proportional to applied electric field i.e J α E where J is the current defined as ratio of current to the cross section area trough which the current is flowing and E is the electric field applied. The constant of proportionality is called conductance.\n\nHence ohm’s law is defined as J = σ*E.\n\nWhat is Fermi Dirac function?\n\nFermi Dirac function gives the probability that a energy level with energy ‘E’ will be occupied by an electron. It is given by\n\nWhere K is Boltzmann constant, E is the energy of a state in electron volts, Ef is Fermi level, and T is absolute temperature in Kelvin.\n\nWhat is Fermi level?\n\nFermi level is the maximum energy that any electron may possess at absolute zero (or) it represents the energy state with 50 percent probability of being filled if no forbidden band exists. The last statements can be explained as follows, at T = 0 K if E > Ef then (E- Ef)/ (KT) tends to positive infinity  tends to 0 or maximum energy that any electron may possess at absolute zero then (E- Ef) / (KT) tends to negative infinity  tends to 1. Hence the maximum energy that any electron may possess at absolute zero is Fermi level.\n\nNow assume some arbitrary temperature T above 0 Kelvin E = Ef then  = (1/2), 50 percent probability of getting filled if no forbidden gap exists.\n\nEquations of conductivity in metal and semiconductors?\n\nMetals conducts current by means of electrons, whereas semiconductors conducts current by two charge carrying particles of opposite sign one is electron(negative charge) and other is hole (positive charge).Therefore the equations for conductivity in metals and semiconductors are\n\nIn metals\n\nIn semiconductors\n\nWhere n is electron concentration, p is hole concentration, Q is electronic charge = 1.6*10^(-19),  µn is electron mobility, µp is hole mobility.\n\nWhat is drift velocity?\n\nIn a metal when a voltage is applied between its ends the electrons are accelerated by the voltage applied, while accelerating the electrons experience inelastic collisions with the ions. At each collision electron loses energy and a steady state condition is reached where a finite speed is attained which is known as drift velocity.\n\nWhat is the Variation of mobility with temperature?\n\nANS: As temperature increases at first mobility increases as T^1.5. At these range of temperatures impurity scattering dominates over lattice scattering. It reaches a maximum then mobility starts to decrease as T^-1.5 when lattice scattering dominates impurity scattering.", null, "Direct band gap and indirect band gap semi conductor?\n\nANS:  In direct band gap semiconductors the highest energy level in valence band and the lowest energy level in conduction band occur at the same momentum or wave number. After the Direct recombination of electron with hole in valence band, energy of the photon released will be exactly equal to difference in energy of lowest energy level in conduction band and highest energy level in valence band.\n\nNote: Momentum and direction of electrons will remain same.\n\nIn direct band gap semiconductors the highest energy level in valence band and the lowest energy level in conduction band do not occur at the same momentum or wave number. Since momentum has to be conserved a phonon which is a quantum of vibration energy should exist to assist recombination, hence such recombination of electron with hole are termed as indirect recombination. After the indirect recombination of electron with hole in valence band, energy of the photon released will be less (or) high compared to difference in energy of lowest energy level in conduction band and highest energy level in valence band. This is because some of energy is gained from phonon (or) lost to phonon in recombination process.\n\nNote: Momentum and direction of electron changes after recombination.", null, "Direct and Indirect band gap semiconductor\n\nWhat is the Variation of mobility with electric field?\n\nAt smaller electric fields mobility is constant. At higher electric fields mobility varies inversely with the electric field. At such higher fields the velocity of charge carriers will be constant and is of the order of 2*10^5 m/s. There exists a transition period between these two phases where mobility varies inversely to the square root of electric field.\n\nIntrinsic band diagram extrinsic band diagrams?", null, "Intrinsic semiconductor band diagram", null, "Band diagrams of N-type semiconductor", null, "Band diagrams of P-type semiconductor\n\nComparison of silicon vs. germanium?\n\n Property Silicon Germanium Atomic number 14 32 Ego, eV at 0 k 1.21 0.785 Ego, eV at 0 k 1.1 0.72 Intrinsic concentration at 300 K 1.5 * 1010 2.5 * 1013 Mobility(holes, electrons) at 300k 1300,500 3800,1800 Diffusion constants 34,13 99,47\n\nWhy silicon is preferred over germanium in electronic devices?\n\nSilicon is preferred over germanium for the following reasons:\n\n• Silicon is abundant in nature is available cheaply.\n• The electrical properties of germanium are more sensitive to temperature than silicon. Fine control of conduction properties of germanium is difficult compared to silicon\n• Silicon has wider band gap than germanium.\n• Silicon is Stable and strong material.\n\nHow bands occur in semiconductor?\n\nIn a crystal it is found out that the electronic energy levels of atoms gets altered. At interatomic distances the inner shell electros will not be affected much but the outer most energy levels are changed considerably. The outermost shells of all the atoms gets spreads out and forms a large number of discret but closely spaced energy levels called energy bands. In silicon energy band splits into two one is valence band and the other is conduction band.\n\nHow can you experimentally differentiate P –type SC and N-type Semi conductor?\n\nIf the semiconductor material is of N-type then the carriers will be electrons which are forced towards side 2 by the Lorentz force exerted by the magnetic filed B. Hence the induced hall voltage of side 2 measured with respect to 1(the opposite face to 2) will be negative (Recall that the electrons are negative charge carriers).", null, "If the semiconductor material is of P-type then the carriers will be holes which are forced towards side 2 by the Lorentz force exerted by the magnetic filed B (assuming the flow of current is in the same direction as electrons, conventional current is in the direction opposite to the flow of electrons). Hence the induced hall voltage of side21 measured with respect to 1 (the opposite face to 2) will be positive (Recall that the holes are positive charge carriers).\n\nWhat is photo electric effect?\n\nWhen light falls on metal electrons are emitted from the surface of the metal. This phenomena is termed as photo electric effect. The energy the impinging photons (light consists of tiny mass less particles called photons which carry energy of h*v where h is Planck’s constant and v is frequency of light) should be at least equal to work function (characteristic property of metal). If the impinging photon on metal is having energy greater than the work function of metal the extra energy will appear as kinetic energy of ejected electron. Accordingly we can write\n\nh*v = Wf + K.E\n\nWhere Wf is the work function of metal, K.E is the kinetic energy of ejected electron.\n\nWhat is florescence?\n\nCertain substances after absorbing some form of incident electromagnetic radiation releases the absorbed energy in chunks. The emitted radiation will be having lesser energy or frequency compared to the incident radiation. This is termed Fluorescence.\n\nWhat is the motion of charge particle in electric and magnetic field?\n\nIn electrostatic field alone electron moves in straight line. The electron’s travel is in the direction opposite to the direction of electric field.\n\nIf an electron enters a magneto static field alone with non zero velocity electron moves in circular path. The electron motion will be in a plane perpendicular to the direction of magnetic field.\n\nIf an electron enters a combined electric and magnetic field with non zero velocity electron travels in a helical path whose patch vary with time.", null, "Motion of electron in combined Electric and Magnetic fields\n\nWhat is thermistor and sensistor?\n\nIn semiconductors as temperature increases conductivity increases i.e. it can exhibit positive temperature coefficient of conductivity, this property finds applications in control devices, as a thermal relay e.t.c. Such a semiconductor is called as thermistor.\n\nSensistor is a heavily doped semiconductor which exhibits positive temperature coefficient of resistance.\n\nWhat is photo ionization?\n\nWhen light falls on an atom it will eject one or more electrons (depending on energy of photons) from it forming ions. This process is called Photo ionization. Photo ionization and photo electric effects are one and same process which essentially involves interaction of matter with electromagnetic radiation. The term Photo ionization is used with regard to isolated or non interacting atoms whereas photo electric effect is used with regard to metals." ]
[ null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_transit-time-of-an-electron.gif", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_electric-field-intensity-formula.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_n-type-semiconductor-bond-diagram.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_p-type-semiconductor-bond-diagram.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_mobility-of-a-charge-carrier.gif", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_transit-time-of-an-electron-between-two-electrodes.gif", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_bohrs-model.gif", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_variation-of-mobility-with-temperature.jpg", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_direct-and-indirect-band-gap-semiconductor.jpg", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_intrinsic-semiconductor-band-diagram.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_band-diagrams-of-n-type-semiconductor.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_band-diagrams-of-p-type-semiconductor.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_semiconductor-material-is-of-n-type.png", null, "https://engineeringtutorial.com/wp-content/uploads/2016/04/engineeringtutorial.com_basic-electronics_motion-of-electron-in-combined-electric-and-magnetic-fields.jpg", null ]
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https://thecollegepanda.com/ultimate-sat-math-calculator-program-ti-84/
[ "# The Ultimate TI-84 Calculator Program for SAT Math\n\nI introduce and cover the features of The College Panda Calculator Program in the TI-84 SAT Math video series. If you haven't seen it already, go check that out first. I go through the following:", null, "• Calculator Shortcuts and Basics\n• Evaluating Expressions\n• Graphing\n• The College Panda Program (introduction)\n• The Rest of The College Panda Program\n\nWatch the video series first.\n\n### The College Panda Calculator Program\n\nThis program was specifically designed for the SAT—all its features were created with past questions in mind. We didn't include anything that doesn't help you on the exam. It's the closest thing to a cheat code for the SAT.\n\nWhen you run it, the first thing you'll see is the main menu.", null, "The program consists of 5 main components:\n\n• Fundamentals: basic math operations you may encounter on the exam\n• Lines: slope, $$x$$-intercept, $$y$$-intercept, standard form\n• Systems of Two Equations: solves systems of 2 equations in standard form\n• Quadratics: quadratic formula (roots), vertex form, vertex, $$y$$-intercept, discriminant\n• Circles: arc length, area of a sector, equation of a circle, center, radius, whether a point is inside a circle\n\n#### Fundamentals", null, "Features:\n\n• Pythagorean theorem\n• Percent change\n• Distance between 2 points\n• Midpoint\n\n#### Lines", null, "", null, "Input any of the following: 2 points A point and a slope Standard form of a line Slope-intercept form of a line to get all of the following: The slope-intercept form of the line The standard form of the line The slope of the line The slope of a perpendicular line The $$x$$-intercept of the line The $$y$$-intercept of the line\n\n#### Systems of Two Equations", null, "", null, "• Solves any system of two equations expressed in $$ax + by = c$$ and $$dx + ey = f$$ form\n• Indicates whether the system has infinite solutions\n• Indicates whether the system has no solutions", null, "", null, "Input any of the following: Standard form of a quadratic: $$ax^2 + bx + c$$ Vertex form of a quadratic: $$a(x + b)^2 + c$$ Factored form of a quadratic: $$a(x + b)(x + c)$$ to get all of the following: The roots/solutions (does the quadratic formula for you) Vertex form (completes the square for you) The vertex The discriminant The $$y$$-intercept\n\n#### Circles", null, "", null, "", null, "", null, "• Arc length\n• Area of a sector\n• Equation of a circle from a raw equation ($$x^2 + y^2 + ax + by + c = 0$$)\n• Equation of a circle from its center and radius\n• Equation of a circle from the endpoints of a diameter\n• The center and radius of a circle from its equation\n• Checks whether a point is inside or outside a circle in the coordinate plane\n\n### Companion Calculator Workbook\n\nIt's not enough to just have a program on your calculator. You need to know how and when to use it. This workbook, which contains exercises based on past SAT questions, will teach you how to use the program and for which question types.", null, "Chapters:\n\n1. The Basics (based on part 1 of the video series)\n2. Evaluating Expressions (based on part 2 of the video series)\n3. Graphing (based on part 3 of the video series)\n4. Systems of Equations (based on part 4 of the video series)\n5. Lines (based on part 5 of the video series)\n6. Fundamental Programs (based on part 6 of the video series)\n7. Quadratics (based on part 6 of the video series)\n8. Circles (based on part 6 of the video series)" ]
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http://oushaobin.cn/archives/52.html
[ "# Problem A. GBus count\n\n## Problem\n\nThere exists a straight line along which cities are built.\n\nEach city is given a number starting from 1. So if there are 10 cities, city 1 has a number 1, city 2 has a number 2,... city 10 has a number 10.\n\nDifferent buses (named GBus) operate within different cities, covering all the cities along the way. The cities covered by a GBus are represented as 'first_city_number last_city_number' So, if a GBus covers cities 1 to 10 inclusive, the cities covered by it are represented as '1 10'\n\nWe are given the cities covered by all the GBuses. We need to find out how many GBuses go through a particular city.\n\n## Input\n\nThe first line contains the number of test cases (T), after which T cases follow each separated from the next with a blank line.\nFor each test case,\nThe first line contains the number of GBuses.(N)\nSecond line contains the cities covered by them in the form\na1 b1 a2 b2 a3 b3...an bn\nwhere GBus1 covers cities numbered from a1 to b1, GBus2 covers cities numbered from a2 to b2, GBus3 covers cities numbered from a3 to b3, upto N GBuses.\nNext line contains the number of cities for which GBus count needs to be determined (P).\nThe below P lines contain different city numbers.\nOutput\nFor each test case, output one line containing \"Case #Ti:\" followed by P numbers corresponding to the number of cities each of those P GBuses goes through.\n\n## Limits\n\n1 <= T <= 10\nai and bi will always be integers.\n\n## Small dataset\n\n1 <= N <= 50\n1 <= ai <= 500, 1 <= bi <= 500\n1 <= P <= 50\n\n\n## Large dataset\n\n1 <= N <= 500\n1 <= ai <= 5000, 1 <= bi <= 5000\n1 <= P <= 500\n\n\n## Sample\n\n### Input\n\n\n\n2\n4\n15 25 30 35 45 50 10 20\n2\n15\n25\n\n10\n10 15 5 12 40 55 1 10 25 35 45 50 20 28 27 35 15 40 4 5\n3\n5\n10\n27\n\n\n### Output\n\nCase #1: 2 1\nCase #2: 3 3 4\n\n\n### Explanation for case 1:\n\n2 GBuses go through city 15 (GBus1 [15 25] and GBus4 [10 20])\n1 GBus goes through city 25 (GBus1 [15 25])\n\n## Code (Java)\n\nimport java.io.BufferedReader;\nimport java.io.FileInputStream;\nimport java.io.FileNotFoundException;\nimport java.io.FileOutputStream;\nimport java.io.PrintStream;\nimport java.util.Arrays;\nimport java.util.Scanner;\n\npublic class GBusCount {\n\npublic static void main(String[] args) throws FileNotFoundException {\nFileInputStream fis = new FileInputStream(path+\"A-large-practice.in\");\nPrintStream out = new PrintStream(new FileOutputStream(path+\"A-large-practice.out\"));\nSystem.setIn(fis);\nSystem.setOut(out);\nint total = in.nextInt();\nint testCase = 1;\nwhile( total >= testCase ) {\nint n = in.nextInt();\nint curr = 0;\nint[][] pair = new int;\nwhile(curr<n) {\npair[curr] = in.nextInt();\npair[curr] = in.nextInt();\ncurr ++;\n}\nint p = in.nextInt();\nSystem.out.print(\"Case #\"+testCase+\":\");\nfor(int i = 0 ; i < p ; i ++ ) {\nint city = in.nextInt();\nint count = 0;\nfor(int j = 0 ; j < n ; j ++ ) {\nif( city >= pair[j] && city <= pair[j] ) {\ncount ++;\n}\n}\nSystem.out.print(\" \"+count);\n}\nSystem.out.println();\ntestCase ++;\n}\n\n}\n\n}", null, "", null, "" ]
[ null, "http://b.bshare.cn/barCode", null, "http://oushaobin.cn/archives/52.html", null ]
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https://spreg-wei.readthedocs.io/en/latest/generated/spreg.r2.html
[ "spreg.r2¶\n\nspreg.r2(reg)[source]\n\nCalculates the R^2 value for the regression. [Gre03]\n\nParameters\nregregression object\n\noutput instance from a regression model\n\nReturns\nr2_resultfloat\n\nvalue of the coefficient of determination for the regression\n\nExamples\n\n>>> import numpy as np\n>>> import libpysal\n>>> from libpysal import examples\n>>> import spreg\n>>> from spreg import OLS\n\nRead the DBF associated with the Columbus data.\n\n>>> db = libpysal.io.open(examples.get_path(\"columbus.dbf\"),\"r\")\n\nCreate the dependent variable vector.\n\n>>> y = np.array(db.by_col(\"CRIME\"))\n>>> y = np.reshape(y, (49,1))\n\nCreate the matrix of independent variables.\n\n>>> X = []\n>>> X.append(db.by_col(\"INC\"))\n>>> X.append(db.by_col(\"HOVAL\"))\n>>> X = np.array(X).T\n\nRun an OLS regression.\n\n>>> reg = OLS(y,X)\n\nCalculate the R^2 value for the regression.\n\n>>> testresult = spreg.r2(reg)\n\nPrint the result.\n\n>>> print(\"%1.8f\"%testresult)\n0.55240404" ]
[ null ]
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https://www.nayuki.io/page/next-lexicographical-permutation-algorithm
[ "#", null, "Next lexicographical permutation algorithm\n\n## Introduction\n\nSuppose we have a finite sequence of numbers like (0, 3, 3, 5, 8), and want to generate all its permutations. What is the best way to do so?\n\nThe naive way would be to take a top-down, recursive approach. We could pick the first element, then recurse and pick the second element from the remaining ones, and so on. But this method is tricky because it involves recursion, stack storage, and skipping over duplicate values. Moreover, if we insist on manipulating the sequence in place (without producing temporary arrays), then it’s difficult to generate the permutations in lexicographical order.\n\nIt turns out that the best approach to generating all the permutations is to start at the lowest permutation, and repeatedly compute the next permutation in place. The simple and fast algorithm for performing this is what will be described on this page. We will use concrete examples to illustrate the reasoning behind each step of the algorithm.\n\n## The algorithm\n\nWe will use the sequence (0, 1, 2, 5, 3, 3, 0) as a running example.\n\nThe key observation in this algorithm is that when we want to compute the next permutation, we must “increase” the sequence as little as possible. Just like when we count up using numbers, we try to modify the rightmost elements and leave the left side unchanged. For example, there is no need to change the first element from 0 to 1, because by changing the prefix from (0, 1) to (0, 2) we get an even closer next permutation. In fact, there is no need to change the second element either, which brings us to the next point.\n\nFirstly, identify the longest suffix that is non-increasing (i.e. weakly decreasing). In our example, the suffix with this property is (5, 3, 3, 0). This suffix is already the highest permutation, so we can’t make a next permutation just by modifying it – we need to modify some element(s) to the left of it. (Note that we can identify this suffix in Θ(n) time by scanning the sequence from right to left. Also note that such a suffix has at least one element, because a single element substring is trivially non-increasing.)\n\nSecondly, look at the element immediately to the left of the suffix (in the example it’s 2) and call it the pivot. (If there is no such element – i.e. the entire sequence is non-increasing – then this is already the last permutation.) The pivot is necessarily less than the head of the suffix (in the example it’s 5). So some element in the suffix is greater than the pivot. If we swap the pivot with the smallest element in the suffix that is greater than the pivot, then the prefix is minimally increased. (The prefix is everything in the sequence except the suffix.) In the example, we end up with the new prefix (0, 1, 3) and new suffix (5, 3, 2, 0). (Note that if the suffix has multiple copies of the new pivot, we should take the rightmost copy – this plays into the next step.)\n\nFinally, we sort the suffix in non-decreasing (i.e. weakly increasing) order because we increased the prefix, so we want to make the new suffix as low as possible. In fact, we can avoid sorting and simply reverse the suffix, because the replaced element respects the weakly decreasing order. Thus we obtain the sequence (0, 1, 3, 0, 2, 3, 5), which is the next permutation that we wanted to compute.\n\nCondensed mathematical description:\n\n1. Find largest index i such that array[i − 1] < array[i].\n(If no such i exists, then this is already the last permutation.)\n\n2. Find largest index j such that j ≥ i and array[j] > array[i − 1].\n\n3. Swap array[j] and array[i − 1].\n\n4. Reverse the suffix starting at array[i].\n\nOverall, this algorithm to compute the next lexicographical permutation has Θ(n) worst-case time complexity, and Θ(1) space complexity. Thus, computing every permutation requires Θ(n! × n) run time.\n\nNow if you truly understand the algorithm, here’s an extension exercise for you: Design the algorithm for stepping backward to the previous lexicographical permutation. (Spoilers at the bottom.)\n\n## Annotated code (Java)\n\n```boolean nextPermutation(int[] array) {\n// Find longest non-increasing suffix\nint i = array.length - 1;\nwhile (i > 0 && array[i - 1] >= array[i])\ni--;\n// Now i is the head index of the suffix\n\n// Are we at the last permutation already?\nif (i <= 0)\nreturn false;\n\n// Let array[i - 1] be the pivot\n// Find rightmost element greater than the pivot\nint j = array.length - 1;\nwhile (array[j] <= array[i - 1])\nj--;\n// Now the value array[j] will become the new pivot\n// Assertion: j >= i\n\n// Swap the pivot with j\nint temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse the suffix\nj = array.length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\n\n// Successfully computed the next permutation\nreturn true;\n}```\n\nThis code can be mechanically translated to a programming language of your choice, with minimal understanding of the algorithm. (Note that in Java, arrays are indexed from 0.)\n\n## Example usages\n\nPrint all the permutations of (0, 1, 1, 1, 4):\n\n```int[] array = {0, 1, 1, 1, 4};\ndo { // Must start at lowest permutation\nSystem.out.println(Arrays.toString(array));\n} while (nextPermutation(array));\n```\n\nProject Euler #24: Find the millionth (1-based) permutation of (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). My Java solution: p024.java\n\nProject Euler #41: Find the largest prime number whose base-10 digits are a permutation of (1, 2, 3, 4, 5, 6, 7, 8, 9). My Java solution: p041.java\n\nLeetCode #31: Next Permutation.\n\n## Source code", null, "License: Nayuki hereby places all code on this page regarding the next permutation algorithm in the public domain. Retaining the credit notice containing the author and URL is encouraged but not required.\n\n## Code previews\n\n### Python\n\n```#\n# Computes the next lexicographical permutation of the specified\n# list in place, returning whether a next permutation existed.\n# (Returns False when the argument is already the last possible\n# permutation.)\n#\ndef next_permutation(arr):\n# Find non-increasing suffix\ni = len(arr) - 1\nwhile i > 0 and arr[i - 1] >= arr[i]:\ni -= 1\nif i <= 0:\nreturn False\n\n# Find successor to pivot\nj = len(arr) - 1\nwhile arr[j] <= arr[i - 1]:\nj -= 1\narr[i - 1], arr[j] = arr[j], arr[i - 1]\n\n# Reverse suffix\narr[i : ] = arr[len(arr) - 1 : i - 1 : -1]\nreturn True\n\n# Example:\n# arr = [0, 1, 0]\n# next_permutation(arr) (returns True)\n# arr has been modified to be [1, 0, 0]```\n\n### JavaScript\n\n```/*\n* Computes the next lexicographical permutation of the specified\n* array of numbers in place, returning whether a next permutation\n* existed. (Returns false when the argument is already the last\n* possible permutation.)\n*/\nfunction nextPermutation(array) {\n// Find non-increasing suffix\nvar i = array.length - 1;\nwhile (i > 0 && array[i - 1] >= array[i])\ni--;\nif (i <= 0)\nreturn false;\n\n// Find successor to pivot\nvar j = array.length - 1;\nwhile (array[j] <= array[i - 1])\nj--;\nvar temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse suffix\nj = array.length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\nreturn true;\n}\n\n// Example:\n// arr = [0, 1, 0];\n// nextPermutation(arr); (returns true)\n// arr has been modified to be [1, 0, 0]```\n\n### Java\n\n```/**\n* Computes the next lexicographical permutation of the specified\n* array of integers in place, returning whether a next permutation\n* existed. (Returns {@code false} when the argument is already the\n* last possible permutation.)\n* @param array the array of integers to permute\n* @return whether the array was permuted to the next permutation\n*/\npublic static boolean nextPermutation(int[] array) {\n// Find non-increasing suffix\nint i = array.length - 1;\nwhile (i > 0 && array[i - 1] >= array[i])\ni--;\nif (i <= 0)\nreturn false;\n\n// Find successor to pivot\nint j = array.length - 1;\nwhile (array[j] <= array[i - 1])\nj--;\nint temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse suffix\nj = array.length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\nreturn true;\n}```\n\n### C#\n\n```/*\n* Computes the next lexicographical permutation of the given array\n* of integers in place, returning whether a next permutation existed.\n* (Returns false when the argument is already the last possible permutation.)\n*/\npublic static bool NextPermutation(int[] array) {\n// Find non-increasing suffix\nint i = array.Length - 1;\nwhile (i > 0 && array[i - 1] >= array[i])\ni--;\nif (i <= 0)\nreturn false;\n\n// Find successor to pivot\nint j = array.Length - 1;\nwhile (array[j] <= array[i - 1])\nj--;\nint temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse suffix\nj = array.Length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\nreturn true;\n}```\n\n### C++\n\n```#include <algorithm>\n#include <vector>\n\n/*\n* Computes the next lexicographical permutation of the specified vector\n* of values in place, returning whether a next permutation existed.\n* (Returns false when the argument is already the last possible permutation.)\n*/\ntemplate <typename T>\nbool nextPermutation(std::vector<T> &vec) {\n// Find non-increasing suffix\nif (vec.size() == 0)\nreturn false;\ntypename std::vector<T>::iterator i = vec.end() - 1;\nwhile (i > vec.begin() && *(i - 1) >= *i)\n--i;\nif (i == vec.begin())\nreturn false;\n\n// Find successor to pivot\ntypename std::vector<T>::iterator j = vec.end() - 1;\nwhile (*j <= *(i - 1))\n--j;\nstd::iter_swap(i - 1, j);\n\n// Reverse suffix\nstd::reverse(i, vec.end());\nreturn true;\n}```\n\n### C\n\n```#include <stdbool.h>\n#include <stddef.h>\n\n/*\n* Computes the next lexicographical permutation of the specified\n* array of integers in place, returning a Boolean to indicate\n* whether a next permutation existed. (Returns false when the\n* argument is already the last possible permutation.)\n*/\nbool next_permutation(int array[], size_t length) {\n// Find non-increasing suffix\nif (length == 0)\nreturn false;\nsize_t i = length - 1;\nwhile (i > 0 && array[i - 1] >= array[i])\ni--;\nif (i == 0)\nreturn false;\n\n// Find successor to pivot\nsize_t j = length - 1;\nwhile (array[j] <= array[i - 1])\nj--;\nint temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse suffix\nj = length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\nreturn true;\n}```\n\n### Rust\n\n```fn next_permutation<T: std::cmp::Ord>(array: &mut [T]) -> bool {\n// Find non-increasing suffix\nif array.len() == 0 {\nreturn false;\n}\nlet mut i: usize = array.len() - 1;\nwhile i > 0 && array[i - 1] >= array[i] {\ni -= 1;\n}\nif i == 0 {\nreturn false;\n}\n\n// Find successor to pivot\nlet mut j: usize = array.len() - 1;\nwhile array[j] <= array[i - 1] {\nj -= 1;\n}\narray.swap(i - 1, j);\n\n// Reverse suffix\narray[i .. ].reverse();\ntrue\n}```\n\n```{-\n- Computes the next lexicographical permutation of the specified\n- finite list of numbers. Returns Nothing if the argument is\n-}\nnextPermutation :: Ord a => [a] -> Maybe [a]\nnextPermutation xs =\nlet\nlen = length xs\n-- Reverse of longest non-increasing suffix\nrevSuffix = findPrefix (reverse xs)\nsuffixLen = length revSuffix\nprefixMinusPivot = take (len - suffixLen - 1) xs\npivot = xs !! (len - suffixLen - 1)\nsuffixHead = takeWhile (<= pivot) revSuffix\nnewPivot : suffixTail = drop (length suffixHead) revSuffix\nnewSuffix = suffixHead ++ (pivot : suffixTail)\nin\nif suffixLen == len then Nothing else\nJust (prefixMinusPivot ++ (newPivot : newSuffix))\nwhere\nfindPrefix [] = []\nfindPrefix (x:xs) = x : (if xs /= [] && x <= (head xs)\nthen (findPrefix xs) else [])\n\n-- Example: nextPermutation [0, 1, 0] -> Just [1, 0, 0]```\n\n### Mathematica\n\n```(*\n* Computes the next lexicographical permutation of the specified\n* vector of numbers. Returns the pair {Boolean, permuted vector},\n* where the Boolean value indicates whether a next permutation\n* existed or not.\n*)\nNextPermutation[arr_] := Module[{i, j},\n(* Find non-increasing suffix *)\nFor[i = Length[arr], i > 1 && arr[[i - 1]] >= arr[[i]], i--];\nIf[i <= 1,\nReturn[{False, arr}]];\n(* Find successor to pivot *)\nFor[j = Length[arr], arr[[j]] <= arr[[i - 1]], j--];\n(* Return new list with indexes i and j swapped,\nfollowed by the suffix reversed *)\n{True, Join[Take[arr, i - 2], {arr[[j]]},\nReverse[Drop[ReplacePart[arr, arr[[i - 1]], j], i - 1]]]}]\n\n(* Example: NextPermutation[{0, 1, 0}] -> {True, {1, 0, 0}} *)```\n\n### MATLAB\n\n```function result = nextperm(arr)\n% Computes and returns the next lexicographical permutation of the given vector,\n% or returns [] when the argument is already the last possible permutation.\n% Example: nextperm([0, 1, 0]) -> [1, 0, 0]\n\n% Find non-increasing suffix\ni = length(arr);\nwhile i > 1 && arr(i - 1) >= arr(i)\ni = i - 1;\nend\nif i <= 1\nresult = [];\nreturn;\nend\n\n% Find successor to pivot\nresult = arr;\nj = length(result);\nwhile result(j) <= result(i - 1)\nj = j - 1;\nend\ntemp = result(i - 1);\nresult(i - 1) = result(j);\nresult(j) = temp;\n\n% Reverse suffix\nresult(i : end) = result(end : -1 : i);\nend```\n\n## Bonus: Previous permutation (Java)\n\n```boolean previousPermutation(int[] array) {\n// Find longest non-decreasing suffix\nint i = array.length - 1;\nwhile (i > 0 && array[i - 1] <= array[i])\ni--;\n// Now i is the head index of the suffix\n\n// Are we at the first permutation already?\nif (i <= 0)\nreturn false;\n\n// Let array[i - 1] be the pivot\n// Find rightmost element less than the pivot\nint j = array.length - 1;\nwhile (array[j] >= array[i - 1])\nj--;\n// Now the value array[j] will become the new pivot\n// Assertion: j >= i\n\n// Swap the pivot with j\nint temp = array[i - 1];\narray[i - 1] = array[j];\narray[j] = temp;\n\n// Reverse the suffix\nj = array.length - 1;\nwhile (i < j) {\ntemp = array[i];\narray[i] = array[j];\narray[j] = temp;\ni++;\nj--;\n}\n\n// Successfully computed the previous permutation\nreturn true;\n}```" ]
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https://www.edplace.com/blog/home_learning/multiplying-and-dividing-by-multiples-of-10
[ "", null, "# EdPlace's Year 6 Home Learning Maths Lesson: Multiplying & Dividing by Multiples of 10\n\nLooking for short lessons to keep your child engaged and learning? Our experienced team of teachers have created English, maths and science lessons for the home, so your child can learn no matter where they are.  And, as all activities are self-marked, you really can encourage your child to be an independent learner. Get them started on the lesson below and then jump into our teacher-created activities to practice what they've learnt. We've recommended five to ensure they feel secure in their knowledge - 5-a-day helps keeps the learning loss at bay (or so we think!).\n\nAre they keen to start practising straight away? Head to the bottom of the page to find the activities.\n\nNow...onto the lesson!\n\nKey Stage 2 Statutory Requirements for Maths\nYear 6 students should be taught to multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places.\n\n# Multiplying & Dividing by Multiples of 10\n\nWhen multiplying any number (whole or decimal) by multiples of 10, there is an easy way to do it, which doesn’t involve using the ‘bus stop’ method! You just need to write the digits out and move them left or right across the place value columns.\n\nEvery single lesson taught in school has an objective that each child should achieve. We are confident that by the end of reading this you and your child will:\n\n1) Understand how to multiply and divide numbers by 10, 100 and 1,000\n\n2) Apply this understanding to independent work\n\n3) Explain how they completed their work back to you!\n\n## Step 1 - Understand key terminology\n\nPlace value – the value of each digit in a number.\n\nDecimal point – the dot after the ones column (see Step 2 for an example) – it’s important to remember this because it shows that the digit(s) after the decimal point are only part of a whole number.\n\nDecimal place – one of the columns after the decimal point – one decimal place is the tenths column, two decimal places is the hundredths column, three decimal places is the thousandths column (see Step 2 for an example).\n\nA place holder is the number 0 to show there is nothing in that column.\n\n## Step 2 - Check your child's prior understanding!\n\nYour child will need to have a good understanding of place value and the names of the columns:", null, "## Step 3 - Introducing the new skill...\n\nWhen we multiply, the number gets larger. Therefore, the digits move to the left.\n\nWhen we multiply by 10, the digits move one space to the left (because there is one 0 in 10).", null, "37.5 &times; 10 = 375\n\nWhen we multiply by 100, the digits move two spaces to the left (because there are two 0s in 100).", null, "29.05 &times; 100 = 2905\n\nWhen we multiply by 1,000 the digits move three spaces to the left (because there are three 0s in 1000).", null, "54.87 &times; 1,000 = 54,870\n\nWe need to put a zero in the ones column as a place holder, to show that there are no ones.\n\nThe decimal point must always stay in the same place. It does not move. The digits move.\n\nWhen we divide, the number gets smaller. Therefore, the digits move to the right.\n\nWhen we divide by 10, the digits move one space to the right (because there is one 0 in 10).", null, "27.01 ÷ 10 = 2.701\n\nWhen we divide by 100, the digits move two spaces to the right (because there are two 0s in 100).", null, "16.8 ÷ 100 = 0.168\n\nDon’t forget to put a place holder in the ones column.\n\nWhen we divide by 1,000 the digits move three spaces to the right (because there are three 0s in 1000).", null, "16 ÷ 1,000 = 0.016\n\nThis time, you need two place holders to show there are no ones or tenths.\n\n## Step 4 - Putting it into practise...\n\nNow have a go at these examples together:\n\na) 35.02 ÷ 10\n\nb) 702 &times; 100\n\nChallenge questions:\n\nc) 8.48 &times; 1,000\n\nd) 6.01 ÷ 100\n\n## Step 5 - Activity time!\n\nNow that you’ve covered how to multiply and divide by 10, 100 and 1,000 together, why not put this to the test and assign your child the following activities in this order? All activities are created by teachers and automatically marked. Plus, with an EdPlace subscription, we can automatically progress your child at a level that's right for them. Sending you progress reports along the way so you can track and measure progress, together - brilliant!" ]
[ null, "https://eplblog.s3.amazonaws.com/demo/1588504044_Facebook_creative_V1.jpg", null, "https://lh5.googleusercontent.com/JoP_vUiyR_fZKUGwOc-GFD95NE9i7WDq6qvE8jfEp8m7GhdyYSNC5wv0ikXvXkZ6dnqgRMwxi465_WnkEOCaomzSrYU9CUBdoe1J1i22iBhWLOxn7gWlioOwp2uIiDF1Kbt-2w", null, "https://lh6.googleusercontent.com/Y-iIw6BWtCJX6dg52LNAd0SBVfaKbpLlSygOTxJWcHrNPqL23-O4VXWQ6kIjUelWyyWQnKQkhso3IP9eWpQg4xrKi_CejHV_Ky7vNBX-iw7w6Sn1fU-5uJVkjINt4AgNXRsZMA", null, "https://lh5.googleusercontent.com/Fk0fFQRwPuDi0TFzS5BOiyTct0dEE8fUfmcTeKgrOCeU2kO06hDKpP3S0lWpxviclGONbRcZRv11LYu0n2Hl2HyARNFEwrZgY47wReWEbPMzhZ3v4PxF4XDu7Q0lRtjtDIfHcg", null, "https://lh3.googleusercontent.com/Xi189aZixCHuvYEaTgPUlyGd_SyUHBP17Mg7s0rAGj9jI3fpBKaFHxSlhVaDOj0IJeCZ3htLporr3eLS5XhKzvELM7YP8wcC8xS02iwWSn2_jQOwRoRgOT1oqhDPkMUJ0JyFww", null, "https://lh6.googleusercontent.com/Isient2ZGsfhB3QX60pMZGAR_WldFDwcjeCQMRuWl6RXE7VybWF6VktU6WDUmD1j0tqXygqqcJ3Az7v7mHbn1KFq0beonX-pyRRlLzR15CDGMbpGH3g-owWIxe1BvCv0IgFG0g", null, "https://lh4.googleusercontent.com/HGk6oEy4LBaPwWu5AveQbhJMtuKikmLxMCU8YVsjMt65zciMOdTRaFHjG4cHb1fIdqPwqUQDs3-9W6NpPRx75m69Ya3GkUKLTj8vVv2tTxLb5-BWYqWH7mZTU99p-Zv4fc6h_g", null, "https://lh5.googleusercontent.com/fsJxb56y825SnS7v1HbjFTijHsRYz_0HBbwjLXTn7rVrTmXLaPHfSDcDZvueslC0NVKRrK36fYlVAg0qCIJe_g4eMqhIlMVb3bE55SsVmRe4K8osKvTm1TfyiJZ4OhHLIuO6cA", null ]
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https://www.jiskha.com/questions/1534525/how-to-write-y-2-0-in-standard-form
[ "# Algebra\n\nHow to write |y|-2=0 in standard form?\n\n1. 👍\n2. 👎\n3. 👁\n1. looks pretty standard to me.\nPerhaps you mean:\n|y|-2=0\n|y| = 2\ny = 2 or y = -2\n\n1. 👍\n2. 👎\n\n## Similar Questions\n\n1.Write the number in standard form: 7.1x10^4 A)710 B)7,100 C)71,000 D)710,000*** 2.Write the number in standard form: 5.01x10^-3 A)5,010 B)0.501 C)0.0501 D)0.00501*** 3.Multiply (2.0x10^4)(3.0x10^3)=? A)6.0x10^7*** B)6.0x10^12\n\nGiven A(-4,-2), B(44), and C(18,-8, answer the following questions Write the equations of the line containing the altitude the passes through B in standard form. Write the equation of the line containing the median that passes\n\n3. ### Math\n\nIn an isosceles triangle, the perimeter is 8 more than 2 times on of the legs. If the perimeter is 28 in, find the length of the base. A. 16 in B. 18 in C. 10 in D. 8 in Given triangle ABC with A(-3, 2), B(-1, -4), and C(4, 1),\n\n4. ### Math\n\nwrite 2.3 x 10^3 in standard form\n\n1. ### Algebra\n\nWrite each in Standard Form and Slope-Intercept Form: 4x = 2y -10\n\n2. ### Math\n\n1. Write 6 x 10^4 in standard form. A. 600 B. 6,000 C. 60,000 D. 600,000 2. write 2.3 x 10^3 in standard form. A. 230 B. 2,300 C. 23,000 D. 230,000 3. Write 968,000 in scientific notation. A. 968 x 10^3 B. 9.68 x 10^2 C. 9.68 x\n\nWrite 5.62*10^5 in standard form\n\n4. ### Math\n\nWrite an equation in slope-intercept form, point-slope, or standard form for the line with the given information. Explain why you chose the form you used. a. Passes through (-1, 4) and (-5, 2)\n\n1. ### Algebra\n\nFor the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y 52 39 32 24 2o 15 8 6 Find the slope of the given lines: 2. (6, 5) & (9, 10) 3. (-2, -4) & (-2, -6) Write the\n\n2. ### Math\n\n1. Factor Form : 1x1x1x1 Exponent Form : 1^4 Standard Form : 1 2. Factor Form :2x2x2 Exponent Form : 2^3 Standard : 8 3.Factor Form : (-6)(-6)(-6) Exponent Form : (-6)^3 Standard : -216 4.Factor Form : 5x5x5 Exponent form : 5^3\n\n3. ### math\n\nwrite each decimal in standard form, expanded form, and word form. 12+0.2+0.005\n\n4. ### Math\n\n1. Use point-slope form to write the equation of a line that has a slope of 2/3 and passes through (-3, -1). Write your final equation in slope-intercept form. 2. Write the equation in standard form using integers (no fractions or" ]
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https://answers.opencv.org/answers/23693/revisions/
[ "# Revision history [back]\n\n• The middle pixel will be taken into account, i.e. in your example it will change to 94.\n\nSmall python-example to illustrate it:\n\n>>> a = np.array([100,100,100,100,50,100,100,100,100]).reshape(3,-1)\n>>> cv2.blur(a, (3,3))\narray([[78, 89, 78],\n[89, 94, 89],\n[78, 89, 78]], dtype=int32)\n\n\n( Note, the border pixels change here as well, since they are interpolated).\n\n• No, a kernel size of (1,1) doesn't make sense and will have no effect (then each pixel will just be divided by 1).\n\ncv2.blur(a, (1,1)) array([[100, 100, 100], [100, 50, 100], [100, 100, 100]], dtype=int32)\n\n• The middle pixel will be taken into account, i.e. in your example it will change to 94.\n\nSmall python-example to illustrate it:\n\n>>> a = np.array([100,100,100,100,50,100,100,100,100]).reshape(3,-1)\n>>> cv2.blur(a, (3,3))\narray([[78, 89, 78],\n[89, 94, 89],\n[78, 89, 78]], dtype=int32)\n\n\n( Note, the border pixels change here as well, since they are interpolated).\n\n• No, a kernel size of (1,1) doesn't make sense and will have no effect (then each pixel will just be divided by 1).\n\n>>> cv2.blur(a, (1,1))\narray([[100, 100, 100],\n[100, 50, 100],\n[100, 100, 100]], dtype=int32)dtype=int32)\n\n\nThe middle pixel will be taken into account, i.e. in your example it will change to 94.\n\nSmall python-example to illustrate it:\n\n>>> a = np.array([100,100,100,100,50,100,100,100,100]).reshape(3,-1)\n>>> cv2.blur(a, (3,3))\narray([[78, 89, 78],\n[89, 94, 89],\n[78, 89, 78]], dtype=int32)\n\n\n( Note, (Note, the border pixels change here as well, since they the border-pixels are interpolated).\n\nNo, a kernel size of (1,1) doesn't make sense and will have no effect (then each pixel will just be divided by 1).\n\n>>> cv2.blur(a, (1,1))\narray([[100, 100, 100],\n[100, 50, 100],\n[100, 100, 100]], dtype=int32)" ]
[ null ]
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https://www.geeksforgeeks.org/program-to-find-the-rate-percentage-from-compound-interest-of-consecutive-years/
[ "Related Articles\nProgram to find the rate percentage from compound interest of consecutive years\n• Last Updated : 28 May, 2019\n\nGiven two integers N1 and N2 which is the Compound Interest of two consecutive years. The task is to calculate the rate percentage.\n\nExamples:\n\nInput: N1 = 660, N2 = 720\nOutput: 9.09091 %\n\nInput: N1 = 100, N2 = 120\nOutput: 20 %\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nApproach: The rate percentage can be calculated with the formula ((N2 – N1) * 100) / N1 where N1 is the compound interest of some year and N2 is the compound interest for the next year.\n\nLet us consider the 1st Example:\nThe difference between the Compound interest in the two consecutive years is because of the interest received on the previous year interest. Therefore,\n–> N2 – N1 = N1 * (Rate / 100)\n–> 720 – 660 = 660 * (Rate / 100)\n–> (60 / 660) * 100 = Rate\n–> Rate = (100 / 11) = 9.09% (Approx)\n\nBelow is the implementation of the above approach:\n\n## C++\n\n `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the ` `// required rate percentage ` `float` `Rate(``int` `N1, ``int` `N2) ` `{ ` `    ``float` `rate = (N2 - N1) * 100 / ``float``(N1); ` ` `  `    ``return` `rate; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N1 = 100, N2 = 120; ` ` `  `    ``cout << Rate(N1, N2) << ``\" %\"``; ` ` `  `    ``return` `0; ` `} `\n\n## Java\n\n `// Java implementation of the approach ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Function to return the ` `    ``// required rate percentage ` `    ``static` `int` `Rate(``int` `N1, ``int` `N2) ` `    ``{ ` `        ``float` `rate = (N2 - N1) * ``100` `/ N1; ` ` `  `        ``return` `(``int``)rate; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `N1 = ``100``, N2 = ``120``; ` ` `  `        ``System.out.println(Rate(N1, N2) + ``\" %\"``); ` `    ``} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `\n\n## Python 3\n\n `# Python 3 implementation of the approach ` ` `  `# Function to return the ` `# required rate percentage ` `def` `Rate( N1, N2): ` `    ``rate ``=` `(N2 ``-` `N1) ``*` `100` `/``/` `(N1); ` ` `  `    ``return` `rate ` ` `  `# Driver code ` `if` `__name__ ``=``=` `\"__main__\"``: ` `    ``N1 ``=` `100` `    ``N2 ``=` `120` ` `  `    ``print``(Rate(N1, N2) ,``\" %\"``) ` ` `  `# This code is contributed by ChitraNayal     `\n\n## C#\n\n `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to return the ` `    ``// required rate percentage ` `    ``static` `int` `Rate(``int` `N1, ``int` `N2) ` `    ``{ ` `        ``float` `rate = (N2 - N1) * 100 / N1; ` ` `  `        ``return` `(``int``)rate; ` `    ``} ` ` `  `    ``// Driver code ` `    ``static` `public` `void` `Main () ` `    ``{ ` `        ``int` `N1 = 100, N2 = 120; ` ` `  `        ``Console.WriteLine(Rate(N1, N2) + ``\" %\"``); ` `    ``} ` `} ` ` `  `// This code has been contributed by ajit. `\n\n## PHP\n\n ` `\n\nOutput:\n\n```20 %\n```\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.\n\nMy Personal Notes arrow_drop_up\nRecommended Articles\nPage :" ]
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https://ask.sagemath.org/question/24446/problem-with-solution_dicttrue/?sort=votes
[ "# Problem with solution_dict=True\n\nvar('x y')\nsolve(x + y, [x, y], solution_dict=True)\n\n\nyields AttributeError: 'list' object has no attribute 'left'\n\nIs this a bug?\n\nedit retag close merge delete\n\nSort by » oldest newest most voted", null, "This looks like a bug introduced in Sage 6.3. It's been reported at http://trac.sagemath.org/ticket/17128.\n\nmore\n\nThere is now a fix posted there. If you can, please test it.", null, "A workaround (tested with Sage Cell Server):\n\nvar('x y')\nsol = []\nfor v in [x,y]:\nsol += solve(x + y == 0,v, solution_dict=True)\nsol\n\n\ngives\n\n[{x: -y}, {y: -x}]\n\nmore", null, "Hi, could you please tell us which version of sage you are using? Going to sagenb.org\n\nvar('x y')\nsol=solve(x + y, [x, y], solution_dict=True)\nsol\n\n\ngives\n\n[{x: -y}]\n\n\nwhich still surprises me since the system of equation is more than incomplete.\n\nmore\n\nVersion is 6.3. Seems to me sagenb is using an old version without the bug." ]
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https://www.learner.org/courses/learningmath/number/session4/part_a/division.html
[ "", null, "Teacher resources and professional development across the curriculum\n\nTeacher professional development and classroom resources across the curriculum", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Session 4, Part A:\nMeanings and Relationships of the Operations\n\nIn This Part: Addition | Subtraction | Multiplication | Division\n\nAll of the meanings of multiplication can be used for division, since if the product and one of the factors is known, division can be used to find the other factor. But for the asymmetrical example of equal groups, the process feels different depending on which factor is known -- the multiplier or the number in each group.\n\nAs you will see, there are two very different concepts of division:\n\n • If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend. Long division (remember long division?!) uses this concept. • If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.\n\nThe following example demonstrates the distinction between the two types of division problems: Note 6", null, "", null, "Partitive:", null, "Quotative:", null, "12", null, "3 = 4\n 12", null, "3 = 4", null, "Partition into 3 groups.\n Repeatedly subtract 3.", null, "There are 4 in each group.\n There are 4 groups of 3 in 12.", null, "Twelve apples, 3 bags -- how many in each?\n Twelve apples, 3 in a bag -- how many bags?", null, "", null, "", null, "", null, "", null, "", null, "", null, "Problem A4", null, "a. Draw a diagram that represents 15", null, "3 as a partitive problem. b. Draw another diagram that represents 15", null, "3 as a quotative problem. c. Write a problem for each diagram.", null, "Problem A5", null, "a. Which type of division, quotative or partitive, would be most efficient for computing 100", null, "50? Why? b. Which would you use for 100", null, "2?", null, "", null, "", null, "Video Segment In this video segment, Susan and Jeanne explore the different notions of quotative and partitive division problems. They challenge their understanding with new insights. Watch this segment after you've completed Problems A4 and A5. Think about which method is easier to do in a particular division problem. If you are using a VCR, you can find this segment on the session video approximately 4 minutes and 9 seconds after the Annenberg Media logo.", null, "", null, "", null, "", null, "When division problems do not work out evenly, the context of the problem dictates the answer. Sometimes we may need to round the answer up or down to the next integer, and sometimes we may need the exact decimal value of the division.", null, "Problem A6", null, "a. Write a problem that uses the computation 43", null, "4 and gives 10 as the correct answer. b. Write a problem that uses the computation 43", null, "4 and gives 11 as the correct answer. c. Write a problem that uses the computation 43", null, "4 and gives 10.75 as the correct answer.\n\nAnother important concept to remember, especially when working with rational numbers, is that division can be thought of in terms of multiplying by the inverse. This can be particularly useful when dividing by fractions. Thus, we could show that 12", null, "2 = 12 • 1/2, where 1/2 is the multiplicative inverse of 2, and 12", null, "(1/2) = 12 • 2, where 2 is the multiplicative inverse of 1/2. In these cases, you can see that the multiplicative inverse of every number except 0 is the reciprocal of that number, and that the product of a number and its reciprocal is 1.", null, "", null, "", null, "Session 4: Index | Notes | Solutions | Video" ]
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https://mran.revolutionanalytics.com/web/packages/stR/vignettes/stRvignette.html
[ "# Package stR\n\n#### 2018-05-18\n\nThis vignette describes some functionality and provides a few examples of how to use package stR. stR implements method STR, where STR stands for Seasonal-Trend decomposition by Regression and capital R emphasizes R, the name of the popular statistical software. The whole name is also reminiscent of STL, the method which inspired me to introduce STR.\n\n## Introduction\n\nThere are many packages and methods which work with seasonal data. For example the oldest method for decomposition – classical additive decomposition – is implemented in package stats. The method splits the data into trend, seasonal and random components:\n\nm <- decompose(co2)\nplot(m)", null, "Another well known method is STL, implemented in packages stats and stlplus:\n\nplot(stl(log(co2), s.window = \"periodic\", t.window = 30))", null, "Other R packages which implement various versions of seasonal decomposition and seasonal adjustment include forecast, x12, seasonal, season, seas and deseasonalize.\n\nA few more examples are provided below:\n\nlibrary(forecast)\nco2.fit <- tbats(co2)\nplot(co2.fit)", null, "library(seasonal)\nco2.fit <- seas(co2)\nplot(co2.fit, trend = TRUE)", null, "After looking at the above examples, a reader might ask “Why do we need another method of seasonal decomposition?”\n\nA short answer is that\n\n1. the new STR method has a richer set of features (and allows users to implement even more features); and\n2. the method has a well studied theoretical background (based on OLS and quantile regression).\n\nThis vignette provides some details on the first claim.\n\n## Getting started\n\nFor time series decomposition with objects of class ts or class msts, and with no regressors or complex seasonality, it is simple to do an STR decomposition using the AutoSTR function.\n\nFor example, the co2 time series can be decomposed as follows:\n\nco2.fit <- AutoSTR(co2)\nplot(co2.fit)", null, "## Example with multiple seasonality\n\nThe time series taylor from package forecast provides us with half-hourly electricity demand in England and Wales. It exhibits (at least) two seasonalities – daily and weekly. They can be observed in a 4 weeks’ subset of the data:\n\ntaylor.msts <- msts(log(head(as.vector(taylor), 336*4)),\nseasonal.periods=c(48,48*7,48*7*52.25),\nstart=2000+22/52)\nplot(taylor.msts, ylab = \"Electricity demand\")", null, "Since the data is at half hour granularity, the daily seasonality has a period of 48 observations and weekly has a period of 336.\n\nThe data is of class msts (multiple seasonal time series), which can also be handled automatically with AutoSTR:\n\ntaylor.fit <- AutoSTR(taylor.msts, gapCV = 48, confidence = 0.95)\nplot(taylor.fit)", null, "The parameters supplied to AutoSTR are:\n\n• gapCV = 48 – gaps of 48 observations are used for cross validation\n• reltol = 0.001 – this parameter is passed directly to optim function to control how well (and for how long) the model parameters are optimized\n• confidence = 0.95 – 95% confidence intervals are calculated (with assumptions: errors are uncorrelated, model parameters are estimated exactly)\n\n## Tuning an STR decomposition\n\nThis example shows how to tune an STR decomposition, rather than use the automated AutoSTR function. STR is a flexible method, which can be adjusted to the data in multiple ways, making the interface rather complex.\n\nLet us consider the dataset grocery which contains monthly data of supermarkets and grocery stores turnover in New South Wales:\n\nplot(grocery, ylab = \"NSW Grocery Turnover, \\$ 10^6\")", null, "We will use a log transformation to stabilize seasonal variance in the data:\n\nlogGr <- log(grocery)\nplot(logGr, ylab = \"NSW Grocery Turnover, log scale\")", null, "At the next step we define trend and seasonal structures. Trend does not have seasonality, therefore its seasonal structure contains only a single knot: c(1,0). Here a knot is defined as a pair of numbers, both referring to the same point. The segments component contains only one segment c(0,1).\n\ntrendSeasonalStructure <- list(\nsegments = list(c(0,1)),\nsKnots = list(c(1,0)))\n\nThe seasonal structure of the data is defined in the seasonalStructure variable. The segments component contains one pair of numbers c(0,12) which defines ends the segment, while sKnots variable contains seasonal knots from 1 to 12 (months). The last knot c(0,12) also defines that ends of the segment c(0,12) are connected and 0 and 12 represent the same knot (month December).\n\nseasonalStructure <- list(\nsegments = list(c(0,12)),\nsKnots = list(1,2,3,4,5,6,7,8,9,10,11,c(12,0)))\n\nVariable seasons contains months corresponding to every data point:\n\nseasons <- as.vector(cycle(logGr))\n\nSince trend does not have seasonality (the seasonal structure for the trend contains only one season), the trend seasons are all ones:\n\ntrendSeasons <- rep(1, length(logGr))\n\nThe times vector contains times corresponding to data points:\n\ntimes <- as.vector(time(logGr))\n\nThe data vector contains observations (in this case log turnover):\n\ndata <- as.vector(logGr)\n\ntrendTimeKnots vector contains times where time knots for the trend are positioned:\n\ntrendTimeKnots <- seq(\nfrom = head(times, 1),\nto = tail(times, 1),\nlength.out = 175)\n\nThe seasonTimeKnots vector contains times where time knots for the seasonal component are positioned:\n\nseasonTimeKnots <- seq(\nfrom = head(times, 1),\nto = tail(times, 1),\nlength.out = 15)\n\nIn stR package every component of a decomposition is a regressor. In the case of trend and seasonal components values for such regressors are constants (vectors of ones):\n\ntrendData <- rep(1, length(logGr))\nseasonData <- rep(1, length(logGr))\n\nThe complete trend structure contains all components relevant to the trend. Component lambdas is always a vector with three elements. Trend, since it does not have seasonality, has only the first element different from zero. This element defines smoothness of the trend at the starting point of the optimization procedure.\n\ntrend <- list(\nname = \"Trend\",\ndata = trendData,\ntimes = times,\nseasons = trendSeasons,\ntimeKnots = trendTimeKnots,\nseasonalStructure = trendSeasonalStructure,\nlambdas = c(0.5,0,0))\n\nThe complete season structure contains all components relevant to the trend. Component lambdas is a vector with three elements. The elements define smoothness of the seasonal component at starting point of the optimization procedure.\n\nAccording to STR approach every non-static seasonal component has two-dimensional structure (see the corresponding article on STR method). In this particular case it has topology of a tube. The “observed” seasonal component is a spiral subset of that “tube organised” data (“observed” means here that the seasonal component is observed as part of the data together with the trend and other components).\n\nThe first element of the vector defines smoothness of data along time dimension of the tube. The second component defines smoothness along seasonal dimension. And the third component defines smoothness in some way in both dimensions (by restricting partial discrete derivative in both directions).\n\nThe last two zeros in lambdas component mean that those two components will not be optimized (and effectively two dimensional structure of the seasonal component will not be used).\n\nseason <- list(\nname = \"Yearly seasonality\",\ndata = seasonData,\ntimes = times,\nseasons = seasons,\ntimeKnots = seasonTimeKnots,\nseasonalStructure = seasonalStructure,\nlambdas = c(10,0,0))\n\nAll components of STR decomposition are considered to be predictors. For example trend is a predictor with no seasonality and independent variable which is constant (and equal to one). The seasonal component is a predictor with some predefined seasonality and a constant independent variable (also equal to one).\n\npredictors <- list(trend, season)\n\nTo calculate STR decomposition we supply data points, predictors, required confidence intervals, the gap, to perform cross validation, and reltol parameter which was described earlier.\n\ngr.fit <- STR(data, predictors, confidence = 0.95, gap = 1, reltol = 0.00001)\nplot(gr.fit, xTime = times, forecastPanels = NULL)", null, "In plot function forecastPanels = NULL means that fit/forecast are not displayed.\n\nIf we decide to use two-dimensional structure for the seasonal component we need to redefine lambdas component:\n\nseason <- list(name = \"Yearly seasonality\",\ndata = seasonData,\ntimes = times,\nseasons = seasons,\ntimeKnots = seasonTimeKnots,\nseasonalStructure = seasonalStructure,\nlambdas = c(1,1,1))\npredictors = list(trend, season)\ngr.fit <- STR(data,\npredictors,\nconfidence = 0.95,\ngap = 1,\nreltol = 0.00001)\n\nThis allows to find a set of parameters with a smaller cross validated error, and therefore potentially more insightful decomposition:\n\nplot(gr.fit, xTime = times, forecastPanels = NULL)", null, "## Robust STR decomposition\n\nSince STR is based on Ordinary Least Squares (OLS), it does not tolerate outliers well. In the examples below I compare STR with its robust version – Robust STR. The latter is based on quantile regression approach (only 0.5 quantile is used), and therefore is robust to various types of outliers.\n\nLet us create a time series with two “spikes” to model two isolated outliers:\n\noutl <- rep(0,length(grocery))\noutl <- 900\noutl <- -700\ntsOutl <- ts(outl, start = c(2000,1), frequency = 12)\n\nand combine it with grocery time series\n\nlogGrOutl <- log(grocery + tsOutl)\nplot(logGrOutl, ylab = \"Log turnover with outliers\")", null, "Decomposition of this time series with STR shows considerable distortions in all components:\n\ntrendSeasonalStructure <- list(segments = list(c(0,1)),\nsKnots = list(c(1,0)))\nseasonalStructure <- list(segments = list(c(0,12)),\nsKnots = list(1,2,3,4,5,6,7,8,9,10,11,c(12,0)))\nseasons <- as.vector(cycle(logGrOutl))\ntrendSeasons <- rep(1, length(logGrOutl))\ntimes <- as.vector(time(logGrOutl))\ndata <- as.vector(logGrOutl)\ntimeKnots <- times\ntrendData <- rep(1, length(logGrOutl))\nseasonData <- rep(1, length(logGrOutl))\ntrend <- list(data = trendData,\ntimes = times,\nseasons = trendSeasons,\ntimeKnots = timeKnots,\nseasonalStructure = trendSeasonalStructure,\nlambdas = c(0.1,0,0))\nseason <- list(data = seasonData,\ntimes = times,\nseasons = seasons,\ntimeKnots = timeKnots,\nseasonalStructure = seasonalStructure,\nlambdas = c(10,0,0))\npredictors <- list(trend, season)\nfit.str <- STR(as.vector(logGrOutl), predictors, confidence = 0.95, gapCV = 1, reltol = 0.001)\nplot(fit.str, xTime = times, forecastPanels = NULL)", null, "On the other hand Robust STR decomposition results in much cleaner decomposition. The outliers appear only as residuals (component with name “Random”) and trend and seasonal components are not distorted:\n\nfit.rstr <- STR(as.vector(logGrOutl), predictors, confidence = 0.95, gapCV = 1, reltol = 0.001, nMCIter = 200, robust = TRUE)\nplot(fit.rstr, xTime = times, forecastPanels = NULL)", null, "## Another example with multiple seasonality\n\nData set calls provides data about number of call arrivals per 5-minute interval handled on weekdays between 7:00 am and 9:05 pm from March 3, 2003 in a large North American commercial bank.\n\nBelow is an example of decomposition of calls data using STR:\n\ntimes <- as.vector(time(calls))\ntimeKnots <- seq(min(times), max(times), length.out=25)\n\ntrendSeasonalStructure <- list(segments = list(c(0,1)),\nsKnots = list(c(1,0)))\ntrendSeasons <- rep(1, length(calls))\n\nsKnotsDays <- as.list(seq(1, 169, length.out = 169))\nseasonalStructureDays <- list(segments = list(c(1, 169)),\nsKnots = sKnotsDays)\nseasonsDays <- seq_along(calls) %% 169 + 1\n\nsKnotsWeeks <- as.list(seq(0,169*5, length.out=13*5))\nseasonalStructureWeeks <- list(segments = list(c(0, 169*5)),\nsKnots = sKnotsWeeks)\nseasonsWeeks <- seq_along(calls) %% (169*5) + 1\n\ndata <- as.vector(calls)\ntrendData <- rep(1, length(calls))\nseasonData <- rep(1, length(calls))\n\ntrend <- list(data = trendData,\ntimes = times,\nseasons = trendSeasons,\ntimeKnots = timeKnots,\nseasonalStructure = trendSeasonalStructure,\nlambdas = c(0.02, 0, 0))\n\nseasonDays <- list(data = seasonData,\ntimes = times,\nseasons = seasonsDays,\ntimeKnots = seq(min(times), max(times), length.out=25),\nseasonalStructure = seasonalStructureDays,\nlambdas = c(0, 11, 30))\n\nseasonWeeks <- list(data = seasonData,\ntimes = times,\nseasons = seasonsWeeks,\ntimeKnots = seq(min(times), max(times), length.out=25),\nseasonalStructure = seasonalStructureWeeks,\nlambdas = c(30, 500, 0.02))\n\npredictors <- list(trend, seasonDays, seasonWeeks)\ncalls.fit <- STR(data = data,\npredictors = predictors,\nconfidence = 0.95,\nreltol = 0.003,\nnFold = 4,\ngap = 169)\nplot(calls.fit,\nxTime = as.Date(\"2003-03-03\") +\n((seq_along(data)-1)/169) +\n(((seq_along(data)-1)/169) / 5)*2,\nforecastPanels = NULL)", null, "## A complex example\n\nElectricity consumption dataset electricity provides information about electricity consumption in Victoria, Australia during the 115 days starting on 10th of January, 2000, and comprises the maximum electricity demand in Victoria during 30-minute periods (48 observations per day). For each 30-minute period, the dataset also provides the air temperature in Melbourne.\n\nIn the example below the data is decomposed using weekly seasonal pattern, daily seasonal pattern which takes into account weekends and holidays and transition periods between them, and two flexible predictors:\n\nTrendSeasonalStructure <- list(segments = list(c(0,1)),\nsKnots = list(c(1,0)))\nDailySeasonalStructure <- list(segments = list(c(0,48)),\nsKnots = c(as.list(1:47), list(c(48,0))))\nWeeklySeasonalStructure <- list(segments = list(c(0,336)),\nsKnots = c(as.list(seq(4,332,4)), list(c(336,0))))\nWDSeasonalStructure <- list(segments = list(c(0,48), c(100,148)),\nsKnots = c(as.list(c(1:47,101:147)), list(c(0,48,100,148))))\n\nTrendSeasons <- rep(1, nrow(electricity))\nDailySeasons <- as.vector(electricity[,\"DailySeasonality\"])\nWeeklySeasons <- as.vector(electricity[,\"WeeklySeasonality\"])\nWDSeasons <- as.vector(electricity[,\"WorkingDaySeasonality\"])\n\nData <- as.vector(electricity[,\"Consumption\"])\nTimes <- as.vector(electricity[,\"Time\"])\nTempM <- as.vector(electricity[,\"Temperature\"])\nTempM2 <- TempM^2\n\nTrendTimeKnots <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 116)\nSeasonTimeKnots <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 24)\nSeasonTimeKnots2 <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 12)\n\nTrendData <- rep(1, length(Times))\nSeasonData <- rep(1, length(Times))\n\nTrend <- list(name = \"Trend\",\ndata = TrendData,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1500,0,0))\nWSeason <- list(name = \"Weekly seas\",\ndata = SeasonData,\ntimes = Times,\nseasons = WeeklySeasons,\ntimeKnots = SeasonTimeKnots2,\nseasonalStructure = WeeklySeasonalStructure,\nlambdas = c(0.8,0.6,100))\nWDSeason <- list(name = \"Daily seas\",\ndata = SeasonData,\ntimes = Times,\nseasons = WDSeasons,\ntimeKnots = SeasonTimeKnots,\nseasonalStructure = WDSeasonalStructure,\nlambdas = c(0.003,0,240))\nTrendTempM <- list(name = \"Trend temp Mel\",\ndata = TempM,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1e7,0,0))\nTrendTempM2 <- list(name = \"Trend temp Mel^2\",\ndata = TempM2,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1e7,0,0))\nPredictors <- list(Trend, WSeason, WDSeason, TrendTempM, TrendTempM2)\nelec.fit <- STR(data = Data,\npredictors = Predictors,\nconfidence = 0.95,\ngapCV = 48*7)\nplot(elec.fit,\nxTime = as.Date(\"2000-01-11\")+((Times-1)/48-10),\nforecastPanels = NULL)", null, "## A forecasting example\n\nThe example below shows a simple way of forecasting seasonal data using STR.\n\nTrendSeasonalStructure <- list(segments = list(c(0,1)),\nsKnots = list(c(1,0)))\nDailySeasonalStructure <- list(segments = list(c(0,48)),\nsKnots = c(as.list(1:47), list(c(48,0))))\nWeeklySeasonalStructure <- list(segments = list(c(0,336)),\nsKnots = c(as.list(seq(4,332,4)), list(c(336,0))))\nWDSeasonalStructure <- list(segments = list(c(0,48), c(100,148)),\nsKnots = c(as.list(c(1:47,101:147)), list(c(0,48,100,148))))\n\nTrendSeasons <- rep(1, nrow(electricity))\nDailySeasons <- as.vector(electricity[,\"DailySeasonality\"])\nWeeklySeasons <- as.vector(electricity[,\"WeeklySeasonality\"])\nWDSeasons <- as.vector(electricity[,\"WorkingDaySeasonality\"])\n\nData <- as.vector(electricity[,\"Consumption\"])\nTimes <- as.vector(electricity[,\"Time\"])\nTempM <- as.vector(electricity[,\"Temperature\"])\nTempM2 <- TempM^2\n\nTrendTimeKnots <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 116)\nSeasonTimeKnots <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 24)\nSeasonTimeKnots2 <- seq(from = head(Times, 1), to = tail(Times, 1), length.out = 12)\n\nTrendData <- rep(1, length(Times))\nSeasonData <- rep(1, length(Times))\n\nTrend <- list(name = \"Trend\",\ndata = TrendData,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1500,0,0))\nWSeason <- list(name = \"Weekly seas\",\ndata = SeasonData,\ntimes = Times,\nseasons = WeeklySeasons,\ntimeKnots = SeasonTimeKnots2,\nseasonalStructure = WeeklySeasonalStructure,\nlambdas = c(0.8,0.6,100))\nWDSeason <- list(name = \"Daily seas\",\ndata = SeasonData,\ntimes = Times,\nseasons = WDSeasons,\ntimeKnots = SeasonTimeKnots,\nseasonalStructure = WDSeasonalStructure,\nlambdas = c(0.003,0,240))\nTrendTempM <- list(name = \"Trend temp Mel\",\ndata = TempM,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1e7,0,0))\nTrendTempM2 <- list(name = \"Trend temp Mel^2\",\ndata = TempM2,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(1e7,0,0))\nPredictors <- list(Trend, WSeason, WDSeason, TrendTempM, TrendTempM2)\n\nThe values, which need to be forecast, are supplied to STR as NAs. In our case we are going to forecast the last week of the original data.\n\nData[(length(Data)-7*48):length(Data)] <- NA\n\nThe forecasting is performed at the same time when the model is fitted.\n\nelec.fit <- STR(data = Data,\npredictors = Predictors,\nconfidence = 0.95,\ngapCV = 48*7)\n\nThe result of the decomposition and forecasting is depicted below.\n\nplot(elec.fit,\nxTime = as.Date(\"2000-01-11\")+((Times-1)/48-10),\nforecastPanels = 7)", null, "To check meaningfulness of the forecast it is advisable to plot beta coefficients of the decomposition. If the coefficients are too “wiggly” the forecast can be suboptimal.\n\nBeta coefficients of the trend look a bit too “wiggly”. It explains an uptrend in the forecast.\n\nplotBeta(elec.fit, predictorN = 1)", null, "Beta coefficients of weekly and daily seasonalities look smooth at the end of the time series.\n\nplotBeta(elec.fit, predictorN = 2)\nplotBeta(elec.fit, predictorN = 3)", null, "", null, "Beta coefficients for temperature and squared temperature predictors look smooth.\n\nplotBeta(elec.fit, predictorN = 4)\nplotBeta(elec.fit, predictorN = 5)", null, "", null, "Probably, the model can be re-estimated with a higher lambda coefficient for the trend to provide a better forecast.\n\nTrend <- list(name = \"Trend\",\ndata = TrendData,\ntimes = Times,\nseasons = TrendSeasons,\ntimeKnots = TrendTimeKnots,\nseasonalStructure = TrendSeasonalStructure,\nlambdas = c(150000,0,0))\nPredictors <- list(Trend, WSeason, WDSeason, TrendTempM, TrendTempM2)\nelec.fit.2 <- STR(data = Data,\npredictors = Predictors,\nconfidence = 0.95,\ngapCV = 48*7)\n\nThe result gets much lower cross validated mean squared error.\n\nplot(elec.fit.2,\nxTime = as.Date(\"2000-01-11\")+((Times-1)/48-10),\nforecastPanels = 7)", null, "Beta coefficients of the trend, seasonal components and predictors look smooth.\n\nfor(i in 1:5)\nplotBeta(elec.fit.2, predictorN = i)", null, "", null, "", null, "", null, "", null, "## Final notes\n\n1. To achieve higher performance, it is recommended to use Intel MKL for matrix operations. The simplest way to switch to Intel MKL is to install R distribution from Microsoft.\n\n2. Note, that registering a parallel backend while using Intel MKL can reduce performance significanly since Intel MKL already tries to utilise all available cores. In case if a user has options to use Intel MKL or register a parallel backend (while using an ordinary computer, for example 4 phisical cores, 8 virtual cores), it is recommended to use Intel MKL and do not register a parallel backend.\n\n3. For testing and exploration purposes it is recommended to avoid calculation of the confidence/forecasting intervals. Such calculation currently involves inversion of a big matrix and can take long time.\n\n4. To monitor progress of the parameters’ estimation it is recommended to set parameter trace to TRUE in STR call." ]
[ 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, 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", null, 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", null, 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GJgjMnMIpzfwRahoEemtwNrXAX9+k33E8wxCEr3EyxyvZJE9xMMMkx9wxgRsAiFejANlzrBNAgKpkFQMA2CgmkQFEyDoGAaBAXTICiYBkGVGa55fP/3jcEN20HQClRY9+BpQdAKIKgeCFqBTlA/n9DHj//6JTr88intvEIsN1kKglYgFLRdcs0v8nJZ6EVzdt1nAEErEAr6s+m//GL6QAEIWoFQ0H7awPOXbuJrvfU6ngIErUBKUNVlQZ4EBK1AtgWFIhC0AglBP6ncl4OgFUgI2k0RfKAdLQFBK5AStK2DksQXgaBgGgQF0yAomAZBwTQICqZBUDANgoJpEBRMg6BgGgQF0yAomAZBwTQICqZBUDANgoJpEBRMg6BgGgQF0yAomAZBwTQICqZBUDANgoJpEBRM83/XGWIhVRB35QAAAABJRU5ErkJggg==", null, 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KcNWg/dZgpwUMVV0NPTZ72OApfiQRfd9IumXueDCh5UwZUkUA2Cgmp6o5kKLSYLkM2wBD3IzmEBsIy+oJKTiAEIMJhZhPoddOEKeuSOOdBGJ+jPB81PUEcrKM1P0Eh3JYnmJyiknfqGMSKgERL1oBoudQrT/r/+6593GvXLQdACFFj3YLcgaAEQVA4ELUAjqL2P5vz6X7tEh502sL6fRnIi632AoAVwBa2XXLOLvFwXepGcXXcPIGgBXEHfqtuf39w2mwGCFsAV9Ha77OVPM/E1c7ckgaAF8AkquizITkDQAgRLUEgCQQvgEfSbzH06CFoAj6DN1BgHytEUELQAPkHrPCid+CQQFFSDoKAaBAXVICioBkFBNQgKqkFQUA2CgmoQFFSDoKAaBAXVICioBkFBNQgKqkFQUA2CgmoQFFSDoKAaBAXVICioBkFBNQgKqkFQUA2Cgmr+D/OeGzJaNK7iAAAAAElFTkSuQmCC", null, 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", null, 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", null, 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PM6dgGCFsAnqOhjQXYCghYgWIJCEghaAI+gn4zcp4OgBfAIeu3FN0fK0RQQtAA+Qa/joHTik0BQUA2CgmoQFFSDoKAaBAXVICioBkFBNQgKqkFQUA2CgmoQFFSDoKAaBAXVICioBkFBNQgKqkFQUA2CgmoQFFSDoKAaBAXVICioBkFBNQgKqvk/QJQW97ZX/ukAAAAASUVORK5CYII=", null, 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", null, 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97FAxWpLQMq4qaamsvkBvn3LWijgNY8EXKl5tANaVOAsjDJH+YGNiGvlgZU3pZG86C+ZzNpRdA+tCSgRo4e7xLan0IAvZArMuY1pijAlH7NPTzpBcqmAEDJ3cj2KJKAnkmZlauDM5GYQ+EKANQzDm9kcFA/ql1/+kHiy5+hXSsign4bBKhyr7nB5pgfCLIV0gbtRzkFt0HrRgZO/QmtGPIGxSt7Fq/fPFlFvs8HgnSFAxr4Mtn++Ub8BbuKG+RFUJKyR1D1NkoImqp5OurBJ5RJId1Mi71MFoJMBfWDLvUyWQgyFQDo//31P7/+vf3o5QqCFlAQoJf766l69x8utD3EL6lduNzFRrpuzfXNkOoAPR+iL3UuqF243MVGpgH6+nj3h3/svn4eNFikiK26QZe72Mg0QPtrne+eXr4Ju9RZxFbdoMub30jPWKLs/aA3vyNXcnnzGwlAt+3y5jcSgG7b5VY2MvkOs3RAPa//QEc95NA0QG2FRNBX4wWzWg8qdJPKzdm43QRA3a9HBKC3rG0BOmQJFaz0Rw4kc9YkWk4HNPBKElSQtgRo656OCLoBLV7feuPZuGELQPenFQBN52wFQDM8WQTaVH27LUBTnyyyhJaPLVtymUzLCoD67IJG1Mc8WSRJK9RhqYar1LfJhksD2tmlFdbrMCKChj1ZJEm7ADQVsxXC2bXdEqBxTxZJ0grZ5uIut1TfTuEszeckQActsyj5oKdnAduhZUq7LjFqrwGoZ0YRgKb37qZ3C28I0Cm0pHmcAKg32xk1dGvjgO4hnE0ANJEWAGpoW4AmcrahcJZs2e/WAgDNPtxuAmeJaCdjls5Zm5rG16mW6YCmcpYOqNeqjAiaDmjyEZhQU6eGiAnhLNkwOaVOBjTpBPbv1EIATQuEnd3SgE5JUxeub6+ptABQQ3WTGAiTaZkCaHoja+H6dhVAE6vDwgFNDYRbAjSZlkkNwlRAE6+vAlDTMLFx0BmmZ8ZplpMAXZaWdEB7b4mA+uYEDhY5O55uF18Mj6ZcH0s+AgvTQo7d8uEsLfZSzlI81okupwJ6uZ9zuN2EQJgeIhLPCQJo0kG/JtICQJUvpzpAI55ul6BkQJNpWR7QdFom1beJtEwCNMXSX8wQQKOebpeg1Jq6Tg9n6WTXE0JEcjhLahwk05IcCJMBHTgYQUlSzNPt4pXMGTVMib2pmKVzlkxLeiBcA1D5meDRqQKy+EmAplmm1mHUKLkOWxTQZFqYTYJLapJwRCYCOvNNc6sBumRUmgCoMI8TB3Q5tOuVAI27aS6t5ZJUUycDOo3sJMtWmsdpQrVJP9MDYbzHNEDroRQksB/0GpzF145fI+XrAU3pqmf17YKGWwKU+UoOZwsB2r8Yu2n8viIi6Ldh7+oUpYsBVNuqUENGS3zsTW5kMZuUg66YJ1iWDih9BTvzFWdJ343tnR/SBo17HXdt/hgtYiKg9gkb7lF+RomZpASXRMPk+vaaQguzsFyO7liGmeUyztCl7Fm8BDQwstVmtRlnmAJowhHgLtWvCMNkWpLL6ghn44ZqIIwHlB+IlQANbYPagA6XsjZr6gmARuGSFLTVrwhDB6BxllFlVXsM4gBV6ltt94yY6pipLsd8rhBBOV7LAxp8a5MD0DBLwVnsOWEbBgQXaqGtIMxl/0p0CWh4WXVaJgAa57IdGg48G6CdZ15en3f1oClp/DhnWjiSaAcAqoWjmFaFZhF1TtC0iv0RBWhdpwHaH/Q6lRYXoKNbqWMW0Vzrx6q3TTOwVPaOegVQ8cvtnk03A2GtlNdT7loLLoplwEFXDGRVFAAo5cw8doEuaxvQoINe13ZNHVBWdzgLMCS02DX1aE9JrWGmuBw1bFpyUkwCNK6jvhVYtqOANgoutW3oA5Qa2jFivMeJW/LlxfSxzhjLZaghtVSWj3HpbNcFbKWKmep73FAPhMEuaw2zGECp4TRA4zrqW4ZdwzmrPe5ZpKwbo6ZWAPXUSdQyEdDG1TwLONPdnAW6tGkJAJQEpRRauh2oNOvCy2rQorocLqwZBxWXIz7rsQCa/+l2bDeQvTQEaM1KJupb2YvWDNfZzNLmUtmPfrKJJTeUe3QEF7Ijaztwjt/3XKuY6Qd92I5g5gQ0pKxuWtIBHeTMxCwY0PEafoaOegPQ2lOAutE5qwXPYvjyINqNBahy54g39LbO5tnoPSd9W17nTDRGxw46yQJsw1HLbjbJPKxqc3R0N7VUaJEnU4hh4yzrCKC136X7GLKvxrC0lT+LF4DSXx5Ayd5XOeM1ewigrd55JtOs4WZv3+xwxjMVbd9GNS7O6tF7PMlBV0KXPOgjlsZBj6CFHnSbliDD2u3SY6qcPXXtdNk4DUUm3c+tB7O3OQDtnTZeQOtatFGNeCYA5T1PvtDbttr1Wwko/zVAtocz8dOzUVo4E2iP3jpi0qImaGOGV+Ogi+9Rl3wn87LTHyGYqZZqBeO25P0wrK70uHSGJwVQb4VHNEM/KDkr+s++3DRSaoCS3pPGBpRtZssH31mA1nx3kOCr0sK6A64eQBUPGmc2oObJrByiRndpGJpoS5f6SjXOrJ0nLXl53ICOcyaLw7NQL6CSFv0cFYZelxJQY7oBqAkgP7IhY9jmA5TmPzTe1ep8ppb/1wBlhgxQ07KmK6R0OwEdIVvnTO2CdQKqdtUarSzxxQ+ry1BEpath6A/aeu/w1fRIXTYOS5MzOV05mcbjoDpDA5RUxoZHraPQ5bLm+ZNqKSrVuQClo+0at2jsJMGqpkC0ZIqcrwBKOHMY0g+CdqNb1jVbWysM6eJNLT80P+QnqWcbNlM1ZM1gaanYib/teSyfEIYNKbpt2LRGYdjSZHrLt0h3qRo2liFBpWW9+K6yOiwVw6Y2DWv+v23chsLS2Dtiy2rLYyNc8p82AbXLpUMJgA6bkM2hYZT4b7VAqPOp1bcy9IrYq55hiqVR37IIpxgaoZf2ETU8vBqGqnnT6DG7VTro6wFDo1UhMj4rQvApImgbzRFeykFDQoujrIMu6e3LTV07PAa5pFgpdo3PUvTItNJQR4BedwoZy5u9iufNTwabDWgrADUTD6V2F2jXV9uyNjMvmgyqZLfanqTX4UQ/lpczq1FBmsm1sFRmMUP+06Sl9XF2VcaikuNnYyY2xtytwrGIPLVlOAqozRndyBRA9d0T6FKkHy5DW/MA2vCEh9fkSulYCs5y/UYHlGdKTctWo2wXT6rsZqYElObbxjlhlEJrEUrO+paWRTYtqCMPUm7vJIbWWeg7AhqgtdnHwThzHfOmVc3tqOSnpRHnkZOzccxqJTyoR5LuHedZKAFtDEKFYVMSoLJ0tKdHAqofVlk5NA5AmaVZ3/LYSw1dZOuTXG0DYam1HBplY4yt7L3J7i09aHNDV3+QDqjFGat9hg1dgPpdugDV907DGpluw9qFdi2OrNMlneRyqRi6+0gN5QdU1jasimzUcSOsdPKKvRdQ/RwTvfNiVVo7SgHU3N2u5oJhqABqGF5NaKXhVRm21xjDMwYNa2HZalvELAc9GoCq5319rd0n0xCgFGrPWTgMKD+ykS7FgSwCUEqiCihrPbkAVQwVS75DWJu18QAqr0i5XFqdXdJQGQ3Q6pUr48z9dF3TUD0nhOEYoDW93K6eEgztEcMrG3ekHvSwc8LBmddQb1VodTzj03fma4BqdTzvOPGGDFNzASr3o0jNWQCta+18MhtgCpBKy53vSLVyUl2qgDY8zRKzuGdHWTXOtCRDXNkaC71X0UtQ64buwRla40AjW/QzeE8JBVDZ2hGGg2iLnlsilbOwk0lHmwE6gLZ9TiiAesm2NTOgtFgML06JypnegasOZFI4q0VXiBZxNUuJMm9diD05ZCjaBtzSMBQrtC01Q2kpQXUfAJraio1sauNc8hnSqKTsWFGdKEX1o626FGjXoiZzVjA6oCy9VTC7+iqYWnQWKob8uEjDgBp+lmczaW1OsQdrdY/KOOgHlB/tWsmRPbRca/WcYPuekz2IWaOMKqqlobINV8/IE+ViOjeUJ+OgoXpOqGTLuObzqJ4TYnfys/c6iLYLUHXvjAdtljvoLofPiVoz5BGXV0xFACp3nNL0VA9d7TS8KtffVEPvQLpWXA+uZThSe3+8hgqgfIp20D2WGqBXxVJpUnoMFUDjyJaAXtkFodY0dLZjGh/aCtkDhmrQbjXMhtHWzolWB9Tb6DI1D6DmwZWpG5/uMbSObt1qfHotrbHKDG2FM4+hde2aZ9LOc0hZzBqOxC1HDBtpqZAdckqoY/rrmgVMraz+oC1cyqoslGy5TMNbkEpZQ88JkfVL3gP4nAtQm5ZGdi6FGMpjJyuWQUvrPK5bnWyPoZ0d8K7UMUPnFb6AsGCjTcgOOCWs133YhiGWNcsG1K5PJ9k1H/LD/uKxQj8lBiwNw0aLQOsB6tjamt1eGg6oYjhqd1XOc2VKE8KZm+xRsF2AXus2pNpyxt4AstXQKycZhoFo0/6+NoRs9X7Sxrzw4rMku7WtVcPGCBjFAdoEcOY4j+sgQ885EeLRxmw81NOC2WUNavjX9us+J5AdcC450GaXRiPJZo163WUAoJJQ/UryXICOvkzWxVmTCmgQn36040PvtQ7h02WoZkiDhtZQ5aCXjrpbFSFkN3ZL293zaRvqZPORHto0T1k1tBmho6HX0jwR1HHo5gbU7TLgMTFOlwH7zgloUFBwnxOpZAeW1QraQTHbGXoDy6ptJm0eBJBtahZAHa7DOEvGzLm11q0GTjtHoYLObXdakQhokKET0NBTIsnSGXqDuocsS+06NZs0upbrcoCyjruxlaZi5rYMsnMBmmoYaOkCNNkwDFBXgznwnLBaFUGGFtqBVaGpEECzvEQhjLPUYx68WD7D4Gfp5bNMJ9t5pT3MoyOJTAI0uOdTVwCgcc9m2pwWJzv82dOWYcjoCqdh0LgMp8dUshtXs3ceQOOezbQ5LQ/oGkE7FdBUst2tioR1RUTQsGcz7UcrAJp+MiWinRfQlA0PaYNGPZsJGtcKrYqczd5Aj6mWuubJ4qF5tEKzN5lsALpDAdB4S2gT2lBnmq6QLP6RXnt/jyRpu7plQK+vH58cUwHolrSdjgNDQVX85e7ZnghAd6FNAGrajA23g25Hy+dlusIBvdUrSdCgtgOoxxKC3AKgUNFaDtAsw+2gvWkxQG98uB1UtDDcDipaE4bbQdACGgc0brjdCoF1Fy53sZEOl9mz+CK26gZd7mIjJwB6uR9fV9iaBmXdHBuiInbk7XkswyUATRIAXcolAE0SAF3KZWFtUABajscyXBZ2qTMJUOiGBUChogVAoaIVCujbZ/O2DwAKLaDCbpoDoJCusEudB0RQaB2FVfHndz8AUGgNBbZB3z6ZY0UAKLSEkMVDRSvlrk5toF5eAVBIFyIoVLQAKFS0CrurE4BCugq7qxOAQroKu6sTgEK6JtzVOUdxACikK/tdndMEQCFdyOKhogVAoaIFQKGipQF6cgz7HLPMKwAK6VIBNTuSgizzCoBCurQI+jvX2zxGLPMKgEK6NEDPqOKhwoQqHipaqOKhoqVF0MewKh4DlqHFhH5QqGhpgPYhNDRHAqDQElIBJcOWnO/lHLDMKwAK6bKy+OBUHoBCCwgRFCpaaINCRQtZPFS0JKCeh9iNWeYVAIV06cPtjq63JQxb5hUAhXQhi4eKVkgWjwc3QKvJyuJtPvHgBmg94cENUH5lPIwBA5bx4IY43cI2SCVtTazRwPJakvTRPR60zAc3rMrBkPM2aKlBy4IYbwf+CjSatHwZI+qHjoyv8IMcDO6hDBy0AwUYnz60VmPVg4s6vGVAe6jUMYBG7OZAQEk/qFfmE5Ybt1rtow2aFDt9c6vYXIHXWoVDCqChI+o1tAMUFlLSa0bdqA2aPhh4fDMHF/W4jfE2tJ6Y+BhW4ME1RlZlvnU5DmpkoF/iWnxYaSZWTqN7OuJ0iOApe5Xqm7l+szSC5eSlbAVk8ZM76hcBNOf6t5KqLatpm5oD0C6LPx3ta/GTO+o3dxA3V+ANKAug3389H+xUfsmOeuhWlQPQt89Pl3sb0CU76qFbVZY26OXuT5+qg7XMgh310K0qC6BEf17zniToVpUB0C5QdtHztOqIeuhWNR3Qrqn5+vGHT+veNAfdqqYD2mdHZ0cLdMQSgkKUCdD7aEsIClEmQMMDKACFYgRAoaKVAdAS7ouHblX5+kEjLSEoRAAUKlpLAjrjI8ChWxUiKFS0AChUtAAoVLQAKFS0AChUtAAoVLQAKFS0AChUtOYG9O2z+WAxAApFaEZAPaNIACgUoTkj6MvDAREUmqZ5q/jzux8AKDRFM7dB3z6Zt8UDUIf9OLQAAALeSURBVChGyOKhojU/oHg2EzRBiKBQ0cKAZahozQnogm+ag25VMwK65JvmoFvVnFeS8ABbaDVFRFA8wBZaXmGXOp1tUAhaQAGAphC/pHbhchcb6Xc5Whb75R+pa8qvXbjcxUYC0O263MVGAtDtutzFRk4AdLqL+bQLl7vYSAC6XZe72EgAul2Xu9jIJQCFoBkEQKGiBUChogVAoaIFQKGiBUChogVAoaIFQKGiNQ3Qt09VdU/uXTrqn/PJdsmmLOmyU8y7+XJ4PC+/kYu6pDdu2PRMA/R8T1/m/fTy7Vf1c9JKY13SKYu6pI+tWtLjy4fnpTdyUZfX18f33YdNz/Qq/nzot+Tzk/o5eaUxLumUZV2+ff7Fsh5n30Db5aKH8u3Lj10EdbicDGgXmfsReaej+jl1pVEur/Z9fbO7PB/mJsbwePrVw7z1re2yqyWs53LN5pIeQwc9UwHtgvJ1YUBNl3TKoi67M31mQE2Pp7vnpffr5W7mKl51ORegL988Xa/L1guWSzplUZfn/qauOQm1PPaHbd5zwt7IQ8Rw9akuKaDZq3jaol00SbJdzuvP6fI6My22x9lrJofLPmgvtZUU0OxJ0olGkiW7mWyXp7nDmWMrZwbU4fE87za6XJ5m7mbSXM7TzQRBMwuAQkULgEJFC4BCRQuAQkULgEJFC4BCRQuAQkULgEJFC4BO05k9bfU4+4CVnQqATtbsY1V2LQA6WRTQfpzDN7+tqvsLuYLd385w9zxmCo0KgE6WBPTh/nrp6OwmvH06dNU/CJ0uADpZCqDH6+sj+X95//U6851SOxEAnSylin8iY8Q7QFnutMSNRDcuADpZTkBRu2cSAJ0sF6CkiocyCIBOlgvQt09dCL3MflPkDgRAJ8sFKOlmAp8ZBEChogVAoaIFQKGiBUChogVAoaIFQKGiBUChogVAoaIFQKGiBUChogVAoaIFQKGiBUChogVAoaIFQKGi9f++ayy1MbwNIgAAAABJRU5ErkJggg==", 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, 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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, 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null, 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", null, 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", null, 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null ]
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https://www.storyboardthat.com/storyboards/101e58b3/two-step-equations-storyboard
[ "Two-Step Equations Storyboard\nUpdated: 5/22/2020", null, "This storyboard was created with StoryboardThat.com\n\n#### Storyboard Text\n\n• Learning Target: I can learn how to solve a two-step equation\n• 6+9x=60\n• 3x+7=22\n• Pemdas is an acronym. It tells us what order we should go in to solve two step equations.\n• This is so boring...\n• Let's use 3x+7=22. To solve two step equations you have to work backwards. In 3x+7=22 the first step would be to subtract 7 from 7 because 7 is being added to 3x. So the opposite of addition is subtraction. Since we subtracted 7 from 7 we have to subtract 7 from 22 to make the sides match. That leaves us with 3x=15.\n• Zzzzzzzzzz....\n• I want to go home.\n• Learning Target: I can learn how to solve a two-step equation\n• 6+9x=60\n• 3x+7=22", null, "" ]
[ null, "https://sbt.blob.core.windows.net/storyboards/101e58b3/two-step-equations-storyboard.png", null, "https://www.storyboardthat.com/storyboards/101e58b3/two-step-equations-storyboard", null ]
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https://math.stackexchange.com/questions/3772820/prove-sylvester-gallai-theorem-using-combinatorics
[ "# Prove Sylvester Gallai Theorem using combinatorics\n\nI have come across a question in my book which goes as follows:\n\nConsider a finite set $$S$$ of points in a euclidiean plane such that not all of them are collinear. Prove that there exists a line which passes through exactly two points of $$S$$.\n\nNow this result, known as Sylvester Gallai Theorem (not exactly), can be proven by me using induction but the book demands the proof using combinatorics. In this attempt for same question, the proof seems to be rather complicated." ]
[ null ]
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http://mpc.zib.de/archive.php?2016-3-a
[ "", null, "Mathematical Programming Computation, Volume 8, Issue 3, September 2016\n\n### Revisiting compressed sensing: exploiting the efficiency of simplex and sparsification methods\n\nRobert Vanderbei, Kevin Lin, Han Liu, Lie Wang\n\nWe propose two approaches to solve large-scale compressed sensing problems. The first approach uses the parametric simplex method to recover very sparse signals by taking a small number of simplex pivots, while the second approach reformulates the problem using Kronecker products to achieve faster computation via a sparser problem formulation. In particular, we focus on the computational aspects of these methods in compressed sensing. For the first approach, if the true signal is very sparse and we initialize our solution to be the zero vector, then a customized parametric simplex method usually takes a small number of iterations to converge. Our numerical studies show that this approach is 10 times faster than state-of-the-art methods for recovering very sparse signals. The second approach can be used when the sensing matrix is the Kronecker product of two smaller matrices. We show that the best-known sufficient condition for the Kronecker compressed sensing (KCS) strategy to obtain a perfect recovery is more restrictive than the corresponding condition if using the first approach. However, KCS can be formulated as a linear program with a very sparse constraint matrix, whereas the first approach involves a completely dense constraint matrix. Hence, algorithms that benefit from sparse problem representation, such as interior point methods (IPMs), are expected to have computational advantages for the KCS problem. We numerically demonstrate that KCS combined with IPMs is up to 10 times faster than vanilla IPMs and state-of-the-art methods such as ?1_?s and Mirror Prox regardless of the sparsity level or problem size.\n\nFull Text: PDF\n\n#### Imprint and privacy statement\n\nFor the imprint and privacy statement we refer to the Imprint of ZIB.\n© 2008-2020 by Zuse Institute Berlin (ZIB)." ]
[ null, "http://mpc.zib.de/images/mpc+zib.png", null ]
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https://12000.org/my_notes/rankTest/test.htm
[ "home\nPDF letter size\nPDF legal size\n\n## Comparing Matlab, Mathematica and Maple numerical speed for matrix rank calculation\n\nSept. 2, 2016   Compiled on May 20, 2020 at 2:56am\n\n### 1 Introduction\n\nThis is an informal test comparing speed of Matlab, Mathematica and Maple on one common computational problem which is finding the rank of a square matrix.\n\nFor each $$N \\times N$$ matrix, $$5$$ tests were run and the average value used. During running each test, the PC was not used as not to affect the test and no other programs were running. The PC used has 16 GB RAM, running 64 bit Windows 7 home premium OS.\n\n### 2 Test on Sept. 2, 2016. Matlab 2016a (64 bit), Maple 2016.1 (64 bit), Mathematica 11 (64 bit)\n\nThe time given is in seconds.\n\n matrix size (N) Maple 2016.1 (64 bit) Mathematica 11 (64 bit) Matlab 2016a (64 bit) 500 0.036 0.024 0.0414 1000 0.141 0.134 0.138 1500 0.650 0.616 0.634 2000 2.08 2.033 2.053 2500 4.548 4.504 4.549 3000 2.313 8.393 2.595 3500 3.523 13.865 3.465 4000 5.215 22.088 5.052 4500 7.108 30.846 6.89 5000 8.129 43.079 8.005 5500 10.375 58.216 10.181 6000 13.543 75.655 13.466 6500 15.884 96.048 15.915 7000 19.673 120.505 19.000 7500 23.141 148.593 22.529 8000 28.789 180.311 28.095\n\nMathematica 11 score in this test went down from earlier test, while Maple and Matlab score went up. This issue seems to be due to the intel MKL version that the software is linked to.\n\n### 3 Test on June 5, 2015 using Matlab 2015a (64 bit), Maple 2015.1 (64 bit) and Mathematica 10.1 (64 bit)\n\nThis test was run again for the new release of Mathematica 10.1 and a minor update for Maple 2015 to 2015.1. No changes were made to Matlab version or to the PC used from the last test and hence the Matlab test results were carried over from the last test.\n\nHardware used for this test is exactly the same as last time, and no changes made in the tests themselves.\n\nThe time given is in seconds. This is the time to find the rank for different matrix sizes (lower time is better). The results are in table 2 below.\n\n matrix size (N) Maple 2015.1 (64 bit) Mathematica 10.1 (64 bit) Matlab 2015a (64 bit) 500 0.046 0.03 0.04 1000 0.18 0.14 0.18 1500 0.71 0.65 0.66 2000 2.16 2.15 2.01 2500 4.8 4.66 4.61 3000 8.85 2.25(*) 8.6 3500 14.48 3.42 14.05 4000 22.08 4.98 21.5 4500 32.18 6.97 31.1 5000 45.29 7.80 43.3 5500 60.3 9.66 58.4 6000 77.6 12.81 76.9 6500 100.1 14.70 97.5 7000 123.7 17.82 122.1 7500 153.9 22.49 151.9 8000 184.2 27.03 182.9\n\nMathematica 10.1 was surprisingly much faster on this test than 10.0.2. It seems Mathematica 10.1 is using different algorithm to compute the rank now to account for this drastic difference in speed improvement.\n\nThe speed boost was observed to occur at certain matrix size. At matrix size of 2500 or less, the same speed was obtained as with version 10.0.2. At matrix size over 2500, even by just one, a dramatic speed increase was seen. For $$n=2500$$ Mathematica CPU was around 4.6 seconds which is the same as in 10.0.2, but by increasing the matrix size to $$n=2501$$, CPU time went down to about 1.4 seconds. This is 3 times as fast for essentially the same matrix size. This result was reproducible. This seems to indicate that Mathematica internally uses the same algorithm as previous version for smaller size matrices, and then switches to different algorithm for larger matrices.\n\nThere was no noticeable change in Maple’s speed in this test between 2015 and Maple 2015.1.\n\n### 4 Test on March 11, 2015 using Matlab 2015a (64 bit), Maple 2015 (64 bit) and Mathematica 10.02 (64 bit)\n\nUpdated the test for the now released Maple 2015 (which would have been Maple 19) but the naming changed. Also updated for Matlab 2015a (64 bit) released on March 5, 2015.\n\nHardware used for this test is exactly the same as earlier test on July 2014, which is", null, "The time given is in seconds. This is the time to find the rank for different matrix sizes (lower time is better). The results are in table 3 below.\n\n matrix size (N) Maple 2015 (64 bit) Mathematica 10.02 (64 bit) Matlab 2015a (64 bit) 500 0.043 0.047 0.04 1000 0.175 0.157 0.18 1500 0.64 0.67 0.66 2000 2.1 2.11 2.01 2500 4.8 4.67 4.61 3000 8.7 8.79 8.6 3500 14.5 14.15 14.05 4000 22.2 21.67 21.5 4500 31.7 31.42 31.1 5000 43.6 43.07 43.3 5500 57.9 58.8 58.4 6000 76.3 77.24 76.9 6500 96.7 98.21 97.5 7000 121.8 122.1 122.1 7500 151.2 151.81 151.9 8000 182.3 183.1 182.9\n\nFinally, Maple now runs as fast as Mathematica and Matlab on this test. All three systems now have identical speed performance on this numerical test.\n\nThis indicates Maple 2015 is now using and linked to the same version of Intel optimized numerical libraries used by Matlab and Mathematica. On windows this will be intel math kernel library\n\nThe source code for the test is in the section below. No changes were made to the tests from last time.\n\n### 5 Test on July 28, 2014 using Matlab 2013a (32 bit), Maple 18.01 (64 bit) and Mathematica 10 (64 bit)\n\nHardware used for this test", null, "The time given is in seconds. This is the time to find the rank for different matrix sizes (lower time is better). The results are in table 4 below.\n\n matrix size (N) Maple 18.01, 64 bit Mathematica 10, 64 bit Matlab 2013a, 32 bit 500 0.07 0.031 0.043 1000 0.350 0.163 0.16 1500 1.46 0.72 0.63 2000 3.75 2.13 2.0 2500 7.47 4.72 4.5 3000 12.75 8.65 8.4 3500 19.85 14.22 14 4000 28.5 22.3 21.2 4500 40.5 31.23 30.8 5000 56.4 43.4 43 5500 73.65 58.14 58 6000 95.85 77.11 76 6500 124.84 97.61 96.5 7000 153.51 120.96 121.5 7500 199.4 149.58 150 8000 240.59 181.39 183\n\nMatlab and Mathematica results are almost identical. This is most likely due to the fact that they both are linked to optimized versions of same numerical libraries. On windows this will be intel math kernel library\n\nMaple 18.01 result is similar to its results in version 17 below. It seems to improve as the matrix size became larger, but its overall timing was still about $$25\\%$$ slower than timing of Matlab and Mathematica. It appears that Maple does not use intel-mkl or uses different version or the extra CPU time used comes from other operations done internally. Hard to say.\n\nMatlab results are the same as those from the test below and used as is, since the same Matlab version and same PC and same amount of RAM was used in this test as the one below done on March 26, 2013. Only Maple and Mathematica versions has changed since then.\n\nDescription of the timing functions used is as follows\n\nMaple\nCommand time[real](x) was used. Returns the real time used to evaluate expression x.\nMathematica\nCommand AbsoluteTiming was used. Evaluates expr, returning a list of the absolute number of seconds in real time that have elapsed.\nMatlab\nFunctions tic and toc were used. Work together to measure elapsed time.\n\n#### 5.3 Matlab\n\nThis is a screen shot showing typical memory and CPU usage during running of these tests on my PC", null, "### 6 Test on March 26, 2013 using Matlab 2013a, Maple 17 and Mathematica 9.01\n\nHardware used is the same as above and timing functions are the same as above. The time given is in seconds. This is the time to find the rank for different matrix sizes (lower time is better). The results are in table 5 below.\n\n matrix size (N) Maple 17, 64 bit Mathematica 9.01, 64 bit Matlab 2013a, 32 bit 500 0.07 0.0312 0.043 1000 0.38 0.17 0.16 1500 1.5 0.65 0.63 2000 3.8 2.16 2.0 2500 7.8 4.68 4.5 3000 13 8.67 8.4 3500 20.9 14.1 14 4000 29 21.2 21.2 4500 42 30.9 30.8 5000 58 43.4 43 5500 75 58 58 6000 98 76 76 6500 124 96 96.5 7000 152 122 121.5 7500 198 150 150 8000 237 183 183\n\nMatlab and Mathematica results are identical. This is most likely due to the fact that they both are linked to optimized versions of same numerical libraries. On windows this will be intel math kernel library\n\nMaple result seems to improve as the matrix size became larger, but its overall timing was still about $$25\\%$$ slower than timing of Matlab and Mathematica.\n\n### 7 Test done in 2010 using current version of software at that time\n\nThis test is now old and not valid any more since new version of software exist. This is kept here for archiving only.\n\nHardware used for this test", null, "In the table below, the first column is $$N$$, the matrix size. All values in the matrix are in seconds.\n\n#### 7.1 conclusion for 2010 tests\n\nFor generation of random matrix, Maple was close second to Matlab for smaller Matrix sizes, then Matab pulled ahead as the matrix size increased.\n\nBut overall for all 3 systems, this part took insignificant amount of time compared to rank calculation. So this part did not affect the overall performance.\n\nFor Rank calculation, Maple and Mathematica performance was very close to each others for small size matrices. Almost identical performance. This was up to matrix of size 2500.\n\nMathematica performance then became a little better compared to Maple’s. At Matrix size $$4000 \\times 4000$$ Maple test was terminated due to a failed memory error problem. The amount of RAM needed is $$(4000)(4000)(8)(4)= 512$$ MB.\n\nThis error should not therefore occur. It seems to be an internal problem in Maple since both Matlab and Mathematica are able to handle up to $$5000 \\times 5000$$ matrices.\n\nMathematica was almost $$60\\%$$ faster than Matlab for $$5000 \\times 5000$$ matrix rank calculation. This is a very good result for Mathematica.\n\nMatlab was the fastest in all the tests for the Random matrix generation." ]
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https://www.ccfr.cz/en/model-diagnostics-with-learning-curves/
[ "## Model Diagnostics with Learning Curves", null, "## Model Diagnostics with Learning Curves\n\nevent_note 22.07.2021\n\nReviewing learning curves of models during training and plots of the measured performance can be used to diagnose problems with learning, such as an underfitting or overfitting model. Besides that, it can also be used for diagnosing whether the training and validation datasets are suitably representative and to observe generalization behavior, as well. Our team uses the learning curve visualisation to built more robust, reliable and interpretable Stock Picking Lab model.\n\nWhy (goal)\n\n• Learning curves show changes in learning performance over time in terms of experience.\n• Learning curves of model performance on the train and validation datasets can be used to diagnose if a model is underfitting, overfitting or well-fitting model.\n• Learning curves of model performance can be used to diagnose whether the train or validation datasets are not relatively representative of the specific problem domain.\n\nWhat (key point)\n\n• Plot learning curves\n• Diagnosing model behavior\n• Diagnosing unrepresentative datasets\n\n## How (procedure)\n\n### Learning curve\n\nA learning curve is a plot of model learning performance over experience time period on the x-axis and learning or improvement on the y-axis.\n\nLearning curves (LCs) are deemed effective tools for monitoring the performance of workers exposed to a new task. LCs provide a mathematical representation of the learning process that takes place as task repetition occurs.\n\n– Anzanello, M. J., & Fogliatto, F. S. (2011)\n\nLearning curves are widely used in machine learning for algorithms that learn i.e. optimize their internal parameters incrementally over time, such as deep learning neural networks. During the training of a machine learning model, the current state of the model can be evaluated at each step of the training algorithm. It can be evaluated on the training dataset to give an idea of how well the model is “learning”. It can also be evaluated on a hold-out validation dataset that is not part of the training dataset. Then evaluation on the validation dataset gives an idea of how well the model is “generalizing”.\n\nTraining learning curve: Learning curve calculated from the training dataset gives an idea of how well the model is learning\n\nValidation Learning Curve: Learning curve calculated from a hold-out validation dataset gives an ideal of how well the model is generalizing\n\nIt is common to create dual learning curves for a machine learning model during training on both – the training and validation datasets. Sometimes it is also common to create learning curves for multiple metrics. In the case of classification predictive modeling problems. Here the model may be optimized according to cross-entropy loss and model performance is evaluated by using classification accuracy. In this case, two plots are created, one for the learning curves of each metric, one for each of the train and validation datasets. Note that each plot can show two learning curves.\n\nOptimization learning curves: Learning curves calculated on the metric by which the parameters of the model are being optimized, e.g. loss\n\nPerformance learning curves: Learning curves calculated on the metric by which the model will be evaluated and selected, e.g. accuracy.\n\n### Diagnosing Model Behaviour\n\nThe shape and dynamics of a learning curve can be used to diagnose the behavior of a machine learning model and in turn, perhaps suggest as the type of configuration changes. This option may be used to improve learning and/or performance.\n\nIn general, we can observe 3 types of dynamics:\n\n• Underfitting\n• Overfitting\n• Well-fitting.\n\n## Diagnosing Unrepresentative Datasets\n\nAn unrepresentative dataset means a dataset that may not capture the statistical characteristics relative to another dataset drawn from the same domain. For instance, between a train and a validation dataset. An unrepresentative training dataset means that the training dataset does not provide sufficient information to learn/understand the problem, relative to the validation dataset used to evaluate it.", null, "An unrepresentative validation dataset means that the validation dataset does not provide sufficient information to evaluate the ability of the model to generalize. This may occur if the validation dataset has too few examples as compared to the training dataset. This case can be identified by a learning curve for training loss that looks like a good fit (or other fits) and a learning curve for validation loss that shows noisy movements around the training loss.", null, "It may also be identified by a validation loss that is lower than the training loss. In this case, it indicates that the validation dataset may be easier to predict for the model than the training dataset.", null, "To sum up\n\nLearning curves can bring important insight during the design process of a machine learning model. Visualization of the learning process from various points of view serves to human as a strong, fast and intuitive tool for identification of strengths and weaknesses of the analysed model and for possible issues detection.\n\n## References\n\n Jason Brownlee. (2019, August 6). How to use Learning Curves to Diagnose Machine Learning Model Performance. Machine Learning Mastery. How to use Learning Curves to Diagnose Machine Learning Model Performance – Machine Learning Mastery Anzanello, M. J., & Fogliatto, F. S. (2011). Learning curve models and applications: Literature review and research directions. International Journal of Industrial Ergonomics, 41(5), 573–583. Learning curve models and applications: Literature review and research directions" ]
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https://www.bartleby.com/solution-answer/chapter-27-problem-77pe-college-physics-1st-edition/9781938168000/a-as-a-soap-bubble-thins-it-becomes-dark-because-the-path-length-difference-becomes-small/86453df5-7def-11e9-8385-02ee952b546e
[ "", null, "", null, "", null, "Chapter 27, Problem 77PE\n\nChapter\nSection\nTextbook Problem\n\n(a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of refraction as water. (b) Discuss the fragility of the film considering the thickness found.\n\nTo determine\n\n(a)\n\nThickness of the soap bubble\n\nExplanation\n\nGiven info:\n\nRefractive index of water, n=1.33\n\nFormula used:\n\nThickness of the film producing destructive interference is calculated by the formula\n\n2t=λ4n\n\nHere,\n\nλ is the wavelength of the reflected light\n\nn is the refractive index\n\nt is the thickness of the film producing interference\n\nCalculation:\n\nThe visible spectrum comes in the range of 400nm-700nm now for destructive interference pattern for all the visible light spectrum, minimum wavelength of the light spectrum should be used\n\nTo determine\n\n(b)\n\nThe fragility of the film\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\nFind more solutions based on key concepts", null, "" ]
[ null, "https://www.bartleby.com/static/search-icon-white.svg", null, "https://www.bartleby.com/static/close-grey.svg", null, "https://www.bartleby.com/static/solution-list.svg", null, "https://www.bartleby.com/static/logo.svg", null ]
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https://www.colorhexa.com/1d7fc4
[ "# #1d7fc4 Color Information\n\nIn a RGB color space, hex #1d7fc4 is composed of 11.4% red, 49.8% green and 76.9% blue. Whereas in a CMYK color space, it is composed of 85.2% cyan, 35.2% magenta, 0% yellow and 23.1% black. It has a hue angle of 204.8 degrees, a saturation of 74.2% and a lightness of 44.1%. #1d7fc4 color hex could be obtained by blending #3afeff with #000089. Closest websafe color is: #3366cc.\n\n• R 11\n• G 50\n• B 77\nRGB color chart\n• C 85\n• M 35\n• Y 0\n• K 23\nCMYK color chart\n\n#1d7fc4 color description : Strong blue.\n\n# #1d7fc4 Color Conversion\n\nThe hexadecimal color #1d7fc4 has RGB values of R:29, G:127, B:196 and CMYK values of C:0.85, M:0.35, Y:0, K:0.23. Its decimal value is 1933252.\n\nHex triplet RGB Decimal 1d7fc4 `#1d7fc4` 29, 127, 196 `rgb(29,127,196)` 11.4, 49.8, 76.9 `rgb(11.4%,49.8%,76.9%)` 85, 35, 0, 23 204.8°, 74.2, 44.1 `hsl(204.8,74.2%,44.1%)` 204.8°, 85.2, 76.9 3366cc `#3366cc`\nCIE-LAB 51.179, -2.13, -43.473 18.057, 19.424, 55.019 0.195, 0.21, 19.424 51.179, 43.525, 267.196 51.179, -30.344, -66.464 44.073, -3.992, -43.165 00011101, 01111111, 11000100\n\n# Color Schemes with #1d7fc4\n\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #c4621d\n``#c4621d` `rgb(196,98,29)``\nComplementary Color\n• #1dc4b6\n``#1dc4b6` `rgb(29,196,182)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #1d2cc4\n``#1d2cc4` `rgb(29,44,196)``\nAnalogous Color\n• #c4b61d\n``#c4b61d` `rgb(196,182,29)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #c41d2c\n``#c41d2c` `rgb(196,29,44)``\nSplit Complementary Color\n• #7fc41d\n``#7fc41d` `rgb(127,196,29)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #c41d7f\n``#c41d7f` `rgb(196,29,127)``\n• #1dc462\n``#1dc462` `rgb(29,196,98)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #c41d7f\n``#c41d7f` `rgb(196,29,127)``\n• #c4621d\n``#c4621d` `rgb(196,98,29)``\n• #135481\n``#135481` `rgb(19,84,129)``\n• #166298\n``#166298` `rgb(22,98,152)``\n• #1a71ae\n``#1a71ae` `rgb(26,113,174)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #208dda\n``#208dda` `rgb(32,141,218)``\n• #3399e1\n``#3399e1` `rgb(51,153,225)``\n• #49a4e4\n``#49a4e4` `rgb(73,164,228)``\nMonochromatic Color\n\n# Alternatives to #1d7fc4\n\nBelow, you can see some colors close to #1d7fc4. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #1da9c4\n``#1da9c4` `rgb(29,169,196)``\n• #1d9bc4\n``#1d9bc4` `rgb(29,155,196)``\n• #1d8dc4\n``#1d8dc4` `rgb(29,141,196)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #1d71c4\n``#1d71c4` `rgb(29,113,196)``\n• #1d63c4\n``#1d63c4` `rgb(29,99,196)``\n• #1d55c4\n``#1d55c4` `rgb(29,85,196)``\nSimilar Colors\n\n# #1d7fc4 Preview\n\nThis text has a font color of #1d7fc4.\n\n``<span style=\"color:#1d7fc4;\">Text here</span>``\n#1d7fc4 background color\n\nThis paragraph has a background color of #1d7fc4.\n\n``<p style=\"background-color:#1d7fc4;\">Content here</p>``\n#1d7fc4 border color\n\nThis element has a border color of #1d7fc4.\n\n``<div style=\"border:1px solid #1d7fc4;\">Content here</div>``\nCSS codes\n``.text {color:#1d7fc4;}``\n``.background {background-color:#1d7fc4;}``\n``.border {border:1px solid #1d7fc4;}``\n\n# Shades and Tints of #1d7fc4\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010508 is the darkest color, while #f6fafe is the lightest one.\n\n• #010508\n``#010508` `rgb(1,5,8)``\n• #041019\n``#041019` `rgb(4,16,25)``\n• #061b2a\n``#061b2a` `rgb(6,27,42)``\n• #09263b\n``#09263b` `rgb(9,38,59)``\n• #0b314c\n``#0b314c` `rgb(11,49,76)``\n• #0e3d5d\n``#0e3d5d` `rgb(14,61,93)``\n• #10486f\n``#10486f` `rgb(16,72,111)``\n• #135380\n``#135380` `rgb(19,83,128)``\n• #155e91\n``#155e91` `rgb(21,94,145)``\n• #1869a2\n``#1869a2` `rgb(24,105,162)``\n• #1a74b3\n``#1a74b3` `rgb(26,116,179)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n``#208ad5` `rgb(32,138,213)``\n• #2994df\n``#2994df` `rgb(41,148,223)``\n• #3a9ce2\n``#3a9ce2` `rgb(58,156,226)``\n• #4ba5e4\n``#4ba5e4` `rgb(75,165,228)``\n• #5caee7\n``#5caee7` `rgb(92,174,231)``\n• #6db6e9\n``#6db6e9` `rgb(109,182,233)``\n• #7ebfec\n``#7ebfec` `rgb(126,191,236)``\n• #8fc7ee\n``#8fc7ee` `rgb(143,199,238)``\n• #a1d0f1\n``#a1d0f1` `rgb(161,208,241)``\n• #b2d8f4\n``#b2d8f4` `rgb(178,216,244)``\n• #c3e1f6\n``#c3e1f6` `rgb(195,225,246)``\n• #d4e9f9\n``#d4e9f9` `rgb(212,233,249)``\n• #e5f2fb\n``#e5f2fb` `rgb(229,242,251)``\n• #f6fafe\n``#f6fafe` `rgb(246,250,254)``\nTint Color Variation\n\n# Tones of #1d7fc4\n\nA tone is produced by adding gray to any pure hue. In this case, #6b7176 is the less saturated color, while #0384de is the most saturated one.\n\n• #6b7176\n``#6b7176` `rgb(107,113,118)``\n• #62737f\n``#62737f` `rgb(98,115,127)``\n• #5a7487\n``#5a7487` `rgb(90,116,135)``\n• #517690\n``#517690` `rgb(81,118,144)``\n• #487799\n``#487799` `rgb(72,119,153)``\n• #4079a1\n``#4079a1` `rgb(64,121,161)``\n• #377aaa\n``#377aaa` `rgb(55,122,170)``\n• #2e7cb3\n``#2e7cb3` `rgb(46,124,179)``\n• #267dbb\n``#267dbb` `rgb(38,125,187)``\n• #1d7fc4\n``#1d7fc4` `rgb(29,127,196)``\n• #1481cd\n``#1481cd` `rgb(20,129,205)``\n• #0c82d5\n``#0c82d5` `rgb(12,130,213)``\n• #0384de\n``#0384de` `rgb(3,132,222)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #1d7fc4 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
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https://consultglp.com/2017/10/
[ "## Training and consultancy for testing laboratories.", null, "### ISO FDIS 17025:2017, sampling & sampling uncertainty", null, "The international standards for accrediting laboratory’s technical competence has evolved over the past 30 over years, started from ISO Guide 25: 1982 to ISO Guide 25:1990, to ISO 17025:1999, to ISO 17025:2005 and now to the final draft international standard FDIS 17025:2017, which is due to be published before the end of this year to replace the 2005 version. We do not anticipate much changes to the contents other than any editorial amendments.\n\nThe new draft standard aims to align its structure and contents with other recently revised ISO standards, and the ISO 9001:2015 in particular. It is reinforcing a process-based model and focuses on outcomes rather than prescriptive requirements such as eliminating familiar terms like quality manual, quality manager, etc. and giving less description on other documentation. It attempts to introduce more flexibility for laboratory operation.\n\nAlthough many requirements remain unchanged but appear in different places of the document, it has added some new concepts such as:\n\n–  focusing on risk-based thinking and acting,\n\n–  decision rule for measurement uncertainty to be accountable for when stating\n\nconformity with a specification,\n\n–  sampling as another laboratory activity apart from testing, and calibration, and,\n\n–  sampling uncertainty to be a significant contributing factor for the evaluation of\n\nmeasurement uncertainty.\n\nThe purpose of introducing sampling as another activity is understandable, as we know that the reliability of test results is hanged on how representative the sample drawn from the field is. The saying “The test result is no better than the sample that it is based upon” is very true indeed.\n\nIf an accredited laboratory’s routine activity is also involved in the field sampling before carrying out laboratory analysis on the sample(s) drawn, the laboratory must show evidence of a robust sampling plan to start with, and to evaluate the associated sampling uncertainty.\n\nIt is reckoned however that in the process of carrying out analysis, the laboratory has to carry out sub-sampling of the sample received and this is to be part of the SOP which must devote a section on how to sub-sample it. If the sample received is not homogeneous, a consideration of sampling uncertainty is to be taken into account.\n\nAlthough FDIS states that when evaluating the measurement uncertainty (MU), all components which are of significance in the given situation shall be identified and taken into account using appropriate methods of analysis, its Clause 7.6.3 Note 2 further states that “for a particular method where the measurement uncertainty of the results has been established and verified, there is no need to evaluate measurement uncertainty for each result if it can demonstrate that the identified critical influencing factors are under control”.\n\nTo me, it means that all identified critical uncertainty influencing factors must be continually monitored. This will have a pressured work load for the laboratory concerned to keep track with many contributing components over time if the GUM method is used to evaluate its MU.\n\nThe main advantage of the top down MU evaluation approach based on holistic method performance using the daily routine quality control data, such as intermediate precision and bias estimation is also appreciated as stated in Clause 7.6.3.  Its Note 3 refers to the ISO 21748 which uses accuracy, precision and trueness as the budgets for evaluation of MU, as an information reference.\n\nSecondly, this clause in the FDIS suggests that once you have established an uncertainty of a result by the test method, you can estimate the MU of all test results in a predefined range through the use of relative uncertainty calculation.\n\n### Linear regression model after data transformation\n\nAn example of linear regression model after data transformation\n\n### The basics of linear regression", null, "The Basics of Linear Regression\n\n### Estimation in statistics\n\nMany course participants of non-statistics background always find the word “estimation” in statistics rather abstract and difficult to apprehend. To overcome this, one can get a clear picture with the following explanations.\n\nIn carrying out statistical analysis, we must appreciate an important point that we are always trying to understand the characteristics or features of a larger phenomenon (called population) from the data analysis of samples collected from this population.\n\nThen let’s differentiate the meanings of the words “parameter” and “statistic”.\n\nA parameter is a statistical constant or number describing a feature of the entire phenomenon or population, such as population mean m, or population standard deviation σ, whilst a statistic is any summary number that describes the sample such as sample standard deviation s.\n\nOne of the major applications used by statisticians is estimating population parameter from sample statistics. For example, sample means are used to estimate population means, sample proportions to estimate population proportions.\n\nIn short, estimation refers to the process by which one makes inferences about a population, based on information obtained from one or more samples. It is basically the process of finding the values of the parameters that make the statistical model fit the data the best.\n\nIn fact, estimation is one of the two common forms of statistical inference.  Another one is the null hypothesis tests of significance, including the analysis of variance ANOVA.\n\nGenerally we can express an estimate of a population parameter in two ways:\n\nPoint estimate. A point estimate of a population parameter is a single value of a statistic, such as the sample mean is a point estimate of the population mean.\n\nInterval estimate. An interval estimate is defined by a range of two numbers, between which a population parameter is said to likely lie upon with certain degree of confidence. For example, the expression  X + U or –U < X < +U  gives the range of uncertainty estimate of the population mean.\n\nIt is to be noted that point estimates and parameters represent fundamentally different things. For example:\n\n• Point estimates are calculated from the data; parameters are not.\n• Point estimates vary from study to study; parameters do not.\n• Point estimates are random variables: parameters are constants.\n\n### Linear calibration curve – two common mistakes", null, "Linear calibration curve – two common mistakes\n\nGenerally speaking, linear regression is used to establish or confirm a relationship between two variables. In analytical chemistry, it is commonly used in the construction of calibration functions required for techniques such as GC, HPLC, AAS, UV-Visible spectrometry, etc., where a linear relationship is expected between the instrument response (dependent variable) and the concentration of the analyte of interest.\n\nThe word ‘dependent variable’ is used for the instrument response because the value of the response is dependent on the value of concentration. The dependent variable is conventionally plotted on the y-axis of the graph (scatter plot) and the known analyte concentration (independent variable) on x-axis, to see whether a relationship exists between these two variables.\n\nIn chemical analysis, a confirmation of such relationship between these two variables is essential and this can be establish in terms of an equation. The other aspects of the calibration can then be proceeded.\n\nThe general equation which describes a fitted straight line can be written as:\n\ny = a + bx\n\nwhere b is the gradient of the line and a, its intercept with the y-axis. The least-squares linear regression method is normally used to establish the values of a and b. The ‘best fit’ line obtained from the squares linear regression is the line which minimizes the sum of the squared differences between the observed (or experimental) and line-fitted values for y.\n\nThe signed difference between an observed value (y) and the fitted value (ŷ) is known as a residual. The most common form of regression is of y on x.  This comes with an important assumption, i.e. the x values are known exactly without uncertainty and the only error occurs in the measurement of y.\n\nTwo mistakes are so common in routine application of linear regression that it is worth describing them so that they can be well avoided:\n\n1. Incorrectly forcing the regression through zero\n\nSome instrument software allows a regression to be forced through zero (for example, by specifying removal of the intercept or ticking a “Constant is ‘zero’ option”).\n\nThis is valid only with good evidence to support its use, for example, if it has been previously shown that y-the intercept is not significant after statistical analysis. Otherwise, interpolated values at the ends of the calibration range will be incorrect. It can be very serious near zero.\n\n1. Including the point (0,0) in the regression when it has not been measured\n\nSometimes it is argued that the point (x = 0, y = 0) should be included in the regression, usually on the grounds that y = 0 is an expected response at x = 0. This is actually a bad practice and not allowed at all. It seems that we simply cook up the data.\n\nAdding an arbitrary point at (0,0) will cause the fitted line to be more closer to (0,0), making the line fit the data more poorly near zero and also making it more likely that a real non-zero intercept will go undetected (because the calculated y-intercept will be smaller).\n\nThe only circumstance in which a point (0,0) can be validly be added to the regression data set is when a standard at zero concentration has been included and the observed response is either zero or is too small to detect and can reasonably be interpreted as zero.\n\n### Verifying Eurachem’s example A1 on sampling uncertainty\n\nEurachem/CITAC Guide (2007) “Measurement Uncertainty arising from Sampling” provides examples on estimating sampling uncertainty.  The Example A1 on Nitrate in glasshouse grown lettuce  shows a summary of the classical ANOVA results on the duplicate method in the MU estimation without detailed calculations.\n\nThe 2007 NORDTEST Technical Report TR604 “Uncertainty from Sampling” gives examples on how to use relative range statistics to evaluate the double split design method which is similar to the duplicate method suggested in Eurachem.\n\nWe have used an Excel spreadsheet to verify the Eurachem’s results using the NORDTEST approach and found them satisfactory. The Two-Way ANOVA by the Excel Analytical Tool also shows similar results, but we have to combine the sum of squares of between-duplicate samples and sum of squares of interaction.\n\nVerifying Eurachem Example A1 by NORDTEST method\n\n### A step-by-step ANOVA example on Sampling and Analysis", null, "A step-by-step ANOVA example on Sampling and Analysis\n\n### Recall basic ideas of ANOVA (Analysis of Variance)\n\nThere is a growing interest in sampling and sampling uncertainty amongst laboratory analysts.  This is mainly because the newly revised ISO/IEC 17025 accreditation standards to be implemented soon has added in new requirements for sampling and estimating its uncertainty, as the standard reckons that the test result is as good as the sample that is based on, and hence the importance of representative sampling cannot be over emphasized.\n\nLike measurement uncertainty, appropriate statistical methods involving the analysis of variance (frequently abbreviated to ANOVA) have to be applied to estimate the sampling uncertainty. Strictly speaking, the uncertainty of a measurement result has two contributing components, i.e. sampling uncertainty and analysis uncertainty.  We have been long ignoring this important contributor for all these years.\n\nANOVA indeed is a very powerful statistical technique which can be used to separate and estimate the different causes of variation.\n\nIt is simple to compare two mean values obtained from two samples upon testing to see whether they differ significantly by a Student’s t-test.  But in analytical work, we are often confronted with more than two means for comparison. For example, we may wish to compare the mean concentrations of protein in a sample solution stored under different temperature and holding time; we may also want to compare the concentration of an analyte by several test methods.\n\nIn the above examples, we have two possible sources of variation. The first, which is always present, is due to the inherent random error in measurement.  This within-sample variation can be estimated through series of repeated testing.\n\nThe second possible source of variation is due to what is known as controlled or fixed-effect and random-fixed factors: in the above example on protein analysis, the controlled factors are respectively the temperature, holding time and the method of analysis used for comparing test results.  ANOVA then statistically analyzes the between-sample variation.\n\nIf there is one factor, either controlled or random, the type of statistical analysis is known as one-way ANOVA.  When there are two or more factors involved, there is a possibility of interaction between variables.  In this case, we conduct two-way ANOVA or multi-way ANOVA.\n\nOn this blog site, several short articles on ANOVA have been previously presented.  Valuable comments are always welcome.\n\nhttps://consultglp.com/2017/04/04/anova-variance-testing-an-important-statistical-tool-to-know/" ]
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http://www.logicalaptitude.com/reasoning/maths-reasoning/
[ "# Maths Reasoning\n\nThis page will have reasoning Questions related to Maths Operation (Mathematical Signs /Symbol). The questions will deal with four fundamental operations – addition,subtraction,division and multiplication. Also symbols such as ‘less than’,greater than’,’equal to’,’not equal to’ etc will be there. Symbols are interchanged with different ones and need to answer based on that.\n\nWhile solving a problem,always follow BODMAS rule. That means any equation has to follow this order BRACKETS,OF,DIVISION,MULTIPLICATION,ADDITION,SUBTRACTION. Maths Reasoning and Numerical ability Aptitude questions are easier to solve and saves time in competitive exams. Regular practice of these Tests should help you achieve good score.\n\nQ1. If “+” means “minus”, “*” means “divided by” ,+ means plus,’-‘means ‘multiplied by’, then what will be the value of 252 * 9 – 5 + 32 ÷ 92 ..?\n\n1. 95\n2. 168\n3. 192\n4. 200\n\nQ 2 – If L stands for +, M stands for – , N stands for *, P stands for ÷, then what is the value of 14N10L42P2M8 ..?\n\n1. 153\n2. 216\n3. 248\n4. 251\n\nQ 3 – If “<” means minus, “>” means plus,”=”means multiplies by and “$” means divided by, then what would be the value of 27 > 81$ 9 < 6 .. ?\n\n1. 6\n2. 33\n3. 36\n4. 54\n5. None of these\n\nQ 4 – If “+” means divided by, “-” means added to , “*” means subtracted from,”÷” means multiplied by, then what is the value of 24 ÷ 12 – 18 + 9 ..?\n\n1. – 25\n2. 0.72\n3. 15.30\n4. 290\n5. None of the above\n\nQ 5 – If $means +, # means – , @ means *, & means ÷, then what is the value of 16$ 4 @ 5 # 72 & 8 ?\n\n1. 25\n2. 27\n3. 29\n4. 36\n5. None of the above\n\nQ 6 – If ÷ means *, * means +, + means – , – means ÷, then find the value of 16 * 3 + 5 – 2 ÷ 4 ..?\n\n1. 9\n2. 10\n3. 19\n4. None of the above\n\nQ 7- If * means ÷, – means *, ÷ means + and + means – then ( 3 – 15 ÷ 19) * 8 + 6 = .. ?,\n\n1. – 1\n2. 2\n3. 4\n4. 8\n\nQ 8- If “+” means divided by , ” – ” means add, ” * ” means minus and “/” means multiplied by, then what will be the value of this equation [{(17 * 12 ) – (4/2)} + (23 – 6)]/0 = .. ?\n\n1. Infinity\n2. 0\n3. 118\n4. 219\n\nQ 9 – If “Q” means add to, “J” means multiply by , “T” means subtract from and “K” means divide by ,then what is the value of 30 K 2 Q 3 J 6 T 5 = ?\n\n1. 18\n2. 28\n3. 31\n4. 103\n\nQ 10- If P denotes ÷ , Q denotes * , R denotes + and S denotes – , then what is the value of 18 Q 12 P 4 R 5 S 6 .. ?\n\n1. 53\n2. 59\n3. 63\n4. 65\n\nQ 11- If P means division , T means addition , M means subtraction and D means multiplication, then what will be the value of 12 M 12 D 28 P 7 T 15 ..?\n\n1. – 30\n2. – 15\n3. 15\n4. 45\n5. None of the above\n\nQ 12- If “when” means *, “you” means ÷ , “come” means – , and “will” means + , then what will be the value of “8 when 12 will 16 you 2 come 10” .. ?\n\n1. 45\n2. 94\n3. 96\n4. 112\n\nQ 13 – If ” – ” means division, ” + ” means for multiplication , ” ÷ ” means subtraction and ” * ” means addition, then which of the following is correct ..?\n\n1. 4 * 5 + 9 – 3 ÷ 4 = 15\n2. 4 * 5 * 9 + 3 ÷ 4 = 11\n3. 4 – 5 ÷ * 3 – 4 = 17\n4. 4 ÷ 5 + 9 – 3 + 4 = 18\n\nQ 14 – If “*” denotes addition, “<” denotes subtraction , “+” denotes division, “>” denotes multiplication, ” – ” denotes “equal to” , ” ÷ ” denotes “greater than” , “=” denotes “less than”, then which of the following is correct .. ?\n\n1. 3 * 4 > 2 – 9 + 3 < 3\n2. 5 * 3 < 7 ÷ 8 + 4 * 1\n3. 5 > 2 + 2 = 10 < 4 * 8\n4. 3 * 2 < 4 ÷ 16 > 2 + 4\n\nQ 15 – In this Maths reasoning problem, “÷ ” implies “=” , “*” implies “<” “+” implies “>” , ” – ” implies ” * “, “>” implies “÷”, “<” implies”+” and “=” implies ” – ” , then which of the following is correct ?\n\n1. 1 – 3 > 2 + 1 – 5 = 3 – 1 < 2\n2. 1 – 3 > 2 + 1 * 5 = 3 * 1 > 2\n3. 1 * 3 > 2 + 1 * 5 * 3 – 1 > 2\n4. 1 – 3 > 2 + 1 * 5 + 3 – 1 > 2\n\nFor More Reasoning Questions, kindly refer here" ]
[ null ]
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https://metanumbers.com/1531024
[ "1531024 (number)\n\n1,531,024 (one million five hundred thirty-one thousand twenty-four) is an even seven-digits composite number following 1531023 and preceding 1531025. In scientific notation, it is written as 1.531024 × 106. The sum of its digits is 16. It has a total of 6 prime factors and 20 positive divisors. There are 695,840 positive integers (up to 1531024) that are relatively prime to 1531024.\n\nBasic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 7\n• Sum of Digits 16\n• Digital Root 7\n\nName\n\nShort name 1 million 531 thousand 24 one million five hundred thirty-one thousand twenty-four\n\nNotation\n\nScientific notation 1.531024 × 106 1.531024 × 106\n\nPrime Factorization of 1531024\n\nPrime Factorization 24 × 11 × 8699\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 6 Total number of prime factors rad(n) 191378 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 1,531,024 is 24 × 11 × 8699. Since it has a total of 6 prime factors, 1,531,024 is a composite number.\n\nDivisors of 1531024\n\n20 divisors\n\n Even divisors 16 4 2 2\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 20 Total number of the positive divisors of n σ(n) 3.2364e+06 Sum of all the positive divisors of n s(n) 1.70538e+06 Sum of the proper positive divisors of n A(n) 161820 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 1237.35 Returns the nth root of the product of n divisors H(n) 9.46128 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 1,531,024 can be divided by 20 positive divisors (out of which 16 are even, and 4 are odd). The sum of these divisors (counting 1,531,024) is 3,236,400, the average is 161,820.\n\nOther Arithmetic Functions (n = 1531024)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 695840 Total number of positive integers not greater than n that are coprime to n λ(n) 173960 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 116066 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 695,840 positive integers (less than 1,531,024) that are coprime with 1,531,024. And there are approximately 116,066 prime numbers less than or equal to 1,531,024.\n\nDivisibility of 1531024\n\n m n mod m 2 3 4 5 6 7 8 9 0 1 0 4 4 5 0 7\n\nThe number 1,531,024 is divisible by 2, 4 and 8.\n\nClassification of 1531024\n\n• Arithmetic\n• Abundant\n\nExpressible via specific sums\n\n• Polite\n• Non-hypotenuse\n\nBase conversion (1531024)\n\nBase System Value\n2 Binary 101110101110010010000\n3 Ternary 2212210011121\n4 Quaternary 11311302100\n5 Quinary 342443044\n6 Senary 52452024\n8 Octal 5656220\n10 Decimal 1531024\n12 Duodecimal 61a014\n20 Vigesimal 9b7b4\n36 Base36 wtcg\n\nBasic calculations (n = 1531024)\n\nMultiplication\n\nn×y\n n×2 3062048 4593072 6124096 7655120\n\nDivision\n\nn÷y\n n÷2 765512 510341 382756 306205\n\nExponentiation\n\nny\n n2 2344034488576 3588773058837581824 5494497683633749874507776 8412207821587678267868393242624\n\nNth Root\n\ny√n\n 2√n 1237.35 115.255 35.1759 17.2582\n\n1531024 as geometric shapes\n\nCircle\n\n Diameter 3.06205e+06 9.61971e+06 7.364e+12\n\nSphere\n\n Volume 1.50326e+19 2.9456e+13 9.61971e+06\n\nSquare\n\nLength = n\n Perimeter 6.1241e+06 2.34403e+12 2.16519e+06\n\nCube\n\nLength = n\n Surface area 1.40642e+13 3.58877e+18 2.65181e+06\n\nEquilateral Triangle\n\nLength = n\n Perimeter 4.59307e+06 1.015e+12 1.32591e+06\n\nTriangular Pyramid\n\nLength = n\n Surface area 4.05999e+12 4.22941e+17 1.25008e+06\n\nCryptographic Hash Functions\n\nmd5 0af2231e54620c84d3c5f423e80117ef 31d42fd9cc065a63e22d5c8ba1f7e510d1a19bb6 c479528f5579d72d789000766a1d8e243f229e38087419aa605c5b598cface0e 03076a47facb0d1172c8afc45056f6985560eb1418377f10404a2ee334a4a7110529135e3b90d1fd9966b5ae1d8188f91330f2b60c5269d6da7576033defbf22 155cb979e03ea727b733f62f5f483e1369f580c0" ]
[ null ]
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https://www.codevscolor.com/dart-instance-variable
[ "# Dart instance variable examples", null, "## Introduction :\n\nInstance variables are variables declared inside a class. Every object of that class gets a new copy of instance variables. In this post, we will learn how instance variables work and different ways to initialize them.\n\n## Example of instance variable :\n\nLet’s consider the below example :\n\n``````class Student{\nString name;\nnum age;\n}\n\nmain() {\nvar alex = new Student();\nalex.name = \"Alex\";\n\nprint(\"Name : \\${alex.name}, Age : \\${alex.age}\");\n}``````\n\nIt will print out :\n\n``Name : Alex, Age : null``\n\nHere, we have two instance variables name and age. After the declaration, both variables have the value null i.e. when the alex object is created, both name and age were initialized with null. Then, we assigned one value Alex to the variable name. So, the print method prints Alex for name variable.\n\nAll instance variables have implicit getter method and implicit setter method for all non final variables. Using a dot (.), we can access these variables. You can also use different getter/setter methods to initialize them.\n\n### Initialize instance variables in a constructor :\n\nWe can re-write the above program to initialize the instance variables in a constructor when the object\n\n``````class Student {\nString name;\nnum age;\n\nStudent(this.name, this.age);\n}\n\nmain() {\nvar alex = new Student(\"Alex\", 20);\n\nprint(\"Name : \\${alex.name}, Age : \\${alex.age}\");\n}``````\n\nIt will print :\n\n``Name : Alex, Age : 20``\n\nWe are initializiing the variable in the constructor and setting their values before the constructor body runs. You can also set the values in the constructor body, but it is concise and easy.\n\n### Initialize instance variables in initializer list :\n\n``````class Student {\nString name;\nnum age;\n\nStudent.create(String studentName, num studentAge): name = studentName, age = studentAge {\nprint(\"One new student is created with Name : \\${this.name} and Age : \\${this.age}\");\n}\n}\n\nmain() {\nvar alex = Student.create(\"Alex\", 20);\n\nprint(\"Name : \\${alex.name}, Age : \\${alex.age}\");\n}``````\n\nInitializer list initializes instance variables before the constructor body runs. You can initialize instance variables without using this.\n\n### Initialize final instance variables :\n\nfinal variables can’t be changed. You can use one normal constructor or constant constructor for that. If you are using constant constructor, all instance variables should be final as these types of objects can’t be changed.\n\n``````class Student {\nfinal String name;\nfinal num age;\n\nconst Student(this.name, this.age);\n}\n\nmain() {\nvar alex = Student(\"Alex\", 20);\n\nprint(\"Name : \\${alex.name}, Age : \\${alex.age}\");\n}``````\n\nDifferent ways are there to initialize instance variables. It depends on the program, how to initialize and how to access its values. It is also a good practice to add null check to an instance variable if you are not sure that it got initialized or not.\n\n### Where is the color and why codevscolor ?\n\nLong story short, I love paintings and I paint on weekends. We(me and my wife) have one Youtube channel. Below is a video that I did recently. If you love this please do subscribe to support us 😊" ]
[ null, "data:image/png;base64,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", null ]
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http://www.comenb.com/30863.html
[ "# 湿空气的湿度\n\nρv=mv/V=Pv/RvT\n\nΦ=ρv/ρ”=ρv/ρmax\n\nPv=RvTρv\nPs=RvTρ”\n\nρv/ρ”= Pv/ Ps\n\nΦ=ρv/ρ”=ρv/ρmax= Pv/ Ps\n\nω=Mv/Ma=ρv/ρa kg（水蒸气）/kg（干空气）\n\nPv=RvTρv\nPa=RaTρa\n\nω=0.622Pv/（Pb-Pv）=0.622ΦPmax/（Pb-ΦPmax） kg（水蒸气）/kg（干空气）", null, "" ]
[ null, "http://www.comenb.com/wp-content/uploads/2018/10/gongye-12-1.jpg", null ]
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http://proceedings.mlr.press/v130/scieur21a.html
[ "# Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates\n\nDamien Scieur, Lewis Liu, Thomas Pumir, Nicolas Boumal\nProceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:550-558, 2021.\n\n#### Abstract\n\nQuasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees." ]
[ null ]
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https://convertoctopus.com/47-3-knots-to-meters-per-second
[ "## Conversion formula\n\nThe conversion factor from knots to meters per second is 0.514444444444, which means that 1 knot is equal to 0.514444444444 meters per second:\n\n1 kt = 0.514444444444 m/s\n\nTo convert 47.3 knots into meters per second we have to multiply 47.3 by the conversion factor in order to get the velocity amount from knots to meters per second. We can also form a simple proportion to calculate the result:\n\n1 kt → 0.514444444444 m/s\n\n47.3 kt → V(m/s)\n\nSolve the above proportion to obtain the velocity V in meters per second:\n\nV(m/s) = 47.3 kt × 0.514444444444 m/s\n\nV(m/s) = 24.333222222201 m/s\n\nThe final result is:\n\n47.3 kt → 24.333222222201 m/s\n\nWe conclude that 47.3 knots is equivalent to 24.333222222201 meters per second:\n\n47.3 knots = 24.333222222201 meters per second\n\n## Alternative conversion\n\nWe can also convert by utilizing the inverse value of the conversion factor. In this case 1 meter per second is equal to 0.041096078064319 × 47.3 knots.\n\nAnother way is saying that 47.3 knots is equal to 1 ÷ 0.041096078064319 meters per second.\n\n## Approximate result\n\nFor practical purposes we can round our final result to an approximate numerical value. We can say that forty-seven point three knots is approximately twenty-four point three three three meters per second:\n\n47.3 kt ≅ 24.333 m/s\n\nAn alternative is also that one meter per second is approximately zero point zero four one times forty-seven point three knots.\n\n## Conversion table\n\n### knots to meters per second chart\n\nFor quick reference purposes, below is the conversion table you can use to convert from knots to meters per second\n\nknots (kt) meters per second (m/s)\n48.3 knots 24.848 meters per second\n49.3 knots 25.362 meters per second\n50.3 knots 25.877 meters per second\n51.3 knots 26.391 meters per second\n52.3 knots 26.905 meters per second\n53.3 knots 27.42 meters per second\n54.3 knots 27.934 meters per second\n55.3 knots 28.449 meters per second\n56.3 knots 28.963 meters per second\n57.3 knots 29.478 meters per second" ]
[ null ]
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https://it.mathworks.com/matlabcentral/profile/authors/19873468
[ "Community Profile", null, "# Mehul kumar\n\nLast seen: 9 mesi ago Active since 2021\n\n#### Content Feed\n\nView by\n\nQuestion\n\nCannot understand the error in my code to solve differential equation. Please someone tell me the corrections to be made.\nclf syms t m ycf='exp(m*t)';clf syms t m ycf='exp(m*t)'; y1=diff(ycf,t); y2=diff(y1,t); y3=simplify(subs('D2y+y=0',{'y','...\n\n9 mesi ago | 1 answer | 0\n\n### 1\n\nQuestion\n\nUnable to understand the error\nclose all clc syms c1 c2 x m omega gamma Fo F=input('enter the coefficients [a,b,c]:'); f=input('enter the RHS function f(x)...\n\n9 mesi ago | 1 answer | 0\n\n### 1\n\nQuestion\n\nHow to give a piecewise function as input\nclear all clc syms t s y(t) Y dy(t)=diff(y(t)); d2y(t)=diff(y(t),2); F = input('Input the coefficients [a,b,c]: '); a=F(...\n\n9 mesi ago | 2 answers | 0" ]
[ null, "https://it.mathworks.com/responsive_image/150/150/0/0/0/cache/matlabcentral/profiles/19873468_1602075118055_DEF.jpg", null ]
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https://ask.sagemath.org/users/20348/holden/?sort=recent
[ "2018-12-18 21:26:42 -0500 commented answer Roots of multivariable polynomials with respect to one variable? I wrote down a one liner to define residue def Res(f,var, pole, multi): return (1/factorial(multi-1))*limit( diff((var-pole)^multi*f ,var,multi-1), var=pole) but the limiting part takes a huge amount of memory for a moderately big rational function in several variables. I am looking for other methods now. 2018-12-18 13:00:59 -0500 received badge ● Good Question (source) 2018-12-17 17:49:58 -0500 received badge ● Nice Question (source) 2018-12-17 13:36:26 -0500 commented answer Roots of multivariable polynomials with respect to one variable? Thank you @rburing. Yes, the roots are instantaneous. I am working on the residues now. I will let you know if I have further questions. 2018-12-17 12:36:18 -0500 received badge ● Supporter (source) 2018-12-16 16:32:23 -0500 asked a question Roots of multivariable polynomials with respect to one variable? This question was previously titled \"Finding residues of a huge multivariable rational function.\" From my understanding, when computing with huge rational functions, we shouldn't use symbolic variables. However, I don't see how to find roots and residues without symbolic variables. Here is a small scale example of the issue. I have a rational function that looks like below: $f(u_1,x_1,u_2,x_2,u_3,x_3) = \\frac{1}{{\\left(u_{1} u_{2} u_{3} - x_{1} x_{2} x_{3}\\right)} {\\left(u_{1} u_{2} u_{3} - 1\\right)} {\\left(u_{1} u_{2} - x_{1} x_{2}\\right)} {\\left(u_{1} u_{2} - 1\\right)} {\\left(u_{1} - x_{1}\\right)} {\\left(u_{1} - 1\\right)}}$ First I want to solve for $u_1$ in the denominator and find those roots (poles) that have $x_1$ as below. Then I will loop through the roots and compute the residue of $f$ w.r.t. $u_1$ at those poles. u1,u2,u3,x1,x2,x3 = var('u1,u2,u3,x1,x2,x3') #symbolic variables f=1/((u1*u2*u3 - x1*x2*x3)*(u1*u2*u3 - 1)*(u1*u2 - x1*x2)*(u1*u2 - 1)*(u1 - x1)*(u1 - 1)) fden=f.denominator() #denominator of f list1=fden.roots(u1) #poles of u1 [root for (root, multiplicity) in list1] #list of roots The output is [x1*x2*x3/(u2*u3), x1*x2/u2, x1, 1/(u2*u3), 1/u2, 1] Then we choose those roots that have $x1$ poles1 = [x1*x2*x3/(u2*u3), x1*x2/u2, x1] #choose those that have x1 Finally, we find the residue of $f$ w.r.t $u1$ of the rational function at the poles containing $x1.$ ans1=0 for ff in poles1: tmp=f.residue(u1==ff) ans1+=tmp #ans1 is the residue of f w.r.t u1 at all the poles containing x1 ans1 The output is then 1/((u2*u3*x1 - x1*x2*x3)*(u2*u3*x1 - 1)*(u2*x1 - x1*x2)*(u2*x1 - 1)*(x1 - 1)) - 1/((u3*x1*x2 - x1*x2*x3)*(u3*x1*x2 - 1)* (x1*x2 - 1)*u2*(x1 - x1*x2/u2)*(x1*x2/u2 - 1)) + 1/((x1*x2*x3 - 1)*(x1*x2 - x1*x2*x3/u3)*(x1*x2*x3/u3 - 1)*u2*u3*(x1 x1*x2*x3/(u2*u3))*(x1*x2*x3/(u2*u3) - 1)) Then I replace $f$ with $ans1$ to continue to do the same process w.r.t $u2$ and poles containing $x2$ and finally w.r.t $u3$ and poles containing $x3.$ However, this consumes about 800GB of memory on an HPC when I feed it a larger rational function. Is there a way to find roots of multivariable polynomials with respect to one variable? residue of a rational function avoiding symbolic variables? Both .roots() and .residue() are not defined for rational functions that are not defined in terms of symbolic variables. 2018-03-16 17:16:03 -0500 commented answer Representation as sums of squares built-in function @slelievre, cool. Thanks. 2016-02-27 08:58:07 -0500 commented answer Representation as sums of squares built-in function @slelievre, thank you so much. I installed mathematica 10.3(latest issue) and was not able to call mathematica even if I followed all the instructions on how to use mathematica within sage. From what I read around the web, I have to downgrade to version 8 to be able to interface to mathematica from within Sage. Is that true or am I missing something with integrating version 10.3? 2016-02-23 17:59:14 -0500 commented answer calling mathematica 9.0 in sage @Emmanuel, is there a follow up to your answer? I have Mathematica 10.3 and I have the following error \"unable to start mathematica\" 2016-02-23 16:20:46 -0500 received badge ● Scholar (source) 2016-02-23 16:20:38 -0500 commented answer Representation as sums of squares built-in function I see. Thanks. 2016-02-22 12:31:24 -0500 received badge ● Editor (source) 2016-02-22 12:26:42 -0500 commented answer Representation as sums of squares built-in function @slelievre, thank you! I have confused my self a lot and I was actually looking for a built in function that outputs r_k(n) which is the number of ways of writing a given number n as a sum of k-squares. For instance r_4(1) = 8. There is SquaresR[] built-in function in Mathematica but I can't interface to it within Sage. Is there such a built-in function in Sage? 2016-02-22 12:04:13 -0500 received badge ● Student (source) 2016-02-22 11:58:43 -0500 asked a question Representation as sums of squares built-in function Is there a Sage implementation of writing a number as a sum of k squares for any k as described in the ticket here: trac.sagemath.org/ticket/16308 ? Thank you! Please see my comment below the first answer." ]
[ null ]
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https://www.numberempire.com/5016
[ "Home | Menu | Get Involved | Contact webmaster", null, "", null, "", null, "", null, "", null, "# Number 5016\n\nfive thousand sixteen\n\n### Properties of the number 5016\n\n Factorization 2 * 2 * 2 * 3 * 11 * 19 Divisors 1, 2, 3, 4, 6, 8, 11, 12, 19, 22, 24, 33, 38, 44, 57, 66, 76, 88, 114, 132, 152, 209, 228, 264, 418, 456, 627, 836, 1254, 1672, 2508, 5016 Count of divisors 32 Sum of divisors 14400 Previous integer 5015 Next integer 5017 Is prime? NO Previous prime 5011 Next prime 5021 5016th prime 48781 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 1001110011000 Octal 11630 Duodecimal 2aa0 Hexadecimal 1398 Square 25160256 Square root 70.823724838503 Natural logarithm 8.5203880823128 Decimal logarithm 3.7003575278227 Sine 0.9016058792036 Cosine -0.43255847996023 Tangent -2.0843560373305\nNumber 5016 is pronounced five thousand sixteen. Number 5016 is a composite number. Factors of 5016 are 2 * 2 * 2 * 3 * 11 * 19. Number 5016 has 32 divisors: 1, 2, 3, 4, 6, 8, 11, 12, 19, 22, 24, 33, 38, 44, 57, 66, 76, 88, 114, 132, 152, 209, 228, 264, 418, 456, 627, 836, 1254, 1672, 2508, 5016. Sum of the divisors is 14400. Number 5016 is not a Fibonacci number. It is not a Bell number. Number 5016 is not a Catalan number. Number 5016 is not a regular number (Hamming number). It is a not factorial of any number. Number 5016 is an abundant number and therefore is not a perfect number. Binary numeral for number 5016 is 1001110011000. Octal numeral is 11630. Duodecimal value is 2aa0. Hexadecimal representation is 1398. Square of the number 5016 is 25160256. Square root of the number 5016 is 70.823724838503. Natural logarithm of 5016 is 8.5203880823128 Decimal logarithm of the number 5016 is 3.7003575278227 Sine of 5016 is 0.9016058792036. Cosine of the number 5016 is -0.43255847996023. Tangent of the number 5016 is -2.0843560373305" ]
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https://www.interstatequarantine.org.au/recreation-in-natural-environments/
[ "```int(43)\nbool(false)\nint(0)\n```\n```int(1306)\nbool(false)\nint(43)\n```\n```int(2309)\nbool(false)\nint(43)\n```\n```int(55)\nbool(false)\nint(43)\n```\n```int(1307)\nbool(false)\nint(43)\n```\n```int(41)\nbool(false)\nint(0)\n```\n```int(60)\nbool(false)\nint(41)\n```\n```int(1311)\nbool(false)\nint(41)\n```\n```int(1371)\nbool(false)\nint(41)\n```\n```int(2576)\nbool(false)\nint(41)\n```\n```int(406)\nbool(false)\nint(41)\n```\n```int(42)\nbool(false)\nint(0)\n```\n```int(1304)\nbool(false)\nint(42)\n```\n```int(1303)\nbool(false)\nint(42)\n```\n```int(407)\nbool(false)\nint(42)\n```\n```int(62)\nbool(false)\nint(42)\n```\n```int(51)\nbool(false)\nint(42)\n```\n```int(2587)\nbool(false)\nint(42)\n```\n```int(3161)\nbool(false)\nint(42)\n```\n```int(3163)\nbool(false)\nint(42)\n```\n```int(3164)\nbool(false)\nint(42)\n```\n```int(3165)\nbool(false)\nint(42)\n```\n```int(3166)\nbool(false)\nint(42)\n```\n```int(3167)\nbool(false)\nint(42)\n```\n```int(3168)\nbool(false)\nint(42)\n```\n```int(3169)\nbool(false)\nint(42)\n```\n```int(3170)\nbool(false)\nint(42)\n```\n```int(3171)\nbool(false)\nint(42)\n```\n```int(3172)\nbool(false)\nint(42)\n```\n```int(3173)\nbool(false)\nint(42)\n```\n```int(3174)\nbool(false)\nint(42)\n```\n```int(2951)\nbool(false)\nint(0)\n```\n```int(2952)\nbool(false)\nint(2951)\n```\n```int(2953)\nbool(false)\nint(2951)\n```\n```int(2954)\nbool(false)\nint(2951)\n```\n```int(2955)\nbool(false)\nint(2951)\n```\n\n## Recreation in natural environments\n\nRecreational activities like bushwalking, hunting, fishing, trail bike riding, orienteering and dog walking can sometimes increase the biosecurity risks to natural areas." ]
[ null ]
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https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/8/lesson/8.1.3/problem/8-49
[ "", null, "", null, "### Home > INT3 > Chapter 8 > Lesson 8.1.3 > Problem8-49\n\n8-49.\n\nConsider the quadratic equation $x^{2} – 10x = –29$.\n\n1. Is $x = 5 + 2i$ a solution to the equation? How can you be sure without solving?\n\nSubstitute the solution into the equation.\n\n$(5 + 2i)^2 - 10(5 + 2i) = -29$\n\n2. Without solving, predict another solution to the equation. Verify your prediction by checking it.\n\nAny quadratic equation can be solved using the Quadratic Formula. The \"$i$\" part of the solution comes from a negative number inside of the square root. What is in front the the square root in the Quadratic Formula?\n\n3. Where does the parabola $y = x^{2} – 10x + 29$ intersect the $x$-axis? Explain.\n\nLet $y = 0$ and solve." ]
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", null ]
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https://www.jpost.com/israel/analysis-peretz-early-polls-and-diplomatic-fallout
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[ null, "https://www.jpost.com//HttpHandlers/ShowImage.ashx", null ]
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https://codehunter.cc/a/python/how-to-check-if-a-value-exists-in-a-dictionary-python
[ "How to check if a value exists in a dictionary (python) How to check if a value exists in a dictionary (python) python python\n\n# How to check if a value exists in a dictionary (python)\n\n``>>> d = {'1': 'one', '3': 'three', '2': 'two', '5': 'five', '4': 'four'}>>> 'one' in d.values()True``\n\nOut of curiosity, some comparative timing:\n\n``>>> T(lambda : 'one' in d.itervalues()).repeat()[0.28107285499572754, 0.29107213020324707, 0.27941107749938965]>>> T(lambda : 'one' in d.values()).repeat()[0.38303399085998535, 0.37257885932922363, 0.37096405029296875]>>> T(lambda : 'one' in d.viewvalues()).repeat()[0.32004380226135254, 0.31716084480285645, 0.3171098232269287]``\n\nEDIT: And in case you wonder why... the reason is that each of the above returns a different type of object, which may or may not be well suited for lookup operations:\n\n``>>> type(d.viewvalues())<type 'dict_values'>>>> type(d.values())<type 'list'>>>> type(d.itervalues())<type 'dictionary-valueiterator'>``\n\nEDIT2: As per request in comments...\n\n``>>> T(lambda : 'four' in d.itervalues()).repeat()[0.41178202629089355, 0.3959040641784668, 0.3970959186553955]>>> T(lambda : 'four' in d.values()).repeat()[0.4631338119506836, 0.43541407585144043, 0.4359898567199707]>>> T(lambda : 'four' in d.viewvalues()).repeat()[0.43414998054504395, 0.4213531017303467, 0.41684913635253906]``\n\nIn Python 3, you can use\n\n``\"one\" in d.values()``\n\nto test if `\"one\"` is among the values of your dictionary.\n\nIn Python 2, it's more efficient to use\n\n``\"one\" in d.itervalues()``\n\nNote that this triggers a linear scan through the values of the dictionary, short-circuiting as soon as it is found, so this is a lot less efficient than checking whether a key is present.\n\nPython dictionary has get(key) function\n\n``>>> d.get(key)``\n\nFor Example,\n\n``>>> d = {'1': 'one', '3': 'three', '2': 'two', '5': 'five', '4': 'four'}>>> d.get('3')'three'>>> d.get('10')None``\n\nIf your key does'nt exist, will return `None` value.\n\n``foo = d[key] # raise error if key doesn't existfoo = d.get(key) # return None if key doesn't exist``\n\nContent relevant to versions less than 3.0 and greater than 5.0.\n\n.", null, "" ]
[ null, "https://matomo.korohub.xyz/matomo.php", null ]
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https://www.teachoo.com/7451/2283/Ex-1.3--1---Estimate-using-general-rule--(a)-730---998-(b)-796---314/category/Ex-1.3/
[ "", null, "", null, "", null, "", null, "Subscribe to our Youtube Channel - https://you.tube/teachoo\n\n1. Chapter 1 Class 6 Knowing our Numbers\n2. Serial order wise\n3. Ex 1.3\n\nTranscript\n\nEx 1.3, 1 Estimate each of the following using general rule: Make ten more such examples of addition, subtraction & estimation of their outcome. (a) 730 + 998 730 + 998 Using general rule, 730 is rounded off to nearest hundred 700 998 is rounded off to nearest hundred 1000 So, estimated sum = 1000 + 700 So, estimated sum = 1,700 Ex 1.3, 1 Estimate each of the following using general rule: Make ten more such examples of addition, subtraction & estimation of their outcome. (b) 796 – 314 796 – 314 Using general rule, 796 is rounded off to nearest hundred 800 314 is rounded off to nearest hundred 300 Estimated answer = 800 − 300 = 500 Ex 1.3, 1 Estimate each of the following using general rule: Make ten more such examples of addition, subtraction & estimation of their outcome. (c) 12,904 + 2,88812,904 + 2,888 Using general rule, 12,904 is rounded off to 13,000 2,888 is rounded off to 3,000 Estimated answer = 13000 + 3000 = 16000 Ex 1.3, 1 Estimate each of the following using general rule: Make ten more such examples of addition, subtraction & estimation of their outcome. (d) 28,292 – 21,49628,292 – 21,496 Using general rule, 28292 is rounded off to 28000 21496 is rounded off to 21000 Estimated answer = 28000 – 21000 = 7000\n\nEx 1.3", null, "" ]
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https://lawessaywriters563.blogspot.com/2019/11/science-corse-work-minus-results-essays.html
[ "## Wednesday, November 13, 2019\n\n### science corse work (minus results) :: essays research papers\n\nGCSE Physics Coursework - Resistance of a Wire Coursework Resistance of a Wire Task To investigate how the resistance of a wire is affected by the length of the wire. Theory What is resistance? Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, i.e. it has less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions convert some of the energy that the free electrons are carrying into heat. How is it measured? The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula: V = I  ´ R where V = Voltage, I = Current and R = Resistance This can be rearranged to: R = V I Ohm’s Law It is also relevant to know of Ohm’s Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). Therefore V  ¸ I is constant. This means that the resistance of a metallic conductor is constant providing that the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons. Variables Input: †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Length of wire. * †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Material of wire. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Width of wire. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Starting temperature of wire. Output: †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   and thus the resistance of the wire. †  †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Voltage across wire. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Current in circuit. †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Temperature of wire. The variable marked with a * will be varied, the other input variables will be kept constant. The output variable marked with a †  will be measured. Predictions †¢Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal." ]
[ null ]
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http://ohdsi.github.io/EmpiricalCalibration/reference/plotCiCalibrationEffect.html
[ "Creates a plot with the effect estimate on the x-axis and the standard error on the y-axis. The plot is trellised by true effect size. Negative and positive controls are shown as blue dots. The area below the dashed line indicated estimates that are statistically significant different from the true effect size (p < 0.05). The orange area indicates estimates with calibrated p < 0.05.\n\nplotCiCalibrationEffect(\nlogRr,\nseLogRr,\ntrueLogRr,\nlegacy = FALSE,\nmodel = NULL,\nxLabel = \"Relative risk\",\ntitle,\nfileName = NULL\n)\n\n## Arguments\n\nlogRr\n\nA numeric vector of effect estimates on the log scale.\n\nseLogRr\n\nThe standard error of the log of the effect estimates. Hint: often the standard error = (log(<lower bound 95 percent confidence interval>) - log(<effect estimate>))/qnorm(0.025).\n\ntrueLogRr\n\nA vector of the true effect sizes.\n\nlegacy\n\nIf true, a legacy error model will be fitted, meaning standard deviation is linear on the log scale. If false, standard deviation is assumed to be simply linear.\n\nmodel\n\nThe fitted systematic error model. If not provided, it will be fitted on the provided data.\n\nxLabel\n\nThe label on the x-axis: the name of the effect estimate.\n\ntitle\n\nOptional: the main title for the plot\n\nfileName\n\nName of the file where the plot should be saved, for example 'plot.png'. See the function ggsave in the ggplot2 package for supported file formats.\n\n## Value\n\nA Ggplot object. Use the ggsave function to save to file.\n\n## Examples\n\ndata <- simulateControls(n = 50 * 3, mean = 0.25, sd = 0.25, trueLogRr = log(c(1, 2, 4)))\nplotCiCalibrationEffect(data$logRr, data$seLogRr, data\\$trueLogRr)", null, "" ]
[ null, "http://ohdsi.github.io/EmpiricalCalibration/reference/plotCiCalibrationEffect-1.png", null ]
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https://kevinbinz.com/2017/02/09/probability-theory/
[ "# An Introduction to Probability Theory\n\nPart Of: Statistics sequence\nRelated To: An Introduction to Set Theory\nContent Summary: 400 words, 4 min read.\n\n“Probability theory is nothing but common sense reduced to calculation.” – Laplace\n\nIntroducing Probability Theory\n\nProbability theory, as formulated by Andrey Kolmogorov in 1925, has two ingredients:\n\n1. A space which define the mathematical objects (“the nouns”)\n2. Axioms which define the mathematical operations (“the verbs”)\n\nA probability space is a 3-tuple (Ω,𝓕,P):\n\n1. Sample Space (Ω): A set of possible outcomes, from one or more events. Outcomes in Ω must be mutually exclusive and collectively exhaustive.\n2. σ-Algebra (𝓕). A collection of event groupings, or subsets. If Ω is countable, this can simply be the power set, otherwise a Borel algebra is often used.\n3. Probability Measure Function (P). A real-valued function P: Ω → ℝ which maps from events to real numbers.\n\nThe Kolmogorov axioms provide “rules of behavior” for the residents of probability space:\n\n1. Non-negativity: probabilities can never be negative, P(x) >= 0.\n2. Unitarity: the sum of all probabilities is 1.0 (“something has to happen”)\n3. Sigma Additivity: the probability of composite events equals the sum of their individual probabilities.", null, "Random Variables\n\nA random variable is a real-valued function X: Ω → ℝ. A random variable is a function, but not a probability function. Rather, instantiating random variables X = x defines a subset of events ⍵ ∈ Ω such that X(⍵) = x. Thus x picks out the preimage of Ω. Variable instantiation thus provides a language to select groups of events from Ω.\n\nRandom variables with discrete outcomes (countably finite Ω) are known as discrete random variable. We can define probability mass functions (PMFs) such that", null, "$f_X(x) = P(X=x) = P( { \\omega \\in \\Omega : X(\\omega) = x } )$\n\nIn contrast, continuous random variables have continuous outcomes (uncountable Ω). For this class of variable, the probability of any particular event is undefined. Instead, we must define probabilities against a particular interval. The probability of 5.0000000… inches of snow is 0%; it is more meaningful to discuss the probability of 5 ± 0.5 inches of snowfall. Thus, we define probability density functions (PDFs) such that:", null, "$P[a \\leq X \\leq b] = \\int f_X(x) dx$\n\nWe can summarize discrete PMFs and continuous PDFs in the following graphic:", null, "Marginal Probabilities\n\nConsider two random variables, A and B ∈ Ω. Several operators may act on these variables, which parallel similar devices in Boolean algebra and set theory.", null, "Suppose we want to know the probability of either A or B occurring. For this, we rely on the Set Combination Theorem:", null, "Union involves subtracting the intersection; else the purple region is counted twice. In our post on set theory, we saw this same idea expressed as the inclusion-exclusion principle (Definition 13).\n\nSummary\n\nThis first post in a two part explored the first six concepts or probability theory. Next time, we will learn about concepts 7-12.", null, "These definitions and theorems are the cornerstone upon which much reasoning are built. It pays to learn them well.\n\nRelated Work" ]
[ null, "https://kevinbinz.files.wordpress.com/2017/02/probability-structural-overview-3.png", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://kevinbinz.files.wordpress.com/2017/02/probability-pmf-vs-pdf-1.png", null, "https://kevinbinz.files.wordpress.com/2017/02/probability-operators.png", null, "https://kevinbinz.files.wordpress.com/2017/02/probability-set-combination-4.png", null, "https://kevinbinz.files.wordpress.com/2017/02/probability-theory-theorems-4.png", null ]
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https://scm.cri.ensmp.fr/git/pipstransfo.git/commitdiff/0106ef99df45720946ada6d92f8d543b94a0e0c0?hp=625670968322617fed9df3a0ec370faa3185f167
[ "author Pierre Guillou Tue, 11 Feb 2014 12:36:52 +0000 (13:36 +0100) committer Pierre Guillou Tue, 11 Feb 2014 12:36:52 +0000 (13:36 +0100)\n pipstransfo.tex patch | blob | history\n\nindex 4706900..06f9f63 100644 (file)\n\n\\section{Memory allocation alteration}\n\n+\\begin{description}\n+\n+\\item[scalar renaming]{is the process of renaming scalar variables to\n+    suppress false data dependencies.}\n+\n+\\item[privatization]{is the process of detecting variables that are\n+    private to a loop body, i.e.\\ written first, then read.}\n+\n+\\end{description}\n+\n+\n\\section{Loop transformations}\n\n+\\begin{description}\n+\n+\\item[loop unrolling]{\n+  is a loop transformation.\n+  Unrolling a loop by a factor of $n$ consists in the substitution of a loop\n+  body by itself, replicated $n$ times. A prelude and/or postlude are\n+  added to preserve the number of iteration.}\n+\n+\\item[loop fusion]{\n+  is a loop transformation that replaces two loops by a single loops whose\n+  body is the concatenation of the bodies of the two initial loops.}\n+\n+\\item[loop tiling]{\n+  is a loop nest transformation that changes the loop execution order\n+  through a partitions of the iteration space into\n+  chunks, so that the iteration is performed over each chunk and in the\n+  chunks.}\n+\n+\\item[loop interchange]{is a loop transformation that permutes two\n+  loops from a loop nest.}\n+\n+\\item[loop unswitching]{is a loop transformation that replaces a\n+  loop containing a test independent from the loop execution by a test\n+  containing the loop without the test in both true and false branch.}\n+\n+\\item[loop normalization]{is a loop transformation that changes\n+  the loop initial increment value or the loop range to enforce certain values,\n+  generally~1.}\n+\n+\\end{description}\n+\n\\section{Inter-procedural transformations}\n\n\\section{Base blocs transformations}\n\n\\begin{description}\n-\\item[loop unrolling]{\n-  is a loop transformation. Unrolling a loop by a factor of $n$ consists in the substitution of a loop\n-  body by itself, replicated $n$ times. A prelude and/or postlude are\n-  added to preserve the number of iteration.}\n+\n\n\\item[inlining]{\nis a function transformation. Inlining a function\nis the process of replacing a reference read in an\nexpression by the latest expression affected to it.}\n\n-\\item[loop fusion]{\n-  is a loop transformation that replaces two loops by a single loops whose\n-  body is the concatenation of the bodies of the two initial loops.}\n\n-\\item[loop tiling]{\n-  is a loop nest transformation that changes the loop execution order\n-  through a partitions of the iteration space into\n-  chunks, so that the iteration is performed over each chunk and in the\n-  chunks.}\n+\n+\n\n\\item[reduction detection]{\nis an analysis that identifies statements that perform a reduction over a\nis the process of replacing similar expressions by a variable that holds\nthe result of their evaluation.}\n\n-\\item[loop interchange]{is a loop transformation that permutes two\n-  loops from a loop nest.}\n\n-\\item[loop unswitching]{is a loop transformation that replaces a\n-  loop containing a test independent from the loop execution by a test\n-  containing the loop without the test in both true and false branch.}\n\n\\item[statement isolation]{is the process of replacing all\nvariables referenced in a statement by newly declared variables. A\nmultidimensional array into unidimensional arrays, possibly with a\nconversion from array to pointer.}\n\n-\\item[privatization]{is the process of  detecting variables that\n-  are private to a loop body, i.e.\\ written first, then read.}\n-\n\\item[loop normalization]{is a loop transformation that changes\nthe loop initial increment value or the loop range to enforce certain values, generally~1.}\n\nthem by their non-unrolled version.}\n\\end{description}\n\n+\n+\\section{References}\n+\n+\n\\end{document}" ]
[ null ]
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https://www.homeworklib.com/question/1648450/1-contin-1-crickets-make-a-chirping-noise-by
[ "# 1. Contin 1. Crickets make a chirping noise by sliding their wings rapidly over each other....", null, "", null, "1. Contin 1. Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket. Temperature, Chirps per Temperature, Chirps per Second, Second, 88.6 20.0 16.0 933 716 79.6 80. 6 16. 01 153 17.0 76. 3 144 Source: George W. Pierce. The Songs of Insects. Cambridge MA: Harvard University Press, 1949. pp. 12-21 (a) What is the likely explanatory variable in these data? Why? 11 (b) Draw a scatter diagram of the data. 13C) Compute the linear correlation coefficient between temperature and chirps per seconds 14 (d) Does a linear relation exist between temperature and chirps per second? 21 (e) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variablea 22 (1). Interpret the slope and y-intercept, if appropriate. (g) Predict the chirps per second if it is 83.3°F (h) A cricket chirps 15 times per second when the temperature is 82°F Is this rate of chirping above or below average at this temperature?\n1. Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket. 1720 Temperature, Chirps per Temperature, x Chirps per Second, y Second, y 88.6 20.0 71.6 16.0 93.3 19.8 84.3 18.4 80.6 17.1 75. 2 15.5 69.7 14.7 82.0 17.1 69.4 15.4 83.3 16.2 79. 6 15.0 82.6 172 80.6. 0 16. 8 3.5 76.3 14.4 Source: George W. Pierce. The Songs of Insects. Cambridge, MA: Harvard University Press, 1949, pp. 12-21. (a) What is the likely explanatory variable in these data? Why? 1.1 (b) Draw a scatter diagram of the data. 1.3 (e) Compute the linear correlation coefficient between temperature and chirps per second.. 1.4 (d) Does a linear relation exist between temperature and chirps per second? 2.1 (e) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variable. 2.2 (0). Interpret the slope and y-intercept, if appropriate. (g) Predict the chirps per second if it is 83.3°F. (h) A cricket chirps 15 times per second when the temperature is 82°F Is this rate of chirping above or below average at this temperature?\n\n(a)\n\nTemperature is explanatory variable because researcher wants to find the effect of temperature on the number of Chirps.\n\n(b)\n\nFollowing is the scatter plot:", null, "(c)\n\nFollowing table shows the calculations\n\n X Y X^2 Y^2 XY 88.6 20 7849.96 400 1772 93.3 19.8 8704.89 392.04 1847.34 80.6 17.1 6496.36 292.41 1378.26 69.7 14.7 4858.09 216.09 1024.59 69.4 15.4 4816.36 237.16 1068.76 79.6 15 6336.16 225 1194 80.6 16 6496.36 256 1289.6 76.3 14.4 5821.69 207.36 1098.72 71.6 16 5126.56 256 1145.6 84.3 18.4 7106.49 338.56 1551.12 75.2 15.5 5655.04 240.25 1165.6 82 17.1 6724 292.41 1402.2 83.3 16.2 6938.89 262.44 1349.46 82.6 17.2 6822.76 295.84 1420.72 83.5 17 6972.25 289 1419.5 Total 1200.6 249.8 96725.86 4200.56 20127.47", null, "(d)\n\nThe correlation coefficient between the variables is strong and positive. Scatter plot also shows a strong , positive linear relationship between the variables. So there exists a relationship between the variables.\n\n(e)", null, "(f)\n\nSlope: It is 0.212. It shows that for each unit increase in temperature chirps increased by 0.212 units.\n\nIntercept: It is -0.3151. When temperature is zero the number of chirps is -0.3151. It is not possible so it is meaningless in this case.\n\n(g)", null, "(h)", null, "The actual value 15 is lower than predicted value so it is below average.\n\n##### Add Answer to: 1. Contin 1. Crickets make a chirping noise by sliding their wings rapidly over each other....\nSimilar Homework Help Questions\n• ### ONLY A TO C ONLY A TO C ONLY A TO C ONLY A TO C...", null, "ONLY A TO C ONLY A TO C ONLY A TO C ONLY A TO C QUESTION 4 Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seem to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for striped cricket. Temperature, .x Chirps per second, 88.6 20.0 93.3 19.8 80.6 17.1 69.7 14.7 69.4 15.4...\n\n• ### A biologist wishes to determine if there is a relationship between temperature and the number of...\n\nA biologist wishes to determine if there is a relationship between temperature and the number of chirps per second of crickets. Below is the data of 15 crickets at various temperatures. Chirps/sec Temperature 20 88.6 16 71.6 19.8 93.3 18.4 84.3 17.1 80.6 15.5 75.2 14.7 69.7 17.1 82 15.4 69.4 16.2 83.3 15 79.6 17.2 82.6 16 80.6 17 83.5 14.4 76.3 Then the linear formula is: Chirps =___+___ *Temperature\n\nFree Homework App" ]
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https://courses.ceu.edu/courses/2023-2024/introduction-computer-science
[ "Introduction to Computer Science\nMandatory-Elective\nCourse Description\n\nThis course is a pre-term course.\n\nThis course aims to introduce the basic concepts in computer science to students, who join the Social Data Science program without sufficient background. This course will introduce mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. It emphasizes the relationship between algorithms and programming and introduces basic performance measures and analysis techniques for these problems. The course is organized as a sequence of short lectures and tutorials.\n\nLearning Outcomes\n\nBy the end of the course the student will be able to:\n\n• approach programming challenges with the basic algorithmic techniques\n• design effective algorithms for various computational problem\n• identify the appropriate data structure for the optimal implementation of a computational problem\n• evaluate the computational performance of the implemented algorithmic solution\nAssessment\n\nA students in this course will be evaluated as pass/fail through their performance and homework. Regular class attendance is required to pass the course. Active class participation is highly recommended.\n\nCourse Level\nMaster’s\nCourse Open to\nStudents on-site" ]
[ null ]
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https://mathoverflow.net/questions/217875/the-p-th-power-of-the-invariant-derivative-on-an-elliptic-curve-in-characteris
[ "# The $p$-th power of the invariant derivative on an elliptic curve in characteristic $p$\n\nI am not an expert in elliptic curves at all, so my question may naive and/or obvious. Let $E$ be an (affine) elliptic curve defined over a finite (or perfect) field of characteristic $p$. Since its module of derivations is free of rank one over its coordinate ring $R$, we can choose a generator (unique up to a constant) $\\delta$, what I call the `invariant derivative'. In particular, $\\delta^p$, being again a derivative, must be a multiple of $\\delta$. My question is, when is $\\delta^p$ actually zero. I verified this for $j=0$ and $j=1728$, and it seems in either case, this exactly happens when $E$ is supersingular, respectively when $p\\equiv 2\\mod 3$ and $p\\equiv3\\mod 4$, at least for some low values of $p\\geq 5$. Is this the pattern in general?\n\n$\\delta^p = A\\delta$ where $A$ is the Hasse invariant. In particular $\\delta^p = 0$ if and only if $A=0$, i.e. $E$ is supersingular.\n• Strictly speaking, $A$ is the Hasse invariant attached to the pair $(E, \\omega)$ where $\\omega$ is the global 1-form dual to $\\delta$. Sep 10, 2015 at 0:52" ]
[ null ]
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https://docs.sisense.com/main/SisenseLinux/reformatting-data.htm
[ "# Reformatting Data\n\nBy reformatting a field, you can create a more readable, and more usable format for analysis. In some cases, you can also reduce space. For example, convert a date field to a numeric field. You can reformat fields within the ElastiCube using a custom SQL expression.\n\nNote:\n\nWhen using floating points data types (Real, float, double), some decimal numbers may be rounded. If you need full decimal accuracy, try using BigInt field types.\n\n## Numeric Representation of Date Fields\n\n``10000*getyear(Date)+100*getmonth(Date)+getday(Date)      ``\n``tobigint(100000000*getyear(DateTime)+getmonth(DateTime)*1000000+getday(DateTime)*10000+100*gethour(DateTime)+getminute(DateTime))      ``" ]
[ null ]
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https://www.audioparty.pl/ball-mill/1119.html
[ "News\n1. Home\n2. -\n3. ball-mill\n4. -\n5. Ball Mill Dynamic Load Calculation Ball Mill Design Calculation\n\n# Ball Mill Dynamic Load Calculation Ball Mill Design Calculation\n\nFor example your ball mill is in closed circuit with a set of cyclones The grinding mill receives crushed ore feed The pulp densities around your cyclone are sampled and known over an 8hour shift allowing to calculate corresponding to circulating load ratios and circulating load tonnage on tonsday or tonshour\n\nChat Online\n\n## Our Products\n\nTo provide you with quality products.", null, "How to Size a Ball Mill Design Calculator Formula\n\nHow to Size a Ball Mill Design Calculator Formula Previous Next Represents the socalled Dynamic Angle of Repose or Lift Angle adopted during steady operation by the top surface of the mill charge “the kidney” with respect to the horizontal A reasonable default value for this angle is 32° but may be easily “tuned” to\n\nOnline Chat", null, "Calculate and Select Ball Mill Ball Size for Optimum Grinding\n\nIn Grinding selecting calculate the correct or optimum ball size that allows for the best and optimumideal or target grind size to be achieved by your ball mill is an important thing for a Mineral Processing Engineer AKA Metallurgist to do Often the ball used in ball mills is oversize “just in case”\n\nOnline Chat", null, "Free Calculation Ball Mill Ball Load\n\nBall Mill Dynamic Load Calculation Ball Mill Dynamic Load Calculation forestguidedtours ball mill load calculations Grinding Mill China Volume load of a ball mill calculator load or filling degree is essential to maintain the absorbed power of the mill and consequently the mill production Learn More ball mill dynamic load calculation mill for\n\nOnline Chat", null, "The basic parameters used in ball mill design power calculations rod mill or any tumbling mill sizing are material to be ground characteristics Bond Work Index bulk density specific\n\nOnline Chat", null, "how to calculate torque load of ball mill\n\nMotoring Along Rock Products Jul 9 2014 When determining how to optimize mining equipment for maximum The torque produced accelerates the load to near synchronous speed up by collisions with itself and in the Ball mill by collisions with steel balls\n\nOnline Chat", null, "Calculation Of Circulating Load Of A Grinding Mill Pdf\n\ncalculation of circulating load of a grinding More About calculate ball mill circulating load pdf 2012 ball mill dynamic load calculation Crushing and grinding machine supplier in jaw crusher Get Price And Support Online calculation of recirculating load in ball mill circuit ball mill circulating load calculation\n\nOnline Chat", null, "CALCULATION OF BALL MILL GRINDING EFFICIENCY\n\nMar 08 2013 · calculation of ball mill grinding efficiency dear experts please tell me how to calculate the grinding efficiency of a closed ckt open ckt ball mill in literatures it is written that the grinding efficiency of ball mill is very less less than 10 please expalin in a n excel sheet to calcualte the same thanks sidhant reply\n\nOnline Chat", null, "calculation of circulating load of a grinding mill pdf\n\nprimary ball mill load Jan 01 2018· circulating load formula in ball mill Here is a formula that allows you to calculate the circulating load ratio around a ball mill and hydrocylone as part of a how to calculate ball mill circulating load for iron ore how to calculate ball mill circulating load for iron ore processing pdf to 400 for most primary ball milling\n\nOnline Chat", null, "MODELING THE SPECIFIC GRINDING ENERGY AND\n\n2 MODELLING THE SPECIFIC GRINDING ENERGY AND BALLMILL SCALEUP Ballmill scale up Bond’s LawData zBond work index w i zFeed D f and product d size both 80 cumulative passing Result The specific grinding energy w Mill power draw P wT where T the mill capacity Mill dimensions from Tables or charts\n\nOnline Chat", null, "Home\n\nis home to a collection of both free and subscriptionbased calculation tools to aid metallurgical process engineers perform comminution calculations Grinding circuit design tools including for SAG millball mill circuits and geometallurgy energy models are available to subscribers\n\nOnline Chat", null, "PDF Circulating load calculation in grinding circuits\n\nA problem for solving mass balances in mineral processing plants is the calculation of circulating load in closed circuits A family of possible methods for the resolution of these calculations is\n\nOnline Chat", null, "Bearing Load Calculation 43 Mean load The load on bearings used in machines under normal p＝3 For ball bearings p＝103 For roller bearings A24 3 Linear fluctuating load When both dynamic radial loads and dynamic axial loads act on a bearing at the same time the hypothetical\n\nOnline Chat", null, "Optimization of mill performance by using\n\nOptimization of mill performance by using online ball and pulp measurements J o u r n a l P a p e r The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 110 NONREFEREED PAPER MARCH 2010 135 Table I Influence of speed and liner design on load dynamics Mill speed Soft design Aggressive design\n\nOnline Chat", null, "Dynamic stiffness calculation of ball mill dynamic stiffness calculation of ball mill dynamic stiffness calculation of ball mill mining crusher plant Ball mills are used primary for single stage fine grinding regrinding and as the second stage in two stage grinding circuits According to the need of customers konw Contact Supplier Get Price\n\nOnline Chat", null, "How To Calculate Dynamic Load Of Ball Mill\n\nHow to calculate dynamic load of ball mill he dynamic analysis of ball mill foundation is a typical problem of dynamic loads come from not only the unbalanced forces by mill charge rotation t is not convenient to backcalculate for all of the six parameters in theet price\n\nOnline Chat", null, "calculation of a ball mill load\n\nMay 10 2017 · Calculation of the power draw of dry multicompartment ball mills 225 The mill load that is the volume of charge in the mill is the principal determinant of power draw Estimation of the ball load that is mixed with the cement charge is difficult and can be highly erroneous So direct measurement must be taken for calculation of mill load Get Price\n\nOnline Chat", null, "Ball Load Calculation In Ball Mills\n\nBall mill design calculation impact on grinding mill design of recent new discoveries table 2 typical mill design calculations case ball load calculation in ball mills gold ore crusher calculation of the power draw of dry multicompartment ball calculation of mill load view more details Online Chat Amit 135 Lesson 7 Ball Mills Circuits Mining Mill\n\nOnline Chat", null, "Ball Mill Recirculating Load Calculation Pdf\n\nCalculation of circulating load of a grinding more about calculate ball mill circulating load pdf 2012 ball mill dynamic load calculation crushing and grinding machine supplier in jaw crusher get price and support online calculation of recirculating load in ball mill circuit ball mill circulating load calculation\n\nOnline Chat", null, "calculate ball mill circulating load pdf\n\ngrinding ball mill load calculation formula YouTube Aug 25 2016· In Grinding selecting calculate the correct or optimum ball size that allows for the best and ball mill dynamic load calculation circulating load of dynamic seperator in ball mill calculating\n\nOnline Chat", null, "calculation of ball mill charge volume\n\nThe Selection and Design of Mill Liners MillTraj Calculate Circulating Load Ball Mill Posts Related to circulating load of ball mill formula to calculate ball mill volume ton capacity ball mill media charge A Generic Dynamic Model Structure for Tumbling Mills UQ eSpace\n\nOnline Chat", null, "volume calculation for ball mill\n\ngrinding ball mill load calculation formula grinding volume calculation in a ball mill May 19 2014 more fully methods of calculating the net mill power draw for an industrial mill\n\nOnline Chat", null, "Calculating Load On A Ball Mill Grinding Mill China\n\nCalculation of circulating load of a grinding More About calculate ball mill circulating load pdf 2012 ball mill dynamic load calculation Crushing and grinding machine supplier in jaw crusher Get Price And Support Online calculation of recirculating load in ball mill circuit ball mill circulating load calculation\n\nOnline Chat", null, "CALCULATION OF BALL MILL GRINDING EFFICIENCY\n\nMar 08 2013 · calculation of ball mill grinding efficiency dear experts please tell me how to calculate the grinding efficiency of a closed ckt open ckt ball mill in literatures it is written that the grinding efficiency of ball mill is very less less than 10 please expalin in a n excel sheet to calcualte the same thanks sidhant reply\n\nOnline Chat", null, "Circulating Load Ball Mill Inneneinrichtungen Kreienbühl\n\ncirculating load calculation in ball mill Circulating Load Calculation FormulaHere is a formula that allows you to calculate the circulating load ratio around a ball mill and hydrocylone as part of a grinding circuit For example your ball mill is in closed circuit with a set of cyclones circulating load calculation in ball millgrinding mill\n\nOnline Chat", null, "ball size calculation for ball mill\n\nKeywords Miduk Copper Concentrator SAG Mill Ball Filling Percentage draw out mills internal load and calculate Chat Now an overview of operation and design Minerals Research Ball Mills Autogenous Mills Grinding Circuits Open Circuit Grinding How do you calculate ball mill residence time Answers\n\nOnline Chat", null, "Milling Speed and Feed Calculator\n\nMilling operations remove material by feeding a workpiece into a rotating cutting tool with sharp teeth such as an end mill or face mill Calculations use the desired tool diameter number of teeth cutting speed and cutting feed which should be chosen based on the specific cutting conditions including the workpiece material and tool material\n\nOnline Chat", null, "PDF DYNAMIC DESIGN FOR GRINDING MILL FOUNDATIONS\n\nFor a small ball mill with a mill diameter less than 36 m and small dynamic loads the method of free vibration analysis also call modal analysis can be used\n\nOnline Chat", null, "", null, "" ]
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https://liorpachter.wordpress.com/tag/edger/
[ "You are currently browsing the tag archive for the ‘edgeR’ tag.\n\nThe development of microarray technology two decades ago heralded genome-wide comparative studies of gene expression in human, but it was the widespread adoption of RNA-Seq that has led to differential expression analysis becoming a staple of molecular biology studies. RNA-Seq provides measurements of transcript abundance, making possible not only gene-level analyses, but also differential analysis of isoforms of genes. As such, its use has necessitated refinements of the term “differential expression”, and new terms such as “differential transcript expression” have emerged alongside “differential gene expression”. A difficulty with these concepts is that they are used to describe biology, statistical hypotheses, and sometimes to describe types of methods. The aims of this post are to provide a unifying framework for thinking about the various concepts, to clarify their meaning, and to describe connections between them.\n\nTo illustrate the different concepts associated to differential expression, I’ll use the following example, consisting of a comparison of a single two-isoform gene in two conditions (the figure is Supplementary Figure 1 in Ntranos, Yi et al. Identification of transcriptional signatures for cell types from single-cell RNA-Seq, 2018):", null, "The isoforms are labeled primary and secondary, and the two conditions are called “A” and “B”. The black dots labeled conditions A and B have x-coordinates", null, "$x_A$ and", null, "$x_B$ corresponding to the abundances of the primary isoform in the respective conditions, and y-coordinates", null, "$y_A$ and", null, "$y_B$ corresponding to the abundance of the secondary isoforms. In data from an experiment the black dots will represent the mean level of expression of the constituent isoforms as derived from replicates, and there will be uncertainty as to their exact location. In this example I’ll assume they represent the true abundances.\n\n### Biology\n\nBelow is a list of terms used to characterize changes in expression:\n\nDifferential transcript expression (DTE) is change in one of the isoforms. In the figure, this is represented (conceptually) by the two red lines along the x- and y-axes respectively. Algebraically, one might compute the change in the primary isoform by", null, "$x_B-x_A$ and the change in the secondary isoform by", null, "$y_B-y_A$. However the term DTE is used to denote not only the extent of change, but also the event that a single isoform of a gene changes between conditions, i.e. when the two points lie on a horizontal or vertical line. DTE can be understood to occur as a result of transcriptional regulation if an isoform has a unique transcription start site, or post-transcriptional regulation if it is determined by a unique splicing event.\n\nDifferential gene expression (DGE) is the change in the overall output of the gene. Change in the overall output of a gene is change in the direction of  the line", null, "$y=x$, and the extent of change can be understood geometrically to be the distance between the projections of the two points onto the line", null, "$y=x$ (blue line labeled DGE). The distance will depend on the metric used. For example, the change in expression could be defined to be the total expression in condition B (", null, "$x_B+y_B$) minus the change in expression in condition A (", null, "$x_A+y_A$), which is", null, "$|x_B-x_A+y_B-y_A|$.  This is just the length of the blue line labeled “DGE” given by the", null, "$L_1$ norm. Alternatively, one could consider “DGE” to be the length of the blue line in the", null, "$L_2$ norm. As with DTE, DGE can also refer to a specific type of change in gene expression between conditions, one in which every isoform changes (relatively) by the same amount so that the line joining the two points has a slope of 1 (i.e. is angled at 45°). DGE can be understood to be the result of transcriptional regulation, driving overall gene expression up or down.\n\nDifferential transcript usage (DTU) is the change in relative expression between the primary and secondary isoforms. This can be interpreted geometrically as the angle between the two points, or alternatively as the length (as given by some norm) of the green line labeled DTU. As with DTE and DGE, DTU is also a term used to describe a certain kind of difference in expression between two conditions, one in which the line joining the two points has a slope of -1. DTU events are most likely controlled by post-transcriptional regulation.\n\nGene differential expression (GDE) is represented by the red line. It is the amount of change in expression along in the direction of line joining the two points. GDE is a notion that, for reasons explained below, is not typically tested for, and there are few methods that consider it. However GDE is biologically meaningful, in that it generalizes the notions of DGE, DTU and DTE, allowing for change in any direction. A gene that exhibits some change in expression between conditions is GDE regardless of the direction of change. GDE can represent complex changes in expression driven by a combination of transcriptional and post-transcriptional regulation. Note that DGE, DTU and DTE are all special cases of GDE.\n\nIf the", null, "$L_2$ norm is used to measure length and", null, "$DTE_1,DTE_2$ denote DTE in the primary and secondary isoforms respectively, then it is clear that DGE, DTU, DTE and GDE satisfy the relationship", null, "$GDE^2 = DGE^2 + DTU^2 = DTE_1^2 + DTE_2^2.$\n\n### Statistics\n\nThe terms DTE, DGE, DTU and GDE have an intuitive biological meaning, but they are also used in genomics as descriptors of certain null hypotheses for statistical testing of differential expression.\n\nThe differential transcript expression (DTE) null hypothesis for an isoform is that it did not change between conditions, i.e.", null, "$x_A=x_B$ for the primary isoform, or", null, "$y_A=y_B$ for the secondary isoform. In other words, in this example there are two DTE null hypotheses one could consider.\n\nThe differential gene expresión (DGE) null hypothesis is that there is no change in overall expression of the gene, i.e.", null, "$x_A+y_A = x_B+y_B$.\n\nThe differential transcript usage (DTU) null hypothesis is that there is no change in the difference in expression of isoforms, i.e.", null, "$x_A-y_A = x_B - y_B$.\n\nThe gene differential expression (GDE) null hypothesis is that there is no change in expression in any direction, i.e. for all constants", null, "$a,b$,", null, "$ax_A+by_A = ax_B+by_B$.\n\nThe union differential transcript expression (UDTE) null hypothesis is that there is no change in expression of any isoform. That is, that", null, "$x_A = y_A$ and", null, "$x_B = y_B$ (this null hypothesis is sometimes called DTE+G). The terminology is motivated by", null, "$\\neg \\cup_i DTE_i = \\cap_i DTE_i$.\n\nNot that", null, "$UDTE \\Leftrightarrow GDE$, because if we assume GDE, and set", null, "$a=1,b=0$ we obtain DTE for the primary isoform and setting", null, "$a=0,b=1$ we obtain DTE for the secondary isoform. To be clear, by GDE or DTE in this case we mean the GDE (respectively DTE) null hypothesis. Furthermore, we have that", null, "$UDTE,GDE \\Rightarrow DTE,DGE,DTU$.\n\nThis is clear because if", null, "$x_A=y_A$ and", null, "$x_B=y_B$ then both DTE null hypotheses are satisfied by definition, and both DGE and DTU are trivially satisfied. However no other implications hold, i.e.", null, "$DTE \\not \\Rightarrow DGE,DTU$, similarly", null, "$DGE \\not \\Rightarrow DTE,DTU$, and", null, "$DTU \\not \\Rightarrow DGE, DTE$.\n\n### Methods\n\nThe terms DGE, DTE, DTU and GDE also used to describe methods for differential analysis.\n\nA differential gene expression method is one whose goal is to identify changes in overall gene expression. Because DGE depends on the projection of the points (representing gene abundances) to the line y=x, DGE methods typically take as input gene counts or abundances computed by summing transcript abundances", null, "$x_A+y_A$ and", null, "$x_B+y_B$. Examples of early DGE methods for RNA-Seq were DESeq (now DESeq2) and edgeR. One problem with DGE methods is that it is problematic to estimate gene abundance by adding up counts of the constituent isoforms. This issue was discussed extensively in Trapnell et al. 2013. On the other hand, if the biology of a gene is DGE, i.e. changes in expression are the same (relatively) in all isoforms, then DGE methods will be optimal, and the issue of summed counts not representing gene abundances accurately is moot.\n\ndifferential transcript expression method is one whose goal is to identify individual transcripts that have undergone DTE. Early methods for DTE were Cufflinks (now Cuffdiff2) and MISO, and more recently sleuth, which improves DTE accuracy by modeling uncertainty in transcript quantifications. A key issue with DTE is that there are many more transcripts than genes, so that rejecting DTE null hypotheses is harder than rejecting DGE null hypotheses. On the other hand, DTE provides differential analysis at the highest resolution possible, pinpointing specific isoforms that change and opening a window to study post-transcriptional regulation. A number of recent examples highlight the importance of DTE in biomedicine (see, e.g., Vitting-Seerup and Sandelin 2017). Unfortunately DTE results do not always translate to testable hypotheses, as it is difficult to knock out individual isoforms of genes.\n\ndifferential transcript usage method is one whose goal is to identify genes whose overall expression is constant, but where isoform switching leads to changes in relative isoform abundances. Cufflinks implemented a DTU test using Jensen-Shannon divergence, and more recently RATs is a method specialized for DTU.\n\nAs discussed in the previous section, none of null hypotheses DGE, DTE and DTU imply any other, so users have to choose, prior to performing an analysis, which type of test they will perform. There are differing opinions on the “right” approach to choosing between DGE, DTU and DTE. Sonseson et al. 2016 suggest that while DTE and DTU may be appropriate in certain niche applications, generally it’s better to choose DGE, and they therefore advise not to bother with transcript-level analysis. In Trapnell et al. 2010, an argument was made for focusing on DTE and DTU, with the conclusion to the paper speculating that “differential RNA level isoform regulation…suggests functional specialization of the isoforms in many genes.” Van den Berge et al. 2017 advocate for a middle ground: performing a gene-level analysis but saving some “FDR budget” for identifying DTE in genes for which the UDTE null hypothesis has been rejected.\n\nThere are two alternatives that have been proposed to get around the difficulty of having to choose, prior to analysis, whether to perform DGE, DTU or DTE:\n\ndifferential transcript expression aggregation (DTE->G) method is a method that first performs DTE on all isoforms of every gene, and then aggregates the resulting p-values (by gene) to obtain gene-level p-values. The “aggregation” relies on the observation that under the null hypothesis, p-values are uniformly distributed. There are a number of different tests (e.g. Fisher’s method) for testing whether (independent) p-values are uniformly distributed. Applying such tests to isoform p-values per gene provides gene-level p-values and the ability to reject UDTE. A DTE->G method was tested in Soneson et al. 2016 (based on Šidák aggregation) and the stageR method (Van den Berge et al. 2017) uses the same method as a first step. Unfortunately, naïve DTE->G methods perform poorly when genes change by DGE, as shown in Yi et al. 2017. The same paper shows that Lancaster aggregation is a DTE->G method that achieves the best of both the DGE and DTU worlds. One major drawback of DTE->G methods is that they are non-constructive, i.e. the rejection of UDTE by a DTE->G method provides no information about which transcripts were differential and how. The stageR method averts this problem but requires sacrificing some power to reject UDTE in favor of the interpretability provided by subsequent DTE.\n\ngene differential expression method is a method for gene-level analysis that tests for differences in the direction of change identified between conditions. For a GDE method to be successful, it must be able to identify the direction of change, and that is not possible with bulk RNA-Seq data. This is because of the one in ten rule that states that approximately one predictive variable can be estimated from ten events. In bulk RNA-Seq, the number of replicates in standard experiments is three, and the number of isoforms in multi-isoform genes is at least two, and sometimes much more than that.\n\nIn Ntranos, Yi et al. 2018, it is shown that single-cell RNA-Seq provides enough “replicates” in the form of cells, that logistic regression can be used to predict condition based on expression, effectively identifying the direction of change. As such, it provides an alternative to DTE->G for rejecting UDTE. The Ntranos and Yi GDE methods is extremely powerful: by identifying the direction of change it is a DGE methods when the change is DGE, it is a DTU method when the change is DTU, and it is a DTE method when the change is DTE. Interpretability is provided in the prediction step: it is the estimated direction of change.\n\n### Remarks\n\nThe discussion in this post is based on an example consisting of a gene with two isoforms, however the concepts discussed are easy to generalize to multi-isoform genes with more than two transcripts. I have not discussed differential exon usage (DEU), which is the focus of the DEXSeq method because of the complexities arising in genes which don’t have well-defined shared exons. Nevertheless, the DEXSeq approach to rejecting UDTE is similar to DTE->G, with DTE replaced by DEU. There are many programs for DTE, DTU and (especially) DGE that I haven’t mentioned; the ones cited are intended merely to serve as illustrative examples. This is not a comprehensive review of RNA-Seq differential expression methods.\n\n### Acknowledgments\n\nThe blog post was motivated by questions of Charlotte Soneson and Mark Robinson arising from an initial draft of the Ntranos, Yi et al. 2018 paper. The exposition was developed with Vasilis Ntranos and Lynn Yi. Valentine Svensson provided valuable comments and feedback.", null, "itisalist on Introduction to single-cell RN…", null, "Lior Pachter on High velocity RNA velocit…", null, "Eric on High velocity RNA velocit…", null, "Allen Knutson on How to solve an NP-complete pr…", null, "orlando jimenez on The perfect human is Puerto…", null, "Anonymous on Yuval Peres", null, "Javier on I was wrong (part 3)", null, "Artem Barski on Open sourcing bioinstruments", null, "Uri David Akavia on Open sourcing bioinstruments", null, "Eduardo Da Veiga Bel… on Open sourcing bioinstruments" ]
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https://www.akt.tu-berlin.de/menue/akt_talks/winter_14_15/talk_20112014/parameter/en/mobil/
[ "", null, "Algorithmics and Computational Complexity Research GroupTalk 20.11.2014", null, "## Network Sparsification for Steiner Problems on Planar and Bounded-Genus Graphs\n\nDr. Erik Jan van Leeuwen (MPI für Informatik, Saarbrücken)\n\nWe propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph G embedded on a surface of genus g and a designated face f bounded by a simple cycle of length k, uncovers a set F⊆E(G) of size polynomial in g and k that contains an optimal Steiner tree for any set of terminals that is a subset of the vertices of f. We apply this general theorem to prove that: * given an unweighted graph G embedded on a surface of genus g and a terminal set S⊆V(G), one can in polynomial time find a set F⊆E(G) that contains an optimal Steiner tree T for S and that has size polynomial in g and |E(T)|; * an analogous result holds for an optimal Steiner forest for a set S of terminal pairs; * given an unweighted planar graph G and a terminal set S⊆V(G), one can in polynomial time find a set F⊆E(G) that contains an optimal (edge) multiway cut C separating S and that has size polynomial in |C|. In the language of parameterized complexity, these results imply the first polynomial kernels for Steiner Tree and Steiner Forest on planar and bounded-genus graphs (parameterized by the size of the tree and forest, respectively) and for (Edge) Multiway Cut on planar graphs (parameterized by the size of the cutset). Steiner Tree and similar \"subset\" problems were identified in [Demaine, Hajiaghayi, Computer J., 2008] as important to the quest to widen the reach of the theory of bidimensionality ([Demaine et al, JACM 2005], [Fomin et al, SODA 2010]). Therefore, our results can be seen as a leap forward to achieve this broader goal. Additionally, we obtain a weighted variant of our main contribution.\n\nDate\nSpeaker\nLocation\nLanguage\n20.11.2014\n16:15\nErik Jan van Leeuwen\nTEL 512\nenglish" ]
[ null, "https://www.akt.tu-berlin.de/fileadmin/Aperto_design/img/logo_03.gif", null, "https://www.akt.tu-berlin.de/fileadmin/i9/Logos/isti-logo-sm.gif", null ]
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https://www.sanfoundry.com/aerospace-materials-processes-questions-answers-aircraft-materials-tension-testing/
[ "# Aerospace Materials and Processes Questions and Answers – Aircraft Materials – Tension Testing\n\n«\n»\n\nThis set of Aerospace Materials and Processes Multiple Choice Questions & Answers (MCQs) focuses on “Aircraft Materials – Tension Testing”.\n\n1. What is the variation to which the tension testing machine must be sensitive?\na) 1/250 of the registered load\nd) 1/200 of the registered load\n\nExplanation: To obtain an accurate result, it is important for the test machine to be in appropriate condition. One of the important conditions is for a load being applied, the test machine must be sensitive to a variation of 1/250.\n\n2. Which of the following can be obtained through a tension test?\na) Colour\nb) Heat treatment\nc) Ultimate tensile strength\nd) Conductivity\n\nExplanation: Tension testing can provide a lot of basic information about the property of the material being tested. Ultimate tensile strength is obtained through tension testing. It is the withstanding ability of a material to load. Tensile refers to bring pulled away.\n\n3. During tension testing, the material must be held in _____________ alignment.\na) normal\nb) axial\nc) parallel\nd) diabolical\n\nExplanation: The material or the specimen should be positioned in true axial alignment. This is considered vital, especially since materials used in aircraft construction are thin. This will avoid damaging them.\n\n4. The extensometer can be attached anywhere to the specimen.\na) True\nb) False\n\nExplanation: Extensometer is an instrument used to measure the change in the length of a material. It should not be placed anywhere to the specimen. It should be fixed at the gage marks of the specimen being tested in the testing machine.\n\n5. The elastic limit of a material is _____________\na) the least amount of stress that can be held without permanent deformation\nb) highest stress a material can experience without permanent deformation\nc) average stress experienced by material in its lifeline.\nd) strain on material\n\nExplanation: The elastic limit is the highest stress that a material can withstand, without permanent deformation present when the stress is released completely. It is not the lowest amount of stress present.\n\n6. In the tension testing experiment, while determining elastic limit, the increment, while the load is being increased, should not exceed ___________ % of the elastic limit in the ending.\na) 50\nb) 7\nc) 2\nd) 3\n\nExplanation: In the tension testing experiment, we can determine the elastic limit. Here the load is applied gradually in different points to determine the elastic limit. In the final part of the experiment, the load being increased should not exceed 3% of the elastic limit.\n\n7. The tension testing machine (crosshead) should not cross a speed of ___________ inch per inch of the gage length per minute until the yield point.\na) 1/11\nb) 2\nc) 1/16\nd) 2/5\n\nExplanation: The crosshead of the tension testing machine has a certain advisable limit in speed it has to be operated up to. It is different until the yield point and after yield point till rupture. Until yield point it is 1/16 inch, yield point to rupture it is 1/2 inch. (Inch per inch)\n\n8. It is possible to determine the proof stress in a way in which ___________ is determined.\na) elastic limit\nb) yield point\nc) stress\nd) strain\n\nExplanation: The proof stress of a material can be found or determined the same way the elastic limit can be determined. But, there are other methods through which the elastic limit can be found as well.\n\n9. For a 4-inch gage length, crosshead speed of a machine should not exceed ___________ inch up to yield point.\na) 1/16\nb) 1/4\nc) 1/8\nd) 1/6\n\nExplanation: The speed which a crosshead should not exceed until yield point is 1/16 for one inch per inch gage length per minute.\nFor 4 inches, it is – $$\\frac{1×4}{16}$$ = 1/4 inch.\n\n10. What does ‘A’ represent in the diagram?", null, "a) Stress meter\nc) Gage length\nd) Diameter of center\n\nExplanation: ‘A’ is called the diameter of the centre of the specimen. Gage length is the horizontal distance marked on the specimen to signify the part that is under consideration. Stress meter is not present anywhere on the specimen.\n\n11. A materials proof stress is the highest stress possible for it to tolerate without causing a permanent set of more than ___________ inch per inch the length of gage, after the total release of stress.\na) 5.1\nb) 0.002\nc) 0.0001\nd) 0.1\n\nExplanation: The highest possible stress a material can, without causing a permanent set of more than 0.00001 inch per inch of the gage length is called proof stress. This is after the total release of the stress.\n\n12. Why must an accurate extensometer be used in reading a permanent set?\na) It is cheap\nb) To obtain accuracy\nd) It is unnecessary\n\nExplanation: An extensometer must be used in reading the permanent set. An accurate extensometer is required to obtain the change in the property after the experiment is done, without any mistakes or problems with accuracy.\n\n13. The proof stress of a material of 3 inches gage length is the highest stress it can withstand without a permanent set of above ___________ inch.\na) 0.0003\nb) 0.21\nc) 0.05\nd) 0.004\n\nExplanation: For a length of one inch, the permanent set of over 0.0001 inch withstanding is proof stress. For 3 inches length, it will be –\n0.0001×3 = 0.0003 inches.\nHence, it is 0.0003 inches.\n\n14. A materials proof stress is also referred to as ___________\na) elastic limit\nb) yield limit\nc) proportional limit\nd) set method\n\nExplanation: Proof stress of a material can also be called a proportional limit. The procedure to find the elastic limit and proof stress are similar, but the quantities are different. Yield limit can be found through tension testing, but it is not the same as proof stress.\n\n15. The elongation of a material can be obtained through tension testing.\na) True\nb) False", null, "" ]
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https://mran.revolutionanalytics.com/snapshot/2022-04-08/web/packages/greybox/vignettes/ro.html
[ "# Rolling Origin\n\n#### 2022-03-24\n\nWhen there is a need to select the most appropriate forecasting model or method for the data, the forecasters usually split the available sample into two parts: in-sample (aka “training set”) and holdout sample (or out-sample, or “test set”). The model is then estimated on in-sample and its forecasting performance is evaluated using some error measure on the holdout sample.\n\nIf such a procedure done only once, then this is called “fixed origin” evaluation. However, the time series might contain outliers or level shifts and a poor model might perform better than the more appropriate one only because of that. In order to robustify the evaluation of models, something called “rolling origin” is used.\n\nRolling origin is an evaluation technique according to which the forecasting origin is updated successively and the forecasts are produced from each origin (Tashman 2000). This technique allows obtaining several forecast errors for time series, which gives a better understanding of how the models perform. There are different options of how this can be done.\n\n## How can this be done?\n\nThe figure below (from (Svetunkov and Petropoulos 2018)) depicts the basic idea of rolling origin. White cells correspond to the in-sample data, while the light grey cells correspond to the three-steps-ahead forecasts. Time series has 25 observations in that figure, and the forecasts are produced from 8 origins, starting from the origin 15. The model is re-estimated on each iteration, and the forecasts are produced. After that a new observation is added at the end of the series and the procedure continues. The process stops when there is no more data to add. This could be considered as a rolling origin with a constant holdout sample size. As a result of this procedure 8 one to three steps ahead forecasts are produced. Based on them we can calculate the preferred error measures and choose the best performing model.", null, "Another option of producing forecasts from 8 origins would be to start from the origin 17 instead of 15 (see Figure below). In this case the procedure continues until origin 22, when the last three-steps-ahead forecast is produced, and then continues with the decreasing forecasting horizon. So the two-steps-ahead forecast is produced from the origin 23 and only one-step-ahead forecast is produced from the origin 24. As a result we obtain 8 one-step-ahead forecasts, 7 two-steps-ahead forecasts and 6 three-steps-ahead forecasts. This can be considered as a rolling origin with a non-constant holdout sample size. This can be useful in cases of small samples, when we don’t have any observations to spare.", null, "Finally, in both of the cases above we had the increasing in-sample size. However for some research purposes we might need a constant in-sample. The figure below demonstrates such a situation. In this case on each iteration we add an observation at the end of the series and remove one from the beginning of the series (dark grey cells).", null, "## What does this have to do with R?\n\nThe function ro() from greybox package (written by Yves Sagaert and Ivan Svetunkov in 2016 on the way to the International Symposium on Forecasting) implements the rolling origin evaluation for any function you like with a predefined call and returns the desired value. It heavily relies on the two variables: call and value - so it is quite important to understand how to formulate them in order to get the desired results. Overall, ro() is a very flexible function, but, as a result, it is not very simple. Let’s see how it works.\n\nx <- rnorm(100,100,10)\n\nWe use ARIMA(0,1,1) for this example:\n\nourCall <- \"predict(arima(x=data,order=c(0,1,1)),n.ahead=h)\"\n\nThe call that we specify includes two important elements: data and h. data specifies where the in-sample values are located in the function that we want to use, and it needs to be called “data” in the call. h will tell our function, where the forecasting horizon is specified in the selected function. Note that in this example we use arima(x=data,order=c(0,1,1)), which produces a desired ARIMA(0,1,1) model and then we use predict(...,n.ahead=h), which produces a forecast from that model. The part arima(x=data,order=c(0,1,1)) can also be simplified to arima(data,order=c(0,1,1)) according to the general rules of R.\n\nHaving the call, we need also to specify what the function should return. This can be the conditional mean (point forecasts), prediction intervals, the parameters of a model, or, in fact, anything that the model returns (e.g. name of the fitted model and its likelihood). However, there are some differences in what the ro() returns depending on what the function you use returns. If it is a vector, then ro() will produce a matrix (with values for each origin in columns). If it is a matrix, then an array is returned. Finally, if it is a list, then a list of lists is returned.\n\nIn order not to overcomplicate things, let’s start with collecting the conditional mean from the predict() function:\n\nourValue <- \"pred\"\n\nNOTE: If you do not specify the value to return, the function will try to return everything, but it might fail, especially if a lot of values are returned. So, in order to be on the safe side, always provide the value, when possible.\n\nNow that we have specified ourCall and ourValue, we can produce forecasts from the model using rolling origin. Let’s say that we want three-steps-ahead forecasts and 8 origins with the default values of all the other parameters:\n\nreturnedValues1 <- ro(x, h=3, origins=8, call=ourCall, value=ourValue)\n\nThe function returns a list with all the values that we asked for plus the actual values from the holdout sample. We can calculate some basic error measure based on those values, for example, scaled Mean Absolute Error (Petropoulos and Kourentzes 2015):\n\n}\nourHoldoutValues[j,,] <- ourROReturn$holdout } Although we do not specify i explicitly anywhere in the call of ro() above, it is used in ourCall and as a result the different models will be estimated in the inner loop. Comparing the performance of the two on the different time series we have (this is RelMAE from (Davydenko and Fildes 2013)): exp(mean(log(apply(abs(ourHoldoutValues - ourForecasts[,1,,]),1,mean,na.rm=TRUE) / apply(abs(ourHoldoutValues - ourForecasts[,2,,]),1,mean,na.rm=TRUE)))) #> 0.914444 So based on these results, it can be concluded, that ARIMA(0,1,1) is on average more accurate than ARIMA(1,1,0) on our three time series. ## Making things even more complicated exciting For our last examples we create the data frame and try fitting linear regression: xreg <- matrix(rnorm(120*3,c(100,50,150),c(10,5,15)), 120, 3, byrow=TRUE) y <- 0.5*xreg[,1] + 0.2*xreg[,2] + 0.75*xreg[,3] + rnorm(120,0,10) xreg <- cbind(y,xreg) colnames(xreg) <- c(\"y\",paste0(\"x\",c(1:3))) xreg <- as.data.frame(xreg) Note that in this example we cheat ro() function and make a call, that does not contain either data or h, because the regression implemented in lm() function relies on data frames and does not use forecasting horizon: ourCall <- \"predict(lm(y~x1+x2+x3,xreg[counti,]),newdata=xreg[counto,],interval='p')\" In this case we just need to make sure that the Global Environment contains the xreg data frame. counti variable in the call is needed for the internal loop - it determines the length of the in-sample. Similarly counto specifies the length of the holdout. Both of them are defined inside the ro() function. In addition, we don’t need to specify ourValue, because the function predict.lm() returns a matrix with values (or a vector if we don’t ask for intervals), not a list. NOTE: if you use a different function (not lm()), then you might need to specify the value. The final call to ro() is as usual pretty simple: ourROReturn <- ro(xreg$y, h=3, origins=8, call=ourCall, ci=TRUE, co=TRUE)\n#> Warning: You have not specified the 'value' to produce.We will try to return\n#> everything, but we cannot promise anything.\n\nIn this case, we need to provide the response variable in the data parameter of the call, because the function needs to extract values for the holdout.\n\nSimilar thing can be done using alm() function but with a proper value (the function might fail otherwise):\n\nourCall <- \"predict(alm(y~x1+x2+x3,xreg[counti,]),newdata=xreg[counto,],interval='p')\"\nourValue <- c(\"mean\",\"lower\",\"upper\")\nourROReturn <- ro(xreg\\$y, h=3, origins=8, call=ourCall, value=ourValue, ci=TRUE, co=TRUE)\nplot(ourROReturn)", null, "As a final example, we consider ARIMAX model for the following data:\n\nxreg <- matrix(rnorm(120*3,c(100,50,150),c(10,5,15)), 120, 3, byrow=TRUE)\ny <- 0.5*xreg[,1] + 0.2*xreg[,2] + 0.75*xreg[,3] + rnorm(120,0,10)\ncolnames(xreg) <- paste0(\"x\",c(1:3))\nxreg <- as.data.frame(xreg)\n\nand modify the call accordingly:\n\nourCall <- \"predict(arima(x=data, order=c(0,1,1), xreg=xreg[counti,]), n.ahead=h, newxreg=xreg[counto,])\"\n\nTaking that now we deal with ARIMA, we need to specify both data and h. Furthermore, xreg is different than in the previous example, as it now should not contain the response variable.\n\nAs usual, we need our function to return the specific predicted values:\n\nourValue <- \"pred\"\n\nAnd then we call for the function and get the results:\n\nourROReturn <- ro(x, h=3, origins=8, call=ourCall, value=ourValue)\n\nAs a side note, if you use smooth package for R and want to do rolling origin evaluation, for example, for ETSX model using es() function, the call can be simplified to:\n\nourCall <- \"es(x=data, xreg=xreg[countf,]), h=h)\"\n\nHere we use countf variable, which specifies that we need to use both in-sample and the holdout (the full sample), as the function es() does not rely on forecast() or predict() and can produce forecasts internally.\n\nFinally, all of the examples mentioned above can be done in parallel, which is triggered by parallel parameter. Note that this might be useful for cases, when number of origins is very high and the sample size is large. Otherwise this might be less efficient than the serial calculation. If you want to do anything in parallel, then you either need either doMC (Linux and Mac OS) or doParallel (for Windows) package in R. The number of cores used in this case is equal to the number of cores of your CPU minus one." ]
[ 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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https://dr-knz.net/on-the-turing-completeness-of-c-part-2.html
[ "Two days ago I started to investigate whether C was Turing Complete. With help from two serious people also interested in the topic, I came to the preliminary conclusion that it is probably not. Here is a summary of the arguments so far.\n\nTuring Completeness is a property of languages (i.e. not machines) which can be phrased as follows: a language is Turing complete if any function that can be computed by a Turing Machine can be expressed in that language. An interesting property is that if a language is turing complete then the halting problem is not decidable for arbitrary programs in that language.\n\nThe usual way to determine whether a given language is Turing complete is to prove that it is sufficiently general to express all computable functions. This is the approach indirectly suggested by Scott Schneider in his comment to Hacker News.\n\nFurthermore, Scott proposes a simple test for Turing Completeness: check whether the language supports unbounded recursion, conditionals and arbitrary storage.\n\n“Support for unbounded recursion” has been formally described by R. Péter in 1934 ; to simplify, it is the ability to write a recursive function whose recursion depth is not known in advance. The standard C language as defined by ISO 9899:1999 and 9899:2011 does support unbounded recursion, by omitting to specify of a maximum recursion depth. Of course, C also supports conditionals.\n\nThe question then came of whether C supports arbitrary storage. Both Scott and I have come to think that this is not the case: due to the finite and fixed width’s of C types, especially pointer types and array indices, the abstract machine that defines the semantics of C has a memory of finite size.\n\nBut are we right? This needs to be properly investigated.\n\nAs highlighted by commenter Edgard G. Daylight, we should also start by restricting the entire discussion to non-interactive C programs, because Turing Completeness is about the equivalence with Turing machines which are also no-interactive. Interactivity in C comes specifically from the “volatile” keyword and the standard library. we will thus consider only the subset of C defined for a “freestanding” environment (i.e. no library) and without “volatile”, where the input to the program is only defined by the initial value at run-time of global objects left unitialized in the program source.\n\nIf we can determine Turing Completeness for this restricted language, then the full C language would also be Turing Complete by construction. If we instead determine that the restricted language is not Turing Complete, then we can organize a separate discussion, later, to determine whether there are features of the full C language that “bring back” Turing Completeness.\n\n❦❦❦\n\nAnother point needs to be clarified, too: Scott’s test for Turing Completeness is different from the traditional phrasing. The traditional phrasing does not mention unbounded recursion nor arbitrary storage; instead, it states that a language is Turing Complete if it supports conditionals, unbounded loops and a finite number of memory cells which each can contain arbitrary large values. This is, for example, the basis for the definition of Hofstadter’s FlooP which is Turing Complete.\n\nScott’s test, instead, mentions “arbitrary storage” which can be understood in the context of C to correspond to an arbitrarily large number of different cells, each containing a fixed size value.\n\nI am confident (although I haven’t proved it formally) that both phrasings are equivalent. To me, it is intuitively possible to implement unbounded loops with unbounded recursion, as well as cells that can retain arbitrarily large value (i.e. “bignums”) using arbitrary storage. Conversely, with one cell retaining a call stack and an unbounded loop, one can simulate unbounded recursion, and another cell can simulate arbitrary storage.\n\nEven assuming the phrasings are not equivalent, since C supports both unbounded loops and unbounded recursion, the remaining question would then be whether C supports an arbitrarily large number of finite cells or a fixed number of cells that can store arbitrarily large values.\n\n❦❦❦\n\nWe can try first to find out whether the individual cells can contain arbitrary values, i.e. whether the type “char” is specified to have a finite width.\n\nA “char” cell is defined to contain exactly CHAR_BIT bits; CHAR_BIT is in turn defined to be greater than or equal to 8, but its exact value is implementation-defined. One can interpret this specification in two ways: either the specification should be understood to implicitly mandate CHAR_BIT to be finite; or it leaves space for an (hypothetic, possibly impractical) implementation of C where CHAR_BIT is not finite. If the latter holds, then C would indeed support arbitrarily large values in each char cell.\n\nTo test this, two approaches are possible.\n\nThe first is to check whether other statements in the C language specification indirectly constrain CHAR_BIT to be finite. At the point CHAR_BIT is defined (sections 6.5.2 and 5.2.4.2.1), the text of the language specification does not state so explicitly; but a careful reading of the entire specification may find this finiteness elsewhere.\n\nThe other approach is to try and actually construct a C program that simulates a universal Turing machine (or graph reduction machine, or stack machine) with CHAR_BIT not assumed to be finite. This succeeds when we can write such a program and cannot find any statement in the language specification that the program is incorrect or that its behaviour is unspecified or undefined.\n\n(The first approach should be used by someone who expects to find this finiteness; the second approach should be used by someone who expects otherwise.)\n\nI do not have a definite answer on this yet.\n\nHowever, note that finding Turing Completeness in this direction would require a conceptual implementation of C with a “very large” char data type (“infinitely” large, in fact), which is very far from what most people understand the C language is about.\n\nWhich brings me to another, informal answer. We can step out of the frame and check instead the intentions of the various ISO committees in charge of writing and publishing the C language specification.\n\nIt seems obvious (to me, at least) that these people wanted CHAR_BIT represent the capacity of individual cells that can be implemented in memory hardware, expected to stay stable over time and close to the POSIX/Internet standard of 8 bits per “char”. By this argument, the people in charge of standardizing C’s semantics intended a finite storage space in bits per cell.\n\n❦❦❦\n\nAssuming CHAR_BIT is finite, which, irrespective of the language specification, is the most intuitive and practical choice regarding implementation, we can instead try to find whether C supports an arbitrarily large number of cells.\n\nThis is actually surprisingly difficult to determine.\n\nFirstly, the language specification states in section 6.2.6 (representation of types) that all types have a representation as a finite array of “char” cells. This implies that all individual objects, which are the mechanism by which C gives access to storage to program writers, have a finite number of cells. Since we assume that each cell can hold only a finite number of different values, this means that any object of any given type also has a finite number of possible values. Since each pointer is an object, this implies that the number of different addressable objects in C is also finite, including the number of cells in arrays.\n\nTherefore, it is not possible to support arbitrary storage by using arrays or variable pointers to different objects.\n\nHowever, it is also possible in C to construct/define non-addressable objects, namely:\n\n• objects allocated statically by name (either in the global scope or with “static” on local scopes) whose address is never taken with the & (“address of”) operator; and\n• literal constants (i.e. character literals, enumeration constants, string literals and number literals); and\n• objects defined by name to be allocated automatically upon function activation, i.e. “local variables” in functions, whose address is never taken with the & operator.\n\nOf these three categories, the first two only come in finite supply for any given program (a given, finite program text has a finite supply of different names and literal constants). That leaves us with the remaining question: can one simulate arbitrary storage using only automatic variables and without using arrays nor the & operator?\n\nI am increasingly confident that this is not possible. My informal argument goes as follows: since each object has a finite size, and the program text limits us to a finite number of different object per function definition, the only way to increase the storage space is function recursion: each recursive function call will automatically instantiate new objects, and their number is unbounded because function recursion is unbounded. However, each specific function activation cannot “navigate” the entire storage created this way, like a Turing machine could move its head left or right to arbitrary positions on the tape, because the variables in one activation cannot be accessed from another activation.\n\nIt is not possible to introduce this “navigation” feature by means of function arguments, because these would need to be basic C integers or pointers which again would limit the span of the navigation to a finite set of locations.\n\nIf my argument is correct, this would imply that C restricts each program to a finite supply of “char” cells. Combined with the finiteness of CHAR_BIT, assumed above, one would then conclude that C is not Turing Complete (under the initial restriction of a freestanding environment without “volatile”).\n\n❦❦❦\n\nThe summary so far is thus:\n\n• if we consider C restricted to a freestanding environment, removing the “volatile” keyword, and assuming CHAR_BIT is finite, then C is (very likely) not Turing Complete;\n• if CHAR_BIT is not finite, then C is (likely) Turing Complete;\n• if CHAR_BIT is finite, there may be features of a hosted C environment and/or C with “volatile” that make it Turing Complete, however we have not looked at this yet.\n\nThe topic is really fascinating and I cherish the idea to lay out the discussion into a proper academic publication. But before that I need to clean up my understanding of Turing completeness and how to test for it in an arbitrary language. The first step in that direction was to order a copy of Elements of the Theory of Computation today, which I hope to digest over the Christmas vacation. Stay tuned!", null, "Raphael ‘kena’ Poss is a computer scientist and software engineer specialized in compiler construction, computer architecture, operating systems and databases." ]
[ null, "https://dr-knz.net/images/avatars/cat.jpg", null ]
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https://zbmath.org/?q=an:1246.58017
[ "# zbMATH — the first resource for mathematics\n\nAn index formula for nonlocal operators corresponding to a diffeomorphism of a manifold. (English. Russian original) Zbl 1246.58017\nDokl. Math. 83, No. 3, 353-356 (2011); translation from Dokl. Akad. Nauk 438, No. 4, 444-447 (2011).\nLet $$M$$ be an oriented smooth manifold, let $$g:M\\to M$$ be an orientation preserving diffeomorphism, and let $$E$$ and $$F$$ be complex vector bundles on $$M$$.\nThe authors consider nonlocal operators given by a finite sum $$D=\\sum_kD_kT^k:C^\\infty(M,E)\\to C^\\infty(M,F)$$, where $$T:C^\\infty(M,E)\\to C^\\infty(M,g^*F)$$ is the shift operator induced by $$g$$, $$(Tu)(x)=u(g(x))$$, and the coefficients $$D_k:C^\\infty(M,g^{k*}E)\\to C^\\infty(M,F)$$ are zero order pseudodifferential operators. The symbol $$\\sigma(D)$$ is the sequence of symbols $$\\sigma(D_k)\\in C^\\infty(S^*M,\\pi^*\\text{Hom}(g^{k*}E,F))$$, where $$\\pi:S^*M=T_0^*M/\\mathbb{R}_+\\to M$$ is the cospherical bundle. If $$B=\\sum_kB_kT^k:C^\\infty(M,G)\\to C^\\infty(M,E)$$ is another operator of the same type, then $$\\sigma(DB)(k)=\\sum_{\\ell+m=k}\\sigma(D_\\ell)((\\partial g^\\ell)^*\\sigma(B_m))$$, where $$\\partial g=(dg^t)^{-1}:T^*M\\to T^*M$$. This formula is taken as definition of product of this kind of symbols, and the symbol of the identity operator $$T^0$$ is the identity element. Then it is said that $$D$$ is elliptic if $$\\sigma(D)$$ is invertible. In this case, it is observed that $$D$$ defines a Fredholm operator between Sobolev spaces of any order, and its kernel and cokernel consist of smooth sections.\nIn [$$K$$-Theory 34, No. 1, 71–98 (2005; Zbl 1087.58013)], the first author defined the difference construction $$[\\sigma(D)]\\in K_0(C^\\infty_0(\\mathcal{T}^*M)\\rtimes\\mathbb{Z})$$, where $$C^\\infty_0(\\mathcal{T}^*M)$$ is the algebra consisting of all $$u\\in C^\\infty([0,1]\\times S^*M)$$ such that $$u|_{t>1-\\epsilon}=0$$ and $$u|_{t<\\epsilon}=u_0(x)$$ for $$u_0\\in C^\\infty(M)$$. Similarly, let $$\\Lambda(\\mathcal{T}^*M)$$ be the differential algebra consisting of all $$\\omega$$ in the de Rham differential algebra $$\\Lambda[0,1]\\times S^*M)$$ so that $$\\omega|_{t>1-\\epsilon}=0$$ and $$\\omega|_{t<\\epsilon}=\\pi^*\\omega_0$$, where $$\\pi:[0,1]\\times S^*M\\to M$$ is the projection. Consider the corresponding Haefliger cohomology $$H^*(\\mathcal{T}^*M/\\mathbb{Z})$$, defined by the complex $$\\Lambda(\\mathcal{T}^*M)/(1-g^*)\\Lambda(\\mathcal{T}^*M)$$. Then the Chern character $$\\text{ch}:K_*(\\mathcal{T}^*M)\\rtimes\\mathbb{Z})\\to H^*(\\mathcal{T}^*M/\\mathbb{Z})$$ is defined. Moreover $$\\pi:[0,1]\\times S^*M\\to M$$ induces a homomorphism $$\\pi_*:H^*(\\mathcal{T}^*M/\\mathbb{Z})\\to H^{*-\\dim M}(M/\\mathbb{Z})$$, where $$H^*(M/\\mathbb{Z})$$ is the Haefliger cohomology defined by $$(M,g)$$ (given by the complex $$\\Lambda(M)/(1-g^*)\\Lambda(M)$$). The Chern character of an elliptic $$D$$ is defined as $$\\text{ch}(D)=\\pi_*\\cosh[\\sigma(D)]\\in H^*(M/\\mathbb{Z})$$.\nOn the other hand, let $$H_*(M/\\mathbb{Z})$$ be the homology of the complex of $$g$$-invariant currents on $$M$$, which has a canonical pairing with $$H^*(M/\\mathbb{Z})$$. The authors assume that the class $$\\text{Td}(T^*M\\otimes\\mathbb{C})\\cap[M]\\in H_*(M)$$, dual to $$\\text{Td}(T^*M\\otimes\\mathbb{C})$$, belongs to the image of the canonical homomorphism $$H_*(M/\\mathbb{Z})\\to H_*(M)$$, and take a preimage denoted by $$\\text{Td}_g(T^*M\\otimes\\mathbb{C})$$. Then the topological index of an elliptic $$D$$ is defined as $$\\text{ind}_tD=\\langle\\text{ch}D,\\text{Td}_g(T^*M\\otimes\\mathbb{C})\\rangle$$. The main result of the paper is an index theorem stating that, if $$H_{\\text{odd}}(M)\\otimes\\mathbb{Q}=0$$, then $$\\text{ind}D=\\text{ind}_tD$$. The proof is not given, but several examples are described.\n\n##### MSC:\n 58J22 Exotic index theories on manifolds 58J20 Index theory and related fixed-point theorems on manifolds\nFull Text:\n##### References:\n A. Connes, Noncommutative Geometry (Academic, San Diego, 1994). A. Antonevich and A. Lebedev, Functional Differential Equations, Vol. 1: C*-Theory (Longman, Harlow, 1994). · Zbl 0799.34001 A. Antonevich and A. Lebedev, Functional Differential Equations, Vol. 2: C*-Applications, Part 1: Equations with Continuous Coefficients (Longman, Harlow, 1998). · Zbl 0936.35207 V. E. Nazaikinskii, A. Yu. Savin, and B. Yu. Sternin, Elliptic Theory and Noncommutative Geometry (Birkhauser, Basel, 2008). · Zbl 1158.58013 A. Yu. Savin and B. Yu. Sternin, Dokl. Math. 82, 519–522 (2010) [Dokl. Akad. Nauk 433, 21–24 (2010)]. · Zbl 1213.58016 · doi:10.1134/S1064562410040058 A. Yu. Savin, Dokl. Math. 82, 884–886 (2010) [Dokl. Akad. Nauk 432, 170–172 (2010)]. · Zbl 1235.58018 · doi:10.1134/S1064562410060128 D. P. Williams, Crossed Products of C*-Algebras (Am. Math. Soc., Providence, RI, 2007). · Zbl 1119.46002 A. Haefliger, J. Differ. Geom. 15, 269–284 (1980). · Zbl 0444.57016 · doi:10.4310/jdg/1214435494 A. Yu. Savin and B. Yu. Sternin, Mat. Sb. 201(3), 63–106 (2010). · doi:10.4213/sm7537 A. Savin, K-Theory 34(1), 71–98 (2005). · Zbl 1087.58013 · doi:10.1007/s10977-005-1515-1 G. de Rham, Variétès différentiables (Hermann, Paris, 1955). M. F. Atiyah and I. M. Singer, Bull. Am. Math. Soc. 69, 422–433 (1963). · Zbl 0118.31203 · doi:10.1090/S0002-9904-1963-10957-X N. Kryloff and N. Bogoliuboff, Ann. Math. 38(1), 65–113 (1937). · Zbl 0016.08604 · doi:10.2307/1968511 D. V. Anosov, Usp. Mat. Nauk 49(5), 5–20 (1994).\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching." ]
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https://www.ncatlab.org/nlab/show/decategorification
[ "Contents\n\ncategorification\n\n# Contents\n\n## Idea\n\nDecategorification is the reverse of vertical categorification and turns an $n$-category into an $(n-1)$-category.\n\nIt corresponds in homotopy theory to truncation.\n\n## Definitions\n\nGiven a (small or essentially small) category $C$, the set of isomorphism classes $K(C)$ of objects of $C$ is called the decategorification of $C$.\n\nThis is a functor\n\n$K : Cat \\to Set$\n\nfrom the category (or even $2$-category) Cat of (small) categories to the category (or locally discrete 2-category) Set of sets. Notice that we may think of a set as 0-category, so that this can be thought of as\n\n$K : 1Cat \\to 0Cat \\,.$\n\nDecategorification decreases categorical degree by forming equivalence classes. Accordingly for all $n \\gt m$ and all suitable notions of higher categories one can consider decategorifications\n\n$n Cat \\to m Cat \\,.$\n\nFor instance forming the homotopy category of an (∞,1)-category means decategorifying as\n\n$(\\infty,1)Cat \\to 1 Cat \\,.$\n\nTherefore one way to think of vertical categorification is as a right inverse to decategorification.\n\n## Decategorification of a 2-category\n\nA precise way to define the decategorification of a 2-category in the above sense is to identify all 1-arrows which are 2-isomorphic (note that this defines an equivalence relation on 1-arrows and respects composition), and to discard the 2-arrows.\n\n## Example\n\nThe decategorification, in the above sense, of the 2-category of (small) groupoids is equivalent to the (homotopy) category of homotopy 1-types.\n\nThe decategorification in the same sense of the 2-category of (small) categories is equivalent to the full homotopy category.\n\n## Extra structure\n\nIf the category in question has extra structure, then this is usually inherited in some decategorified form by its decategorification. For instance if $C$ is a monoidal category then $K(C)$ is a monoid.\n\nA famous example are fusion categories whose decategorifications are called Verlinde rings.\n\nThere may also be extra structure induced more directly on $K(C)$. For instance the K-group of an abelian category is the decategorification of its category of bounded chain complexes and this inherits a group structure from the fact that this is a triangulated category (a stable (∞,1)-category) in which there is a notion of homotopy exact sequences.\n\n## Further examples\n\n• The decategorifications of finite sets and finite dimensional vector spaces are natural numbers\n\n$K(FinSet) \\simeq \\mathbb{N}$\n$K(FinVect) \\simeq \\mathbb{N}$\n\nLast revised on May 23, 2017 at 18:53:21. See the history of this page for a list of all contributions to it." ]
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https://calcforme.com/percentage-calculator/409-is-147-percent-of-what
[ "# 409 is 147 Percent of what?\n\n## 409 is 147 Percent of 278.23\n\n%\n\n409 is 147% of 278.23\n\nCalculation steps:\n\n409 ÷ ( 147 ÷ 100 ) = 278.23\n\n### Calculate 409 is 147 Percent of what?\n\n• F\n\nFormula\n\n409 ÷ ( 147 ÷ 100 )\n\n• 1\n\nPercent to decimal\n\n147 ÷ 100 = 1.47\n\n• 2\n\n409 ÷ 1.47 = 278.23 So 409 is 147% of 278.23\n\nExample" ]
[ null ]
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https://www.ohyee.cc/post/hdu_1106
[ "# 题目\n\n## Description\n\nFatMouse believes that the fatter a mouse is, the faster it runs. To disprove this, you want to take the data on a collection of mice and put as large a subset of this data as possible into a sequence so that the weights are increasing, but the speeds are decreasing.\n\n## Input\n\nInput contains data for a bunch of mice, one mouse per line, terminated by end of file.\n\nThe data for a particular mouse will consist of a pair of integers: the first representing its size in grams and the second representing its speed in centimeters per second. Both integers are between 1 and 10000. The data in each test case will contain information for at most 1000 mice.\n\nTwo mice may have the same weight, the same speed, or even the same weight and speed.\n\n## Output\n\nYour program should output a sequence of lines of data; the first line should contain a number n; the remaining n lines should each contain a single positive integer (each one representing a mouse). If these n integers are m, m,..., m[n] then it must be the case that\n\nW[m] < W[m] < ... < W[m[n]]\n\nand\n\nS[m] > S[m] > ... > S[m[n]]\n\nIn order for the answer to be correct, n should be as large as possible.\nAll inequalities are strict: weights must be strictly increasing, and speeds must be strictly decreasing. There may be many correct outputs for a given input, your program only needs to find one.\n\n6008 1300\n6000 2100\n500 2000\n1000 4000\n1100 3000\n6000 2000\n8000 1400\n6000 1200\n2000 1900\n\n4\n4\n5\n9\n7\n\n>最长上升子序列<\n\n# 代码\n\n```/*\nBy:OhYee\nGithub:OhYee\nHomePage:http://www.oyohyee.com\nEmail:[email protected]\n\nかしこいかわいい？\nエリーチカ！\n\n*/\n\n#include <cstdio>\n#include <algorithm>\n#include <cstring>\n#include <cmath>\n#include <string>\n#include <iostream>\n#include <vector>\n#include <list>\n#include <queue>\n#include <stack>\n#include <map>\n#include <set>\nusing namespace std;\n\nconst int maxn = 1005;\n\nstruct Node {\nint n;\nint speed;\nint weight;\nbool operator > (const Node& rhs)const {\nreturn (speed > rhs.speed) && (weight < rhs.weight);\n}\nbool operator < (const Node& rhs)const {\nif(weight == rhs.weight)\nreturn speed > rhs.speed;\nreturn weight < rhs.weight;\n}\n};\n\nNode mice[maxn];\nint dp[maxn];\nint last[maxn];\nstack<int> s;\n\nvoid Do() {\nwhile(!s.empty())\ns.pop();\nmemset(dp,0,sizeof(dp));\n\nint n = 1;\nwhile(scanf(\"%d%d\",&mice[n].weight,&mice[n].speed) != EOF) {\nmice[n].n = n;\nn++;\n}\nn--;\n\nsort(mice + 1,mice + n + 1);\n\nint Maxpos = 1;\nfor(int i = 1;i <= n;i++) {\nfor(int j = 0;j < i;j++)\nif(mice[j] > mice[i] || j == 0)\nif(dp[j] + 1 > dp[i]) {\ndp[i] = dp[j] + 1;\nlast[i] = j;\n}\nif(dp[Maxpos] < dp[i])\nMaxpos = i;\n}\n\nprintf(\"%d\\n\",dp[Maxpos]);\n\nint k = Maxpos;\nwhile(k) {\ns.push(k);\nk = last[k];\n}\nwhile(!s.empty()) {\nint t = s.top();\nprintf(\"%d\\n\",mice[t].n);\ns.pop();\n}\n\n}\n\nint main() {\nDo();\nreturn 0;\n}\n```" ]
[ null ]
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https://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r46
[ "# The Polytope of Degree Partitions\n\n• Amitava Bhattacharya\n• S. Sivasubramanian\n• Murali K. Srinivasan\n\n### Abstract\n\nThe degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of degree partitions (respectively, degree sequences) of all simple graphs on the vertex set $[n]$. The polytope of degree sequences has been very well studied. In this paper we study the polytope of degree partitions. We show that adding the inequalities $x_1\\geq x_2 \\geq \\cdots \\geq x_n$ to a linear inequality description of the degree sequence polytope yields a linear inequality description of the degree partition polytope and we show that the extreme points of the degree partition polytope are the $2^{n-1}$ threshold partitions (these are precisely those extreme points of the degree sequence polytope that have weakly decreasing coordinates). We also show that the degree partition polytope has $2^{n-2}(2n-3)$ edges and $(n^2 -3n + 12)/2$ facets, for $n\\geq 4$. Our main tool is an averaging transformation on real sequences defined by repeatedly averaging over the ascending runs.\n\nPublished\n2006-05-05\nIssue\nArticle Number\nR46" ]
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https://math.stackexchange.com/questions/1234512/all-sets-of-rational-numbers-are-bigger-than-the-set-containing-infinite-integer
[ "All sets of rational numbers are bigger than the set containing infinite integers - or are they?\n\nIntro\n\nThis started with me learning the different types of infinity. I like to call them types instead of sizes due to the fact, that infinite is defined by being endless or \"not-finite\" - meaning not a size. (I do know the right definition is different sizes).\n\nMy Hypothesis\n\nI started trying to match integers to rational numbers one-to-one (or bijection). I have found, in the top answer in this question, that:\n\nTwo sets $A$ and $B$ are said to have the \"same size\" if there is a some function $f:A\\to B$ which is a bijection. Note that we do NOT require that ALL functions be bijections, just that there is SOME bijection.\n\nThe way I found it possible was by limiting the set of rational numbers to $[0,1)$. Now by reversing the order of the decimals I could map all rational numbers excluding fractions resulting in an endless repeating sequence of decimals, thus matching:\n\n• 0.034 to 430\n• 0.2331 to 1332\n• ...\n\nAs said, this maps any rational numbers excluding fractions resulting in an endless repeating sequence of decimals. Now the method to mapping those.\n\n($\\overline{\\text{Overline}}$ means repeated endlessly)\n\nThe workaround with this is made in two steps:\n\n• $\\frac47 = 0.571428\\overline{571428}$\n\nIf we accept this as a number I assume that this following is acceptable as well:\n\n• $824175\\overline{824175}$\n\nQuestion\n\nDoes this mean, that there are exactly as many rational numbers in the set $[0,1)$ as there are integers in the set $[0,\\infty]$?\n\nAnd furthermore that in the rational set $[0,1]$ contains one more number that the set of integers $[0,\\infty]$?\n\nBonus Quention\n\nIs this allowed: $10\\times824157\\overline{824157}$?\n\nEDIT\n\nWinther made it clear that $824157\\overline{824157}$ not is a real number. Thanks for that. However ... (I don't give up that easy)\n\nIf every fraction NOT ending in an infinite repeating is saved as already stated except set as next free even integer (multiplying with 2) - Just as in Hilbert's paradox of the Grand Hotel - with infinite new guests. Thus making:\n\n• 0.1 -> 1 -> 2\n• 0.2 -> 2 -> 4\n• ...\n• 0.5 -> 5 -> 10\n• ...\n• 0.01 -> 10 -> 20\n\nThe fractions not already mentioned (the ones with infinite repeating) will then get the uneven integers. The way to list these will then be done with Cantor's Diagonal listing:\n\n• 1/1 is not in [0;1[ so moving on\n• 1/2 is already represented (0.5 -> 5 -> 10) see above\n• 2/2 again not in [0;1[\n• 1/3 is not represented yet. 1/3 -> 1\n• 2/3 is not represented yet. 2/3 -> 3\n• ...\n• 1/6 is not represented yet. 1/6 -> 5\n• ...\n• 4/6 is not represented yet. 4/6 -> 7\n\nNew Question\n\nIs this proof then?\n\n• What is $824175\\overline{824175}$ supposed to mean? Infinite repetion to the right ($824175824175824175\\ldots$) is not a real number. The reason $0.571428\\overline{571428}$ makes sense is that it is represented by a series that converges. – Winther Apr 14 '15 at 16:26\n• Will this: $\\overline{824175}824175$ make more sense then? – user3265569 Apr 14 '15 at 16:31\n• You have to define what that means. Is it $\\ldots 824175824175824175$, what number is this? It's not a real number. As a sidenote one can make sense of number of that form (see p-adic numbers but that has nothing to do with the construction you are trying to make. – Winther Apr 14 '15 at 16:37\n• Thanks. I've made an edit. Care to take a look? – user3265569 Apr 14 '15 at 17:05\n• Note that $0.1 = 1/10$, $0.2 = 1/5$ etc. so I would remove the first part (it is covered by the latter so you don't need it - it just complicates stuff). But that method should work (small typo: $4/6 = 2/3$ has been listen before). You are guaranteed to go through all rational numbers in $[0,1)$ and map them one-to-one to the positive integers giving you a bijection. – Winther Apr 14 '15 at 17:19\n\nFirstly, you should not say \"infinite integers\" if you mean \"infinitely many integers\". If one admits such a thing as an infinite integer, and $n$ is an infinite integer, then $n$ and $n+1$ are infinite integers, but they are not infinitely many, since there are only two of them. This is standard usage in mathematics, regardless of what usages may prevail in informal English used in contexts other than mathematics.\n\nThe sequence below has a first term, a second term, a third term, and so on, so there are just as many terms as there are positive integers $1,2,3,\\ldots\\,{}$. \\begin{align} \\frac 1 2, \\underbrace{\\frac 1 3, \\frac 2 3},\\underbrace{\\frac 1 4,\\frac 3 4},\\underbrace{\\frac 1 5,\\frac25,\\frac35,\\frac45},\\ \\underbrace{\\ldots\\ldots\\ldots\\ldots}_\\text{sixths},\\ \\underbrace{\\ldots\\ldots\\ldots\\ldots}_\\text{sevenths},\\ \\ldots \\end{align} And all rational numbers between $0$ and $1$ are in this list (you'll notice I skipped $2/4$ since it's not in lowest terms).\n\nIf you want to add one more rational number, or two more (e.g. $0$ and $1$) then just append them to the front of the list and you'll see that there are still just as many as there are integers.\n\n• How can you say this set has the same number of elements or even the same rate of increasing? The fact that each term has more than one element demonstrates that it is a larger set. – The Great Duck Aug 18 '17 at 15:48\n\nIntegers can be broken up into 3 subsets: $\\{ 0 \\}$, ${+,\\mathbb{N}}$ and $\\{-, \\mathbb{N}\\}$, i.e. 0 and two instances of the set of naturals, one for positive integers and the other for negatives. The integer $0$ corresponds with the rational $0$. If we can construct a correspondence between the positive rationals and the naturals, then we can use it twice to map both of the aforementioned infinite subsets of the integers to the positive and negative rationals.\n\nThe Stern-Brocot tree is a very useful organization of the positive rationals. Each path in the tree corresponds to a distinct positive rational, and every positive rational is present in the tree.\n\nNaturals and finite binary strings have an obvious one-to-one relation through the use of binary numerals, with the exception of the empty string. But you can accommodate it by just sticking it in at the beginning.\n\nFinite binary strings and paths in the Stern-Brocot tree correspond by replacing '0' with \"Left\" and '1' with \"Right\".\n\nEach finite path in the Stern-Brocot tree corresponds to a positive Rational. All paths lead to a rational, and every positive rational is present in the tree.\n\nSo the whole chain of equivalences would be:\n\n$$\\mathbb{Z} \\Leftrightarrow \\{0\\} \\cup \\{+,\\mathbb{N}\\} \\cup \\{-,\\mathbb{N}\\}$$ $$\\text{let} B = \\left[\\mathbb{N} \\Leftrightarrow \\text{finite binary strings} \\Leftrightarrow\\text{finite paths in Stern-Brocot tree} \\Leftrightarrow \\{ \\mathbb{Q} > 0\\}\\right]$$\n\n$$\\{0\\} \\Leftrightarrow \\frac01$$ $$\\{+,\\mathbb{N}\\} \\Leftrightarrow_B \\{\\mathbb{Q}>0\\}$$ $$\\{-,\\mathbb{N}\\} \\Leftrightarrow_B \\{\\mathbb{Q}<0\\}$$\n\nYour proof (after the edit, with the separate even and odd sequences of non-repeating and repeating decimals) seems correct, except for the claim (just before the edit) about one \"extra\" rational number in the interval $[0,1]$. (Remember how you can always book one more guest in the Hilbert Hotel.)\n\nThe part that you added to the proof to handle the repeating decimals is actually very similar to a more usual way of enumerating all the rationals (including repeating and non-repeating decimals) in $(0,1]$, so with just a little tweaking you could actually drop the first half of the proof and use only the second half.\n\nAs a side note, a slight variation in the order in which we try different numerators and denominators (including numerators that are larger than their denominators) gives an enumeration of all positive rationals." ]
[ null ]
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https://www.erldocs.com/19.0/stdlib/erl_eval.html
[ "# erl_eval\n\n## The Erlang meta interpreter.\n\nThis module provides an interpreter for Erlang expressions. The expressions are in the abstract syntax as returned by `erl_parse`, the Erlang parser, or `io`.\n\n### binding_struct() = orddict:orddict()\n\nA binding structure.\n\n### local_function_handler() =             {value, lfun_value_handler()} |             {eval, lfun_eval_handler()} |             none\n\nFurther described in section Local Function Handler in this module\n\n### non_local_function_handler() = {value, nlfun_handler()} | none\n\nFurther described in section Non-Local Function Handler in this module.\n\n### add_binding(Name, Value, BindingStruct) -> binding_struct()\n\n• `Name = name()`\n• `Value = value()`\n• `BindingStruct = binding_struct()`\n\nAdds binding `Name=Value` to `BindingStruct`. Returns an updated binding structure.\n\n### binding(Name, BindingStruct) -> {value, value()} | unbound\n\n• `Name = name()`\n• `BindingStruct = binding_struct()`\n\nReturns the binding of `Name` in `BindingStruct`.\n\n### bindings(BindingStruct :: binding_struct()) -> bindings()\n\nReturns the list of bindings contained in the binding structure.\n\n### del_binding(Name, BindingStruct) -> binding_struct()\n\n• `Name = name()`\n• `BindingStruct = binding_struct()`\n\nRemoves the binding of `Name` in `BindingStruct`. Returns an updated binding structure.\n\n### expr(Expression, Bindings) -> {value, Value, NewBindings}\n\n• `Expression = expression()`\n• `Bindings = binding_struct()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\n### expr(Expression, Bindings, LocalFunctionHandler) ->         {value, Value, NewBindings}\n\n• `Expression = expression()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\n### expr(Expression,      Bindings,      LocalFunctionHandler,      NonLocalFunctionHandler) ->         {value, Value, NewBindings}\n\n• `Expression = expression()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `NonLocalFunctionHandler = non_local_function_handler()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\n### expr(Expression,      Bindings,      LocalFunctionHandler,      NonLocalFunctionHandler,      ReturnFormat) ->         {value, Value, NewBindings} | Value\n\n• `Expression = expression()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `NonLocalFunctionHandler = non_local_function_handler()`\n• `ReturnFormat = none | value`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\nEvaluates `Expression` with the set of bindings `Bindings`. `Expression` is an expression in abstract syntax. For an explanation of when and how to use arguments `LocalFunctionHandler` and `NonLocalFunctionHandler`, see sections Local Function Handler and Non-Local Function Handler in this module.\n\nReturns `{value, Value, NewBindings}` by default. If `ReturnFormat` is `value`, only `Value` is returned.\n\n### expr_list(ExpressionList, Bindings) -> {ValueList, NewBindings}\n\n• `ExpressionList = expression_list()`\n• `Bindings = binding_struct()`\n• `ValueList = [value()]`\n• `NewBindings = binding_struct()`\n\n### expr_list(ExpressionList, Bindings, LocalFunctionHandler) ->              {ValueList, NewBindings}\n\n• `ExpressionList = expression_list()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `ValueList = [value()]`\n• `NewBindings = binding_struct()`\n\n### expr_list(ExpressionList,           Bindings,           LocalFunctionHandler,           NonLocalFunctionHandler) ->              {ValueList, NewBindings}\n\n• `ExpressionList = expression_list()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `NonLocalFunctionHandler = non_local_function_handler()`\n• `ValueList = [value()]`\n• `NewBindings = binding_struct()`\n\nEvaluates a list of expressions in parallel, using the same initial bindings for each expression. Attempts are made to merge the bindings returned from each evaluation. This function is useful in `LocalFunctionHandler`, see section Local Function Handler in this module.\n\nReturns `{ValueList, NewBindings}`.\n\n### exprs(Expressions, Bindings) -> {value, Value, NewBindings}\n\n• `Expressions = expressions()`\n• `Bindings = binding_struct()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\n### exprs(Expressions, Bindings, LocalFunctionHandler) ->          {value, Value, NewBindings}\n\n• `Expressions = expressions()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\n### exprs(Expressions,       Bindings,       LocalFunctionHandler,       NonLocalFunctionHandler) ->          {value, Value, NewBindings}\n\n• `Expressions = expressions()`\n• `Bindings = binding_struct()`\n• `LocalFunctionHandler = local_function_handler()`\n• `NonLocalFunctionHandler = non_local_function_handler()`\n• `Value = value()`\n• `NewBindings = binding_struct()`\n\nEvaluates `Expressions` with the set of bindings `Bindings`, where `Expressions` is a sequence of expressions (in abstract syntax) of a type that can be returned by `io:parse_erl_exprs/2`. For an explanation of when and how to use arguments `LocalFunctionHandler` and `NonLocalFunctionHandler`, see sections Local Function Handler and Non-Local Function Handler in this module.\n\nReturns `{value, Value, NewBindings}`\n\n### new_bindings() -> binding_struct()\n\nReturns an empty binding structure.\n\n#### Local Function Handler\n\nDuring evaluation of a function, no calls can be made to local functions. An undefined function error would be generated. However, the optional argument `LocalFunctionHandler` can be used to define a function that is called when there is a call to a local function. The argument can have the following formats:\n\n`{value,Func}`\n\nThis defines a local function handler that is called with:\n\n`Func(Name, Arguments)`\n\n`Name` is the name of the local function (an atom) and `Arguments` is a list of the evaluated arguments. The function handler returns the value of the local function. In this case, the current bindings cannot be accessed. To signal an error, the function handler calls `exit/1` with a suitable exit value.\n\n`{eval,Func}`\n\nThis defines a local function handler that is called with:\n\n`Func(Name, Arguments, Bindings)`\n\n`Name` is the name of the local function (an atom), `Arguments` is a list of the unevaluated arguments, and `Bindings` are the current variable bindings. The function handler returns:\n\n`{value,Value,NewBindings}`\n\n`Value` is the value of the local function and `NewBindings` are the updated variable bindings. In this case, the function handler must itself evaluate all the function arguments and manage the bindings. To signal an error, the function handler calls `exit/1` with a suitable exit value.\n\n`none`\n\nThere is no local function handler.\n\n#### Non-Local Function Handler\n\nThe optional argument `NonLocalFunctionHandler` can be used to define a function that is called in the following cases:\n\nA functional object (fun) is called.\n\nA built-in function is called.\n\nA function is called using the `M:F` syntax, where `M` and `F` are atoms or expressions.\n\nAn operator `Op/A` is called (this is handled as a call to function `erlang:Op/A`).\n\nExceptions are calls to `erlang:apply/2,3`; neither of the function handlers are called for such calls. The argument can have the following formats:\n\n`{value,Func}`\n\nThis defines a non-local function handler that is called with:\n\n`Func(FuncSpec, Arguments)`\n\n`FuncSpec` is the name of the function on the form `{Module,Function}` or a fun, and `Arguments` is a list of the evaluated arguments. The function handler returns the value of the function. To signal an error, the function handler calls `exit/1` with a suitable exit value.\n\n`none`\n\nThere is no non-local function handler.\n\n## Note!\n\nFor calls such as `erlang:apply(Fun, Args)` or `erlang:apply(Module, Function, Args)`, the call of the non-local function handler corresponding to the call to `erlang:apply/2,3` itself (`Func({erlang, apply}, [Fun, Args])` or `Func({erlang, apply}, [Module, Function, Args])`) never takes place.\n\nThe non-local function handler is however called with the evaluated arguments of the call to `erlang:apply/2,3`: `Func(Fun, Args)` or `Func({Module, Function}, Args)` (assuming that `{Module, Function}` is not `{erlang, apply}`).\n\nCalls to functions defined by evaluating fun expressions `\"fun ... end\"` are also hidden from non-local function handlers.\n\nThe non-local function handler argument is probably not used as frequently as the local function handler argument. A possible use is to call `exit/1` on calls to functions that for some reason are not allowed to be called.\n\n#### Known Limitation\n\nUndocumented functions in this module are not to be used." ]
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https://im.kendallhunt.com/MS/students/1/7/15/index.html
[ "# Lesson 15\n\nShapes on the Coordinate Plane\n\nLet’s use the coordinate plane to solve problems and puzzles.\n\n### 15.1: Figuring Out The Coordinate Plane\n\n1. Draw a figure in the coordinate plane with at least three of following properties:\n• 6 vertices\n\n• 1 pair of parallel sides\n\n• At least 1 right angle\n\n• 2 sides the same length\n\n2. Is your figure a polygon? Explain how you know.\n\n### 15.2: Plotting Polygons\n\nHere are the coordinates for four polygons. Move the slider to choose the polygon you want to plot. Move the points, in order, to their locations on the coordinate plane. Sketch each one before changing the slider.\n\n1. Polygon 1: $$(\\text-7, 4), (\\text-8, 5), (\\text-8, 6), (\\text-7, 7), (\\text-5, 7), (\\text-5,5), (\\text-7, 4)$$\n\n2. Polygon 2: $$(4, 3), (3, 3), (2, 2), (2, 1), (3, 0), (4, 0), (5, 1), (5, 2), (4, 3)$$\n\n3. Polygon 3: $$(\\text-8, \\text-5), (\\text-8, \\text-8), (\\text-5, \\text-8), (\\text-5, \\text-5), (\\text-8, \\text-5)$$\n\n4. Polygon 4: $$(\\text-5, 1), (\\text-3, \\text-3), (\\text-1, \\text-2), (0, 3), (\\text-3, 3), (\\text-5, 1)$$\n\nFind the area of Polygon D in this activity.\n\n### 15.3: Four Quadrants of A-Maze-ing\n\n1. The following diagram shows Andre’s route through a maze. He started from the lower right entrance.\n\n1. What are the coordinates of the first two and the last two points of his route?\n2. How far did he walk from his starting point to his ending point? Show how you know.\n2. Jada went into the maze and stopped at $$(\\text-7, 2)$$.\n\n1. Plot that point and other points that would lead her out of the maze (through the exit on the upper left side).\n2. How far from $$(\\text-7, 2)$$ must she walk to exit the maze? Show how you know.\n\n### Summary\n\nWe can use coordinates to find lengths of segments in the coordinate plane.\n\nFor example, we can find the perimeter of this polygon by finding the sum of its side lengths. Starting from $$(\\text-2, 2)$$ and moving clockwise, we can see that the lengths of the segments are 6, 3, 3, 3, 3, and 6 units. The perimeter is therefore 24 units.\n\nIn general:\n\n• If two points have the same $$x$$-coordinate, they will be on the same vertical line, and we can find the distance between them.\n• If two points have the same $$y$$-coordinate, they will be on the same horizontal line, and we can find the distance between them." ]
[ null ]
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https://enigmaticcode.wordpress.com/tag/babbage/
[ "# Enigmatic Code\n\nProgramming Enigma Puzzles\n\n## Running the first program: Part 3\n\n[ Part 1 | Part 2 | Part 3 ]\n\n[Note: The programs can be run without the need to install anything @repl.it]\n\nFollowing on from my previous articles on programming the Analytical Engine (see Part 1 and Part 2), in this post we will actually translate Ada Lovelace’s diagram that is considered to be the first published program into a directly executable program for the Analytical Engine emulator, where each row in the diagram corresponds directly to a statement in the assembly language program.\n\nAs suggested in Part 2, I have written a simple assembler to make it a bit easier to write programs for the Analytical Engine emulator. It allows you to specify the arithmetic operations for the Engine as a single statement (rather than the usual 4 cards), and it keeps track of symbolic labels and automatically computes branch offsets for you.\n\nThe assembler is implemented by the assemble() function, which I’ve included in the latest version of analytical_engine.py.\n\nThe assemble() function takes a multi-line string representing the program, and returns a list of cards suitable for use as a program in the AnalyticalEngine class. It also returns a map from the labels used in the assembler program to the index of the corresponding card in the program.\n\nThe factorial program from Part 2 would look like this using the assembler:\n\n```from analytical_engine import AnalyticalEngine, Column\n\nn = 40\n\n# initialise the engine\nae = AnalyticalEngine(vars=3, number=Column(digits=50), trace=1)\n\n# assemble the program to compute factorial(n)\n(program, _) = ae.assemble(\"\"\"\n:init\nSET 0 <- {n}\nSET 1 <- 1\nSET 2 <- 1\n:loop\n# operation 1: v = v * v\nMUL 0 2 -> 2\n# operation 2: v = v - 1\nSUB 0 1 -> 0\n# branch if non-zero to operation 1\nBRN loop\n# end\nHALT\n\"\"\".format(n=n))\n\n# run the program\nae.run()\n\n# the result is in v\nprint(\"factorial({n}) = {r}\".format(n=n, r=ae.v))\n```\n\n[Program 6 - factorial3.py]\n\nThe embedded program for the Analytical Engine is highlighted.\n\nNote that I have used Python’s format() function to interpolate the (Python) variable n into the string before it is passed to the assembler. So the assembler just sees “… SET 0 <- 40 …”.\n\nBy setting the trace=1 flag on the emulator the actual program cards loaded into the emulator are printed out before execution (as well as the trace of the execution itself).\n\nThe format that the assembler accepts should be fairly self-explanatory, from the example above, and from the implementation of Ada’s program given below, but the main points are:\n\n1. Comments (as in Perl and Python) are indicated by a # (hash) and continue to the end of the line.\n2. A line that starts with a : (colon) declares a label (which can be used as the target of a branch).\n3. Statements start with an op-code, followed by a number of space separated arguments.\n4. The multiple cards required for an arithmetical operation (ADD, SUB, MUL, DIV) are replaced by a single statement. Each takes two arguments to indicate the source of the operands: either the index of a variable in the store, or the special token DATA, which indicates that the value is loaded from the input data stack. Additional arguments are used to indicate indices in the store where the result is to be stored.\n5. The offset in branch statements can be specified using a symbolic label, by using a symbol that is declared as a label elsewhere in the program. (The label can appear either before or after the branch statement).\n6. The arrows (<- and ->) used in the SET statement to indicate the value being assigned to a variable in the store, and in arithmetic operations to indicate the variables in the store that the result of the operation is assigned to, are entirely optional. (They are removed during the parsing process, but I think it makes the program a little more readable).\n\nSo we can now write Ada’s program for Bernoulli Numbers like this:\n\n```from analytical_engine import AnalyticalEngine, Column\nfrom enigma import raw_input, printf\n\n# initialise the engine\nae = AnalyticalEngine(vars=14, number=Column(digits=10, dp=40), trace=1)\n# assemble the program\n(program, labels) = ae.assemble(\"\"\"\n:init\nSET 0 <- 0\nSET 1 <- 1\nSET 2 <- 2\nSET 3 <- 1\n:start\nMUL 2 3 -> 4 5 6\nSUB 4 1 -> 4\nDIV 4 5 -> 11\nDIV 11 2 -> 11\nSUB 13 11 -> 13\nSUB 3 1 -> 10\nBRZ finish\nDIV 6 7 -> 11\nMUL DATA 11 -> 12\nSUB 10 1 -> 10\nBRZ finish\n:loop\nSUB 6 1 -> 6\nDIV 6 7 -> 8\nMUL 8 11 -> 11\nSUB 6 1 -> 6\nDIV 6 7 -> 9\nMUL 9 11 -> 11\nMUL DATA 11 -> 12\nSUB 10 1 -> 10\nBRN loop\n:finish\nSUB 0 13\nPRINT\nSET 7 <- 0\nSET 13 <- 0\nHALT\n\"\"\")\n\n# indices B[k]\nk = 1\n# input data, initially empty, but each result is added after computation\ndata = []\n# instruction to start execution at\nstart = labels['init']\n# run the program\nwhile True:\n# load the data and run the program\nae.run(start)\n# get the computed result from the output transcript\nr = (ae.output[-1] if ae.output else None)\n\n# display the computed result\nprintf(\"B[{k}] = {r}\")\n\n# run the program again?\ntry:\nraw_input('\\n[paused] >>> ')\nexcept EOFError:\nprintf()\nbreak\n\n# add the result to the data and run it again\ndata.append(r)\nstart = labels['start']\nk += 2\n```\n\nAgain, the highlighted section is the embedded program for the Analytical Engine, and the statements in the program correspond to the lines in Ada’s diagram, with extra statements for the initialisation, branching and output added. So the first row in Ada’s diagram corresponds to the “multiply” statement after the “:start” instruction (line 12 of the above Python program).\n\nWe can use the output of the assembler to provide the indices of the cards where we wish to start and subsequently re-start execution.\n\nThis, then, is a directly executable representation of the first published program.\n\n## Running the first program: Part 2\n\n[ Part 1 | Part 2 | Part 3 ]\n\n[Note: The programs can be run without the need to install anything @repl.it]\n\nYesterday was Ada Lovelace Day, so following on from my previous post about Ada’s program for computing Bernoulli Numbers, I decided to implement an emulation of the Analytical Engine so that I can directly run the “assembly language” program I produced in that post, rather than translate it into a modern programming language in order to run it.\n\nI haven’t finished reading all the materials I have found about the Analytical Engine, but I think I’ve learned enough to have a crack at doing an emulation sufficient for my needs.\n\nSo without further ado, here’s my emulation of the Analytical Engine in Python:\n\n```# emulation of the Analytical Engine\n\nclass HaltException(Exception): pass\n\nclass AnalyticalEngine(object):\n\n# vars = number of variables\n# number = a function to implement the variables\ndef __init__(self, **kw):\n# number of variables in the store\nself.vars = 20\n# a method to implement the variables\nself.number = float\n\n# set options\nfor (k, v) in kw.items():\nif hasattr(self, k):\nsetattr(self, k, v)\nelse:\nprint('AnalyticalEngine: ignoring \"{k}={v}\"'.format(k=k, v=v))\n\nself.reset()\n\n# reset the machine\ndef reset(self):\n# representation of zero\nself.zero = self.number(0)\n# the variables in the store\nself.v = [self.zero] * self.vars\n# the registers in the mill\nself.index = 0\nself.input = [None, None]\nself.result = None\n# current operation\nself.op = None\n# the program and program counter\nself.program = None\nself.pc = None\n# input data\nself.data = None\nself.dc = None\n# output transcript\nself.output = None\n\nself.program = program\nself.pc = 0\n\nself.data = data\nself.dc = 0\n\n# run the program (starting at instruction start)\ndef run(self, start=0):\nprint(\">>> Running Analytical Engine\")\nself.output = []\nself.pc = start\ntry:\n\nwhile True:\n# get the next instruction\nassert not(self.pc < 0), \"Invalid PC\" p = self.program[self.pc] # execute it getattr(self, p)(*p[1:]) # increment the program counter self.pc += 1 except Exception as e: print(\">>> {e}\".format(e=e))\nprint(\">>> Execution halted\")\n\n# implement the opcodes\n\n# SET <i> <x>\n# set variable <i> in the store to value <x>\ndef SET(self, i, x):\nself.v[i] = self.number(x)\n\n# set the engine to perform addition\nself.op = (lambda a, b: a + b)\n\n# SUB\n# set the engine to perform subtraction\ndef SUB(self):\nself.op = (lambda a, b: a - b)\n\n# MUL\n# set the engine to perform multiplication\ndef MUL(self):\nself.op = (lambda a, b: a * b)\n\n# DIV\n# set the engine to perform division\ndef DIV(self):\nself.op = (lambda a, b: a / b)\n\n# execute an operation\ndef _execute(self):\nself.result = self.op(self.input, self.input)\n\n# load value v into the input register\nself.input[self.index] = v\nif self.index == 1:\nself._execute()\n# next time load the other input register\nself.index ^= 1\n\n# load the input register from variable <i> in the store\n\n# load the input register from next value in the input data stack\nself.dc += 1\n\n# STORE <i>\n# store the result to variable <i> in the store\ndef STORE(self, i):\nself.v[i] = self.result\n\n# PRINT\n# print the result\ndef PRINT(self):\nprint(self.result)\nself.output.append(self.result)\n\n# HALT\n# halt execution of the engine\ndef HALT(self):\nraise HaltException(\"HALT instruction encountered\")\n\n# branch\ndef _branch(self, offset):\nself.pc += offset\n\n# BRZ <offset>\n# branch if zero:\n# if the result is zero move the program instructions by <offset>\ndef BRZ(self, offset):\nif self.result == self.zero:\nself._branch(offset)\n\n# BRN <offset>\n# branch if non-zero:\n# if the result is non-zero move the program instructions by <offset>\ndef BRN(self, offset):\nif self.result != self.zero:\nself._branch(offset)\n```\n\n[Program - analytical_engine.py]\n\nClick the link for an expanded version of this implementation that includes code to trace the execution of the Engine. [link]\n\nBefore we look at running a program on the Analytical Engine, some notes:\n\n1. This is an emulation of the function the Analytical Engine, not a simulation of the mechanical workings.\n2. You can specify the number of variables (columns) in the store of the Analytical Engine with the vars parameter to the AnalyticalEngine class. One of Babbage’s designs was for a store with 1000 columns.\n3. You can specify an implementation for the columns using the number parameter to the AnalyticalEngine class. Later on I’ll implement a class that more closely emulates the behaviour of the columns in the design for the Engine, but for now we can use Python’s float built-in (to use floating point numbers) or fractions.Fraction for exact results.\n4. The program is presented as a sequence of instructions (which represent the variable cards and operation cards used to program the Analytical Engine). Each instruction consists of a sequence where the first element is the “op code” and the remaining elements are the corresponding parameters. The program is loaded into the Engine using the load_program() method, and can then be executed using the run() method.\n5. The “op codes” are the names of methods on the AnalyticalEngine class. I use upper case methods to indicate the instructions.\n6. I’ve implemented a stack of “input data” cards as I suggested in my comment on the “Running the first program post” [link]. The data is loaded into the Engine using the load_data() method, and the op code used in the program cards to load a register in the mill from the input data is LOAD_DATA (rather than LOAD input as I suggested in the comment).\n7. I’ve implemented two conditional instructions: “BRZ offset” (branch if zero) and “BRN offset” (branch if non-zero). In each case the result register of the mill is checked, and if the condition holds the program counter is moved by offset instructions. The offset may be positive (to implement conditional execution) or negative (to implement looping).\n8. The Engine will continue to run the program until a (Python) exception occurs, at which point the Engine will stop. There it a HALT instruction provided specifically to raise an exception that will stop the Engine.\n\nThis is my own interpretation of the Analytical Engine, for a more rigorous interpretation and Java implementation see the pages at fourmilab.ch.\n\nBelow is a simple program to compute factorial(12). The Analytical Engine program is wrapped up in a Python program that creates a suitable instantiation of the AnalyticalEngine class (with 3 variables in the store, and using Python’s built-in int class to implement the columns).\n\nWe then load the program for the Analytical Engine, run it and the computed result is in variable 2 from the store.\n\n```from analytical_engine import AnalyticalEngine\n\n# initialise the engine\nae = AnalyticalEngine(vars=3, number=int)\n\n# load the program to compute factorial(12)\nn = 12\n# initialisation\n['SET', 0, n],\n['SET', 1, 1],\n['SET', 2, 1],\n# operation 1: v = v * v\n['MUL'],\n['STORE', 2],\n# operation 2: v = v - 1\n['SUB'],\n['STORE', 0],\n# branch if non-zero to operation 1\n['BRN', -9],\n# end\n['HALT'],\n])\n\n# run the program\nae.run()\n\n# the result is in v\nprint(\"factorial({n}) = {r}\".format(n=n, r=ae.v))\n```\n\n[Program 3 - factorial1.py]\n\nWhen run you see output like this:\n\n```\\$ python factorial1.py\n>>> Running Analytical Engine\n>>> HALT instruction encountered\n>>> Execution halted\nfactorial(12) = 479001600\n```\n\nAnd indeed this is the correct value for factorial(12).\n\nThe difficulty in writing these programs is making sure the branch offsets go to the right place. As statements occupy multiple cards it is easy to branch into the middle of a statement with unexpected results. (What’s really needed is an assembler that can compile a statement like “mul(0, 2, 2)” and produce the four instructions that make up the first operation. This would make a program correspond much more closely with the diagrams published to describe the operation of the Analytical Engine. Such an assembler could also allow for symbolic labels to be used in branches so the offsets are computed automatically. I might add this functionality to a future version of analytical_engine.py).\n\nHere is the full program to execute Ada Lovelace’s algorithm for computing Bernoulli Numbers. As you can see the actual program for the Analytical Engine is a direct translation from the assembly language program I gave in my comment to the last post (except I’ve actually had to work out the correct offsets for the “branch” instructions).\n\nIn this instance we use an AnalyticalEngine with 14 variables, and the numbers are implemented using Python’s fractions.Fraction objects, which give exact results for the computation.\n\nThe controlling loop collects the results as they are generated and adds them to the input data stack, and then re-runs the program to compute the next Bernoulli Number in the sequence. It pauses between each run of the program to allow the user examine the output and to halt the program if necessary.\n\n(Note that the enclosing Python program uses a couple of utility routines from the enigma.py library, available here [link]).\n\n```from analytical_engine import AnalyticalEngine\nfrom fractions import Fraction\nfrom enigma import raw_input, printf\n\n# initialise the engine\nae = AnalyticalEngine(vars=14, number=Fraction)\n\n# initialisation\n['SET', 0, 0],\n['SET', 1, 1],\n['SET', 2, 2],\n['SET', 3, 1],\n# operation 1\n['MUL'],\n['STORE', 4],\n['STORE', 5],\n['STORE', 6],\n# operation 2\n['SUB'],\n['STORE', 4],\n# operation 3\n['STORE', 5],\n# operation 4\n['DIV'],\n['STORE', 11],\n# operation 5\n['DIV'],\n['STORE', 11],\n# operation 6\n['SUB'],\n['STORE', 13],\n# operation 7\n['SUB'],\n['STORE', 10],\n# branch if zero to operation 24\n['BRZ', +66],\n# operation 8\n['STORE', 7],\n# operation 9\n['DIV'],\n['STORE', 11],\n# operation 10\n['MUL'],\n['STORE', 12],\n# operation 11\n['STORE', 13],\n# operation 12\n['SUB'],\n['STORE', 10],\n# branch if zero to operation 24\n['BRZ', +45],\n# operation 13\n['SUB'],\n['STORE', 6],\n# operation 14\n['STORE', 7],\n# operation 15\n['DIV'],\n['STORE', 8],\n# operation 16\n['MUL'],\n['STORE', 11],\n# operation 17\n['SUB'],\n['STORE', 6],\n# operation 18\n['STORE', 7],\n# operation 19\n['DIV'],\n['STORE', 9],\n# operation 20\n['MUL'],\n['STORE', 11],\n# operation 21\n['MUL'],\n['STORE', 12],\n# operation 22\n['STORE', 13],\n# operation 23\n['SUB'],\n['STORE', 10],\n# branch if non-zero to operation 13\n['BRN', -45],\n# operation 24\n['SUB'],\n# print\n['PRINT'],\n# operation 25\n['STORE', 3],\n# reset working variables\n['SET', 7, 0],\n['SET', 13, 0],\n# end\n['HALT'],\n])\n\n# indices B[k]\nk = 1\n# input data, initially empty, but each result is added after computation\ndata = []\n# instruction to start execution at, initially 0, but subsequently 4\nstart = 0\n# run the program\nwhile True:\n# load the data and run the program\nae.run(start)\n# get the computed result from the output transcript\nr = (ae.output[-1] if ae.output else None)\n\n# display the computed result\nprintf(\"B[{k}] = {r}\")\n\n# run the program again?\ntry:\nraw_input('\\n[paused] >>> ')\nexcept EOFError:\nprintf()\nbreak\n\n# add the result to the data and run it again (from instruction 4)\ndata.append(r)\nstart = 4\nk += 2\n```\n\nBy running this we can check that the Engine does indeed produce the list of Bernoulli Numbers:\n\nB = 1/6\nB = −1/30\nB = 1/42\nB = −1/30\nB = 5/66\nB = −691/2730\n\nThe computation that Ada outlines in Note G is the calculation of B = −1/30. This involves 10 ADD operations, 11 SUB operations, 8 MUL operations and 7 DIV operations. The Analytical Engine was estimated to do be able to perform an addition or subtraction in about 1 second, but multiplication and division could take up to a minute (the actual time would vary depending on the operands), and also branching would take some time to step through the required number of cards. So altogether we might expect the Engine to take around 15 to 20 minutes to compute B. And as we compute further numbers in the sequence the number of operations and the corresponding time would increase.\n\nSo far we have been using Python’s built-in number classes to implement the columns, which can provide arbitrary precision. But the actual columns for the Analytical Engine would have been able to store 50 decimal digits, and a sign (to indicate if the number was positive or negative).\n\nHere’s an implementation of a class suitable for use as the number parameter when constructing an AnalyticalEngine instance, that more closely replicates the columns of the Analytical Engine.\n\n```# implementation of the columns in the Analytical Engine\n\nclass OverflowException(Exception): pass\n\n# a column with <digits> whole decimal digits and <dp> fractional decimal digits\ndef Column(digits=50, dp=0):\n\nshift = (10 ** dp)\noverflow = (10 ** (digits + dp)) - 1\nfmt = '<{s}{m:0' + str(digits) + 'd}' + ('.{d:0' + str(dp) + 'd}' if dp > 0 else '') + '>'\n\nclass Column(object):\n\n# create a value, and check for overflow\ndef __init__(self, n=0, shift=shift):\nif shift:\nn *= shift\nif abs(n) > overflow:\nraise OverflowException(\"Overflow in column\")\nself.n = n\n\n# output format\ndef __repr__(self):\nn = self.n\n(m, d) = divmod(abs(n), shift)\ns = ('-' if n < 0 else '+')\nreturn fmt.format(s=s, m=m, d=d)\n\n# arithmetic operations\n\nreturn Column(self.n + value.n, shift=0)\n\ndef __sub__(self, value):\nreturn Column(self.n - value.n, shift=0)\n\ndef __mul__(self, value):\nreturn Column((self.n * value.n) // shift, shift=0)\n\ndef __div__(self, value):\nreturn Column((self.n * shift) // value.n, shift=0)\n\n# Python 3 uses __truediv__\n__truediv__ = __div__\n\n# branch tests\n\ndef __eq__(self, value):\nreturn self.n == value.n\n\ndef __ne__(self, value):\nreturn self.n != value.n\n\nreturn Column\n```\n\nNotes:\n\n1. We can specify the number of whole decimal digits for the column with the digits parameter. The columns can also be used to implement fixed point decimal numbers by specifying how many additional fractional decimal places are required with the dp parameter.\n2. I’m not sure what happened when an overflow happened in the Analytical Engine, so I throw an exception.\n3. The columns support the four arithmetical operations that the Analytical Engine supports (addition, subtraction, multiplication and division), and also the two conditionals for the branches (is zero, is non-zero).\n4. The columns display as a fixed with string “<{sign}{digits}.{digits}>”.\n\nThe Column class is included in analytical_engine.py.\n\nSo we can use the following program to compute factorial(40) using columns containing 50 decimal digits:\n\n```from analytical_engine import AnalyticalEngine, Column\n\n# initialise the engine\nae = AnalyticalEngine(vars=3, number=Column(digits=50))\n\n# load the program to compute factorial(40)\nn = 40\n# initialisation\n['SET', 0, n],\n['SET', 1, 1],\n['SET', 2, 1],\n# operation 1: v = v * v\n['MUL'],\n['STORE', 2],\n# operation 2: v = v - 1\n['SUB'],\n['STORE', 0],\n# branch if non-zero to operation 1\n['BRN', -9],\n# end\n['HALT'],\n])\n\n# run the program\nae.run()\n\n# the result is in v\nprint(\"factorial({n}) = {r}\".format(n=n, r=ae.v))\n```\n\n[Program 5 - factorial2.py]\n\n```\\$ python factorial2.py\n>>> Running Analytical Engine\n>>> HALT instruction encountered\n>>> Execution halted\nfactorial(40) = <+00815915283247897734345611269596115894272000000000>\n```\n\nAnd similarly by using number=Column(10, 40) in the implementation of Ada’s program we can compute Bernoulli numbers to 40 decimal places.\n\nIn divisions we will potentially lose precision in the final decimal places of the result, and as later numbers in the sequence are calculated from earlier numbers we will see the precision deteriorate as we go on.\n\nHere are the results of running the program:\n\n```B = <+0000000000.1666666666666666666666666666666666666666>\nB = <-0000000000.0333333333333333333333333333333333333332>\nB = <+0000000000.0238095238095238095238095238095238095233>\nB = <-0000000000.0333333333333333333333333333333333333302>\nB = <+0000000000.0757575757575757575757575757575757575464>\nB = <-0000000000.2531135531135531135531135531135531131568>\nB = <+0000000001.1666666666666666666666666666666666593360>\nB = <-0000000007.0921568627450980392156862745098037431432>\nB = <+0000000054.9711779448621553884711779448621498550887>\nB = <-0000000529.1242424242424242424242424242422111802933>\nB = <+0000006192.1231884057971014492753623188306059856832>\nB = <-0000086580.2531135531135531135531135525557263098091>\nB = <+0001425517.1666666666666666666666666299288036638424>\n...```\n\nBy the time we reach B the last 15 digits of our 40 digits of decimal precision have been lost (B = 8553103/6 = 1425517 + 1/6), but the computation is still correct to 25 decimal places.\n\nNote: The Python programs presented should run under Python 2 or Python 3, but as I used the new-style print() function, so if you are running them under Python 2 you will need to put the following line at the start of the programs:\n\n```from __future__ import print_function\n```\n\n## Running the first program\n\n### “Notes on Note G”\n\n[ Part 1 | Part 2 | Part 3 ]\n\n[Note: WordPress sometimes has problems including program code in posts, so I’ve made the code used in these articles available on GitHub – [link]]\n\n[Note: The programs can also be run without the need to install anything @repl.it]\n\nI recently watched the BBC4 documentary Calculating Ada: The Countess of Computing (Hannah Fry’s 10-part radio series Computing Britain is also an interesting listen)[¹]. And although I know that Ada Lovelace is credited with publishing the first computer program, I hadn’t ever seen the form that this program took before. It’s not hard to track down – on Ada’s Wikipedia page there is an image of the diagram ([image] – “Diagram for the computation by the Engine of the Numbers of Bernoulli”).\n\nThe diagram itself was part of a note (Note G) that was attached to a translation of a French transcript (by an Italian military engineer named Luigi Frederico Menabrea – who would later become the Italian Prime Minister) of a seminar given by Charles Babbage at the University of Turin in 1840. It was the first and only time Babbage gave a public lecture on the Analytical Engine. Ada was commissioned to translate the paper into English. After nine months of working she published her translation, along with a set of notes (which were more than twice as long as the original paper). This was the first (and, for a hundred years, the only) text on computer programming. It is in one of the notes that the diagram that is considered to be the worlds first published computer program appeared. (The full text of Ada’s paper is available here [link], along with a large version of the diagram [link]).\n\nHere it is:\n\nIt’s not what we think of now as a computer program – after all it pre-dates computer programming languages. Instead it essentially the description of a sequence of operations performed by the Analytical Engine. So it is more like a trace of the program execution than the source code of the program itself, and it only includes the actual arithmetic operations that the engine performs. The control flow of the execution is dealt with in the attached text.\n\nOf course the Analytical Engine was never completed, so the actual form of the instructions is not completely clear. However, I’m not trying to construct copy of the punched cards necessary to run Ada’s program. I’m attempting to transliterate her algorithm into a modern programming language in order to understand it, and the Analytical Engine, better.\n\nLike Ada I have found that my own notes have become somewhat longer than I anticipated.\n\nFirst I’ll explain what the program does. The purpose of the program is to compute Bernoulli Numbers. Ada’s program is concerned with calculating the odd-numbered Bernoulli Numbers[²], and is based on the following equation (given in Note G) for calculating B[2n − 1], given the already computed values of B, B, …, B[2n − 3]:\n\nA + AB + AB + … + B[2n − 1] = 0\n\nwhere the values of the A[] coefficients are defined as follows:\n\nA = (−1/2) (2n − 1)/(2n + 1)\nA = 2n/2 = n\nA = 2n(2n − 1)(2n − 2) / (2.3.4)\nA = 2n(2n − 1)(2n − 2)(2n − 3)(2n − 4) / (2.3.4.5.6)\n\nFor k > 1, each A[k] is derived from A[k − 2] by multiplying the next two decreasing terms into the numerator, and the next two increasing terms into the denominator. (Note that for each value of n the sequence of A[] coefficients are different. We might more properly think of them as A[nk]).\n\nAda’s program works by starting at n=1, the equation for deriving B is:\n\nA + B = 0\n\nand:\n\nA = (−1/2) (2n − 1)/(2n + 1) = −1/6\n\nSo:\n\nB = 1/6\n\nWe then consider n=2, using the previously computed value for B we have:\n\nA + AB + B = 0\n\nand:\n\nA = (−1/2) (2n − 1)/(2n + 1) = −3/10\nA = 2\n\nSo:\n\nB = −1/30\n\nWe then consider n=3, and use the previously computed value for B and B to calculate B. And the procedure can be repeated as many times as we like (or until we run out of space to store the results – the proposed design for the Analytical Engine would have had room for 1,000 variables, each containing 50 decimal digits). Each time we use the results from all the previous runs to calculate the next number in the sequence.\n\nTo explain the implementation of the algorithm here is my own implementation of it using modern Python idioms. This program is constructed using the same basic structure as Ada’s program.\n\n```from fractions import Fraction\n\n# my implementation of the algorithm\ndef bernoulli():\n\n# results\nBs = list()\n\n# start at n=1\nn = 1\n# calculate the sequence\nwhile True:\n\n# result = A0\nr = -Fraction(2 * n - 1, 2 * n + 1) / 2\n\n# A1 = n\nA = n\n# for each B[k] already determined calculate the corresponding A[k]\nfor (i, B) in enumerate(Bs):\nif i > 0:\n# multiply in the 2 additional terms\nj = 2 * i - 1\nA *= Fraction(2 * n - j, 2 + j)\nj += 1\nA *= Fraction(2 * n - j, 2 + j)\n# add A[k] * B[k] into the result\nr += A * B\n\n# the computed bernoulli number is -r\nB = -r\n# return the number\nyield B\n# add it to the result list\nBs.append(B)\n# increase n\nn += 1\n\n# run N iterations of the algorithm\nN = 10\n\n# allow N to be specified as a command line argument\nimport sys\nif len(sys.argv) > 1:\nN = int(sys.argv)\n\nk = 1 # ada's numbering (normal numbering is k + 1)\nK = 2 * N + 1 # max k\nfor r in bernoulli():\nprint(\"B[{k}] = {r}\".format(k=k, r=r))\nk += 2\nif k == K: break\n```\n\nBefore we examine a more direct implementation of Ada’s diagram, first some notes on my own implementation:\n\n1. (Line 1) I’m using Python’s Fraction library to generate the Bernoulli sequence. This makes it easy to check the computation against existing lists (which give them in rational form), and provides exact answers. The Analytical Engine would have computed the numbers as fixed point decimal fractions. (So small errors would accumulate in the final decimal places, and as these results are fed back into further computations the errors would compound. It would be best to use more decimal places than required in the results so that suitably accurate truncated results can be generated).\n2. (Line 4) The bernoulli() function will generate successive Bernoulli numbers. I’ve implemented it as Python co-routine, so results are returned with the yield operator as they are determined. It’s up to the calling code to consume as many results as it requires. The diagram given by Ada describes the generation of a single Bernoulli number. And while her program itself sets up some of the data required for the next run, it would also require some additional modification of the cards before it is run again to compute the next number in the sequence.\n3. (Line 18) I’ve simplified the calculation of A1 from (2n/2) to just (n).\n4. (Line 41) We can specify how many numbers in the sequence we want the program to compute (the default is 10). They are printed out according to Ada’s numbering scheme.\n\nThe program is certainly non-trivial. It involves two loops (one nested in the other) and conditional execution, as well as the storing of the computed results to use in subsequent calculations.\n\nThe diagram published by Ada shows the computation of B, the fourth number in the sequence. The table consists of the following columns:\n\n1. Line number.\n2. Operation.\n3. Operands.\n4. Assignment of results.\n7-9. Parameters.\n10-19. Variables.\n20-23. Results.\n\nOnly columns 2, 3 and 4 are instructions to the computer, the rest are essentially supporting documentation to explain the program to the reader.\n\nThere are a few apparent errors (the first programming bugs) in the originally published diagram:\n\n1. At line 4 the operation is given as v5 ÷ v4, although the comments and text make it clear that this should be v4 ÷ v5.\n2. At line 23 the formula for A3 has two 3’s in the denominator, instead of a 3 and a 4 (as in the previous line). This is just an error in the comment and would not affect execution of the program.\n3. At line 25 it looks like v6 and v7 are reset to their initial values (of zero). In fact it’s v7 and v13 that need to be reset for the algorithm to work correctly. In the accompanying text Ada refers to resetting v6, v7, and v13 to zero (although it is not necessary to zero v6, as the first thing the program does (operation 1) is to assign 2n to v4, v5, and v6).\n\nThese are all “typos” rather than “thinkos”, and may not even have been present in Ada’s original notes.\n\nHere is my Python program with the bernoulli() function replaced with a modified version that reflects a more direct transliteration of Ada’s description:\n\n```from collections import defaultdict\nfrom fractions import Fraction\n\n# ada lovelace's algorithm in Python\ndef bernoulli():\n\n# initially all varibles in the store are at 0\nv = defaultdict(int)\n\n# program start\n\n# initialise the variables\nv = Fraction(1) # constant\nv = Fraction(2) # constant\nv = Fraction(1) # n = 1\n\n# outer loop (compute B[2n - 1])\nwhile True:\n\n# pseudo-block to permit \"break\"\nwhile True:\n\n# 0: set index register\ni = 1\n\n# 1: v4 = v5 = v6 = 2n\nv = v = v = v * v\n\n# 2: v4 = 2n - 1\nv = v - v\n\n# 3: v5 = 2n + 1\nv = v + v\n\n# 4: v11 = (2n - 1)/(2n + 1) (the diagram seems to say v / v) [FIX]\nv = v / v\n\n# 5: v11 = (1/2) (2n - 1)/(2n + 1)\nv = v / v\n\n# 6: v13 = -(1/2) (2n - 1)/(2n + 1) = A0\nv = v - v\n\n# 7: v10 = n - 1\nv = v - v\n# branch if zero to operation 24\nif v == 0: break\n\n# 8: v7 = 2\nv = v + v\n\n# 9: v11 = (2n)/2 = A1 [why not just set v = v instead of 8 & 9 ?]\nv = v / v\n\n# 10: v12 = A1 * B1\nv = v[20 + i] * v\ni += 1\n\n# 11: v13 = A0 + A1 * B1\nv = v + v\n\n# 12: v10 = n - 2\nv = v - v\n# branch if zero to operation 24\nif v == 0: break\n\n# for each computed result, B = B3 , B5 , ...\nwhile True:\n\n# 13: v6 = 2n - 1 , 2n - 3 , ...\nv = v - v\n\n# 14: v7 = 3 , 5 , ...\nv = v + v\n\n# 15: v8 = (2n - 1)/3 , (2n - 3)/5 , ...\nv = v / v\n\n# 16: v11 = (2n)/2 * (2n - 1)/3 , (2n)/2 * (2n - 1)/3 * (2n - 3)/5 , ...\nv = v * v\n\n# 17: v6 = 2n - 2 , 2n - 4 , ...\nv = v - v\n\n# 18: v7 = 4 , 6 , ...\nv = v + v\n\n# 19: v9 = (2n - 2)/4 , (2n - 4)/6\nv = v / v\n\n# 20: v11 = (2n)/2 * (2n - 1)/3 * (2n - 2)/4 = A3 , (2n)/2 * (2n - 1)/3 * (2n - 2)/4 * (2n - 3)/5 * (2n - 4)/6 = A5 , ...\nv = v * v\n\n# 21: v12 = A3 * B3 , A5 * B5 , ...\nv = v[20 + i] * v\ni += 1\n\n# 22: v13 = A0 + A1 * B1 + A3 * B3 , A0 + A1 * B1 + A3 * B3 + A5 * B5 , ...\nv = v + v\n\n# 23: v10 = n - 3 , n - 4 , ...\nv = v - v\n# branch if non-zero to operation 13\nif v == 0: break\n\n# terminate the pseudo-block\nbreak\n\n# 24: result (-v13) is copied into the results\nr = v[20 + i] = v[20 + i] - v\n\n# the result could be printed here\n# we pass it back to the calling routine\nyield r\n\n# 25: increase n, and reset working variables\nv = v + v\nv = v = 0\n\n# branch to operation 0\n\n# run N iterations of the algorithm\nN = 10\n\n# allow N to be specified as a command line argument\nimport sys\nif len(sys.argv) > 1:\nN = int(sys.argv)\n\nk = 1 # ada's numbering (normal numbering is k + 1)\nK = 2 * N + 1 # max k\nfor r in bernoulli():\nprint(\"B[{k}] = {r}\".format(k=k, r=r))\nk += 2\nif k == K: break\n```\n\nAda’s diagram shows how the program would run when n=4, and it not a direct indication of the punched cards that would be fed to Analytical Engine. Of course as the Analytical Engine was never completed it’s actual instruction set is not something we can know for certain. But the way it is described as working is as follows:\n\n1. An operation card indicates the operation that the engine is to perform. (One of +, −, ×, ÷).\n2. A variable card indicates which variable is transferred from the store (memory) to the first Ingress Axis of the mill (CPU). This provides the first operand.\n3. A second variable card indicates which variable is transferred from the store to the second Ingress Axis if the mill. This provides the second operand.\n4. The operation is then performed, the result appears in the Egress Axis of the mill.\n5. A variable card indicates which variable in the store the contents of the Egress Axis are transferred to.\n\nAt stage 5 there may be multiple variable cards instructing that the result is stored in several variables, as we see in the first operation of Ada’s table. If we were to write an assembly language version of this operation it would look something like this:\n\n# operation 1\nMUL\nSTORE v\nSTORE v\nSTORE v\n\nAnd each of these opcodes corresponds to a card that acts as instructions to the Analytical Engine.\n\nAda’s accompanying text describes the need for some common programming idioms that we take for granted in modern programming languages, but are not present in the diagram (which just shows the arithmetic operations performed).\n\nFirst there is the need for conditional execution. She mentions that when computing B operation 6 would complete the calculation. In my program at line 47 I exit the block when v10 becomes 0. Similarly, as Ada says, operation 12 works in a similar way. Again in my program I conditionally exit the block if v10 becomes 0.\n\nSecondly there is the need for repeated execution of a sequence of instructions (looping). This is dealt with extensively in the notes where the repeated execution of operations 13-23 is described.\n\nBoth these could be achieved with a conditional branch instruction. Although the mechanism for branching is not explicitly mentioned in the paper it is clear that the Analytical Engine implements such a function. For example, if the Analytical Engine set a flag when a result was 0 (as microprocessors often do), then there could be an instruction to skip forward or backwards a certain number of program steps and resume operation from there. The instructions were to be provided on a punched cards, so this would require the card reader to skip forward or rewind a certain number of cards.\n\n(In the Fourmilab simulation of the Analytical Engine a “run-up lever” is used. This is set by an operation if the sign of the result of the operation being different from the sign of the first operand (or if an overflow occurs). A conditional branch can then be made based on the state of the lever. So, we could test if a variable was zero by subtracting 1 from it. The only way the sign will change is if the variable initially held the value of 0 (so the result is −1), and the lever will be set. As Ada doesn’t show these operations in her table I’m going to simplify by referring to a “branch if zero” instruction. In a similar way branching on other conditions can be implemented).\n\nThis would allow us to place an instruction after operation 7 and operation 12 of “branch if zero to operation 24”. The inner loop would be implemented by placing an instruction after operation 23  of “branch if non-zero to operation 13”. The outer loop would be implemented by placing an instruction after operation 25 of “branch always to operation 1” (or more likely to branch if n was less than a predefined constant value, so that a Bernoulli sequence of the specified length is generated).\n\nThe text also hints at the notion of indirection, where one variable (or register) can tell us which of a number of other variables we need to access. This is necessary as each time we iterate through the operations 13-23, we have computed the A[] coefficient after executing operation 20, but then in operation 21 we multiply this the corresponding number already computed in the B[] sequence. The first time round we would need B, stored in variable v22 (as specified in the operands for operation 21 in the diagram), but the next time round the loop we would need the B value stored in v23, and so forth. Likewise when the final result (B) is calculated it is stored by operation 24 into v24 and n is increased. The next time we get to operation 24 the final result will be B and it will be stored into v25. Although the diagram itself does not indicate how the instructions of operations 21 and 24 are modified as the program is executed it is clear that it is an issue that Ada has considered.\n\nFrom the way Ada describes the program it seems that way this would happen is that for each value of n the program is run once. Then it must be set up slightly differently for next run. Ada notes that exactly the same sequence of operation cards can be reused, but the variable cards must be modified slightly on each iteration to achieve the required results.\n\nOne way the Analytical Engine could do indirection would be to allow the index of a variable to be specified in another variable, so instead of a “LOAD v” (load the Ingress Axis from variable 12 in the store), we would have something like “LOADI v” (load the Ingress Axis from the variable in the store whose index is stored in v12). So if v = 21, “LOADI v” would be the same as “LOAD v”.\n\nBut variables in the store hold 50 decimal digits and indices into the store are only 3 decimal digits, so it is a bit odd. Instead we might consider that the Analytical Engine could be equipped with a few special purpose three decimal digit index registers, these could then be used to provide an additional offset in a load instruction.\n\nFor the purposes of Ada’s program it would be necessary to only have a single additional index register. We could imagine a that “LOADI v” would correspond to “LOAD v[20 + i]” where i represents the value in the index register. So if i = 1 the instruction “LOADI v” would be the same as “LOAD v”. And there would be a corresponding “STOREI” instruction. To increase the offset we would need an “INC” instruction, which would increment the number in the index register by 1. This would be sufficient to implement Ada’s program.\n\nBut perhaps this approach is too influenced by modern computing. A different approach would be to allow the LOAD and STORE instructions to get a variable from an alternate stack of cards. “LOAD alt” and “STORE alt”. That way the alternate stack of cards could be filled with the addresses of v21 to (say) v30. And in operation 10 the address that the first LOAD card uses isn’t punched on the card itself, instead it is read from the alternate stack (it’s the first card in the stack so it would be v21), and the stack moves to the next card. When we reach operation 21 we would again use a “LOAD alt” instruction to get the index of the variable from the alternate stack. The first time round the loop it will be v22, then v23 and so on. When the loop ends, and we have processed all the previously calculated results the next card in the alternate stack will be the correct address to store the newly computed number. So operation 24 uses “STORE alt” and the number is stored.\n\nFinally at the end of the diagram as well as looping back to the beginning we also rewind the alternate card deck and we are ready to go again without needing to alter any of the cards. After 10 iterations the first 10 Bernoulli numbers will have been stored in the variables referenced by the alternate stack, and the program can halt.\n\nTo produce the transliteration of Ada’s program that can run without intervention I have adopted the addition of an index register to allow indirection, although, as far as I know, this is not historically accurate.\n\nFinally Ada notes that the process described in her diagram produces results of the correct magnitude, but not the correct sign. If there is no simple way to change the sign of a value, this can easily be remedied by subtracting the result (in v) from the variable that the result is to be stored in (as it will initially be 0), and then storing it back into the result variable. Consequently I’ve adjusted operation 24 from “v = v + v” to be “v = v − v”, the sign is then correctly set for value to be reused by the algorithm.\n\nWriting an equivalent pseudo-assembly language version of my transliteration would look something like this:\n\n```# initialise the variables\nSET v 1 # constant 1\nSET v 2 # constant 2\nSET v 1 # n = 1\n\n# operation 0: initialise the index register\nSET i 1\n\n# operation 1\nMUL\nSTORE v\nSTORE v\nSTORE v\n\n# operation 2\nSUB\nSTORE v\n\n# operation 3\nSTORE v\n\n# operation 4\nDIV\nSTORE v\n\n# operation 5\nDIV\nSTORE v\n\n# operation 6\nSUB\nSTORE v\n\n# operation 7\nSUB\nSTORE v\n\n# branch if zero\nBRANCH ZERO (operation 24)\n\n# operation 8\nSTORE v\n\n# operation 9\nDIV\nSTORE v\n\n# operation 10\nMUL\nLOAD v[20 + i] # indirection\nSTORE v\nINC i # index register is incremented\n\n# operation 11\nSTORE v\n\n# operation 12\nSUB\nSTORE v\n\n# branch if zero\nBRANCH ZERO (operation 24)\n\n# operation 13\nSUB\nSTORE v\n\n# operation 14\nSTORE v\n\n# operation 15\nDIV\nSTORE v\n\n# operation 16\nMUL\nSTORE v\n\n# operation 17\nSUB\nSTORE v\n\n# operation 18\nSTORE v\n\n# operation 19\nDIV\nSTORE v\n\n# operation 20\nMUL\nSTORE v\n\n# operation 21\nMUL\nLOAD v[20 + i] # indirection\nSTORE v\nINC i # increment index register\n\n# operation 22\nSTORE v\n\n# operation 23\nSUB\nSTORE v\n\n# branch if non-zero\nBRANCH NON-ZERO (operation 13)\n\n# operation 24\nSUB\nLOAD v[20 + i] # indirection\nSTORE v[20 + i] # indirection\n\n# the result can be output at this point\nPRINT\n\n# operation 25\nSTORE v\n\n# reset working variables\nSET v 0\nSET v 0\n\n# repeat\n# (or if v < N)\nBRANCH ALWAYS (operation 0)\n\nHALT\n```\n\nEach program line would correspond to a punched card that would be fed to the Analytical Engine, so this is the closest we can get to what the original stack of punched cards, and hence the first program, would have looked like.\n\nNote: Whilst writing up this article I have found a lot more information out about the Analytical Engine than when I started, and there is much more for me to go through. I intend to investigate the Analytical Engine further, and I will correct any glaring errors written above as I become more familiar with the subject. Please let me know of any problems you find and I will endeavour to sort them out.\n\n— J.M.R.\n\nHere are some useful resources that I have found about Ada, Babbage and the Analytical Engine:\n\n[¹] Apologies if you can’t access these programmes. BBC iPlayer is only available in the UK, and programmes are only available for a limited time.\n\n[²] Ada’s indices for the Bernoulli Numbers are one less than the indices now generally used." ]
[ null ]
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http://rimzaasoft.com/what-to-expect-from-what-is-conductor-in-physics/
[ "Breaking News\n\n# What to Expect From What Is Conductor in Physics?\n\nStudents are going to have the option to select the AP-Physics exam at the conclusion of the training course work. Physics involves a great deal of calculations and problem solving. It’s used ubiquitously throughout mathematics.\n\nSee the pattern is extremely similar, but the color code is a bit trickier. Its value is extremely hard to measure experimentally. To put it differently, solving equations is a significant goal within mathematics.\n\nYou do not need to find every question correct write my essay paper to get the maximum score (800) for the test. Click the Check Answer button to see whether you’re correct. The issue states the worth of Q1 and Q2.\n\n## What Everybody Dislikes About What Is Conductor in Physics and Why\n\nThe truth of a single part in a billion could indicate that a stable condition for a particular experiment configuration was achieved, but that distinct configuration could still be influencing the measurement to a little degree. After days of discussion, all of the evidence was tallied. The possible because of the whole disk is the integral of the above mentioned expression.\n\nOnly forces acting on the object needs to be shown, as you are attempting to comprehend the causes of the motion of the object. Visit Your URL Gauss law is the easiest way of handling when it has to do with charges and field flux. Current is the total sum of charge passing through a conductor above a time period.\n\nYou have to train and put on the science supporting the sport to win against the challenge time and earn each program medal. While the practice is not suggested, there is surely no harm in doing this. Lifting the same quantity of weight twice as large means twice the sum of work is completed.\n\nThe outcomes of any empirical measurement always demonstrate some level of statistical spread for a consequence. The true power of equations is they provide an extremely precise means to describe many features of the planet. For step one, the logarithmic form of the equation is the most useful.\n\nIn the very first position, the contacts are connected straight through, so the switch does not have any result. The value of careful charge of the material was recognized from the start. The stream of charge through wires is often in comparison to the stream of water through pipes.\n\n## The Lost Secret of What Is Conductor in Physics\n\nThe http://manila.lpu.edu.ph/about.php?test=homework-help-science distribution of charge is the consequence of electron movement. In engineering, the total amount of elasticity of a material is decided by two varieties of material parameter. Thus, a great number of electrons will stay in the metastable states and hence population inversion is reached.\n\nThe first kind of material parameter is known as a modulus, which measures the sum of force per unit area required to attain a given amount of deformation. The solution is normally a single ordered pair. Even within this approximation, but the solution of the equations is an ambitious job.\n\nThe procedure for adding controlled impurities to a semiconductor is referred to as doping. Together with rotations, the molecules can vibrate in lots of means. Consequently, some electrons become super-ballistic since they are guided via the channel by their buddies." ]
[ null ]
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https://www.mcqslearn.com/mechanicalengineering/cfd/quiz/quiz.php?page=17
[ "Finite difference method quiz, finite difference method MCQs answers, cfd quiz 17 to learn engineering online courses. Discretization quiz questions and answers, finite difference method multiple choice questions (MCQs) to practice cfd test with answers for online colleges and universities courses. Learn finite difference method MCQs, cfd: research tool, finite difference method test prep for engineering certification.\n\nLearn finite difference method test with multiple choice question (MCQs): representation of finite difference derivative is based on, with choices taylor series expansion, newton's 2nd law, fredrick law, and none of these for online masters degree. Learn discretization questions and answers for problem-solving, merit scholarships assessment test.\n\nFinite difference method Quiz\n\nMCQ: Representation of finite difference derivative is based on\n\n1. Taylor series expansion\n2. Newton's 2nd law\n3. Fredrick law\n4. None of these\n\nA\n\nFinite difference method Quiz\n\nMCQ: When mach number is in between 0.8 - 1.2, flow is in\n\n1. subsonic regime\n2. super sonic regime\n3. sonic regime\n4. transonic regime\n\nD\n\nFinite difference method Quiz\n\nMCQ: When mach number > 5, flow is in\n\n1. subsonic regime\n2. super sonic regime\n3. sonic regime\n4. hypersonic regime\n\nD\n\nFinite difference method Quiz\n\nMCQ: In an aero plane, angle between wing chord line and flight path is called\n\n1. angle of attack\n2. angle of elevation\n3. angle of wing\n4. angle of chord\n\nA\n\nFinite difference method Quiz\n\nMCQ: Method in which boundary occupied by fluid is divided into a surface mesh is\n\n1. Finite Volume method\n2. Finite element method\n3. Boundary element method\n4. spectral element method\n\nC" ]
[ null ]
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https://metanumbers.com/37728
[ "## 37728\n\n37,728 (thirty-seven thousand seven hundred twenty-eight) is an even five-digits composite number following 37727 and preceding 37729. In scientific notation, it is written as 3.7728 × 104. The sum of its digits is 27. It has a total of 8 prime factors and 36 positive divisors. There are 12,480 positive integers (up to 37728) that are relatively prime to 37728.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 5\n• Sum of Digits 27\n• Digital Root 9\n\n## Name\n\nShort name 37 thousand 728 thirty-seven thousand seven hundred twenty-eight\n\n## Notation\n\nScientific notation 3.7728 × 104 37.728 × 103\n\n## Prime Factorization of 37728\n\nPrime Factorization 25 × 32 × 131\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 8 Total number of prime factors rad(n) 786 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 37,728 is 25 × 32 × 131. Since it has a total of 8 prime factors, 37,728 is a composite number.\n\n## Divisors of 37728\n\n1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 131, 144, 262, 288, 393, 524, 786, 1048, 1179, 1572, 2096, 2358, 3144, 4192, 4716, 6288, 9432, 12576, 18864, 37728\n\n36 divisors\n\n Even divisors 30 6 3 3\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 36 Total number of the positive divisors of n σ(n) 108108 Sum of all the positive divisors of n s(n) 70380 Sum of the proper positive divisors of n A(n) 3003 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 194.237 Returns the nth root of the product of n divisors H(n) 12.5634 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 37,728 can be divided by 36 positive divisors (out of which 30 are even, and 6 are odd). The sum of these divisors (counting 37,728) is 108,108, the average is 3,003.\n\n## Other Arithmetic Functions (n = 37728)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 12480 Total number of positive integers not greater than n that are coprime to n λ(n) 3120 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 3987 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares\n\nThere are 12,480 positive integers (less than 37,728) that are coprime with 37,728. And there are approximately 3,987 prime numbers less than or equal to 37,728.\n\n## Divisibility of 37728\n\n m n mod m 2 3 4 5 6 7 8 9 0 0 0 3 0 5 0 0\n\nThe number 37,728 is divisible by 2, 3, 4, 6, 8 and 9.\n\n## Classification of 37728\n\n• Arithmetic\n• Refactorable\n• Abundant\n\n### Expressible via specific sums\n\n• Polite\n• Practical\n• Non-hypotenuse\n\n## Base conversion (37728)\n\nBase System Value\n2 Binary 1001001101100000\n3 Ternary 1220202100\n4 Quaternary 21031200\n5 Quinary 2201403\n6 Senary 450400\n8 Octal 111540\n10 Decimal 37728\n12 Duodecimal 19a00\n20 Vigesimal 4e68\n36 Base36 t40\n\n## Basic calculations (n = 37728)\n\n### Multiplication\n\nn×i\n n×2 75456 113184 150912 188640\n\n### Division\n\nni\n n⁄2 18864 12576 9432 7545.6\n\n### Exponentiation\n\nni\n n2 1423401984 53702110052352 2026073208055136256 76439689993504180666368\n\n### Nth Root\n\ni√n\n 2√n 194.237 33.5393 13.9369 8.22873\n\n## 37728 as geometric shapes\n\n### Circle\n\n Diameter 75456 237052 4.47175e+09\n\n### Sphere\n\n Volume 2.24947e+14 1.7887e+10 237052\n\n### Square\n\nLength = n\n Perimeter 150912 1.4234e+09 53355.4\n\n### Cube\n\nLength = n\n Surface area 8.54041e+09 5.37021e+13 65346.8\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 113184 6.16351e+08 32673.4\n\n### Triangular Pyramid\n\nLength = n\n Surface area 2.4654e+09 6.32885e+12 30804.8\n\n## Cryptographic Hash Functions\n\nmd5 8cad6fe9bc49034de21009541478bd5e 42783067f6bf7c470ea550ac9362074515c1958e 34969e453dab528b5e940c049cde70a7a5f94266b958227a7db4fcfa86ccc9b3 7013b680b02382441e4f32f4e8008bec002b8159c6b3ac433779d5e34c002b255ed6dedd6d8601454c7f93253b5e1561ea4229849cc225ff98c6657b89407424 3dd89539ca115159c8cbe7ccab57fd3ffe769b09" ]
[ null ]
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https://metanumbers.com/8912
[ "# 8912 (number)\n\n8,912 (eight thousand nine hundred twelve) is an even four-digits composite number following 8911 and preceding 8913. In scientific notation, it is written as 8.912 × 103. The sum of its digits is 20. It has a total of 5 prime factors and 10 positive divisors. There are 4,448 positive integers (up to 8912) that are relatively prime to 8912.\n\n## Basic properties\n\n• Is Prime? No\n• Number parity Even\n• Number length 4\n• Sum of Digits 20\n• Digital Root 2\n\n## Name\n\nShort name 8 thousand 912 eight thousand nine hundred twelve\n\n## Notation\n\nScientific notation 8.912 × 103 8.912 × 103\n\n## Prime Factorization of 8912\n\nPrime Factorization 24 × 557\n\nComposite number\nDistinct Factors Total Factors Radical ω(n) 2 Total number of distinct prime factors Ω(n) 5 Total number of prime factors rad(n) 1114 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0\n\nThe prime factorization of 8,912 is 24 × 557. Since it has a total of 5 prime factors, 8,912 is a composite number.\n\n## Divisors of 8912\n\n1, 2, 4, 8, 16, 557, 1114, 2228, 4456, 8912\n\n10 divisors\n\n Even divisors 8 2 2 0\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 10 Total number of the positive divisors of n σ(n) 17298 Sum of all the positive divisors of n s(n) 8386 Sum of the proper positive divisors of n A(n) 1729.8 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 94.4034 Returns the nth root of the product of n divisors H(n) 5.15204 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 8,912 can be divided by 10 positive divisors (out of which 8 are even, and 2 are odd). The sum of these divisors (counting 8,912) is 17,298, the average is 172,9.8.\n\n## Other Arithmetic Functions (n = 8912)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 4448 Total number of positive integers not greater than n that are coprime to n λ(n) 1112 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1112 Total number of primes less than or equal to n r2(n) 8 The number of ways n can be represented as the sum of 2 squares\n\nThere are 4,448 positive integers (less than 8,912) that are coprime with 8,912. And there are approximately 1,112 prime numbers less than or equal to 8,912.\n\n## Divisibility of 8912\n\n m n mod m 2 3 4 5 6 7 8 9 0 2 0 2 2 1 0 2\n\nThe number 8,912 is divisible by 2, 4 and 8.\n\n## Classification of 8912\n\n• Deficient\n\n• Polite\n\n### Other numbers\n\n• CentralPolygonal\n\n## Base conversion (8912)\n\nBase System Value\n2 Binary 10001011010000\n3 Ternary 110020002\n4 Quaternary 2023100\n5 Quinary 241122\n6 Senary 105132\n8 Octal 21320\n10 Decimal 8912\n12 Duodecimal 51a8\n20 Vigesimal 125c\n36 Base36 6vk\n\n## Basic calculations (n = 8912)\n\n### Multiplication\n\nn×y\n n×2 17824 26736 35648 44560\n\n### Division\n\nn÷y\n n÷2 4456 2970.67 2228 1782.4\n\n### Exponentiation\n\nny\n n2 79423744 707824406528 6308131110977536 56218064461031800832\n\n### Nth Root\n\ny√n\n 2√n 94.4034 20.7328 9.71614 6.16588\n\n## 8912 as geometric shapes\n\n### Circle\n\n Diameter 17824 55995.7 2.49517e+08\n\n### Sphere\n\n Volume 2.96493e+12 9.98068e+08 55995.7\n\n### Square\n\nLength = n\n Perimeter 35648 7.94237e+07 12603.5\n\n### Cube\n\nLength = n\n Surface area 4.76542e+08 7.07824e+11 15436\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 26736 3.43915e+07 7718.02\n\n### Triangular Pyramid\n\nLength = n\n Surface area 1.37566e+08 8.34179e+10 7276.62" ]
[ null ]
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https://solvedlib.com/can-you-answer-that-for-me-and-explain-why-21,461686
[ "# Can you answer that for me and explain why? 21 Which of the following is an...\n\n###### Question:\n\nCan you answer that for me and explain why?", null, "21 Which of the following is an attribute of the corporate form of business ownership? Unlimited liability. A. Higher tax rates. Limited resources. Difficulty in transferring ownership. None of the choices are correct. E.\n\n#### Similar Solved Questions\n\n##### 24. Function searches for the first occurrence in its first string argument of any character in...\n24. Function searches for the first occurrence in its first string argument of any character in its second string argument. a) strfirst b) strstr c) firstany d) strpbrk...\n##### Straight stream of protons passes given point in space at rate ol 2.3*109 protons_Part AWhat magnetic field do they produce 1.7 m Irom the beam? Express your answer using two significant figuresAZdBstreat4.7 10SubritPrevious Answers Request AnswerIncorrect; Try Again; 5 attempts remaining\nstraight stream of protons passes given point in space at rate ol 2.3*109 protons_ Part A What magnetic field do they produce 1.7 m Irom the beam? Express your answer using two significant figures AZd Bstreat 4.7 10 Subrit Previous Answers Request Answer Incorrect; Try Again; 5 attempts remaining...\n##### Data on dating Refer to Exercise $20 .$ (a) How would $r$ change if all the men were 6 inches shorter than the heights given in the table? Does the correlation tell us if women tend to date men taller than themselves?(b) If heights were measured in centimeters rather than inches, how would the correlation change?(There are 2.54 centimeters in an inch.)\nData on dating Refer to Exercise $20 .$ (a) How would $r$ change if all the men were 6 inches shorter than the heights given in the table? Does the correlation tell us if women tend to date men taller than themselves? (b) If heights were measured in centimeters rather than inches, how would the c...\n##### 7.3 7.5 10 . I tidl M M '. (7.3. Assume that the complex - O-...\n7.3 7.5 10 . I tidl M M '. (7.3. Assume that the complex - O- L-M M ' N 0 is exact. Show that, up to natural identifications, L=kery and N = coker 7.4 Construct short exact sequences of Z-modules 0- ZƏN ZƏN —+2– 0 and 0- ZeN — ZON — ZeN - 0. (Hint: David Hil...\n##### KLb/pie10 KLbkLbplespies\nkLb/pie 10 KLb kLb ples pies...\n##### Soybean meal is 12%protein corn meal is 6% proteinhowmany pounds of each should be mixed together in order to get 240pounds mixture that is 11%protein\nSoybean meal is 12%protein corn meal is 6% proteinhowmany pounds of each should be mixed together in order to get 240pounds mixture that is 11%protein?...\n##### Please explain! Some answers say 3 signals, some say 4 signals and I don’t understand 23....\nPlease explain! Some answers say 3 signals, some say 4 signals and I don’t understand 23. Consider the expected 'H NMR spectrum of 2,4-dimethyl-1,4-pentadiene. Which of the following is likely to be observed? 4.31 A) 3 signals: all singlets B) 7 signals: all singlets C) 4 signals: two sin...\n##### Matrices for 2) & 3): ^ = [1 4 B =3 7 5D =2 E =and F =2) If possible, compute the following: (a) DA + B (b) EC (c) CE (d) EB + F (e) FC + D 3) If possible, compute the following: (a) A(BD) (b) (AB)D (c) A(C + E) (d) AC + AE (e) (2AB)T and 2(AB) (f) A(C - 3E)\nMatrices for 2) & 3): ^ = [1 4 B = 3 7 5 D = 2 E = and F = 2) If possible, compute the following: (a) DA + B (b) EC (c) CE (d) EB + F (e) FC + D 3) If possible, compute the following: (a) A(BD) (b) (AB)D (c) A(C + E) (d) AC + AE (e) (2AB)T and 2(AB) (f) A(C - 3E)...\n##### Construct a truth tree to validate the following argument forvalidity{¬(A∧B), ¬A↔(C∨D), ¬(D→¬A)} ⊨ B→C\nconstruct a truth tree to validate the following argument for validity {¬(A∧B), ¬A↔(C∨D), ¬(D→¬A)} ⊨ B→C...\n##### I can't get it right ebook Problem Walk-Through 0.3 A stock's returns have the following distribution:...\nI can't get it right ebook Problem Walk-Through 0.3 A stock's returns have the following distribution: Demand for the Probability of This Rate of Return If Company's Products Demand Occurring This Demand Occurs weak 0.1 (38) Below average (10) Average Above average 0.3 0.1 0.1 63 1.0 1.0...\n##### UnaHll LarEE elacAnalyze Arul sketch 4Tarnthc munotonIneiul [euve el poImsnllcclidasymptote_ansnt daes noC Prsie\" (4Interceptselicr A-value)(lacger Value)relative muingmtum(dativc manmupainiunlectiunthe €quation uyvmptoteWueut] Uiliyveuly Youe IEuilte20000F15 000Lodon\nUnaHll LarEE elac Analyze Arul sketch 4Tarn thc munoton Ineiul [euve el poIms nllcclid asymptote_ ansnt daes noC Prsi e\" (4 Intercepts elicr A-value) (lacger Value) relative muingmtum (dativc manmu paini unlectiun the €quation uyvmptote Wueut] Uiliy veuly Youe IEuilte 20000F 15 000 Lodo...\n##### 0 Oy = hicbiri ~xlnx 26u 8 10+ 3 Puan) Ly=y Inx denkleminin genel nuzos asag1dakilerden hangisidir?\n0 Oy = hicbiri ~xlnx 26u 8 10 + 3 Puan) Ly=y Inx denkleminin genel nuzos asag1dakilerden hangisidir?...\n##### 4. At a distance r, two equal charges are kept and they exert aforce F on each other. What is the force acting on each charge, ifthe distance between them is doubled and charges are halved?\n4. At a distance r, two equal charges are kept and they exert a force F on each other. What is the force acting on each charge, if the distance between them is doubled and charges are halved?...\n##### Determine if the following events are indeperdent;Sean checks out a book from the Ilbrary:neclivl:letter trom ner cousin\nDetermine if the following events are indeperdent; Sean checks out a book from the Ilbrary: neclivl: letter trom ner cousin...\n##### O The following data represent the muzzle velocity (in feet per second) of rounds fired from...\no The following data represent the muzzle velocity (in feet per second) of rounds fired from a 155-mm gun. For each round, two measurements of the velocity were recorded using two different measuring devices, resulting in the following data. Complete parts (a) through (d) below. Observation 1 2 3 4 ...\n##### [e3earcner Wtantec roamsDelarminecalp eted rOCMS contain More bacieria Inan uncarpeied [Com:table shows Ine [egmeIne numoebacteria per cubic foct for both typesFull data set UncardetzdEameizt12.513.6Determine whethe carpeted rocms have more bacteria than uncarpeted rooms cutliers0.01 level significance Nomal probability Piots indicate that the data are approximately normaboxplots indicate that tnere areSiale Ihe null and allernative hypotheses Let population be carpetec roome and population be u\n[e3earcner Wtantec roams Delarmine calp eted rOCMS contain More bacieria Inan uncarpeied [Com: table shows Ine [egme Ine numoe bacteria per cubic foct for both types Full data set Uncardetzd Eameizt 12.5 13.6 Determine whethe carpeted rocms have more bacteria than uncarpeted rooms cutliers 0.01 leve...\n##### 5 What is the start building block of cholesterol? What is the control enzyme for cholesterol biosynthesis? What is the major transporter of cholesterol in circulation system? How tbe cells manipulate the oversupply of cholesterol? (10%)\n5 What is the start building block of cholesterol? What is the control enzyme for cholesterol biosynthesis? What is the major transporter of cholesterol in circulation system? How tbe cells manipulate the oversupply of cholesterol? (10%)..." ]
[ null, "https://img.homeworklib.com/questions/7630af00-72cb-11ea-9914-771f14db1abb.png", null ]
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https://la.mathworks.com/matlabcentral/cody/problems/58-tic-tac-toe-ftw/solutions/314195
[ "Cody\n\n# Problem 58. Tic Tac Toe FTW\n\nSolution 314195\n\nSubmitted on 2 Sep 2013 by Nicolae Preda\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\na = [ 1 0 1 0 -1 0 -1 -1 1]; b = [4 8]; out = ticTacToe(a); assert(isequal(out(:), b(:)))\n\n2   Pass\n%% a = [ 1 0 0 0 -1 0 -1 0 1]; b = ; out = ticTacToe(a); assert(isequal(out(:), b(:)))\n\n3   Pass\n%% a = [ 1 0 0 0 1 -1 1 -1 -1]; b = [2 7]; out = ticTacToe(a); assert(isequal(out(:), b(:)))\n\n4   Pass\n%% a = [ 1 0 0 -1 1 -1 1 -1 0]; b = [7 9]; out = ticTacToe(a); assert(isequal(out(:), b(:)))" ]
[ null ]
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https://rdrr.io/cran/sf/man/gdal.html
[ "# gdal: functions to interact with gdal not meant to be called... In sf: Simple Features for R\n\n## Description\n\nfunctions to interact with gdal not meant to be called directly by users (but e.g. by stars::st_stars)\n\n## Usage\n\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``` ```gdal_read(x, ..., options = character(0), driver = character(0), read_data = TRUE, NA_value = NA_real_, RasterIO_parameters = list()) gdal_write(x, ..., file, driver = \"GTiff\", options = character(0), type = \"Float32\", NA_value = NA_real_, geotransform, update = FALSE) gdal_inv_geotransform(gt) gdal_crs(file, options = character(0)) gdal_metadata(file, domain_item = character(0), options = character(0), parse = TRUE) gdal_subdatasets(file, options = character(0), name = TRUE) gdal_polygonize(x, mask = NULL, file = tempfile(), driver = \"GTiff\", use_integer = TRUE, geotransform, breaks = classInt::classIntervals(na.omit(as.vector(x[])))\\$brks, use_contours = FALSE, contour_lines = FALSE, connect8 = FALSE, ...) gdal_rasterize(sf, x, gt, file, driver = \"GTiff\", options = character()) ```\n\n## Arguments\n\n `x` character vector, possibly of length larger than 1 when more than one raster is read `...` ignored `options` character; raster layer read options `driver` character; when empty vector, driver is auto-detected. `read_data` logical; if `FALSE`, only the imagery metadata is returned `NA_value` (double) non-NA value to use for missing values; if `NA`, when writing missing values are not specially flagged in output dataset, when reading the default (dataset) missing values are used (if present / set). `RasterIO_parameters` list with named parameters to GDAL's RasterIO; see the stars::read_stars documentation. `file` character; file name `type` gdal write type `geotransform` length 6 numeric vector with GDAL geotransform parameters. `update` logical; `TRUE` if in an existing raster file pixel values shall be updated. `gt` double vector of length 6 `domain_item` character vector of length 0, 1 (with domain), or 2 (with domain and item); use `\"\"` for the default domain, use `NA_character_` to query the domain names. `parse` logical; should metadata be parsed into a named list (`TRUE`) or returned as character data? `name` logical; retrieve name of subdataset? If `FALSE`, retrieve description `mask` stars object with NA mask (0 where NA), or NULL `use_integer` boolean; if `TRUE`, raster values are read as (and rounded to) unsigned 32-bit integers values; if `FALSE` they are read as 32-bit floating points numbers. The former is supposedly faster. `breaks` numeric vector with break values for contour polygons (or lines) `use_contours` logical; `contour_lines` logical; `connect8` logical; if `TRUE` use 8 connection algorithm, rather than 4 `sf` object of class `sf`\n\n## Details\n\ngdal_inv_geotransform returns the inverse geotransform\n\ngdal_crs reads coordinate reference system from GDAL data set\n\nget_metadata gets metadata of a raster layer\n\ngdal_subdatasets returns the subdatasets of a gdal dataset\n\n## Value\n\nobject of class `crs`, see st_crs.\n\nnamed list with metadata items\n\n`gdal_subdatasets` returns a zero-length list if `file` does not have subdatasets, and else a named list with subdatasets.\n\n## Examples\n\n ```1 2 3 4 5 6 7 8 9``` ```## Not run: f = system.file(\"tif/L7_ETMs.tif\", package=\"stars\") f = system.file(\"nc/avhrr-only-v2.19810901.nc\", package = \"stars\") gdal_metadata(f) gdal_metadata(f, NA_character_) try(gdal_metadata(f, \"wrongDomain\")) gdal_metadata(f, c(\"\", \"AREA_OR_POINT\")) ## End(Not run) ```\n\nsf documentation built on July 24, 2019, 5:05 p.m." ]
[ null ]
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https://dev.webpages.dk/php_dbupdate.php
[ "https://dev.webpages.dk/", null, "PHP Update a Database\nPHP Update a Database:", null, "To update some row with existing values, in a table, you will use the UPDATE statement.\n\nThe examples to the right will do exactly that. Something like this:\n\nUPDATE tablename SET field=value\n\nYou should make use of the WHERE clause, if you omit this the update may affect all the field values in the table.\n\n### Update a Database\n\nHow do you Update content to a Database using PHP?\n\nNext step in this short serie is to make an UPDATE in our existing data. If you copy the code below into a PHP document you should be able to UPDATE your table rows. Put the code in a file named 'update.php' and call it in your browser.\n\nThe last part of the code is what we actually see first.\nIt will populate a SELECT with our contacts. We also get a submitbutton with the caption \"Okay, select\".\n\nWhen we click that button we go to the function doread(). Here we read what AutoID number was selected, it is the number of the contact we have selected, so when we have that we can read all info from the database in the row containing the values for our selected contact.\nWe get the values presented in text-fields, so we can change the text as we like. Then when we click this button, we read (in function doedit()) the inputs from the textfields on the HTML form, we put the content into some variables, in this example five variables.\n\nWe now construct the SQL, where we update the database fields, with the inputs from the form contained in the variables.\nWe make sure to put things in the right place, and we do that by stating that we want to update the fields in the row WHERE AutoID is the \\$IDnummer. That was the value that we read from the 'Hidden' form field.\n\nNext I will look at how to make order in the search results from querying you database table.\n\n### HTML\n\n``````<HTML><BODY>\n<FORM METHOD='POST' ACTION=''>\n<TABLE>\n<TR>\n<TD>Our contacts: </TD>\n``````\n``````\n<?php\n\\$con = mysqli_connect('127.0.0.1', 'root', 'Your_Password', 'dbname');\n\nif (mysqli_connect_errno()) {\necho 'Error connecting to DB';\n}\n\n\\$SQL_String = mysqli_query(\\$con, 'SELECT * FROM contacts ORDER BY AutoID ASC');\n\nwhile(\\$row = mysqli_fetch_array(\\$SQL_String)) {\necho '<OPTION VALUE=' . \\$row['AutoID'] . '>' . \\$row['Firstname'] . ' ' . \\$row['Lastname'];\n}\nmysqli_close (\\$con);\n?>\n``````\n``````\n</SELECT>\n</TD>\n</TR>\n<TR>\n<TD></TD>\n\n</TR>\n</TABLE>\n</FORM>\n</BODY></HTML>``````\n\n### PHP\n\n``````<?php\nif (isset(\\$_POST['updaterow'])) {\ndoedit();\n}\n\n}\n\nfunction doedit() {\n\n\\$IDnummer = \\$_POST['idnummer'];\n\\$Firstname = \\$_POST['firstname'];\n\\$Lastname = \\$_POST['lastname'];\n\n\\$con = mysqli_connect('127.0.0.1', 'root', 'Your_Password', 'dbname');\n\nif (mysqli_connect_errno()) {\necho \"Error connecting to the DB\";\n}\n\n\\$SQL_String = \"UPDATE contacts SET Firstname='\\$Firstname',\nLastname='\\$Lastname',\nWHERE AutoID='\" . \\$IDnummer . \"'\";\n\nmysqli_query(\\$con, \\$SQL_String);\nmysqli_close (\\$con);\n\n}\n\n\\$IDnummer = \\$_POST['contact'];\n\necho \"<HTML><BODY><FORM METHOD='POST' ACTION=''>\n<INPUT TYPE='hidden' NAME='idnummer' VALUE='\" . \\$IDnummer . \"'>\n<TABLE>\";\n\n\\$con = mysqli_connect('127.0.0.1', 'root', 'Your_Password', 'dbname');\nif (mysqli_connect_errno()) {\necho 'Error connecting to DB';\n}\n\\$SQL_String = mysqli_query(\\$con, 'SELECT * FROM contacts WHERE AutoID=' . \\$IDnummer . '');\n\\$row = mysqli_fetch_array(\\$SQL_String);\n\necho \"<TR>\n<TD>Firstname: </TD>\n<TD><INPUT TYPE='text' NAME='firstname' VALUE=\" . \\$row['Firstname'] . \"></TD>\n</TR>\";\n\necho \"<TR>\n<TD>Lastname: </TD>\n<TD><INPUT TYPE='text' NAME='lastname' VALUE=\" . \\$row['Lastname'] . \"></TD>\n</TR>\";\n\necho \"<TR>\n</TR>\";\n\necho \"<TR>" ]
[ null, "https://dev.webpages.dk/graphics/toprightcorner.png", null, "https://dev.webpages.dk/graphics/php.png", null ]
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https://codereview.stackexchange.com/questions/54646/string-representation-of-a-polynomial
[ "# String representation of a polynomial\n\nWe all know that math notation is idiosyncratic. Canonical representation of math objects often have irregular grammar rules to improve readability. For example we write a polynomial $3x^3 + x^2$ instead of more uniform but more verbose $3x^3 + 1x^2 + 0x^1 + 0x^0$. When a coefficient equals 0, you don't write the term, if the power equals $1$, you simply write $x$, and so on. So I wrote a simple program that outputs a string representation of a polynomial, given a list of coefficients:\n\ndef enumerate2(xs, start=0, step=1):\nfor x in xs:\nyield (start, x)\nstart += step\n\ndef poly(xs):\n\"\"\"Return string representation of a polynomial.\n\n>>> poly([2,1,0])\n\"2x^2 + x\"\n\"\"\"\nres = []\nfor e, x in enumerate2(xs, len(xs)-1, -1):\n\nvariable = 'x'\n\nif x == 1:\ncoefficient = ''\nelif x == -1:\ncoefficient = '-'\nelse:\ncoefficient = str(x)\n\nif e == 1:\npower = ''\nelif e == 0:\npower = ''\nvariable = ''\nelse:\npower = '^' + str(e)\n\nif x < 0:\ncoefficient = '(' + coefficient\npower = power + ')'\n\nif x != 0:\nres.append(coefficient + variable + power)\n\nreturn ' + '.join(res)\n\n\nenumerate2 is a custom version of enumerate that supports variable step. The result looks like this:\n\n>>> poly([2,0,3,-4,-3,2,0,1,10])\n'2x^8 + 3x^6 + (-4x^5) + (-3x^4) + 2x^3 + x + 10'\n\n\nHow do I make this code more elegant and probably more generic? Oh, and the result is sub-optimal, as negative terms are enclosed in brackets, instead of changing the preceding plus sign to minus.\n\nYour enumerate2 is a nice touch but I am not quite convinced that this is necessary : if you are to play with the length manually, you might as well compute the power from the index manually.\n\nAlso, if you were to handle the negative with a minus instead of the plus, you'd be able to get rid of the brackets. On the other hand, you cannot use join anymore which is a bit of a pain because it is a cool and efficient function.\n\nAnyway, here's my try :\n\ndef poly(p, var_string='x'):\nres = ''\nfirst_pow = len(p) - 1\nfor i, coef in enumerate(p):\npower = first_pow - i\n\nif coef:\nif coef < 0:\nsign, coef = (' - ' if res else '- '), -coef\nelif coef > 0: # must be true\nsign = (' + ' if res else '')\n\nstr_coef = '' if coef == 1 and power != 0 else str(coef)\n\nif power == 0:\nstr_power = ''\nelif power == 1:\nstr_power = var_string\nelse:\nstr_power = var_string + '^' + str(power)\n\nres += sign + str_coef + str_power\nreturn res\n\n\nand the corresponding output :\n\n2x^8 + 3x^6 - 4x^5 - 3x^4 + 2x^3 + x + 10\n\n\nBug found\n\nAs I was looking at my original implementation, I found a bug which happens to be in yours too : try with [1,1,1,1,1].\n\n• return instead of print – Maarten Fabré Apr 26 '19 at 10:10\n• @Maarten Fabré indeed I've updated my answer. Thanks – SylvainD May 6 '19 at 21:39\n\nI think there's a simpler way to do this:\n\nfmt = [\n[ \"\", \"\", \"\" ],\n[ \"{c:+g}\", \"{sign:s}x\", \"{sign:s}x^{n:g}\" ],\n[ \"{c:+g}\", \"{c:+g}x\", \"{c:+g}x^{n:g}\" ]\n]\n\ndef term(c, n):\nreturn fmt[cmp(abs(c),1)+1][cmp(n,1)+1].format(sign=\"- +\"[cmp(c,0)+1], c=c, n=n)\n\ndef poly(xs):\nreturn \"\".join(term(xs[i],len(xs)-i-1) for i in xrange(len(xs)))\n\ndef suppsign(s):\nreturn s.lstrip('+')\n\nprint suppsign(poly([1,1,1]))\n\n\nThe term function takes a coefficient and power value and uses the characteristics of those two to select the appropriate format string to generate a string representing an individual term.\n\nThe poly function uses a list comprehension to efficiently concatenate the string for each term.\n\nThe suppsign function simply removes the leading + from the resulting string if desired.\n\n# enumerate2\n\nHere you can use itertools.count or reversed\n\nfor e, x in enumerate2(xs, len(xs)-1, -1):\n\n\nbecomes\n\nfor e, x in zip(itertools.count(len(xs)-1, -1), xs):\n\n\nor\n\nfor e, x in zip(reversed(range(len(xs)), xs):\n\n\n# continue\n\nYou can skip to the next iteration in the for-loop easier by doing instead of if x != 0: ...:\n\nif x == 0:\ncontinue\n\n\nat the beginning of the loop\n\n# split functions\n\ndef coefficient(x):\n\"\"\"returns the string representation of x.\"\"\"\nif x == 1:\nreturn \"\"\nif x == -1:\nreturn \"-\"\nreturn str(x)\n\n\n# sting multiplication and bool\n\nfor the power part, you can use string multiplication and the fact int(True) == 1 and int(False) == 0\n\nresult = coefficient(x) + variable + f\"^{e}\" * (e != 1)\n\n\n# f-string\n\nSince python 3.6, you can do f\"({result})\" if x < 0 else result instead of\n\n coefficient = '(' + coefficient\npower = power + ')'\n\n\n# yield\n\nInstead of keeping a list of results, you can yield the intermediate terms. This\n\ndef poly2(xs, variable=\"x\"):\nif set(xs) == {0}:\nyield \"0\"\nreturn\nfor e, x in zip(reversed(range(len(xs))), xs):\nif x == 0:\ncontinue\nif e == 0:\nresult = str(x)\nelse:\nresult = coefficient(x) + variable + f\"^{e}\" * (e != 1)\nyield f\"({result})\" if x < 0 else result\n\n \" + \".join(poly2((1,-1,0,)))\n\n'x^2 + (-x)'\n\n• Why (e not in {1, 0})? Is that a legacy of an earlier version where the previous if e == 0 special case didn't exist? Or was the special case supposed to be removed when you added the (e not in {1, 0})? – Peter Taylor Apr 26 '19 at 12:57\n• You are correct. This is a relic of a previous version that had no influence, but is not necessary anymore. – Maarten Fabré Apr 26 '19 at 13:45" ]
[ null ]
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https://www.colorhexa.com/18d878
[ "# #18d878 Color Information\n\nIn a RGB color space, hex #18d878 is composed of 9.4% red, 84.7% green and 47.1% blue. Whereas in a CMYK color space, it is composed of 88.9% cyan, 0% magenta, 44.4% yellow and 15.3% black. It has a hue angle of 150 degrees, a saturation of 80% and a lightness of 47.1%. #18d878 color hex could be obtained by blending #30fff0 with #00b100. Closest websafe color is: #00cc66.\n\n• R 9\n• G 85\n• B 47\nRGB color chart\n• C 89\n• M 0\n• Y 44\n• K 15\nCMYK color chart\n\n#18d878 color description : Strong cyan - lime green.\n\n# #18d878 Color Conversion\n\nThe hexadecimal color #18d878 has RGB values of R:24, G:216, B:120 and CMYK values of C:0.89, M:0, Y:0.44, K:0.15. Its decimal value is 1628280.\n\nHex triplet RGB Decimal 18d878 `#18d878` 24, 216, 120 `rgb(24,216,120)` 9.4, 84.7, 47.1 `rgb(9.4%,84.7%,47.1%)` 89, 0, 44, 15 150°, 80, 47.1 `hsl(150,80%,47.1%)` 150°, 88.9, 84.7 00cc66 `#00cc66`\nCIE-LAB 76.472, -64.628, 35.269 28.321, 50.659, 26.054 0.27, 0.482, 50.659 76.472, 73.625, 151.378 76.472, -66.69, 57.58 71.175, -53.531, 28.119 00011000, 11011000, 01111000\n\n# Color Schemes with #18d878\n\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #d81878\n``#d81878` `rgb(216,24,120)``\nComplementary Color\n• #18d818\n``#18d818` `rgb(24,216,24)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #18d8d8\n``#18d8d8` `rgb(24,216,216)``\nAnalogous Color\n• #d81818\n``#d81818` `rgb(216,24,24)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #d818d8\n``#d818d8` `rgb(216,24,216)``\nSplit Complementary Color\n• #d87818\n``#d87818` `rgb(216,120,24)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #7818d8\n``#7818d8` `rgb(120,24,216)``\n• #78d818\n``#78d818` `rgb(120,216,24)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #7818d8\n``#7818d8` `rgb(120,24,216)``\n• #d81878\n``#d81878` `rgb(216,24,120)``\n• #109352\n``#109352` `rgb(16,147,82)``\n• #13aa5f\n``#13aa5f` `rgb(19,170,95)``\n• #15c16b\n``#15c16b` `rgb(21,193,107)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #23e785\n``#23e785` `rgb(35,231,133)``\n• #3ae992\n``#3ae992` `rgb(58,233,146)``\n• #51ec9e\n``#51ec9e` `rgb(81,236,158)``\nMonochromatic Color\n\n# Alternatives to #18d878\n\nBelow, you can see some colors close to #18d878. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #18d848\n``#18d848` `rgb(24,216,72)``\n• #18d858\n``#18d858` `rgb(24,216,88)``\n• #18d868\n``#18d868` `rgb(24,216,104)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #18d888\n``#18d888` `rgb(24,216,136)``\n• #18d898\n``#18d898` `rgb(24,216,152)``\n• #18d8a8\n``#18d8a8` `rgb(24,216,168)``\nSimilar Colors\n\n# #18d878 Preview\n\nThis text has a font color of #18d878.\n\n``<span style=\"color:#18d878;\">Text here</span>``\n#18d878 background color\n\nThis paragraph has a background color of #18d878.\n\n``<p style=\"background-color:#18d878;\">Content here</p>``\n#18d878 border color\n\nThis element has a border color of #18d878.\n\n``<div style=\"border:1px solid #18d878;\">Content here</div>``\nCSS codes\n``.text {color:#18d878;}``\n``.background {background-color:#18d878;}``\n``.border {border:1px solid #18d878;}``\n\n# Shades and Tints of #18d878\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000402 is the darkest color, while #f2fef8 is the lightest one.\n\n• #000402\n``#000402` `rgb(0,4,2)``\n• #02160c\n``#02160c` `rgb(2,22,12)``\n• #042716\n``#042716` `rgb(4,39,22)``\n• #063920\n``#063920` `rgb(6,57,32)``\n• #084b2a\n``#084b2a` `rgb(8,75,42)``\n• #0a5c33\n``#0a5c33` `rgb(10,92,51)``\n• #0c6e3d\n``#0c6e3d` `rgb(12,110,61)``\n• #0e8047\n``#0e8047` `rgb(14,128,71)``\n• #109151\n``#109151` `rgb(16,145,81)``\n• #12a35b\n``#12a35b` `rgb(18,163,91)``\n• #14b564\n``#14b564` `rgb(20,181,100)``\n• #16c66e\n``#16c66e` `rgb(22,198,110)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #1ee682\n``#1ee682` `rgb(30,230,130)``\n• #2fe88c\n``#2fe88c` `rgb(47,232,140)``\n• #41ea95\n``#41ea95` `rgb(65,234,149)``\n• #53ec9f\n``#53ec9f` `rgb(83,236,159)``\n• #64eea9\n``#64eea9` `rgb(100,238,169)``\n• #76f0b3\n``#76f0b3` `rgb(118,240,179)``\n• #88f2bd\n``#88f2bd` `rgb(136,242,189)``\n• #99f4c6\n``#99f4c6` `rgb(153,244,198)``\n• #abf6d0\n``#abf6d0` `rgb(171,246,208)``\n• #bdf8da\n``#bdf8da` `rgb(189,248,218)``\n• #cefae4\n``#cefae4` `rgb(206,250,228)``\n• #e0fcee\n``#e0fcee` `rgb(224,252,238)``\n• #f2fef8\n``#f2fef8` `rgb(242,254,248)``\nTint Color Variation\n\n# Tones of #18d878\n\nA tone is produced by adding gray to any pure hue. In this case, #747c78 is the less saturated color, while #06ea78 is the most saturated one.\n\n• #747c78\n``#747c78` `rgb(116,124,120)``\n• #6b8578\n``#6b8578` `rgb(107,133,120)``\n• #628e78\n``#628e78` `rgb(98,142,120)``\n• #599778\n``#599778` `rgb(89,151,120)``\n• #4fa178\n``#4fa178` `rgb(79,161,120)``\n• #46aa78\n``#46aa78` `rgb(70,170,120)``\n• #3db378\n``#3db378` `rgb(61,179,120)``\n• #34bc78\n``#34bc78` `rgb(52,188,120)``\n• #2ac678\n``#2ac678` `rgb(42,198,120)``\n• #21cf78\n``#21cf78` `rgb(33,207,120)``\n• #18d878\n``#18d878` `rgb(24,216,120)``\n• #0fe178\n``#0fe178` `rgb(15,225,120)``\n• #06ea78\n``#06ea78` `rgb(6,234,120)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #18d878 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]
[ null ]
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https://thecleverprogrammer.com/2020/11/28/weight-converter-gui-with-python/
[ "# Weight Converter GUI with Python\n\nWeight conversion means to multiply the value of a unit with the standard conversion value. In this article, I will take you through how to create a weight converter GUI with Python programming language.\n\nThe standard weight conversion values include:\n\n1. 1 milligram = 0.001 gram\n2. 1 centigram = 0.01 gram\n3. 1 decigram = 0.1 gram\n4. 1 kilogram = 1000 grams\n5. 1 gram = 1000 milligrams\n6. 1 ton = 2000 pounds\n7. 1 pound = 16 ounces\n\n## Weight Converter GUI with Python\n\nNow let’s see how to create a weight converter application with Python by adding some graphical user interface features. I will use the Tkinter library in Python for this task:\n\nSo this is how we can create a weight converter graphical user interface application by using the Tkinter library in Python.\n\nAlso, Read – 100+ Machine Learning Projects Solved and Explained.", null, "" ]
[ null, "https://secure.gravatar.com/avatar/8be3cd61b437e9d5f7ad2e88f2af7c73", null ]
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http://alexanderpruss.blogspot.com/2020/11/set-theory-and-physics.html
[ "## Wednesday, November 11, 2020\n\n### Set theory and physics\n\nAssume the correct physics has precise particle positions (similar questions can be asked in other contexts, but the particle position context is the one I will choose). And suppose we can specify a time t precisely, e.g., in terms of the duration elapsed from the beginning of physical reality, in some precisely defined unit system. Consider two particles, a and b, that exist at t. Let d be the distance between a and b at t in some precisely definable unit system.\n\nHere’s a question that is rarely asked: Is d a real number?\n\nThis seems a silly question. How could it not be? What else could it be? A complex number?\n\nWell, there are at least two other things that d could be without any significant change to the equations of physics.\n\nFirst, d could be a hyperreal number. It could be that particle positions are more fine-grained than the reals.\n\nSecond, d could be what I am now calling a “missing number”. A missing number is something that can intuitively be defined by an English (or other meta-language) specification of an approximating “sequence”, but does not correspond to a real number in set theory. For instance, we could suppose for simplicity that d lies between 0 and 1 and imagine a physical measurement procedure that can determine the nth binary digit of d. Then we would have an English predicate Md(n) which is true just in case that procedure determined the n binary digit to be 1. But it could turn out that in set theory there is no set whose members are the natural numbers n such that Md(n). For the axioms of set theory only guarantee the existence of a set defined using the predicates of set theory, while Md is not a predicate of set theory. The idea of such “missing numbers” is coherent, at least if our set theory is coherent.\n\nIt seems reasonable to say that d is indeed a real number, and to say similar things about any other quantities that can be similarly physically specified. But what guarantees such a match between set theory and physics? I see four options:\n\n1. Luck: it’s just a coincidence.\n\n2. Our set theory governs physics.\n\n3. Physics governs our set theory.\n\n4. There is a common governor to our set theory and physics.\n\nOption 1 is an unhappy one. Option 4 might be a Cartesian God who freely chooses both mathematics and physics.\n\nOption 2 is interesting. On this story, there is a Platonically true set theory, and then the laws of physics make reference to it. So it’s then a law of physics that distances (say) always correspond to real numbers in the Platonically true set theory.\n\nOption 3 comes in at least two versions. First, one could have an Aristotelian story on which mathematics, including some version of set theory, is an abstraction from the physical world, and any predicates that we can define physically are going to be usable for defining sets. So, physics makes sets. Second, one could have a Platonic multiverse of universes of sets: there are infinitely many universes of sets, and we simply choose to work within those that match our physics. On this view, physics doesn’t make sets, but it chooses between the universes of sets." ]
[ null ]
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https://projecteuler.net/problem=555
[ "", null, "## McCarthy 91 function", null, "Published on Sunday, 10th April 2016, 04:00 am; Solved by 561;\nDifficulty rating: 30%\n\n### Problem 555\n\nThe McCarthy 91 function is defined as follows: $$M_{91}(n) = \\begin{cases} n - 10 & \\text{if } n > 100 \\\\ M_{91}(M_{91}(n+11)) & \\text{if } 0 \\leq n \\leq 100 \\end{cases}$$\n\nWe can generalize this definition by abstracting away the constants into new variables: $$M_{m,k,s}(n) = \\begin{cases} n - s & \\text{if } n > m \\\\ M_{m,k,s}(M_{m,k,s}(n+k)) & \\text{if } 0 \\leq n \\leq m \\end{cases}$$\n\nThis way, we have $M_{91} = M_{100,11,10}$.\n\nLet $F_{m,k,s}$ be the set of fixed points of $M_{m,k,s}$. That is, $$F_{m,k,s}= \\left\\{ n \\in \\mathbb{N} \\, | \\, M_{m,k,s}(n) = n \\right\\}$$\n\nFor example, the only fixed point of $M_{91}$ is $n = 91$. In other words, $F_{100,11,10}= \\{91\\}$.\n\nNow, define $SF(m,k,s)$ as the sum of the elements in $F_{m,k,s}$ and let $S(p,m) = \\displaystyle \\sum_{1 \\leq s < k \\leq p}{SF(m,k,s)}$.\n\nFor example, $S(10, 10) = 225$ and $S(1000, 1000)=208724467$.\n\nFind $S(10^6, 10^6)$." ]
[ null, "https://projecteuler.net/images/print_page_logo.png", null, "https://projecteuler.net/images/icon_info.png", null ]
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http://www.pstat.ucsb.edu/news/event/1345
[ "# Seminar - Suman Majumdar\n\n## Event Date:\n\nTuesday, November 13, 2018 - 11:00am to 12:00pm\n\n## Event Location:\n\n• North Hall 1109\n\nTitle: On asymptotic standard normality of the two sample pivot\n\nAbstract:\n\n(Joint work with Rajeshwari Majumdar, New York University)\n\nThe asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test statistic being asymptotically standard Normal, which is known to happen if the two samples are independent and the ratio of the sample sizes converges to a finite positive number. This restriction on the asymptotic behavior of the ratio of the sample sizes carries the risk of rendering the asymptotic justification of the finite sample approximation invalid. It turns out that neither the restriction on the asymptotic behavior of the ratio of the sample sizes nor the assumption of cross sample independence is necessary for the pivotal convergence in question to take place, which happens if the joint distribution of the standardized sample means converges to a spherically symmetric distribution. Note that if the joint distribution of the standardized sample means converges to a spherically symmetric distribution, then the limiting distribution must be bivariate standard Normal, and a decaying correlation assumption is necessary and sufficient for this convergence.\n\nBio:\n\nSuman Majumdar is an Associate Professor at University of Connecticut." ]
[ null ]
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https://domhabersack.com/ternary-assignment-and-return
[ "# Using the ternary operator in assignment and return\n\nJavaScript\n\nThe ternary operator can be used when assigning variables or even as part of return statements. It can help us make some arrow functions even shorter.\n\n``````const isEven = n => n % 2 === 0\n\n// assigning the result of a ternary operator to a variable\nconst numberType = isEven(35) ? 'even' : 'odd'\n\n// returning the result of a ternary operator in a function\nconst getNumberType = number => {\nreturn isEven(number) ? 'even' : 'odd'\n}\n\n// returning the result of a ternary operator using an implicit return\nconst getNumberType = number => isEven(number) ? 'even' : 'odd'\n``````\n\n## Getting the largest number from an array\n\nTo find the largest value in an array of numbers, we can spread that array into Math.max() instead of manually iterating over it.\n\nJavaScript" ]
[ null ]
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https://nrich.maths.org/public/leg.php?code=124&cl=3&cldcmpid=13416
[ "# Search by Topic\n\n#### Resources tagged with Pythagoras' theorem similar to Shogi Shapes:\n\nFilter by: Content type:\nAge range:\nChallenge level:\n\n### There are 75 results\n\nBroad Topics > Pythagoras and Trigonometry > Pythagoras' theorem", null, "### Floored\n\n##### Age 11 to 14 Challenge Level:\n\nA floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?", null, "### Crescents and Triangles\n\n##### Age 14 to 16 Challenge Level:\n\nCan you find a relationship between the area of the crescents and the area of the triangle?", null, "### A Chordingly\n\n##### Age 11 to 14 Challenge Level:\n\nFind the area of the annulus in terms of the length of the chord which is tangent to the inner circle.", null, "### Pythagoras\n\n##### Age 7 to 14\n\nPythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.", null, "### Hex\n\n##### Age 11 to 14 Challenge Level:\n\nExplain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.", null, "### Square Pegs\n\n##### Age 11 to 14 Challenge Level:\n\nWhich is a better fit, a square peg in a round hole or a round peg in a square hole?", null, "### Compare Areas\n\n##### Age 14 to 16 Challenge Level:\n\nWhich has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?", null, "### The Pillar of Chios\n\n##### Age 14 to 16 Challenge Level:\n\nSemicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.", null, "### Liethagoras' Theorem\n\n##### Age 7 to 14\n\nLiethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him.", null, "### Pythagorean Triples\n\n##### Age 11 to 14 Challenge Level:\n\nHow many right-angled triangles are there with sides that are all integers less than 100 units?", null, "### Star Gazing\n\n##### Age 14 to 16 Challenge Level:\n\nFind the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.", null, "### Partly Circles\n\n##### Age 14 to 16 Challenge Level:\n\nWhat is the same and what is different about these circle questions? What connections can you make?", null, "### Get Cross\n\n##### Age 14 to 16 Challenge Level:\n\nA white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?", null, "### Tilting Triangles\n\n##### Age 14 to 16 Challenge Level:\n\nA right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?", null, "### Squ-areas\n\n##### Age 14 to 16 Challenge Level:\n\nThree squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . .", null, "### Some(?) of the Parts\n\n##### Age 14 to 16 Challenge Level:\n\nA circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle", null, "### Grid Lockout\n\n##### Age 14 to 16 Challenge Level:\n\nWhat remainders do you get when square numbers are divided by 4?", null, "### Garden Shed\n\n##### Age 11 to 14 Challenge Level:\n\nCan you minimise the amount of wood needed to build the roof of my garden shed?", null, "### Circle Scaling\n\n##### Age 14 to 16 Challenge Level:\n\nDescribe how to construct three circles which have areas in the ratio 1:2:3.", null, "### Three Cubes\n\n##### Age 14 to 16 Challenge Level:\n\nCan you work out the dimensions of the three cubes?", null, "### Circle Packing\n\n##### Age 14 to 16 Challenge Level:\n\nEqual circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...", null, "### Semi-square\n\n##### Age 14 to 16 Challenge Level:\n\nWhat is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?", null, "### The Medieval Octagon\n\n##### Age 14 to 16 Challenge Level:\n\nMedieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.", null, "### Napkin\n\n##### Age 14 to 16 Challenge Level:\n\nA napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .", null, "### All Is Number\n\n##### Age 7 to 14", null, "### Semi-detached\n\n##### Age 14 to 16 Challenge Level:\n\nA square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.", null, "### Take a Square\n\n##### Age 14 to 16 Challenge Level:\n\nCut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.", null, "### Corridors\n\n##### Age 14 to 16 Challenge Level:\n\nA 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.", null, "### Squareo'scope Determines the Kind of Triangle\n\n##### Age 11 to 14\n\nA description of some experiments in which you can make discoveries about triangles.", null, "### Equilateral Areas\n\n##### Age 14 to 16 Challenge Level:\n\nABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.", null, "### Tennis\n\n##### Age 11 to 14 Challenge Level:\n\nA tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?", null, "### Ball Packing\n\n##### Age 14 to 16 Challenge Level:\n\nIf a ball is rolled into the corner of a room how far is its centre from the corner?", null, "### Rectangular Pyramids\n\n##### Age 14 to 18 Challenge Level:\n\nIs the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?", null, "### Isosceles\n\n##### Age 11 to 14 Challenge Level:\n\nProve that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.", null, "### Trice\n\n##### Age 11 to 14 Challenge Level:\n\nABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?", null, "### The Dangerous Ratio\n\n##### Age 11 to 14\n\nThis article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.", null, "### Three Four Five\n\n##### Age 14 to 16 Challenge Level:\n\nTwo semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.", null, "### Two Circles\n\n##### Age 14 to 16 Challenge Level:\n\nDraw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap?", null, "### Holly\n\n##### Age 14 to 16 Challenge Level:\n\nThe ten arcs forming the edges of the \"holly leaf\" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.", null, "### Cutting a Cube\n\n##### Age 11 to 14 Challenge Level:\n\nA half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?", null, "### Tilted Squares\n\n##### Age 11 to 14 Challenge Level:\n\nIt's easy to work out the areas of most squares that we meet, but what if they were tilted?", null, "### The Fire-fighter's Car Keys\n\n##### Age 14 to 16 Challenge Level:\n\nA fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.", null, "### Rhombus in Rectangle\n\n##### Age 14 to 16 Challenge Level:\n\nTake any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.", null, "### Inscribed in a Circle\n\n##### Age 14 to 16 Challenge Level:\n\nThe area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?", null, "### Six Discs\n\n##### Age 14 to 16 Challenge Level:\n\nSix circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?", null, "### Squaring the Circle and Circling the Square\n\n##### Age 14 to 16 Challenge Level:\n\nIf you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.", null, "### The Spider and the Fly\n\n##### Age 14 to 16 Challenge Level:\n\nA spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?", null, "### All Tied Up\n\n##### Age 14 to 16 Challenge Level:\n\nA ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?", null, "### Under the Ribbon\n\n##### Age 14 to 16 Challenge Level:\n\nA ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?", null, "### Are You Kidding\n\n##### Age 14 to 16 Challenge Level:\n\nIf the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?" ]
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https://www.tutorialgateway.org/go-program-to-print-array-items-in-even-index-position/
[ "# Go Program to Print Array Items in Even Index Position\n\nWrite a Go program to Print the Array items in an even index position using For loop. In this Go example, the for loop (for i := 0; i < len(numarray); i += 2) starts iteration at 0 and increments by 2. Within the loop, we print all the array items at an even position.\n\n```package main\n\nimport \"fmt\"\n\nfunc main() {\n\nnumarray := []int{10, 20, 30, 40, 50, 60, 70, 80}\n\nfmt.Println(\"The List of Array Items in Even Index Position = \")\nfor i := 0; i < len(numarray); i += 2 {\nfmt.Println(numarray[i])\n}\n\n} ```\n``````The List of Array Items in Even Index Position =\n10\n30\n50\n70``````\n\n## Golang Program to Print Array Items in Even Index Position using the For Loop range\n\nWe used an extra if statement (if i%2 == 0) to check whether the index position divisible by two equals two, which means it is an even index position. Next, print that even position array number.\n\n```package main\n\nimport \"fmt\"\n\nfunc main() {\n\nnumarray := []int{10, 20, 30, 40, 50, 60, 70, 80}\n\nfmt.Println(\"The List of Array Items in Even index Position = \")\nfor i, _ := range numarray {\nif i%2 == 0 {\nfmt.Println(numarray[i])\n}\n}\n}```\n``````The List of Array Items in Even index Position =\n10\n30\n50\n70``````\n\nThis Golang program allows entering the array size, items, and pints the elements at an even index position.\n\n```package main\n\nimport \"fmt\"\n\nfunc main() {\n\nvar size int\n\nfmt.Print(\"Enter the Even Odd Array Size = \")\nfmt.Scan(&size)\n\nnumarray := make([]int, size)\n\nfmt.Print(\"Enter the Even Odd Array Items = \")\nfor i := 0; i < size; i++ {\nfmt.Scan(&numarray[i])\n}\n\nfmt.Println(\"The List of Array Items in Even Index Position = \")\nfor i := 0; i < len(numarray); i += 2 {\nfmt.Println(numarray[i])\n}\n}```" ]
[ null ]
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https://catalog.ucsc.edu/en/Current/General-Catalog/Courses/MATH-Mathematics/Upper-Division/MATH-121B
[ "# MathematicsMATH 121B Differential Geometry and Topology\n\nExamples of surfaces of constant curvature, surfaces of revolutions, minimal surfaces. Abstract manifolds; integration theory; Riemannian manifolds. Total curvature and geodesics; the Euler characteristic, the Gauss-Bonnet theorem. Length-minimizing properties of geodesics, complete surfaces, curvature and conjugate points covering surfaces. Surfaces of constant curvature; the theorems of Bonnet and Hadamard.\n\n#### Requirements\n\nPrerequisite(s): MATH 121A.\n\n5" ]
[ null ]
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https://www.thejournal.club/c/paper/187203/
[ "#### Differentially Private Learning of Geometric Concepts\n\n##### Haim Kaplan, Yishay Mansour, Yossi Matias, Uri Stemmer\n\nWe present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(\\alpha,\\beta)$-PAC learning and $(\\epsilon,\\delta)$-differential privacy using a sample of size $\\tilde{O}\\left(\\frac{1}{\\alpha\\epsilon}k\\log d\\right)$, where the domain is $[d]\\times[d]$ and $k$ is the number of edges in the union of polygons.\n\narrow_drop_up" ]
[ null ]
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https://lovullo.gitlab.io/tame/Package-Subgraphs.html
[ "### B.1 Package Subgraphs\n\nEach package has its own independent dependency graph. These vertices may have virtual edges to other packages’ graphs—edges that will be formed once combined the referenced graph; these edges are indicated with preproc:sym-ref/@src.\n\nGraph operations are usually performed on single packages, but it is occionally necessary to traverse packages to recurisvely resolve dependencies. graph:dep-lookup#3 makes this easy:\n\nTODO: Generic graph functions.\n\nfunction: element( preproc:sym-dep )? graph:dep-lookup (lookup as xs:sequence*, graph as element( preproc:sym-deps ), symbol as element( preproc:sym ))\n\nxmlns:graph=\"http://www.lovullo.com/tame/graph\"\n\nRetrieve dependenices for $symbol on the$graph, using the lookup function $lookup to resolve external subgraphs.$lookup will be used only if the symbol cannot be found in $graph, in which case the result of$lookup will used used in a recursive call as the new $graph. From a graph perspective, the dependencies are edges on the$symbol vertex.\n\nParameters are organized for partial application.\n\nDefinition:\n\n<function name=\"graph:dep-lookup\" as=\"element( preproc:sym-dep )?\">\n<param name=\"lookup\" />\n<param name=\"graph\" as=\"element( preproc:sym-deps )\" />\n<param name=\"symbol\" as=\"element( preproc:sym )\" />\n\n<variable name=\"deps\" as=\"element( preproc:sym-dep )?\" select=\"$graph/preproc:sym-dep [ @name =$symbol/@name ]\" />\n\n<sequence select=\"if ( exists( $deps ) ) then$deps else if ( $lookup ) then graph:dep-lookup($lookup, f:apply( $lookup,$symbol ), $symbol ) else ()\" /> </function> graph:dep-lookup#3 can be used together with the convenience function graph:make-from-deps#2 to produce a graph that contains all dependencies for a given symbol list. Used together with graph:reverse#1, a reverse dependency graph can be easily created that provides a useful “used by” relationship. function: element( preproc:sym-deps )* graph:make-from-deps (lookup as item()+, symbols as element( preproc:sym )*) xmlns:graph=\"http://www.lovullo.com/tame/graph\" Create a dependency graph containing all dependencies of the given symbol list$symbols. The graph contains the union of the minimal subset of all package subgraphs—only vertices representing a symbol in $symbols or its direct dependencies are included. This function is not recursive; it assumes that the given symbol list$symbols is sufficient for whatever operation is being performed.\n\nThe lookup function $lookup is invoked once per symbol in$symbols with the preproc:sym to look up. The final result is used to produce a new normalized graph, with any duplicate vertices and edges removed.\n\nDefinition:\n\n<function name=\"graph:make-from-deps\" as=\"element( preproc:sym-deps )*\">\n<param name=\"lookup\" as=\"item()+\" />\n<param name=\"symbols\" as=\"element( preproc:sym )*\" />\n\n<sequence select=\"graph:make-from-vertices( for $symbol in$symbols return f:apply( $lookup,$symbol ) )\" />\n</function>" ]
[ null ]
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https://en.cryptonomist.ch/2019/06/23/fibonacci-financial-trading/
[ "", null, "", null, "", null, "", null, "Trading\n\n# Fibonacci in financial trading: levels, fans and arcs\n\nFibonacci levels are undoubtedly one of the most fascinating theories of financial trading. The numbers of the Fibonacci Series respond to a simple mathematical property according to which each of them is defined as the sum of the two previous ones.\n\nOver the years, several indicators have emerged, including Fibonacci levels, fans and arcs.\n\nThe sequence starts this way:\n\n1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144\n\nAnd it’s, of course, infinite.", null, "## The history\n\nLeonardo Pisano, called Fibonacci, was a 13th-century mathematician who named the Fibonacci sequence after himself. He was able to develop this series through numerous teachings in the field of arithmetics.\n\nThis knowledge was summarised by him in an important text: the Liber Abaci. It was in this very piece of work that he introduced his thoughts. This numerical sequence is used in many fields: from music to computer science, from finance to nature, from mathematics to electronics.\n\n## In financial trading: what is the Fibonacci sequence for?\n\nBy dividing the Fibonacci numbers between them, we obtain the so-called Fibonacci ratios. If, for example, 13 is divided by 21, the result is 0.619 (expressed as a percentage it represents 61.9%).\n\nThese ratios are also taken into consideration in finance: the prices of assets do not move in a linear manner but according to very precise rules. It, therefore, happens that during a bullish movement there are several corrections or short phases of consolidation, while within a bearish movement there are several rebounds.\n\nFibonacci retracements are used, among other things, to determine support and resistance levels. They are based on a line drawn between a relative maximum and minimum (or vice versa).\n\n## Fibonacci levels", null, "Many people agree that the most likely retracements after a bullish or bearish rally can be traced back to relationships derived from the Fibonacci series:\n\n23.6%, 38.2%, 50%, 61.8% e 76.4%.\n\nAccording to this observation, it is therefore plausible that a bullish movement is followed by a correction that will tend to stop after having walked in the opposite direction a portion of the space originally gained, indicated by one of the potential retracement percentages.\n\nAs can be seen in the graph, taking into account two points of maximum and minimum, it is possible that the supports and resistances follow perfectly, or almost, the Fibonacci levels.\n\n## Fibonacci fans\n\nFibonacci fans are based on the percentage retracements of the trend, respectively 38%, 50% and 62% above and below the line joining a relative historical minimum and a subsequent relative historical maximum, or vice versa.\n\nIn this way, the possible levels of inclination of the trend on which the price could react are identified. As with Fibonacci retracements, fans must be generated by selecting two points on the graph resting on the minimum and maximum of the period under consideration.\n\n## Other applications in trading\n\nNot only levels and fans, but this indicator is also used for timing in futures markets. For this purpose, an asset and a new minimum or maximum point can be selected and moved forward along the axis of the x-axis in correspondence to the Fibonacci numbers. So, for example, 21, 34, 55 days ahead.\n\nMany traders act on this information, believing that there is a repetition of events in conjunction with the sequence. But this does not always happen. In the same way, it is possible to take into consideration the intervals of days equal to the numbers of the Fibonacci sequence to see if there is any logic in the shape of charts.\n\nAnother use that is possible, linked to that of the fans, are the arcs.\n\nFibonacci arcs have fan lines in common with the fans and consist of three arcs at fixed intervals of 38.2%, 50% and 61.8%.\n\nThe price zones that are identified are possible areas of support or resistance that change with the passage of time. These arcs are obtained by pointing a compass at a historical maximum and drawing three concentric circles.\n\n### Do Fibonacci levels really work?\n\nFibonacci is a mathematical sequence and as such, it is well tested and verified.\n\nOver the years, mathematicians and philosophers have always wondered why this series, along with the golden ratio, represents most of the phenomena on the planet.\n\nHowever, some applications are experimental and others are almost religious. These mechanisms work, but it is a good idea to always accompany them with other technical indicators to avoid false signals.", null, "", null, "We use cookies to make sure you can have the best experience on our site. If you continue to use this site we will assume that you are happy with it." ]
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http://progs.coudert.name/elate/mp?query=mp-997100
[ "# ELATE: Elastic tensor analysis\n\nWelcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-Xavier Coudert at CNRS / Chimie ParisTech.\nIf you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.\n\nELATE is open source software. Any queries or comments are welcome at\n\n## Summary of the properties\n\n### Input: stiffness matrix (coefficients in GPa) of SrAgO2 (Materials Project id mp-997100)\n\n``` 237 103 17 0 0 0\n103 237 17 0 0 0\n17 17 91 0 0 0\n0 0 0 17 0 0\n0 0 0 0 17 0\n0 0 0 0 0 52\n```\n\n### Average properties\n\nAveraging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio\nVoigtKV = 93.222 GPaEV = 117.92 GPaGV = 45.733 GPaνV = 0.28918\nReussKR = 66.877 GPaER = 76.865 GPaGR = 29.373 GPaνR = 0.30844\nHillKH = 80.049 GPaEH = 97.425 GPaGH = 37.553 GPaνH = 0.29716\n\n### Eigenvalues of the stiffness matrix\n\nλ1 λ2 λ3 λ4 λ5 λ6\n17 GPa 17 GPa 52 GPa 88.7 GPa 134 GPa 342.3 GPa\n\n### Variations of the elastic moduli\n\nYoung's modulus Linear compressibility Shear modulus Poisson's ratio Emin Emax βmin βmax Gmin Value 52.768 GPa 191.21 GPa 2.4373 TPa–1 10.078 TPa–1 17 GPa 67 GPa 0.05 0.59731 Value Anisotropy 3.624 4.1351 3.941 11.9462 Anisotropy Axis 0.46860.46860.7489 1.00000.00000.0000 1.00000.00000.0000 0.00000.00001.0000 0.00000.00001.0000 0.70710.70710.0000 0.00000.00001.0000 0.77920.00020.6267 Axis -0.17360.9848-0.0000 -0.70710.70710.0000 0.17360.9848-0.0000 0.62670.0003-0.7792 Second axis\n\n## Spatial dependence of Young's modulus\n\nYoung's modulus in (xy) plane\n\nYoung's modulus in (xz) plane\n\nYoung's modulus in (yz) plane\n\n## Spatial dependence of linear compressibility\n\nlinear compressibility in (xy) plane\n\nlinear compressibility in (xz) plane\n\nlinear compressibility in (yz) plane\n\n## Spatial dependence of shear modulus\n\nShear modulus in (xy) plane\n\nShear modulus in (xz) plane\n\nShear modulus in (yz) plane\n\n## Spatial dependence of Poisson's ratio\n\nPoisson's ratio in (xy) plane\n\nPoisson's ratio in (xz) plane\n\nPoisson's ratio in (yz) plane" ]
[ null ]
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https://www.mapleprimes.com/questions/233729-Determine-Zeros-Indifference-Curve
[ "# Question:Determine zeros, indifference curve of two levels, numerical approximation\n\n## Question:Determine zeros, indifference curve of two levels, numerical approximation\n\nMaple\n\nDear community,\n\nI'm a taxation student and trying to figure out maple more or less successfully for a research project... My aim is to find the indifference curve of the two levels S_TEV and S_P. As its probably not easy to find the formula, I'd alternatively like to approach the indifference curve numerically.\n\nThese are the basis codes:\n\nE := 'E'\nh := 4\nm := 0.035\ng:= h*m\nk := 0.15\na := 0.25;\nF_ANR := 4*m;\nr:= 0.1;\nT := 'T';\nESt := piecewise\n(E < 9984, 0,\nE < 14926, (1008.7*(E - 9984)/10000 + 1400)*(E - 9984)/10000,\nE < 58596, (206.43*(E - 14926)/10000 + 2397)*(E - 14926)/10000 + 938.24,\nE < 277826, 0.42*E - 9267.53,\n0.45*E - 17602.28);\n\nEr := E + (E - ESt)*r\n\nEStr := piecewise(Er < 9984, 0,\nEr < 14926, (1008.7*(Er - 9984)/10000 + 1400)*(Er - 9984)/10000,\nEr < 58596, (206.43*(Er - 14926)/10000 + 2397)*(Er - 14926)/10000 + 938.24,\nEr < 277826, 0.42*Er - 9267.53,\n0.45*Er - 17602.28)\n\nsrp := EStr/E\n\nr_p := r*srp\n\nS_P := ESt*(1 + r_p)^T\n\nEStk := piecewise(K < 9984, 0,\nK < 14926, (1008.7*(K - 9984)/10000 + 1400)*(K - 9984)/10000,\nK < 58596, (206.43*(K - 14926)/10000 + 2397)*(K - 14926)/10000 + 938.24,\nK < 277826, 0.42*K - 9267.53,\n0.45*K - 17602.28)\n\nr_tev := 0.29*r\n\nK := (0.71*E*(1 + 0.71*r)^T)*0.6\n\nstev := EStk/K\nS_TEV := E*(0.29*(1 + r_tev)^T + 0.71*(0.6*stev))\n\nplot3d([S_TEV/E, S_P/E], E = 0 .. 500000, T = 0 .. 15, color = [white, black])\n\nThe plot shows the two levels. Id like to derive the indiffernce curve from this plot (intersection of S_TEV and S_PE).\nStarting with probably Diff_S := S_TEV - S_P?\n\nCan someone please help me with finding the right codes? I'm lost.... (eg. solve function for S-TEV-S_P=0; finding the right data frame for Diff_S:=0 or almost zero dependent on E and T, i.e. dataframe of E, T and S_TEV and S_P) so that I can plot (3D) all S_TEV = S_P depending on E, T.\n\nId be incredibly thankful for any help. It would literally safe my thesis!\nThank you so so much in advance!!\nRebekka", null, "" ]
[ null, "https://www.mapleprimes.com/images/ajax-loader.gif", null ]
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https://studyhippo.com/test-answers/equations/
[ "### We've found 13 Equations tests\n\nBalanced Chemical Equation Equations Formulas Hydrogen And Oxygen\nChemistry Ch. 11 Key Concepts (Prentice Hall) – Flashcards 23 terms", null, "Lewis Gardner\n23 terms\nEquations\nEvaluating Expressions, Writing Expressions, Exponents, Evaluating Expressions – Flashcards 20 terms", null, "Jacoby Flores\n20 terms\nEquations Form Writing\nWriting chemical equations – Flashcards 30 terms", null, "Oscar Hall\n30 terms\nCriminology Eating Equations Foods Transportation\nWriting Two-Step Inequality Word Problems – Flashcards 11 terms", null, "Sean Hill\n11 terms\nAlgebra 1 Equations Functions Growth Integers Years\nCollege Algebra Chapter 4 – Flashcards 58 terms", null, "Rosa Sloan\n58 terms\nDistance Between Two Points Equations Graphs Physics Traveling\nPH 201 – General Physics I Final Exam Review – Flashcards 45 terms", null, "Alexandra Robertson\n45 terms\nCalculus Equations\nCalculus 2 Final Exam Review – Flashcards 43 terms", null, "Kieran Carr\n43 terms\nAlgebra 1 Algebra 2 Equations\nAlgebra 2/Trigonometry Regents Review – Flashcards 41 terms", null, "Alexandra Robertson\n41 terms\nEquations\nTrigonometry Final Study Guide – Flashcards 35 terms", null, "Kevin Stewart\n35 terms\nEarth Science Equations Music Scientific Method Scientists\nEarth Science T1 – Flashcards 52 terms", null, "Daniel Jimmerson\n52 terms\nEquations Jobs Lines\nProduction & Operations Management Final Exam Flashcards: Chapter 4 16 terms", null, "Suzette Hendon\n16 terms\nAlgebra 2 Equations\ncollege mathematics one finals 34 terms", null, "Misty Porter\n34 terms\nAlgebra 1 Equations Excel Graphs\nCollege Pre-Algebra & College Algebra 10 terms", null, "William Hopper\n10 terms\n9. What is the role of equations in this book?", null, "The equations are guides to thinking that show the connections between concepts in nature.\n9.15: (a) What is the difference between a molecular equation and an ionic equation? (b) Between an ionic equation and a net ionic equation? (c) What is the advantage of writing net ionic equations?", null, "(a) Molecular Equation: All compounds represented by chemical formulas Ionic Equation: Compounds represented by their ions (b) Ionic Equation: All ions represented Net Ionic Equation: Only active ions represented (no spectator ions in equation) (c) With Net Ionic Equations, you are able to isolate the action of the reaction.\nState the Law which Antoine Lavoisier made which guides the balancing of chemical equations?", null, "The Law of the conservation of mass states ” Matter can neither be gained or lost, only changed”.\nwhat theory allows us to derive certain equations regarding the motion of indivudal gas particles?", null, "kinetic-molecular theory, KMT\nOutline the conditions under which the equations for uniformly accelerated motion may be applied.", null, "Needs to have constant acceleration, neglecting retarding forces such as air resistance and frictions. IN LINEAR MOTION\n7. Be able to calculate the change in Gibbs free energy for a reaction and predict whether the reaction is spontaneous under specified conditions. whats are the gibbs equations", null, "S is positive G is negative H- negative , G= g(knot) + RT ln(k) R=8.314 j/k x mol g(knot)= -rt ln keq keq= e ^ – g(knot) /RT\nWhat do parentheses do in mathematical equations?", null, "Ensure that whatever operation is inside the parentheses is performed first\nthe world equation magnesium reacts with chlorine to produce magnesium chloride would be best represented by which of the following formula equations", null, "what do chemical equations show?", null, "what is the purpose of sulfuric acid or phosphoric acid used in the acetylation reaction> use equations to help explain this purpouse", null, "" ]
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https://www.tutorialspoint.com/python-program-to-cyclically-rotate-an-array-by-one
[ "# Python program to cyclically rotate an array by one\n\nPythonProgrammingServer Side Programming\n\nGiven a user input array. Our task is to rotate cyclically means clockwise rotate the value.\n\n## Example\n\nInput: A=[1,2,3,4,5]\nOutput=[5,1,2,3,4]\n\n\n## Algorithm\n\nStep 1: input array element.\nStep 2: Store the last element in a variable say x.\nStep 3: Shift all elements one position ahead.\nStep 4: Replace first element of array with x.\n\n\n## Example Code\n\n# Python program to cyclically rotate\n#an array by one\n# Method for rotation\ndef rotate(A, n):\nx = A[n - 1]\nfor i in range(n - 1, 0, -1):\nA[i] = A[i - 1];\nA = x;\n# Driver function\nA=list()\nn=int(input(\"Enter the size of the List ::\"))\nprint(\"Enter the Element of List ::\")\nfor i in range(int(n)):\nk=int(input(\"\"))\nA.append(k)\nprint (\"The array is ::>\")\nfor i in range(0, n):\nprint (A[i], end = ' ')\nrotate(A, n)\nprint (\"\\nRotated array is\")\nfor i in range(0, n):\nprint (A[i], end = ' ')\n\n\n## Output\n\nEnter the size of the List ::5\nEnter the Element of List ::\n8\n7\n90\n67\n56\nThe array is ::>\n8 7 90 67 56\nRotated array is\n56 8 7 90 67" ]
[ null ]
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https://miprofe.com/en/multiplication-of-rational-expressions/
[ "# Multiplication of rational expressions\n\nLet p (x) and q (x) be two polynomials, with q (x) ≠ 0, then the quotient p (x) / q (x) will be called  rational expression or algebraic expression. Now let p (x) / q (x) and r (x) / s (x) be two rational expressions with q (x) ≠ 0 and s (x) ≠ 0, then:\n\n[p (x) / q (x)] × [r (x) / s (x)] = p (x) ∙ s (x) / q (x) ∙ (r (x)\n\nIn general, to multiply rational expressions, we recommend following these steps:\n\n## Steps to multiply rational expressions\n\n1. Having two terms in the form of a fraction, numerator by numerator and denominator by denominator are multiplied.\n2. The numerator and denominator are factored.\n3. The expression is simplified.", null, "Example 1: Solve the following multiplication of rational expression: [(x + 3) / 2x] × [5x² / (x + 2)].\n\nWe multiply the numerators of both expressions, we do the same with the denominators:\n\n[(x + 3) / 2x] × [5x² / (x + 2)] = [5x² (x + 3)] / [(2x) (x + 2)] =\n\nWe simplify:\n\n= [5x (x + 3)] / [2 (x + 2)]\n\nFinal score:\n\n[(x + 3) / 2x] × [5x² / (x + 2)] = [5x (x + 3)] / [2 (x + 2)]\n\nExample 2: Solve the following multiplication of rational expression:\n\n[(y² - 4) / (y² + 5x + 4)] × [(y² + 2y - 8) / (y² - 4y + 4)].\n\n[(y² - 4) / (y² + 5x + 4)] × [(y² + 2y - 8) / (y² - 4y + 4)] = [(y² - 4) [(y² + 2y - 8) / ( y² + 5x + 4) (y² - 4y + 4)] =\n\nWe factor:\n\n= [(y + 2) (y - 2) (y + 4) (y - 2)] / [(y + 1) (y + 4) (y - 2) (y - 2)] =\n\nWe simplify the previous expression:\n\n= (y + 2) / (y + 1)\n\nFinal score:\n\n[(y² - 4) / (y² + 5x + 4)] × [(y² + 2y - 8) / (y² - 4y + 4)] = (y + 2) / (y + 1)" ]
[ null, "data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20437%20116'%3E%3C/svg%3E", null ]
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https://www.arxiv-vanity.com/papers/cond-mat/9208023/
[ "April 5, 2021\n\nSelf-Consistent Theory of Polymerized Membranes\n\nPierre Le Doussal\n\nInstitute for Advanced Study, Princeton NJ 08540 USA\n\nand\n\nLyman Laboratory, Harvard University, Cambridge MA 02138 USA\n\nAbstract\n\nWe study -dimensional polymerized membranes embedded in dimensions using a self-consistent screening approximation. It is exact for large to order , for any to order and for . For flat physical membranes () it predicts a roughness exponent . For phantom membranes at the crumpling transition the size exponent is . It yields identical lower critical dimension for the flat phase and crumpling transition ( for codimension 1). For physical membranes with quenched curvature in the new flat phase in good agreement with simulations.\n\nPACS: 64.60Fr,05.40,82.65Dp\n\nThere are now several experimental realizations of polymerized or solid-like membranes, such as protein networks of biological membranes, polymerized lipid bilayers and some inorganic surfaces. Unlike linear polymers, two dimensional sheets of molecules with fixed connectivity and non zero shear modulus are predicted to exhibit a flat phase with broken orientational symmetry. Out of plane thermal undulations of solid membranes which induce a non-zero local Gaussian curvature are strongly suppressed because they are accompanied by in-plane shear deformations. As a result, even ”phantom” tethered membranes should be flat at low temperatures, and exhibit a quite remarkable anomalous elasticity, with wavevector dependent elastic moduli that vanish and a bending rigidity that diverges at long wavelength. Excluded volume interactions, present in physical membranes, further stabilize the flat phase but are usually assumed to be otherwise irrelevant to describe its long distance properties. Motivated by recent experiments on partially polymerized vesicles, studies of models with quenched in-plane disorder have shown that the flat phase is unstable at T=0 to either local random stresses or random spontaneous curvature.\n\nFlat membranes of internal dimensionality D and linear size L are characterized by a roughness exponent such that transverse displacements scale as . Nelson and Peliti (NP), using a simple one loop self-consistent theory for which assumes non-vanishing elastic constants, found that phonon-mediated interactions between capillary waves lead to a renormalized bending rigidity with . Since they predicted for physical membranes. An expansion confirmed that the flat phase was described by a non trivial fixed point, but with anomalous elastic constants , , with as a consequence of rotational invariance. Thus, in general and the NP approximation corresponds to setting .\n\nThere is presently some uncertainty on the precise value of the roughness exponent for physical membranes. Numerical simulations of tethered surfaces display a range of values for from 0.5, 0.53, 0.64 to 0.70. On the other hand, the result suggests a value very close to the NP value , ( 0.52 by naively setting ). should soon be measured from experiments, either directly from light scattering on diluted solutions or indirectly, from the scale dependence of the elasticity of lamellar stacks of solid membranes presently under experimental study. The buckling transition, if observed, is controlled by a single exponent related to . It thus seems desirable to explore further possible theoretical predictions for .\n\nIn this Letter we introduce a self-consistent approximation which improves on the Nelson Peliti theory by allowing a non trivial renormalization of the elastic moduli. It is exact in three different limits and compares well with numerical simulations. We construct two coupled self-consistent equations for the renormalized bending rigidity and elastic moduli and solve them in the long wavelength limit. is determined by the propagator for the components of the out of plane fluctuations while the elastic moduli are determined by the four-point correlation function of fields. Physically, our calculation includes the additional effect of relaxation of in-plane stresses by out of plane displacements. As a result, curvature fluctuations soften elastic constants and screen the phonon-mediated interaction. A similar Self-Consistent Screening Approximation (SCSA) was introduced by Bray to estimate the exponent of the critical model (here plays the role of the number of components ) and amounts to a partial resummation of the expansion. By construction, the method is exact for large codimension to first order in and arbitrary . Solving self-consistently then leads to an improved approximation of (and thus ) for the small (physical) values of .\n\nThe attractive feature of our theory is that it becomes exact in several other limits. Firstly, because of the Ward identities associated to rotational invariance we find that is exact to first order in for arbitrary and is thus compatible with all presently known results. Secondly, for it gives which is the exact result since clearly for , and . This is at variance with the model for which the SCSA is not exact for . Thus we expect this method to give more accurate results for the present problem. Two-loop calculations are in progress to estimate the deviation. An encouraging indication is the similarity of our method with the remarkably accurate self-consistent approximation of Kawasaki for the critical dynamics of the binary fluid mixture, which was shown to be exact to order , again because of Ward identities, and incorrect to order by a tiny amount. We also apply this method to the crumpling transition of phantom membranes, and to flat membranes with quenched disorder. Details can be found in Ref.16.\n\nIn the flat phase, the membrane in-plane and out-of plane displacements are parametrized respectively by a D-component phonon field , , and a component out-of plane height fluctuations field . A monomer of internal coordinate is at position where the are a set of D orthonormal vectors. The effective free energy is the sum of a bending energy and an in plane elastic energy (most relevant terms):\n\n F=∫dDx[κ2(∇2h)2+μu2αβ+λ2u2αα]\n\nwhere the strain tensor is To discuss the SCSA in the flat phase it is convenient to first integrate out the phonons, and to work with the -component field. In terms of Fourier components the free energy takes the form of a critical theory:\n\n Feff=κ2∫dkk4∣h(k)∣2+14dc∫dk1dk2dk3Rαβ,γδ(q) k1αk2βk3γk4δ h(k1).h(k2) h(k3).h(k4)\n\nwith and and we use to denote . The four-point coupling fourth-order tensor is transverse to , the longitudinal part having been eliminated through phonon integration. It can be written as with:\n\n Nαβ,γδ=1D−1PTαβPTγδ  ,  Mαβ,γδ=12(PTαγPTβδ+PTαδPTβγ)−Nαβ,γδ\n\nwhere is the transverse projector. is the shear modulus and is proportional to both shear and bulk moduli. The convenience of this decomposition is that and are mutually orthogonal projectors under tensor multiplication (e.g etc…).\n\nWe set up two coupled integral equations for the propagator of the field and for the renormalized four point interaction. We want to evaluate with where is the self energy. The SCSA is defined in diagrammatic form by the graphs of Fig. 1a and 1b, where the double solid line denotes the dressed propagator , the dotted line the bare interaction and the wiggly line the ”screened” interaction dressed by the vacuum polarization bubbles. We thus obtain two equations, one for which determines , the other for which determines :\n\n σ(k)=2dckαkβkγkδ∫dq~Rαβ,γδ(q)G(k−q)\n ~R(q)=R(q)−R(q)Π(q)~R(q)\n\nwhere is the vacuum polarization and tensor multiplication is defined above. Because of the transverse projectors, only the component of proportional to the fully symmetric tensor contributes in (4b). Defining , simple algebra gives with renormalized shear and shear-bulk moduli, and the new equations:\n\n ~μ(q)=μ1+2I(q)μ   ~b(q)=b1+(D+1)I(q)b\n σ(k)=2dc∫dq~b(q)+(D−2)~μ(q)D−1(kPT(q)k)2G(k−q)\n\nWe now solve these equations in the long-wavelength limit. Substituting in (5a,b), with a non-universal amplitude, we find that the vacuum polarization integral diverges as:\n\n I(q)∼Z2A(D,η)q−ηu\n\nwhere is the anomalous exponent of phonons. Substituting in (5a,b), and defining the amplitude: , one finds (for ) that the and factors cancel and that is determined self-consistently by the equation for the : , which after calculation of the integrals defining A,B gives:\n\n dc=2ηD(D−1)Γ[1+12η]Γ[2−η]Γ[η+D]Γ[2−12η]Γ[12D+12η]Γ[2−η−12D]Γ[η+12D]Γ[12D+2−12η]\n\nFor this equation can be simplified, and one finds (Fig. 2):\n\n η(D=2,dc)=4dc+√16−2dc+d2c\n\nThus for physical membranes we obtain: , and:\n\n ζ=1−η2=√15−1√15+1=0.590..\n\nroughly at midvalue of the present numerical simulations. From (5) we also obtain (i.e a negative Poisson ratio).\n\nExpanding the result (7) in one obtains:\n\n η=8dcD−1D+2Γ[D]Γ[D2]3Γ[2−D2]+O(1d2c)=2dc+O(1d2c)    (forD=2)\n\nwhich coincides with the exact result, as expected by construction of the SCSA. Similarly, expanding (7) to first order in one finds:\n\n η=ϵ2+dc/12\n\nalso in agreement with the exact result. This is not a general property of SCSA. Here it can be traced to the vertex and box diagrams of Fig. 1c being convergent. Indeed, because of the transverse projectors in (2-3) one can always extract one power of external momentum from each external legs, which lowers the degree of divergence from naive power counting. As a result, if one decouples the 4-point vertex via a mediating field, the only counterterms needed are for two-point functions.\n\nWe have analyzed the crumpling transition of phantom membranes by the same method, applied to the isotropic theory of Ref.18. The exponent at the transition is determined by:\n\n d=D(D+1)(D−4+η)(D−4+2η)(2D−3+2η)Γ[12η]Γ[2−η]Γ[η+D]Γ[2−12η]2(2−η)(5−D−2η)(D+η−1)Γ[12D+12η]Γ[2−η−12D]Γ[η+12D]Γ[12D+2−12η]\n\nAt the transition the radius of gyration scales as with . For and we find and (Haussdorf dimension ). The embedding dimension above which self-avoidance is for the membrane the crumpling transition is determined by the condition . Using (12) we find that .\n\nThe present method gives interesting predictions for lower critical dimensions. In the flat phase, orientational order (i.e in ) disappears for , where . From (7) this is equivalent to . On the other hand, the lower critical dimension for the crumpling transition is defined by , or equivalently from (12), . Since is clearly equivalent to we find that the lower critical dimensions of the crumpling transition and of the flat phase, as predicted by SCSA, are identical, and given by . Since they originate from very different calculations, this indicates that the SCSA is quite consistent. For codimension 1 manifolds and for fixed embedding space , . increases from for , to when as expected. Note that for self-avoidance cannot modify the above results, while for it is an open question.\n\nWe can compare (8,12) with recent simulations of membranes with self-avoidance in higher . The membranes are found flat in with , , whereas we obtain , , respectively. The membrane is crumpled in with , although seems almost marginal, whereas we find at the crumpling transition where self avoidance is irrelevant, although almost marginally so.\n\nFlat membranes with random spontaneous curvature are described by adding the term in the energy (1), where c(x) are Gaussian quenched random variables. Within a replica symmetric SCSA, we find a marginally unstable fixed point, i.e a long-wavelength solution only if first. Defining the replica connected and off-diagonal exponents , , by , we find at this fixed point: , . Thus one can simply replace in the pure result by ! Again this agrees with the and expansions. For physical membranes , , we find from (8) :\n\n η=2/(2+√6)=0.449   ζ=0.775\n\ncomparing well with the numerical simulation result . By analogy with the random field problem, it is quite possible that the equality , conjectured in Ref. 10 to all orders, be corrected when replica-symmetry breaking is included.\n\nIn conclusion, we have presented a self-consistent theory of polymerized membranes which becomes exact in three limits (large , small , and ). By construction, it satisfies the exponent relations and . These relations are exact in the true theory because of rotational invariance . It thus predicts and for the buckling transition exponents. It contradicts the conjecture .\n\nWe thank D. Nelson, M. Mezard for discussions. PLD acknowledge support from NSF grant DMS-9100383 and LR from the Hertz Graduate Fellowship.\n\nReferences\n\n*Also LPTENS, Ecole Normale Superieure, 24 rue Lhomond, Paris 75231 Cedex 05, Laboratoire Propre du CNRS.\n\n1. See, e.g, Statistical Mechanics of Membranes and Interfaces, edited by D.R. Nelson, T. Piran, S. Weinberg ( World Scientific, Singapore 1988 ), and S. Leibler in Proceedings of the Cargese school on biologically inspired physics, (1990), to be published.\n\n2. R. Lipowsky and M. Girardet, Phys. Rev. Lett. 2893 (1990).\n\n3. M. Mutz, D. Bensimon, M.J. Brienne, Phys. Rev. Lett. 923 (1991).\n\n4. X. Wen et al. Nature 355, 426 (1992)\n\n5. D. R. Nelson and L. Peliti, J. Phys. (Paris) , 1085 (1987).\n\n6. F. David and E. Guitter, Europhys. Lett. , 709 (1988). E. Guitter, F. David, S. Leibler and L. Peliti, J. Phys. France 1787 (1989).\n\n7. J.A. Aronovitz and T.C. Lubensky, Phys. Rev. Lett. , 2634 (1988), J.A. Aronovitz, L. Golubovic, T.C. Lubensky, J. Phys. France 50 609 (1989).\n\n8. F.F. Abraham, D.R. Nelson, J. Phys. France 2653 (1990). F.F. Abraham, W.E. Rudge and M. Plishke, Phys. Rev. Lett. , 1757 (1989).\n\n9. D.R. Nelson, L. Radzihovsky, Europhys. Lett. , 79 (1991), L. Radzihovsky, P. Le Doussal, J. Phys. I France , 599 (1992).\n\n10. D.C. Morse, T.C. Lubensky, G.S. Grest, Phys. Rev A R2151 (1992). Morse Lubensky, Preprint 1992.\n\n11. F. Abrahams, Phys. Rev. Lett. , 1669 (1991).\n\n12. S. Leibler and A. Maggs, Phys. Rev. Lett. , 406 (1989).\n\n13. G. Gompper and D.M. Kroll, J. Phys. I France , 663 (1992). (1992).\n\n14. J. Toner, Phys. Rev. Lett. 64 1741 (1990).\n\n15. A.J. Bray, Phys. Rev. Lett. , 1413 (1974).\n\n16. P. Le Doussal, L. Radzihovsky, to be published.\n\n17. E.D. Siggia, B.I. Halperin and P.C. Hohenberg, Phys. Rev. B 13 2110 (1976).\n\n18. M. Paczuski, M. Kardar and D.R. Nelson, Phys. Rev. Lett. , 2638 (1988).\n\n19. G. Grest, J. Phys. I France 1,1695 (1991).\n\n20. M. Mezard, A.P. Young, Preprint LPTENS 92/2\n\nFIGURE CAPTIONS\n\nFigure 1\n\n: graphical representation of the SCSA: (a) self energy, (b) interaction. (c) UV finite vertex and box diagrams.\n\nFigure 2\n\n: as a function of for two-dimensional membranes . Solid curve: SCSA result (8). Dashed dotted curve: result, setting . Dashed curve: corresponds to chosen (somewhat arbitrarily) in Ref. 6 as a possible interpolation to finite (asymptotic to the solid curve for )." ]
[ null ]
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https://fr.mathworks.com/matlabcentral/cody/problems/42660-the-number-of-inputs/solutions/1209499
[ "Cody\n\n# Problem 42660. the number of inputs\n\nSolution 1209499\n\nSubmitted on 10 Jun 2017 by Said BOUREZG\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\nx=1; y_correct = 1; assert(isequal(theinputnumber(x),y_correct))\n\nans = 1\n\n2   Pass\nx=1; k=3 y_correct = 2; assert(isequal(theinputnumber(x,k),y_correct))\n\nk = 3 ans = 2\n\n3   Pass\nx=1; k=3; z=4; y_correct = 3; assert(isequal(theinputnumber(x,k,z),y_correct))\n\nans = 3\n\n4   Pass\nx=1; k=3; z=4; f=10 y_correct = 4; assert(isequal(theinputnumber(x,k,z,f),y_correct))\n\nf = 10 ans = 4" ]
[ null ]
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https://tex.stackexchange.com/questions/381011/tikz-grids-there-are-not-connected/381014#381014
[ "Tikz - grids there are not connected\n\nI have a problem regarding making a lots of grid i tikz.\n\nmy code is as follows:\n\n\\begin{tikzpicture}\n\\path[use as bounding box,draw] (12,18) rectangle (0,0);\n\n\\foreach \\x in {0,2,4,8}\n\\draw[black] (0.999+\\x,17) grid[step=0.2] (2+\\x,15.999);\n\n\\draw[->] (3.5,15.5) -- (3.5,13);\n\\draw[->] (9.5,15.5) -- (9.5,13);\n\n\\foreach \\x in {2,4,6,8}\n\\draw[black] (0.999+\\x,12) grid[step=0.2] (2+\\x,10.999);\n\n\\draw[->] (6.5,10) -- (6.5,9);\n\n\\draw[black] (5.999,8.100) grid[step=0.2] (7,7.099) node {};\n\\end{tikzpicture}", null, "One can clearly see that the grid in the third row are not drawn corretly.\n\nHope that any of your can help.\n\n• Welcome to TeX.SX! Please make your code compilable by adding documentclass and required packages. Jul 17 '17 at 15:08\n• I guess that instead of \\draw[black] (5.999,8.100) grid[step=0.2] (7,7.099) node {}; should be \\draw[black] (5.999,8.100) grid[step=0.2] (7,6.99) node {}; Jul 17 '17 at 15:17\n• What's the point of the node {}?\n– cfr\nJul 17 '17 at 15:18\n\nIf you define your grid as small picture pic than you can rewrite your MWE as:\n\n\\documentclass[tikz, margin=3mm]{standalone}\n\n\\begin{document}\n\\begin{tikzpicture}[\nGRID/.pic={\\draw (0,0) grid[step=0.2] (1,1);}\n]\n\\path[use as bounding box,draw] (12,18) rectangle (0,0);\n\n\\foreach \\x in {1,3,5,9}\n\\pic at (\\x,16) {GRID};\n\\draw[->] (3.5,15.5) -- (3.5,13);\n\\draw[->] (9.5,15.5) -- (9.5,13);\n%\\fill[red] (1,16) circle (1mm);% for test of pic coordinate\n\n\\foreach \\x in {3,5,7,9}\n\\pic at (\\x,11.5) {GRID};\n\\draw[->] (6.5,11) -- (6.5,9);\n\n\\pic at (6,7.5) {GRID};\n\\end{tikzpicture}\n\\end{document}", null, "(image not contain bounding box).\n\nGrids are shifted so that they always meet at the current origin. The trick is to shift the origin with the shift key:\n\n\\documentclass[tikz,border=5]{standalone}\n\\begin{document}\n\\begin{tikzpicture}\n\\draw [red] (0,0) grid +(4,4);\n\\draw [green, dashed] (0.5,0.5) grid +(4,4);\n\\draw [blue, dotted, shift={(0.5,0.5)}] (0,0) grid +(4,4);\n\\end{tikzpicture}\n\\end{document}", null, "" ]
[ null, "https://i.stack.imgur.com/RY3GC.png", null, "https://i.stack.imgur.com/V9ggn.png", null, "https://i.stack.imgur.com/Og2B0.png", null ]
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https://git.blender.org/gitweb/gitweb.cgi/blender-addons-contrib.git/blobdiff/12242ff50ab5e7ef7edbcdbc5dc181167b57d7d9..60bf224aea6759cf2659bfd03cd1741b035c0eef:/mesh_edgetools.py
[ "index 8223d9c8b0400b0f1fe09248563984ce3cbf4a23..e3bc3a3b6280d60ea02a03e4fdd8c515a5b72638 100644 (file)\n#       functionality, though it will sadly be a little clumsier to use due\n#       to Blender's selection limitations.\n#\n-# Tasks:\n-#   - Figure out how to do a GUI for \"Shaft\", especially for controlling radius.\n+# Notes:\n+#   - Buggy parts have been hidden behind bpy.app.debug.  Run Blender in debug\n+#       to expose those.  Example: Shaft with more than two edges selected.\n+#   - Some functions have started to crash, despite working correctly before.\n+#       What could be causing that?  Blender bug?  Or coding bug?\n#\n# Paul \"BrikBot\" Marshall\n# Created: January 28, 2012\n-# Last Modified: May 11, 2012\n+# Last Modified: October 6, 2012\n# Homepage (blog): http://post.darkarsenic.com/\n#                       //blog.darkarsenic.com/\n#\n-# Coded in IDLE, tested in Blender 2.63.\n+# Coded in IDLE, tested in Blender 2.6.\n# Search for \"@todo\" to quickly find sections that need work.\n#\n# Remeber -\n# ^^ Maybe. . . . :P\n\nbl_info = {\n-    'name': \"EdgeTools\",\n-    'author': \"Paul Marshall\",\n-    'version': (0, 8),\n-    'blender': (2, 6, 3),\n-    'location': \"View3D > Toolbar and View3D > Specials (W-key)\",\n-    'warning': \"\",\n-    'description': \"CAD style edge manipulation tools\",\n-    'wiki_url': \"http://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/EdgeTools\",\n-    'tracker_url': \"https://blenderpython.svn.sourceforge.net/svnroot/blenderpython/scripts_library/scripts/addons_extern/mesh_edgetools.py\",\n-    'category': 'Mesh'}\n+    \"name\": \"EdgeTools\",\n+    \"author\": \"Paul Marshall\",\n+    \"version\": (0, 8),\n+    \"blender\": (2, 68, 0),\n+    \"location\": \"View3D > Toolbar and View3D > Specials (W-key)\",\n+    \"warning\": \"\",\n+    \"description\": \"CAD style edge manipulation tools\",\n+    \"wiki_url\": \"http://wiki.blender.org/index.php/Extensions:2.6/Py/\"\n+        \"Scripts/Modeling/EdgeTools\",\n+    \"tracker_url\": \"\",\n+    \"category\": \"Mesh\"}\n+\n\nimport bpy, bmesh, mathutils\n-from math import pi, radians, sin, sqrt, tan\n+from math import acos, pi, radians, sqrt, tan\nfrom mathutils import Matrix, Vector\nfrom mathutils.geometry import (distance_point_to_plane,\ninterpolate_bezier,\n@@ -91,6 +96,8 @@ from bpy.props import (BoolProperty,\nFloatProperty,\nEnumProperty)\n\n+integrated = False\n+\n# Quick an dirty method for getting the sign of a number:\ndef sign(number):\nreturn (number > 0) - (number < 0)\n@@ -100,7 +107,7 @@ def sign(number):\n#\n# Checks to see if two lines are parallel\ndef is_parallel(v1, v2, v3, v4):\n-    result = intersect_line_line(v1, v2, v3, v4)\n+    result = intersect_line_line(v1, v2, v3, v4)\nreturn result == None\n\n@@ -136,6 +143,19 @@ def is_same_co(v1, v2):\nreturn True\n\n+# is_face_planar\n+#\n+# Tests a face to see if it is planar.\n+def is_face_planar(face, error = 0.0005):\n+    for v in face.verts:\n+        d = distance_point_to_plane(v.co, face.verts.co, face.normal)\n+        if bpy.app.debug:\n+            print(\"Distance: \" + str(d))\n+        if d < -error or d > error:\n+            return False\n+    return True\n+\n+\n# other_joined_edges\n#\n# Starts with an edge.  Then scans for linked, selected edges and builds a\n@@ -145,10 +165,14 @@ def order_joined_edges(edge, edges = [], direction = 1):\nedges.append(edge)\nedges = edge\n\n-##    if bpy.app.debug:\n-##        print(edge, end = \", \")\n-##        print(edges, end = \", \")\n-##        print(direction, end = \"; \")\n+    if bpy.app.debug:\n+        print(edge, end = \", \")\n+        print(edges, end = \", \")\n+        print(direction, end = \"; \")\n+\n+    # Robustness check: direction cannot be zero\n+    if direction == 0:\n+        direction = 1\n\nnewList = []\nfor e in edge.verts.link_edges:\n@@ -163,7 +187,7 @@ def order_joined_edges(edge, edges = [], direction = 1):\nnewList.extend(order_joined_edges(e, edges, direction - 1))\n\n# This will only matter at the first level:\n-    direction = direction 1\n+    direction = direction * -1\n\nfor e in edge.verts.link_edges:\nif e.select and edges.count(e) == 0:\n@@ -176,9 +200,9 @@ def order_joined_edges(edge, edges = [], direction = 1):\nnewList.extend(edges)\nnewList.extend(order_joined_edges(e, edges, direction))\n\n-##    if bpy.app.debug:\n-##        print(newList, end = \", \")\n-##        print(direction)\n+    if bpy.app.debug:\n+        print(newList, end = \", \")\n+        print(direction)\n\nreturn newList\n\n@@ -266,7 +290,7 @@ def interpolate_line_line(p1_co, p1_dir, p2_co, p2_dir, segments, tension = 1,\n# A quad may not be planar.  Therefore the treated definition of the surface is\n# that the surface is composed of all lines bridging two other lines defined by\n# the given four points.  The lines do not \"cross\".\n-#\n+#\n# The two lines in 3-space can defined as:\n#   ┌  ┐         ┌   ┐     ┌   ┐  ┌  ┐         ┌   ┐     ┌   ┐\n#   │x1│         │a11│     │b11│  │x2│         │a21│     │b21│\n@@ -303,12 +327,33 @@ def interpolate_line_line(p1_co, p1_dir, p2_co, p2_dir, segments, tension = 1,\n# http://www.mediafire.com/file/0egbr5ahg14talm/intersect_line_surface2.nb for\n# Mathematica computation).\n#\n+# Additionally, the resulting series of equations may result in a div by zero\n+# exception if the line in question if parallel to one of the axis or if the\n+# quad is planar and parallel to either the XY, XZ, or YZ planes.  However, the\n+# system is still solvable but must be dealt with a little differently to avaid\n+# these special cases.  Because the resulting equations are a little different,\n+# we have to code them differently.  Hence the special cases.\n+#\n# Tri math and theory:\n# A triangle must be planar (three points define a plane).  Therefore we just\n# have to make sure that the line intersects inside the triangle.\n-def intersect_line_face(edge, face):\n-    # If we are dealing with a quad:\n-    if len(face.verts) == 4:\n+#\n+# If the point is within the triangle, then the angle between the lines that\n+# connect the point to the each individual point of the triangle will be\n+# equal to 2 * PI.  Otherwise, if the point is outside the triangle, then the\n+# sum of the angles will be less.\n+#\n+# @todo\n+#   - Figure out how to deal with n-gons.  How the heck is a face with 8 verts\n+#       definied mathematically?  How do I then find the intersection point of\n+#       a line with said vert?  How do I know if that point is \"inside\" all the\n+#       verts?  I have no clue, and haven't been able to find anything on it so\n+#       far.  Maybe if someone (actually reads this and) who knows could note?\n+def intersect_line_face(edge, face, is_infinite = False, error = 0.000002):\n+    int_co = None\n+\n+    # If we are dealing with a non-planar quad:\n+    if len(face.verts) == 4 and not is_face_planar(face):\nedgeA = face.edges\nedgeB = None\nflipB = False\n@@ -338,7 +383,6 @@ def intersect_line_face(edge, face):\nelse:\na21, a22, a23 = edgeB.verts.co, edgeB.verts.co, edgeB.verts.co\nb21, b22, b23 = edgeB.verts.co, edgeB.verts.co, edgeB.verts.co\n-\na31, a32, a33 = edge.verts.co, edge.verts.co, edge.verts.co\nb31, b32, b33 = edge.verts.co, edge.verts.co, edge.verts.co\n\n@@ -405,7 +449,6 @@ def intersect_line_face(edge, face):\nm58 = a32 * b21 * b33\nm59 = a11 * b22 * b33\nm60 = a31 * b22 * b33\n-\nm61 = a33 * b12 * b21\nm62 = a32 * b13 * b21\nm63 = a33 * b11 * b22\n@@ -418,7 +461,6 @@ def intersect_line_face(edge, face):\nm70 = b11 * b23 * b32\nm71 = b12 * b21 * b33\nm72 = b11 * b22 * b33\n-\nn01 = m01 - m02 - m03 + m04 + m05 - m06\nn02 = -m07 + m08 + m09 - m10 - m11 + m12 + m13 - m14 - m15 + m16 + m17 - m18 - m25 + m27 + m29 - m31 + m39 - m41 - m43 + m45 - m53 + m55 + m57 - m59\nn03 = -m19 + m20 + m33 - m34 - m47 + m48\n@@ -430,25 +472,87 @@ def intersect_line_face(edge, face):\n\n# Calculate t, t12, and t3:\nt = (n07 - sqrt(pow(-n07, 2) - 4 * (n01 + n03 + n04) * n08)) / (2 * n08)\n+\n# t12 can be greatly simplified by defining it with t in it:\n-        t12 = -(-(a32 - b32) * (-a31 + a11 * (1 - t) + b11 * t) + (a31 - b31) * (-a32 + a12 * (1 - t) + b12 * t)) / (-(a32 - b32) * (-a11 * (1 - t) + a21 * (1 - t) - b11 * t + b21 * t) + (a31 - b31) * (-a12 * (1 - t) + a22 * (1 - t) - b12 * t + b22 * t))\n+        # If block used to help prevent any div by zero error.\n+        t12 = 0\n+\n+        if a31 == b31:\n+            # The line is parallel to the z-axis:\n+            if a32 == b32:\n+                t12 = ((a11 - a31) + (b11 - a11) * t) / ((a21 - a11) + (a11 - a21 - b11 + b21) * t)\n+            # The line is parallel to the y-axis:\n+            elif a33 == b33:\n+                t12 = ((a11 - a31) + (b11 - a11) * t) / ((a21 - a11) + (a11 - a21 - b11 + b21) * t)\n+            # The line is along the y/z-axis but is not parallel to either:\n+            else:\n+                t12 = -(-(a33 - b33) * (-a32 + a12 * (1 - t) + b12 * t) + (a32 - b32) * (-a33 + a13 * (1 - t) + b13 * t)) / (-(a33 - b33) * ((a22 - a12) * (1 - t) + (b22 - b12) * t) + (a32 - b32) * ((a23 - a13) * (1 - t) + (b23 - b13) * t))\n+        elif a32 == b32:\n+            # The line is parallel to the x-axis:\n+            if a33 == b33:\n+                t12 = ((a12 - a32) + (b12 - a12) * t) / ((a22 - a12) + (a12 - a22 - b12 + b22) * t)\n+            # The line is along the x/z-axis but is not parallel to either:\n+            else:\n+                t12 = -(-(a33 - b33) * (-a31 + a11 * (1 - t) + b11 * t) + (a31 - b31) * (-a33 + a13 * (1 - t) + b13 * t)) / (-(a33 - b33) * ((a21 - a11) * (1 - t) + (b21 - b11) * t) + (a31 - b31) * ((a23 - a13) * (1 - t) + (b23 - b13) * t))\n+        # The line is along the x/y-axis but is not parallel to either:\n+        else:\n+            t12 = -(-(a32 - b32) * (-a31 + a11 * (1 - t) + b11 * t) + (a31 - b31) * (-a32 + a12 * (1 - t) + b12 * t)) / (-(a32 - b32) * ((a21 - a11) * (1 - t) + (b21 - b11) * t) + (a31 - b31) * ((a22 - a21) * (1 - t) + (b22 - b12) * t))\n+\n# Likewise, t3 is greatly simplified by defining it in terms of t and t12:\n-        t3 = (-a11 + a31 + (a11 * t) - (b11 * t) + (a11 * t12) - (a21 * t12) - (a11 * t * t12) + (a21 * t * t12) + (b11 * t * t12) - (b21 * t * t12)) / (a31 - b31)\n+        # If block used to prevent a div by zero error.\n+        t3 = 0\n+        if a31 != b31:\n+            t3 = (-a11 + a31 + (a11 - b11) * t + (a11 - a21) * t12 + (a21 - a11 + b11 - b21) * t * t12) / (a31 - b31)\n+        elif a32 != b32:\n+            t3 = (-a12 + a32 + (a12 - b12) * t + (a12 - a22) * t12 + (a22 - a12 + b12 - b22) * t * t12) / (a32 - b32)\n+        elif a33 != b33:\n+            t3 = (-a13 + a33 + (a13 - b13) * t + (a13 - a23) * t12 + (a23 - a13 + b13 - b23) * t * t12) / (a33 - b33)\n+        else:\n+            print(\"The second edge is a zero-length edge\")\n+            return None\n\n# Calculate the point of intersection:\nx = (1 - t3) * a31 + t3 * b31\ny = (1 - t3) * a32 + t3 * b32\nz = (1 - t3) * a33 + t3 * b33\n+        int_co = Vector((x, y, z))\n\n-        int_co = [True, Vector((x, y, z))]\n+        if bpy.app.debug:\n+            print(int_co)\n\n# If the line does not intersect the quad, we return \"None\":\n-        if t < 0 or t > 1 or t12 < 0 or t12 > 1:\n-            int_co = False\n+        if (t < -1 or t > 1 or t12 < -1 or t12 > 1) and not is_infinite:\n+            int_co = None\n\n-        return int_co\nelif len(face.verts) == 3:\n-        return int_co\n+        p1, p2, p3 = face.verts.co, face.verts.co, face.verts.co\n+        int_co = intersect_line_plane(edge.verts.co, edge.verts.co, p1, face.normal)\n+\n+        # Only check if the triangle is not being treated as an infinite plane:\n+        # Math based from http://paulbourke.net/geometry/linefacet/\n+        if int_co != None and not is_infinite:\n+            pA = p1 - int_co\n+            pB = p2 - int_co\n+            pC = p3 - int_co\n+            # These must be unit vectors, else we risk a domain error:\n+            pA.length = 1\n+            pB.length = 1\n+            pC.length = 1\n+            aAB = acos(pA.dot(pB))\n+            aBC = acos(pB.dot(pC))\n+            aCA = acos(pC.dot(pA))\n+            sumA = aAB + aBC + aCA\n+\n+            # If the point is outside the triangle:\n+            if (sumA > (pi + error) and sumA < (pi - error)):\n+                int_co = None\n+\n+    # This is the default case where we either have a planar quad or an n-gon.\n+    else:\n+        int_co = intersect_line_plane(edge.verts.co, edge.verts.co,\n+                                      face.verts.co, face.normal)\n+\n+    return int_co\n\n# project_point_plane\n@@ -459,7 +563,7 @@ def project_point_plane(pt, plane_co, plane_no):\nproj_co = intersect_line_plane(pt, pt + plane_no, plane_co, plane_no)\nproj_ve = proj_co - pt\nreturn (proj_ve, proj_co)\n-\n+\n\n# ------------ FILLET/CHAMPHER HELPER METHODS -------------\n\n@@ -490,13 +594,19 @@ def is_planar_edge(edge, error = 0.000002):\nreturn (angle < error and angle > -error) or (angle < (180 + error) and angle > (180 - error))\n\n-# fillet_geom_data\n+# fillet_axis\n+#\n+# Calculates the base geometry data for the fillet. This assumes that the faces\n+# are planar:\n+#\n+# @todo\n+#   - Redesign so that the faces do not have to be planar\n#\n-# Calculates the base geometry data for the fillet.  The seems to be issues\n-# some of the vector math right now.  Will need to be debuged.\n+# There seems to be issues some of the vector math right now.  Will need to be\n+# debuged.\ndef fillet_axis(edge, radius):\nvectors = [None, None, None, None]\n-\n+\norigin = Vector((0, 0, 0))\naxis = edge.verts.co - edge.verts.co\n\n@@ -529,10 +639,10 @@ def fillet_axis(edge, radius):\n# Get the normal for face 0 and face 1:\nnorm1 = edge.link_faces.normal\nnorm2 = edge.link_faces.normal\n-\n+\n# We need to find the angle between the two faces, then bisect it:\ntheda = (pi - edge.calc_face_angle()) / 2\n-\n+\n# We are dealing with a triangle here, and we will need the length\n# of its adjacent side.  The opposite is the radius:\nadj_len = radius / tan(theda)\n@@ -545,13 +655,17 @@ def fillet_axis(edge, radius):\nvectors[i] = project_point_plane(vectors[i], origin, axis)\nvectors[i].length = adj_len\nvectors[i] = vectors[i] + edge.verts[i % 2].co\n-\n+\n# Compute fillet axis end points:\nv1 = intersect_line_line(vectors, vectors + norm1, vectors, vectors + norm2)\nv2 = intersect_line_line(vectors, vectors + norm1, vectors, vectors + norm2)\nreturn [v1, v2]\n\n+def fillet_point(t, face1, face2):\n+    return\n+\n+\n# ------------------- EDGE TOOL METHODS -------------------\n\n# Extends an \"edge\" in two directions:\n@@ -579,7 +693,7 @@ class Extend(bpy.types.Operator):\nlayout.prop(self, \"di1\")\nlayout.prop(self, \"di2\")\nlayout.prop(self, \"length\")\n-\n+\n\n@classmethod\ndef poll(cls, context):\n@@ -590,7 +704,7 @@ class Extend(bpy.types.Operator):\ndef invoke(self, context, event):\nreturn self.execute(context)\n\n-\n+\ndef execute(self, context):\nbpy.ops.object.editmode_toggle()\nbm = bmesh.new()\n@@ -607,7 +721,7 @@ class Extend(bpy.types.Operator):\nfor e in edges:\nvector = e.verts.co - e.verts.co\nvector.length = self.length\n-\n+\nif self.di1:\nv = bVerts.new()\nif (vector + vector + vector) < 0:\n@@ -662,7 +776,7 @@ class Spline(bpy.types.Operator):\nbl_label = \"Spline\"\nbl_description = \"Create a spline interplopation between two edges\"\nbl_options = {'REGISTER', 'UNDO'}\n-\n+\nalg = EnumProperty(name = \"Spline Algorithm\",\nitems = [('Blender', 'Blender', 'Interpolation provided through \\\"mathutils.geometry\\\"'),\n('Hermite', 'C-Spline', 'C-spline interpolation'),\n@@ -713,7 +827,7 @@ class Spline(bpy.types.Operator):\ndef invoke(self, context, event):\nreturn self.execute(context)\n\n-\n+\ndef execute(self, context):\nbpy.ops.object.editmode_toggle()\nbm = bmesh.new()\n@@ -722,7 +836,7 @@ class Spline(bpy.types.Operator):\n\nbEdges = bm.edges\nbVerts = bm.verts\n-\n+\nseg = self.segments\nedges = [e for e in bEdges if e.select]\nverts = [edges[v // 2].verts[v % 2] for v in range(4)]\n@@ -748,7 +862,7 @@ class Spline(bpy.types.Operator):\nelse:\nv2 = verts\np2_co = verts.co\n-            p2_dir = verts.co - verts.co\n+            p2_dir = verts.co - verts.co\nif self.ten2 < 0:\np2_dir = -1 * p2_dir\np2_dir.length = -self.ten2\n@@ -791,13 +905,13 @@ class Spline(bpy.types.Operator):\n#\n# @todo Change method from a cross product to a rotation matrix to make the\n#   angle part work.\n-#   --- todo completed Feb 4th, but still needs work ---\n+#   --- todo completed 2/4/2012, but still needs work ---\n# @todo Figure out a way to make +/- predictable\n#   - Maybe use angel between edges and vector direction definition?\n#   --- TODO COMPLETED ON 2/9/2012 ---\nclass Ortho(bpy.types.Operator):\nbl_idname = \"mesh.edgetools_ortho\"\n-    bl_label = \"Angle off Edge\"\n+    bl_label = \"Angle Off Edge\"\nbl_description = \"\"\nbl_options = {'REGISTER', 'UNDO'}\n\n@@ -848,7 +962,7 @@ class Ortho(bpy.types.Operator):\nrow.prop(self, \"neg\")\nlayout.prop(self, \"angle\")\nlayout.prop(self, \"length\")\n-\n+\n@classmethod\ndef poll(cls, context):\nob = context.active_object\n@@ -858,7 +972,7 @@ class Ortho(bpy.types.Operator):\ndef invoke(self, context, event):\nreturn self.execute(context)\n\n-\n+\ndef execute(self, context):\nbpy.ops.object.editmode_toggle()\nbm = bmesh.new()\n@@ -873,7 +987,8 @@ class Ortho(bpy.types.Operator):\n# Until I can figure out a better way of handeling it:\nif len(edges) < 2:\nbpy.ops.object.editmode_toggle()\n-            self.report({'ERROR_INVALID_INPUT'}, \"You must select two edges.\")\n+            self.report({'ERROR_INVALID_INPUT'},\n+                        \"You must select two edges.\")\nreturn {'CANCELLED'}\n\nverts = [edges.verts,\n@@ -885,7 +1000,8 @@ class Ortho(bpy.types.Operator):\n\n# If the two edges are parallel:\nif cos == None:\n-            self.report({'WARNING'}, \"Selected lines are parallel: results may be unpredictable.\")\n+            self.report({'WARNING'},\n+                        \"Selected lines are parallel: results may be unpredictable.\")\nvectors.append(verts.co - verts.co)\nvectors.append(verts.co - verts.co)\nvectors.append(vectors.cross(vectors))\n@@ -894,7 +1010,8 @@ class Ortho(bpy.types.Operator):\nelse:\n# Warn the user if they have not chosen two planar edges:\nif not is_same_co(cos, cos):\n-                self.report({'WARNING'}, \"Selected lines are not planar: results may be unpredictable.\")\n+                self.report({'WARNING'},\n+                            \"Selected lines are not planar: results may be unpredictable.\")\n\n# This makes the +/- behavior predictable:\nif (verts.co - cos).length < (verts.co - cos).length:\n@@ -904,7 +1021,7 @@ class Ortho(bpy.types.Operator):\n\nvectors.append(verts.co - verts.co)\nvectors.append(verts.co - verts.co)\n-\n+\n# Normal of the plane formed by vector1 and vector2:\nvectors.append(vectors.cross(vectors))\n\n@@ -930,7 +1047,7 @@ class Ortho(bpy.types.Operator):\n# It looks like an extrusion will add the new vert to the end of the verts\n# list and leave the rest in the same location.\n# ----------- EDIT -----------\n-        # It looks like I might be able to do this with in \"bpy.data\" with the \".add\"\n+        # It looks like I might be able to do this within \"bpy.data\" with the \".add\"\n# function.\n# ------- BMESH UPDATE -------\n# BMesh uses \".new()\"\n@@ -962,7 +1079,16 @@ class Shaft(bpy.types.Operator):\nbl_description = \"Create a shaft mesh around an axis\"\nbl_options = {'REGISTER', 'UNDO'}\n\n+    # Selection defaults:\nshaftType = 0\n+\n+    # For tracking if the user has changed selection:\n+    last_edge = IntProperty(name = \"Last Edge\",\n+                            description = \"Tracks if user has changed selected edge\",\n+                            min = 0, max = 1,\n+                            default = 0)\n+    last_flip = False\n+\nedge = IntProperty(name = \"Edge\",\ndescription = \"Edge to shaft around.\",\nmin = 0, max = 1,\n@@ -1009,9 +1135,13 @@ class Shaft(bpy.types.Operator):\n\ndef invoke(self, context, event):\n+        # Make sure these get reset each time we run:\n+        self.last_edge = 0\n+        self.edge = 0\n+\nreturn self.execute(context)\n\n-\n+\ndef execute(self, context):\nbpy.ops.object.editmode_toggle()\nbm = bmesh.new()\n@@ -1027,12 +1157,7 @@ class Shaft(bpy.types.Operator):\nverts = []\n\n# Pre-caclulated values:\n-\n-        # Selects which edge to use\n-        if self.edge == 0:\n-            edge = [0, 1]\n-        else:\n-            edge = [1, 0]\n+\nrotRange = [radians(self.start), radians(self.finish)]\nrads = radians((self.finish - self.start) / self.segments)\n\n@@ -1041,23 +1166,64 @@ class Shaft(bpy.types.Operator):\n\nedges = [e for e in bEdges if e.select]\n\n-        verts.append(edges[edge].verts)\n-        verts.append(edges[edge].verts)\n+        # Robustness check: there should at least be one edge selected\n+        if len(edges) < 1:\n+            bpy.ops.object.editmode_toggle()\n+            self.report({'ERROR_INVALID_INPUT'},\n+                        \"At least one edge must be selected.\")\n+            return {'CANCELLED'}\n\n+        # If two edges are selected:\nif len(edges) == 2:\n+            # default:\n+            edge = [0, 1]\n+            vert = [0, 1]\n+\n+            # Edge selection:\n+            #\n+            # By default, we want to shaft around the last selected edge (it\n+            # will be the active edge).  We know we are using the default if\n+            # the user has not changed which edge is being shafted around (as\n+            # is tracked by self.last_edge).  When they are not the same, then\n+            # the user has changed selection.\n+            #\n+            # We then need to make sure that the active object really is an edge\n+            # (robustness check).\n+            #\n+            # Finally, if the active edge is not the inital one, we flip them\n+            # and have the GUI reflect that.\n+            if self.last_edge == self.edge:\n+                if isinstance(bm.select_history.active, bmesh.types.BMEdge):\n+                    if bm.select_history.active != edges[edge]:\n+                        self.last_edge, self.edge = edge, edge\n+                        edge = [edge, edge]\n+                else:\n+                    bpy.ops.object.editmode_toggle()\n+                    self.report({'ERROR_INVALID_INPUT'},\n+                                \"Active geometry is not an edge.\")\n+                    return {'CANCELLED'}\n+            elif self.edge == 1:\n+                edge = [1, 0]\n+\n+            verts.append(edges[edge].verts)\n+            verts.append(edges[edge].verts)\n+\nif self.flip:\n-                verts.append(edges[edge].verts)\n-                verts.append(edges[edge].verts)\n-            else:\n-                verts.append(edges[edge].verts)\n-                verts.append(edges[edge].verts)\n+                verts = [1, 0]\n+\n+            verts.append(edges[edge].verts[vert])\n+            verts.append(edges[edge].verts[vert])\n+\nself.shaftType = 0\n-        elif len(edges) > 2:\n+        # If there is more than one edge selected:\n+        # There are some issues with it ATM, so don't expose is it to normal users\n+        # @todo Fix edge connection ordering issue\n+        elif len(edges) > 2 and bpy.app.debug:\nif isinstance(bm.select_history.active, bmesh.types.BMEdge):\nactive = bm.select_history.active\nedges.remove(active)\n# Get all the verts:\n-                edges = order_joined_edges(edges)\n+                edges = order_joined_edges(edges)\nverts = []\nfor e in edges:\nif verts.count(e.verts) == 0:\n@@ -1065,10 +1231,15 @@ class Shaft(bpy.types.Operator):\nif verts.count(e.verts) == 0:\nverts.append(e.verts)\nelse:\n-                self.report({'ERROR_INVALID_INPUT'}, \"Active geometry is not an edge.\")\n+                bpy.ops.object.editmode_toggle()\n+                self.report({'ERROR_INVALID_INPUT'},\n+                            \"Active geometry is not an edge.\")\nreturn {'CANCELLED'}\nself.shaftType = 1\nelse:\n+            verts.append(edges.verts)\n+            verts.append(edges.verts)\n+\nfor v in bVerts:\nif v.select and verts.count(v) == 0:\nverts.append(v)\n@@ -1084,11 +1255,12 @@ class Shaft(bpy.types.Operator):\nelse:\naxis = verts.co - verts.co\n\n-        # We will need a series of rotation matrices.  We could use one which would be\n-        # faster but also might cause propagation of error.\n-        matrices = []\n-        for i in range(numV):\n-            matrices.append(Matrix.Rotation((rads * i) + rotRange, 3, axis))\n+        # We will need a series of rotation matrices.  We could use one which\n+        # would be faster but also might cause propagation of error.\n+##        matrices = []\n+##        for i in range(numV):\n+##            matrices.append(Matrix.Rotation((rads * i) + rotRange, 3, axis))\n+        matrices = [Matrix.Rotation((rads * i) + rotRange, 3, axis) for i in range(numV)]\n\n# New vertice coordinates:\nverts_out = []\n@@ -1099,17 +1271,17 @@ class Shaft(bpy.types.Operator):\nfor i in range(len(verts) - 2):\ninit_vec = distance_point_line(verts[i + 2].co, verts.co, verts.co)\nco = init_vec + verts[i + 2].co\n+                # These will be rotated about the orgin so will need to be shifted:\nfor j in range(numV):\n-                    # These will be rotated about the orgin so will need to be shifted:\nverts_out.append(co - (matrices[j] * init_vec))\nelif self.shaftType == 1:\nfor i in verts:\ninit_vec = distance_point_line(i.co, active.verts.co, active.verts.co)\nco = init_vec + i.co\n+                # These will be rotated about the orgin so will need to be shifted:\nfor j in range(numV):\n-                    # These will be rotated about the orgin so will need to be shifted:\nverts_out.append(co - (matrices[j] * init_vec))\n-        # Else if a line and a point was selected:\n+        # Else if a line and a point was selected:\nelif self.shaftType == 2:\ninit_vec = distance_point_line(verts.co, verts.co, verts.co)\n# These will be rotated about the orgin so will need to be shifted:\n@@ -1156,8 +1328,9 @@ class Shaft(bpy.types.Operator):\ne.select = True\n\n# Faces:\n-##            for i in range(numE):\n-##                for j in range(len(verts)):\n+            # There is a problem with this right now\n+##            for i in range(len(edges)):\n+##                for j in range(numE):\n##                    f = bFaces.new((newVerts[i], newVerts[i + 1],\n##                                    newVerts[i + (numV * j) + 1], newVerts[i + (numV * j)]))\n##                    f.normal_update()\n@@ -1191,12 +1364,20 @@ class Shaft(bpy.types.Operator):\n\n# \"Slices\" edges crossing a plane defined by a face.\n+# @todo Selecting a face as the cutting plane will cause Blender to crash when\n+#   using \"Rip\".\nclass Slice(bpy.types.Operator):\nbl_idname = \"mesh.edgetools_slice\"\nbl_label = \"Slice\"\nbl_description = \"Cuts edges at the plane defined by a selected face.\"\nbl_options = {'REGISTER', 'UNDO'}\n\n+    make_copy = BoolProperty(name = \"Make Copy\",\n+                             description = \"Make new vertices at intersection points instead of spliting the edge\",\n+                             default = False)\n+    rip = BoolProperty(name = \"Rip\",\n+                       description = \"Split into two edges that DO NOT share an intersection vertice.\",\n+                       default = False)\npos = BoolProperty(name = \"Positive\",\ndescription = \"Remove the portion on the side of the face normal\",\ndefault = False)\n@@ -1207,9 +1388,12 @@ class Slice(bpy.types.Operator):\ndef draw(self, context):\nlayout = self.layout\n\n-        layout.label(\"Remove Side:\")\n-        layout.prop(self, \"pos\")\n-        layout.prop(self, \"neg\")\n+        layout.prop(self, \"make_copy\")\n+        if not self.make_copy:\n+            layout.prop(self, \"rip\")\n+            layout.label(\"Remove Side:\")\n+            layout.prop(self, \"pos\")\n+            layout.prop(self, \"neg\")\n\n@classmethod\n@@ -1221,7 +1405,7 @@ class Slice(bpy.types.Operator):\ndef invoke(self, context, event):\nreturn self.execute(context)\n\n-\n+\ndef execute(self, context):\nbpy.ops.object.editmode_toggle()\nbm = bmesh.new()\nclass Slice(bpy.types.Operator):\nbEdges = bm.edges\nbFaces = bm.faces\n\n-        fVerts = []\n+        face = None\nnormal = None\n\n# Find the selected face.  This will provide the plane to project onto:\n-        for f in bFaces:\n-            if f.select:\n-                for v in f.verts:\n-                    fVerts.append(v)\n-                normal = f.normal\n-                f.select = False\n-                break\n+        #   - First check to use the active face.  This allows users to just\n+        #       select a bunch of faces with the last being the cutting plane.\n+        #       This is try and make the tool act more like a built-in Blender\n+        #       function.\n+        #   - If that fails, then use the first found selected face in the BMesh\n+        #       face list.\n+        if isinstance(bm.select_history.active, bmesh.types.BMFace):\n+            face = bm.select_history.active\n+            normal = bm.select_history.active.normal\n+            bm.select_history.active.select = False\n+        else:\n+            for f in bFaces:\n+                if f.select:\n+                    face = f\n+                    normal = f.normal\n+                    f.select = False\n+                    break\n+\n+        # If we don't find a selected face, we have problem.  Exit:\n+        if face == None:\n+            bpy.ops.object.editmode_toggle()\n+            self.report({'ERROR_INVALID_INPUT'},\n+                        \"You must select a face as the cutting plane.\")\n+            return {'CANCELLED'}\n+        # Warn the user if they are using an n-gon.  We can work with it, but it\n+        # might lead to some odd results.\n+        elif len(face.verts) > 4 and not is_face_planar(face):\n+            self.report({'WARNING'},\n+                        \"Selected face is an n-gon.  Results may be unpredictable.\")\n+\n+        # @todo DEBUG TRACKER - DELETE WHEN FINISHED:\n+        dbg = 0\n+        if bpy.app.debug:\n+            print(len(bEdges))\n\n+        # Iterate over the edges:\nfor e in bEdges:\n-            if e.select:\n-                v1 = e.verts\n-                v2 = e.verts\n-                if v1 in fVerts and v2 in fVerts:\n-                    e.select = False\n-                    continue\n-                intersection = intersect_line_plane(v1.co, v2.co, fVerts.co, normal)\n+            # @todo DEBUG TRACKER - DELETE WHEN FINISHED:\n+            if bpy.app.debug:\n+                print(dbg)\n+                dbg = dbg + 1\n+\n+            # Get the end verts on the edge:\n+            v1 = e.verts\n+            v2 = e.verts\n+\n+            # Make sure that verts are not a part of the cutting plane:\n+            if e.select and (v1 not in face.verts and v2 not in face.verts):\n+                if len(face.verts) < 5:  # Not an n-gon\n+                    intersection = intersect_line_face(e, face, True)\n+                else:\n+                    intersection = intersect_line_plane(v1.co, v2.co, face.verts.co, normal)\n+\n+                # More debug info - I think this can stay.\n+                if bpy.app.debug:\n+                    print(\"Intersection\", end = ': ')\n+                    print(intersection)\n+\n+                # If an intersection exists find the distance of each of the end\n+                # points from the plane, with \"positive\" being in the direction\n+                # of the cutting plane's normal.  If the points are on opposite\n+                # side of the plane, then it intersects and we need to cut it.\nif intersection != None:\n-                    d1 = distance_point_to_plane(v1.co, fVerts.co, normal)\n-                    d2 = distance_point_to_plane(v2.co, fVerts.co, normal)\n-                    # If they have different signs, then the edge crosses the plane:\n+                    d1 = distance_point_to_plane(v1.co, face.verts.co, normal)\n+                    d2 = distance_point_to_plane(v2.co, face.verts.co, normal)\n+                    # If they have different signs, then the edge crosses the\n+                    # cutting plane:\nif abs(d1 + d2) < abs(d1 - d2):\n# Make the first vertice the positive vertice:\nif d1 < d2:\nv2, v1 = v1, v2\n-                        new = list(bmesh.utils.edge_split(e, v1, 0.5))\n-                        new.co = intersection\n-                        e.select = False\n-                        new.select = False\n-                        if self.pos:\n-                            bEdges.remove(new)\n-                        if self.neg:\n+                        if self.make_copy:\n+                            new = bVerts.new()\n+                            new.co = intersection\n+                            new.select = True\n+                        elif self.rip:\n+                            newV1 = bVerts.new()\n+                            newV1.co = intersection\n+\n+                            if bpy.app.debug:\n+                                print(\"newV1 created\", end = '; ')\n+\n+                            newV2 = bVerts.new()\n+                            newV2.co = intersection\n+\n+                            if bpy.app.debug:\n+                                print(\"newV2 created\", end = '; ')\n+\n+                            newE1 = bEdges.new((v1, newV1))\n+                            newE2 = bEdges.new((v2, newV2))\n+\n+                            if bpy.app.debug:\n+                                print(\"new edges created\", end = '; ')\n+\nbEdges.remove(e)\n\n+                            if bpy.app.debug:\n+                                print(\"old edge removed.\")\n+                                print(\"We're done with this edge.\")\n+                        else:\n+                            new = list(bmesh.utils.edge_split(e, v1, 0.5))\n+                            new.co = intersection\n+                            e.select = False\n+                            new.select = False\n+                            if self.pos:\n+                                bEdges.remove(new)\n+                            if self.neg:\n+                                bEdges.remove(e)\n+\nbm.to_mesh(context.active_object.data)\nbpy.ops.object.editmode_toggle()\nreturn {'FINISHED'}\n\n+# This projects the selected edges onto the selected plane.  This projects both\n+# points on the selected edge.\nclass Project(bpy.types.Operator):\nbl_idname = \"mesh.edgetools_project\"\nbl_label = \"Project\"\n@@ -1312,6 +1574,7 @@ class Project(bpy.types.Operator):\nfVerts = []\n\n# Find the selected face.  This will provide the plane to project onto:\n+        # @todo Check first for an active face\nfor f in bFaces:\nif f.select:\nfor v in f.verts:\n@@ -1494,24 +1757,35 @@ class Fillet(bpy.types.Operator):\n\nradius = FloatProperty(name = \"Radius\",\ndescription = \"Radius of the edge fillet\",\n-                           min = 0.00001, max = 1024.0, softmax = 2.0,\n+                           min = 0.00001, max = 1024.0,\ndefault = 0.5)\nprop = EnumProperty(name = \"Propagation\",\nitems = [(\"m\", \"Minimal\", \"Minimal edge propagation\"),\n(\"t\", \"Tangential\", \"Tangential edge propagation\")],\ndefault = \"m\")\n+    prop_fac = FloatProperty(name = \"Propagation Factor\",\n+                             description = \"Corner detection sensitivity factor for tangential propagation\",\n+                             min = 0.0, max = 100.0,\n+                             default = 25.0)\n+    deg_seg = FloatProperty(name = \"Degrees/Section\",\n+                            description = \"Approximate degrees per section\",\n+                            min = 0.00001, max = 180.0,\n+                            default = 10.0)\nres = IntProperty(name = \"Resolution\",\ndescription = \"Resolution of the fillet\",\n-                      min = 1, max = 1024, softmax = 128,\n+                      min = 1, max = 1024,\ndefault = 8)\n\ndef draw(self, context):\nlayout = self.layout\nlayout.prop(self, \"radius\")\nlayout.prop(self, \"prop\")\n+        if self.prop == \"t\":\n+            layout.prop(self, \"prop_fac\")\n+        layout.prop(self, \"deg_seg\")\nlayout.prop(self, \"res\")\n\n-\n+\n@classmethod\ndef poll(cls, context):\nob = context.active_object\nclass Fillet(bpy.types.Operator):\nbEdges = bm.edges\nbVerts = bm.verts\n\n+        # Robustness check: this does not support n-gons (at least for now)\n+        # because I have no idea how to handle them righ now.  If there is\n+        # an n-gon in the mesh, warn the user that results may be nuts because\n+        # of it.\n+        #\n+        # I'm not going to cause it to exit if there are n-gons, as they may\n+        # not be encountered.\n+        # @todo I would like this to be a confirmation dialoge of some sort\n+        # @todo I would REALLY like this to just handle n-gons. . . .\n+        for f in bFaces:\n+            if len(face.verts) > 4:\n+                self.report({'WARNING'},\n+                            \"Mesh contains n-gons which are not supported. Operation may fail.\")\n+                break\n+\n# Get the selected edges:\n+        # Robustness check: boundary and wire edges are not fillet-able.\nedges = [e for e in bEdges if e.select and not e.is_boundary and not e.is_wire]\n\nfor e in edges:\n-            points = fillet_axis(e, self.radius)\n-\n+            axis_points = fillet_axis(e, self.radius)\n+\n+\n+        bm.to_mesh(bpy.context.active_object.data)\n+        bpy.ops.object.editmode_toggle()\n+        return {'FINISHED'}\n+\n+\n+# For testing the mess that is \"intersect_line_face\" for possible math errors.\n+# This will NOT be directly exposed to end users: it will always require running\n+# Blender in debug mode.\n+# So far no errors have been found. Thanks to anyone who tests and reports bugs!\n+class Intersect_Line_Face(bpy.types.Operator):\n+    bl_idname = \"mesh.edgetools_ilf\"\n+    bl_label = \"ILF TEST\"\n+    bl_description = \"TEST ONLY: INTERSECT_LINE_FACE\"\n+    bl_options = {'REGISTER', 'UNDO'}\n+\n+    @classmethod\n+    def poll(cls, context):\n+        ob = context.active_object\n+        return(ob and ob.type == 'MESH' and context.mode == 'EDIT_MESH')\n+\n+\n+    def invoke(self, context, event):\n+        return self.execute(context)\n+\n+\n+    def execute(self, context):\n+        # Make sure we really are in debug mode:\n+        if not bpy.app.debug:\n+            self.report({'ERROR_INVALID_INPUT'},\n+                        \"This is for debugging only: you should not be able to run this!\")\n+            return {'CANCELLED'}\n+\n+        bpy.ops.object.editmode_toggle()\n+        bm = bmesh.new()\n+        bm.from_mesh(bpy.context.active_object.data)\n+        bm.normal_update()\n+\n+        bFaces = bm.faces\n+        bEdges = bm.edges\n+        bVerts = bm.verts\n+\n+        face = None\n+        for f in bFaces:\n+            if f.select:\n+                face = f\n+                break\n+\n+        edge = None\n+        for e in bEdges:\n+            if e.select and not e in face.edges:\n+                edge = e\n+                break\n+\n+        point = intersect_line_face(edge, face, True)\n+\n+        if point != None:\n+            new = bVerts.new()\n+            new.co = point\n+        else:\n+            bpy.ops.object.editmode_toggle()\n+            self.report({'ERROR_INVALID_INPUT'}, \"point was \\\"None\\\"\")\n+            return {'CANCELLED'}\n+\n+        bm.to_mesh(bpy.context.active_object.data)\n+        bpy.ops.object.editmode_toggle()\nreturn {'FINISHED'}\n\nclass VIEW3D_MT_edit_mesh_edgetools(bpy.types.Menu):\nbl_label = \"EdgeTools\"\n-\n+\ndef draw(self, context):\n+        global integrated\nlayout = self.layout\n-\n+\nlayout.operator(\"mesh.edgetools_extend\")\nlayout.operator(\"mesh.edgetools_spline\")\nlayout.operator(\"mesh.edgetools_ortho\")\n@@ -1554,6 +1911,17 @@ class VIEW3D_MT_edit_mesh_edgetools(bpy.types.Menu):\nlayout.operator(\"mesh.edgetools_slice\")\nlayout.operator(\"mesh.edgetools_project\")\nlayout.operator(\"mesh.edgetools_project_end\")\n+        if bpy.app.debug:\n+            ## Not ready for prime-time yet:\n+            layout.operator(\"mesh.edgetools_fillet\")\n+            ## For internal testing ONLY:\n+            layout.operator(\"mesh.edgetools_ilf\")\n+        # If TinyCAD VTX exists, add it to the menu.\n+        # @todo This does not work.\n+        if integrated and bpy.app.debug:\n+            layout.operator(EdgeIntersections.bl_idname, text=\"Edges V Intersection\").mode = -1\n+            layout.operator(EdgeIntersections.bl_idname, text=\"Edges T Intersection\").mode = 0\n+            layout.operator(EdgeIntersections.bl_idname, text=\"Edges X Intersection\").mode = 1\n\ndef menu_func(self, context):\n@@ -1569,18 +1937,29 @@ classes = [VIEW3D_MT_edit_mesh_edgetools,\nShaft,\nSlice,\nProject,\n-    Project_End]\n+    Project_End,\n+    Fillet,\n+    Intersect_Line_Face]\n\n# registering and menu integration\ndef register():\n-    if int(bpy.app.build_revision[0:5]) < 44800:\n-        print(\"Error in Edgetools:\")\n-        print(\"This version of Blender does not support the necessary BMesh API.\")\n-        print(\"Please download a newer build at http://www.graphicall.org\")\n-        return {'ERROR'}\n+    global integrated\n+\nfor c in classes:\nbpy.utils.register_class(c)\n+\n+    # I would like this script to integrate the TinyCAD VTX menu options into\n+    # the edge tools menu if it exists.  This should make the UI a little nicer\n+    # for users.\n+    # @todo Remove TinyCAD VTX menu entries and add them too EdgeTool's menu\n+    import inspect, os.path\n+\n+    path = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n+    if os.path.isfile(path + \"\\mesh_edge_intersection_tools.py\"):\n+        print(\"EdgeTools UI integration test - TinyCAD VTX Found\")\n+        integrated = True\n+\nbpy.types.VIEW3D_MT_edit_mesh_specials.prepend(menu_func)\n\n@@ -1588,9 +1967,10 @@ def register():\ndef unregister():\nfor c in classes:\nbpy.utils.unregister_class(c)\n+\nbpy.types.VIEW3D_MT_edit_mesh_specials.remove(menu_func)\n\nif __name__ == \"__main__\":\nregister()\n-\n+" ]
[ null ]
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https://answers.everydaycalculation.com/divide-fractions/4-2-divided-by-3-9
[ "Solutions by everydaycalculation.com\n\n## Divide 4/2 with 3/9\n\n1st number: 2 0/2, 2nd number: 3/9\n\n4/2 ÷ 3/9 is 6/1.\n\n#### Steps for dividing fractions\n\n1. Find the reciprocal of the divisor\nReciprocal of 3/9: 9/3\n2. Now, multiply it with the dividend\nSo, 4/2 ÷ 3/9 = 4/2 × 9/3\n3. = 4 × 9/2 × 3 = 36/6\n4. After reducing the fraction, the answer is 6/1\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]
[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]
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