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[ "", null, "# Strange points order of Intersection.CurveLine\n\nHello guys,\nHere is my problem:I use “Rhino.Geometry.Intersect.Intersection.CurveLine(Crv,Line,tolerance,overlapTolerance)” to find the intersected points between a curve and a line.if the input line is a single one,the point order is normal.But if a list of lines,the order is abnormal.I do not know how to figure it out.Please help me to get the surposed points order.\nBest Regards.\nMy codes and screenshots are below:\ninput parameters:Line Line0, Line Line1, Polyline BasePolyline\n\n``````List<Line> Lines = new List<Line>(){Line0,Line1};\nNurbsCurve CrvBP = BasePolyline.ToNurbsCurve();\nList < Point3d > LptsA = new List<Point3d>(){};\nfor(int i = 0;i < Lines.Count;i++)\n{\nLine iLine = Lines[i];\nvar events = Rhino.Geometry.Intersect.Intersection.CurveLine(CrvBP, iLine, 0.01, 0.01);\nfor(int j = 0;j < events.Count;j++)\n{\nvar ccx_ets = events[j];\n}\n}\nA = LptsA;\n``````\n\nThe fact confused me is that the points order is normal in some cases like below:\n\nWhere do you have the Curve Seam on that polygon?\n\nI don’t know this, but my guess is that the “hits” are counted along the curve starting from the seam and ending at the seam. So if the Seam is between 7 and 4 (in the first picture), then pt 4 is closest to the start and then comes 5, 6, 7 which are closer to the end of the curve. Just a wild guess…\n\nIn any case, all the numbers are increasing while going in the same direction along the curve.\n\n// Rolf\n\nHi RIL,\nThank you very much.I test the seam you suggested and the output meets your guess.It is absolutely true that all the numbers are increasing while going in the same direction along the curve.And I use “System.Linq” to sort out the problem.My solutions is below:\n\n``````List<Line> Lines = new List<Line>(){Line0,Line1};\nNurbsCurve CrvBP = BasePolyline.ToNurbsCurve();\nList < Point3d > Lpts = new List<Point3d>(){};\nfor(int i = 0;i < Lines.Count;i++)\n{\nList < Point3d > LptsA = new List<Point3d>(){};\nLine iLine = Lines[i];\nvar events = Rhino.Geometry.Intersect.Intersection.CurveLine(CrvBP, iLine, 0.01, 0.01);\nfor(int j = 0;j < events.Count;j++)\n{\nvar ccx_ets = events[j];\nvar SortList = LptsA.OrderBy(p => p.Y).ThenBy(p => p.X).ToList();//using System.Linq;\nLptsA = SortList;\n}\n}\nA = Lpts;``````\n1 Like\n\nAfter defining the slave (in inner Loop)/master (in outer Loop) order … is just a simple matter of sync sorting ccx pts and params (the classic ArraySort thingy, that is). See attached.\n\nCurve_Ccx_SortPtsParams_EntryLevel_V1.gh (133.7 KB)\n\n1 Like\n\nHi Peter,\nI really appreciate your precious advice.Your method is a general solution and totally settles the matter.Thank you very much.\n\nBTW: For BIG N of slave/master curves there’s faster ways to cut the mustard than the ArraySort … but for “reasonable” collections is more or less OK.\n\nBTW: By the book (and common sense) one needs to split the C# in 2 parts: the first does the ccx job(s) and the second does the visualization part: is rather stupid to re-solve everything just for inspecting a slave/master combo. So as an exercise do the right thing." ]

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[ "# Function compute_derivative_kernels¶\n\n## Function Documentation¶\n\nvoid compute_derivative_kernels(cv::OutputArray kx_, cv::OutputArray ky_, const size_t dx, const size_t dy, const size_t scale)\n\nCompute Scharr derivative kernels for sizes different than 3.\n\nParameters\n• kx_ – The derivative kernel in x-direction\n\n• ky_ – The derivative kernel in y-direction\n\n• dx – The derivative order in x-direction\n\n• dy – The derivative order in y-direction\n\n• scale – The kernel size" ]

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[ "# Guillaume Rioux RAS\n\n### Guillaume Rioux RAS\n\nGuillaume Rioux went undrafted for the NFL out of Laval in 2013.\n\nHe recorded a Relative Athletic Score of 1.74, out of a possible 10.0. RAS is a composite metric on a 0 to 10 scale based on the average of all of the percentile for each of the metrics the player completed either at the Combine or pro day.\n\nHe had a recorded height of 5090 that season, recorded as XYYZ where X is feet, YY is inches, and Z is eighths of an inch. That correlates to 5 feet, 9 and 0/8 of an inch or 69.0 inches, or 175.26 centimeters. This correlates to a 0.88 score out of 10.0.\n\nHe recorded a weight of 180 in pounds, which is approximately 81 kilograms. This correlates to a 2.0 score out of 10.0.\n\nBased on his weight, he has a projected 40 yard dash time of 4.43. This is calculated by taking 0.00554 multiplied by his weight and then adding 3.433.\n\nAt the Combine, he recorded a 40 yard dash of 4.68 seconds. This was a difference of 0.25 seconds from his projected time. This forty time correlates to a 1.69 score out of 10.0.\n\nUsing Bill Barnwell’s calculation, this Combine 40 time gave him a Speed Score of 75.04.\n\nThe time traveled between the 20 and 40 yard lines is known as the Flying Twenty. As the distance is also known, we can calculate the player’s speed over that distance. The time he traveled the last twenty yards at the Combine was 1.95 seconds. Over 20 yards, we can calculate his speed in yards per second to 10.26. Taking into account the distance in feet (60 feet), we can calculate his speed in feet per second to 30.77. Breaking it down further, we can calculate his speed in inches per second to 369.23. Knowing the feet per second of 30.77, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 21.0 in the last 20 yards of his run.\n\nAt the Combine, he recorded a 20 yard split of 2.73 seconds. This correlates to a 1.97 score out of 10.0.\n\nWe can calculate the speed traveled over the second ten yards of the 40 yard dash easily, as the distance and time are both known. The time he traveled the second ten yards at the Combine was 1.08 seconds. Over 10 yards, we can calculate his speed in yards per second to 9.26. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 27.78. Breaking it down further, we can calculate his speed in inches per second to 333.33. Knowing the feet per second of 27.78, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 18.9 in the second ten yards of his run.\n\nAt the Combine, he recorded a 10 yard split of 1.65 seconds. This correlates to a 1.89 score out of 10.0.\n\nThe time he traveled the first ten yards at the Combine was 1.65 seconds. Over 10 yards, we can calculate his speed in yards per second to 6.0. Taking into account the distance in feet (30 feet), we can calculate his speed in feet per second to 18.0. Breaking it down further, we can calculate his speed in inches per second to 218.0. Knowing the feet per second of 18.0, we can calculate the approximate miles per hour by multiplying that value by 0.681818 to give us a calculated MPH of 12.3 in the first ten yards of his run.\n\nAt the Combine, he recorded a bench press of 13 repetitions of 225 pounds. This correlates to a 4.57 score out of 10.0.\n\nAt the Combine, he recorded a vertical jump of 33.5 inches. This correlates to a 4.29 score out of 10.0.\n\nAt the Combine, he recorded a broad jump of 902, which is recorded as FII or FFII . where F is feet and I is inches. This correlates to a 0.96 score out of 10.0.\n\nAt the Combine, he recorded a 5-10-5 or 20 yard short shuttle of 3.91 seconds. This correlates to a 9.88 score out of 10.0.\n\nAt the Combine, he recorded a 3 cone L drill of 6.99 seconds. This correlates to a 4.86 score out of 10.0.\n\nThis player did not record any measurements at their pro day that we were able to find. If they recorded Combine measurements, they stood on them.\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]

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[ "Please see my updated post:Convert RGB(A) output to Hex Color\n\nMy current project uses Farbtastic which is a fantastic jQuery plugin which allows users to visually choose a color for an element. The problem I ran into was loading a default color from the element:\n\njQuery returns the element color in RGB format\ndocument.write( \\$('#myElement').css('background-color') );\n// outputs: rgb(34, 34, 34)\n\nbut Farbtastic uses the hex color format, just like the CSS.\n#myElement { background-color: #222222 }\nI found this really nice script (by R0bb13) which converts RGB to hex. This script requires the input variable to be in an array \"[34,34,34]\". In order to make the script use an RGB format \"rgb(34,34,34)\", I had to add one line to the script to remove the \"rgb\" and parenthesis and then convert (split) the result into an array...\n\nUpdate #2 (allows entering an rgba value - opacity is ignored)\n\nUpdated (removing internal function):\n//Function to convert hex format to a rgb color\nfunction rgb2hex(orig){\nvar rgb = orig.replace(/\\s/g,'').match(/^rgba?\\((\\d+),(\\d+),(\\d+)/i);\nreturn (rgb && rgb.length === 4) ? \"#\" +\n(\"0\" + parseInt(rgb,10).toString(16)).slice(-2) +\n(\"0\" + parseInt(rgb,10).toString(16)).slice(-2) +\n(\"0\" + parseInt(rgb,10).toString(16)).slice(-2) : orig;\n}\nHere is an example of how to use this code with jQuery:\ndocument.write( rgb2hex(\\$('#myElement').css('background-color')) );\n// outputs: #222222\nHere is the original code from this post (not nearly as efficient as the updated script):\n//Function to convert hex format to a rgb color\nfunction rgb2hex(rgb) {\nvar hexDigits = [\"0\",\"1\",\"2\",\"3\",\"4\",\"5\",\"6\",\"7\",\"8\",\"9\",\"a\",\"b\",\"c\",\"d\",\"e\",\"f\"];\nrgb = rgb.match(/^rgb\\((\\d+),\\s*(\\d+),\\s*(\\d+)\\)\\$/);\nfunction hex(x) {\nreturn isNaN(x) ? \"00\" : hexDigits[(x - x % 16) / 16] + hexDigits[x % 16];\n}\nreturn \"#\" + hex(rgb) + hex(rgb) + hex(rgb);\n}\n\n1.", null, "2.", null, "thank you so much :)\n\n3.", null, "I've added an alternative method that doesn't require an array, *smack head* just use the built in functions (duh LOL)\n\n4.", null, "Nice one motty, great post! Would you consider writing some jQuery posts for my blog? http://jquery4u.com obviously will be some incentives. Cheers. Sam\n\n5.", null, "Just for info !\n\nThis script breaks awfully when encountering a css3 rgba string !\n\nrgba(0,0,0,0)\n\nhttp://www.zenelements.com/blog/css3-rgb-rgba-color-opacity/\n\n6.", null, "Thanks Kim! I modified the script a bit, here is a demo.\n\n7.", null, "yeeesssss, excellent and simple\n\n8.", null, "Thank you! Worked like a charm here!\n\n9.", null, "" ]

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[ "# Demonstration of Pypi package OCaml for polyglot notebook¶\n\nTL;DR: this Pypi ocaml package allows to embed a real and complete OCaml runtime (with full standard library) in an IPython console or Jupyter notebook running IPython kernel (Python 3). OCaml functions and tiny programs can then be called directly from the IPython/Jupyter console, and results can be printed, or affected to Python variables! It even supports Currying multi-argument functions!\n\nSee also: note, if you really want to use OCaml in a Jupyter notebook, the best solution is OCaml-jupyter kernel! (i opened an issue there to present this to the developer, just for his curiosity)\n\n## Introduction¶\n\nSee this issue I opened and assigned to myself.\n\nIf you run this:\n\nIn :\n!pip3 install ocaml\n\n\nThen you can use basic OCaml expressions and standard library... from IPython or Jupyter notebook with IPython kernel, without having to install OCaml yourself on your laptop! It's pre-compiled. I don't know what version thought...\n\nIn :\nimport ocaml\n\nIn :\nanswer_to_life = %ocaml 40 + 2\n\nIn :\nprint(answer_to_life)\nprint(type(answer_to_life)) # a real integer!\n\n42\n<class 'int'>\n\n\nIt would be a great project to show to students studying Python and C and OCaml : this tiny IPython magic makes the link between Python and OCaml (one way) using OCaml compiled as a dynamic extension to CPython 😍 !\n\n## Reference and missing documentation of ocaml Pypi package¶\n\nThis Jupyter notebook uses the ocaml v0.0.11 package from Pypi.\n\nThere is no documentation, I asked the author, who works at JaneStreet and he redirected me to this blog post by JaneStreet.\n\nApparently, being professional developers doesn't mean they restrain themselves from shipping unfinished and undocumented packages to Pypi. Okay... Why? It seems highly unprofessional! I understand being in a hurry, but then just don't publish to Pypi, and let user install it using pip but from a Git repository:\n\n$pip install git+https://github.com/<Username>/<Projects> Their blog post states Note that this package is not currently very well polished but it should give some ideas of what can be done through this Python-OCaml integration. But come on, writing a short README or description in the setup.py is the least that they should do... I don't do that! See my Pypi packages on https://pypi.org/user/Naereen/: • lempel-ziv-complexity (Last released on Dec 19, 2019): Fast implementation of the Lempel-Ziv complexity function. • SMPyBandits (Last released on Oct 25, 2019): SMPyBandits: Open-Source Python package for Single- and Multi-Players multi-armed Bandits algorithms. • parcoursup (Last released on Nov 14, 2018): ParcourSup.py : un clone en Python 3 de ParcoursSup, écrit à but didactique. • generatewordcloud (Last released on Oct 16, 2016): A simple Python (2 or 3) script to generate a PNG word-cloud image from a bunch of text files. Based on word_cloud. • ansicolortags (Last released on Jul 2, 2016): ansicolortags brings a simple and powerful way to use colours in a terminal application with Python 2 and 3. Let's show the current version of the package, just for reference: In : %load_ext watermark In : %watermark -v -p ocaml CPython 3.6.9 IPython 7.16.1 ocaml 0.0.11 ## A first example¶ As for other languages binding, we can have either a full cell, starting with %%ocaml : In : %%ocaml print_endline \"Hello world from OCaml running in Jupyter (from IPython)!\";; Hello world from OCaml running in Jupyter (from IPython)! Natively, IPython/Jupyter supports lots of \"magic commands\", and especially %%bash, %%perl, %%javascript and %%ruby interface to famous scripting languages, and a generic %%script one. In : %%bash echo \"Hello world from Bash running in Jupyter (from IPython)\" Hello world from Bash running in Jupyter (from IPython) In : %%script bash echo \"Hello world from Bash running in Jupyter (from IPython)\" Hello world from Bash running in Jupyter (from IPython) Not that it has been possible, since a long time, to call an OCaml toplevel like this! In : %%script ocaml print_endline \"Hello world from OCaml running in Jupyter (from IPython)!\";; OCaml version 4.05.0 Findlib has been successfully loaded. Additional directives: #require \"package\";; to load a package #list;; to list the available packages #camlp4o;; to load camlp4 (standard syntax) #camlp4r;; to load camlp4 (revised syntax) #predicates \"p,q,...\";; to set these predicates Topfind.reset();; to force that packages will be reloaded #thread;; to enable threads # Hello world from OCaml running in Jupyter (from IPython)! - : unit = () # But it does nothing else than opening a sub-process, running ocaml command, feeding it the content of the cell, and then exiting. • Cons: It's not so pretty, as it prints all this startup messages. I thought we could silent them, like python -q (quiet) option... but we can't! • Pros: it shows the value of each line, so it can be used to quickly check something, if needed... ## More full %%ocaml cells¶ In : %%ocaml let sum : (int list -> int) = List.fold_left (+) 0 in let a_list (n:int) : int list = Array.to_list (Array.init n (fun i -> i*i+30)) in for n = 300000 to 300010 do Format.printf \"\\nList of size %2.i had sum = %4.i.%!\" n (sum (a_list n)); done;; List of size 300000 had sum = 8999955009050000. List of size 300001 had sum = 9000045009050030. List of size 300002 had sum = 9000135009650061. List of size 300003 had sum = 9000225010850095. List of size 300004 had sum = 9000315012650134. List of size 300005 had sum = 9000405015050180. List of size 300006 had sum = 9000495018050235. List of size 300007 had sum = 9000585021650301. List of size 300008 had sum = 9000675025850380. List of size 300009 had sum = 9000765030650474. List of size 300010 had sum = 9000855036050585. As I was saying, using %%script ocaml allows to quickly check things, like for instance the interface of a module! In : %%script ocaml #show Array;; OCaml version 4.05.0 Findlib has been successfully loaded. Additional directives: #require \"package\";; to load a package #list;; to list the available packages #camlp4o;; to load camlp4 (standard syntax) #camlp4r;; to load camlp4 (revised syntax) #predicates \"p,q,...\";; to set these predicates Topfind.reset();; to force that packages will be reloaded #thread;; to enable threads # module Array : sig external length : 'a array -> int = \"%array_length\" external get : 'a array -> int -> 'a = \"%array_safe_get\" external set : 'a array -> int -> 'a -> unit = \"%array_safe_set\" external make : int -> 'a -> 'a array = \"caml_make_vect\" external create : int -> 'a -> 'a array = \"caml_make_vect\" external create_float : int -> float array = \"caml_make_float_vect\" val make_float : int -> float array val init : int -> (int -> 'a) -> 'a array val make_matrix : int -> int -> 'a -> 'a array array val create_matrix : int -> int -> 'a -> 'a array array val append : 'a array -> 'a array -> 'a array val concat : 'a array list -> 'a array val sub : 'a array -> int -> int -> 'a array val copy : 'a array -> 'a array val fill : 'a array -> int -> int -> 'a -> unit val blit : 'a array -> int -> 'a array -> int -> int -> unit val to_list : 'a array -> 'a list val of_list : 'a list -> 'a array val iter : ('a -> unit) -> 'a array -> unit val iteri : (int -> 'a -> unit) -> 'a array -> unit val map : ('a -> 'b) -> 'a array -> 'b array val mapi : (int -> 'a -> 'b) -> 'a array -> 'b array val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a val fold_right : ('b -> 'a -> 'a) -> 'b array -> 'a -> 'a val iter2 : ('a -> 'b -> unit) -> 'a array -> 'b array -> unit val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array val for_all : ('a -> bool) -> 'a array -> bool val exists : ('a -> bool) -> 'a array -> bool val mem : 'a -> 'a array -> bool val memq : 'a -> 'a array -> bool val sort : ('a -> 'a -> int) -> 'a array -> unit val stable_sort : ('a -> 'a -> int) -> 'a array -> unit val fast_sort : ('a -> 'a -> int) -> 'a array -> unit external unsafe_get : 'a array -> int -> 'a = \"%array_unsafe_get\" external unsafe_set : 'a array -> int -> 'a -> unit = \"%array_unsafe_set\" end # ## Using OCaml returned values from Python¶ This package allows to use dynamically defined OCaml functions from Python, the same way it can be done for other languages lke Julia or R (see this blog post if you never saw these possibilities, or this one). For instance: In : b = %ocaml true print(type(b), b) s = %ocaml \"OK ?\" print(type(s), s) i = %ocaml 2021 print(type(i), i) f = %ocaml 2.99792458 print(type(f), f) <class 'bool'> True <class 'str'> OK ? <class 'int'> 2021 <class 'float'> 2.99792458 So booleans, strings, integers and floats get perfectly mapped from OCaml values to Python native values. In : l = %ocaml [1, 3, 5] print(type(l), l) a = %ocaml [|2; 4; 6|] print(type(a), a) t = %ocaml (23, 02, 2021) print(type(t), t) <class 'list'> [(1, 3, 5)] <class 'list'> [2, 4, 6] <class 'tuple'> (23, 2, 2021) So 'a list, 'a array and 'a * 'b * .. heterogeneous tuples get perfectly mapped from OCaml values to Python native values! But it's not perfect, as for instance OCaml has a char type (similar to the one in C) but Python only has strings, so this'll fail: ValueError: ocaml error (Failure\"unknown type char\") In : c = %ocaml 'C' print(type(c), c) --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-183-19c1c29bb9b1> in <module> ----> 1 c = get_ipython().run_line_magic('ocaml', \"'C'\") 2 print(type(c), c) /usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py in run_line_magic(self, magic_name, line, _stack_depth) 2324 kwargs['local_ns'] = sys._getframe(stack_depth).f_locals 2325 with self.builtin_trap: -> 2326 result = fn(*args, **kwargs) 2327 return result 2328 /usr/local/lib/python3.6/dist-packages/ocaml/__init__.py in ocaml(line) 13 def ocaml(line): 14 with sys_pipes(): ---> 15 return toploop.get(line) 16 17 del ocaml ValueError: ocaml error (Failure\"unknown type char\") And for functions: In : sum_ocaml_1 = %ocaml let sum : (int list -> int) = List.fold_left (+) 0 in sum In : print(sum_ocaml_1, type(sum_ocaml_1)) <built-in method anonymous_closure of PyCapsule object at 0x7ff259159120> <class 'builtin_function_or_method'> In : sum_ocaml_1 ([1, 2, 3, 4, 5]) # 15 Out: 15 Or simply In : sum_ocaml_2 = %ocaml List.fold_left (+) 0 In : sum_ocaml_2 ([1, 2, 3, 4, 5]) # 15 Out: 15 What about user defined types? In : %%ocaml type state = TODO | DONE | Unknown of string;; let print_state (s:state) = match s with | TODO -> Format.printf \"TODO%!\" | DONE -> Format.printf \"DONE%!\" | Unknown status -> Format.printf \"%s%!\" status ;; print_state TODO;; TODO It fails: SyntaxError: ocaml evaluation error on lines 1:11 to 1:15 Error: > 1: let out = (type TODO | DONE);; Syntax error: operator expected. In : t = %ocaml type TODO | DONE Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-191-92828381558a>\", line 1, in <module> t = get_ipython().run_line_magic('ocaml', 'type TODO\\xa0| DONE') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2326, in run_line_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 15, in ocaml return toploop.get(line) File \"<string>\", line unknown SyntaxError: ocaml evaluation error on lines 1:11 to 1:15 Error: > 1: let out = (type TODO | DONE);; Syntax error: operator expected. Indeed the %ocam magic only works for expression, with no ;;. ## More datatypes conversions to Python?¶ We can still explore: • references, let x = ref 1 • polymorphic functions like let smaller (x: 'a) (y: 'a) : true = x < y • 'a option type • functions with labels • records • polymorphic variants ? Fore reference, see https://github.com/janestreet/ppx_python#conversions ### References - fail¶ In : xref = %ocaml ref 1 --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-198-8acf58a91aa8> in <module> ----> 1 xref = get_ipython().run_line_magic('ocaml', 'ref 1') /usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py in run_line_magic(self, magic_name, line, _stack_depth) 2324 kwargs['local_ns'] = sys._getframe(stack_depth).f_locals 2325 with self.builtin_trap: -> 2326 result = fn(*args, **kwargs) 2327 return result 2328 /usr/local/lib/python3.6/dist-packages/ocaml/__init__.py in ocaml(line) 13 def ocaml(line): 14 with sys_pipes(): ---> 15 return toploop.get(line) 16 17 del ocaml ValueError: ocaml error (Failure\"unknown type ref\") ### Polymorphic function - works!¶ In : cons = %ocaml fun hd tl -> hd :: tl print(cons, type(cons)) <built-in method anonymous_closure of PyCapsule object at 0x7ff259179f30> <class 'builtin_function_or_method'> In : cons(10)([20, 30]) Out: [10, 20, 30] In : cons(1.0)([2.0, 30]) Out: [1.0, 2.0, 30] Woooo, somehow OCaml accepted a polymorphic list at some point? In : head, tail = %ocaml List.hd, List.tl In : a_list = [1, 2, 3] a_list.append(a_list) head(a_list), tail(a_list) Out: (1, [2, 3, [1, 2, 3, [...]]]) Another example: In : smaller = %ocaml fun (x: int) (y: int) -> x < y print(smaller) help(smaller) <built-in method anonymous_closure of PyCapsule object at 0x7ff25cf80a20> Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance int -> int -> bool In : smaller_poly = %ocaml fun (x: 'a) (y: 'a) -> x < y print(smaller_poly) help(smaller_poly) <built-in method anonymous_closure of PyCapsule object at 0x7ff259179ea0> Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance pyobject -> pyobject -> bool ### Option type¶ In : none = %ocaml None print(none, type(none)) None <class 'NoneType'> In : some_int = %ocaml Some 42 print(some_int, type(some_int)) 42 <class 'int'> In : # instinguishable from None, so that's weird! some_None = %ocaml Some None print(some_None, type(some_None)) None <class 'NoneType'> Note that this limitation was explained: Note that this makes the two OCaml values [Some None] and [None] indistinguishable on the Python side as both are represented using None. ### Functions with labels - labels get erased¶ In : # val fold_left : f:('a -> 'b -> 'a) -> init:'a -> 'b list -> 'a fold_left = %ocaml ListLabels.fold_left print(fold_left, type(fold_left)) help(fold_left:) <built-in method anonymous_closure of PyCapsule object at 0x7ff259179f00> <class 'builtin_function_or_method'> Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance pyobject -> pyobject -> pyobject -> pyobject -> (pyobject) list -> pyobject In : fold_left(lambda x: lambda y: x + y)(0)([1, 2, 3, 4, 5]) Out: 15 ### Record - fail¶ In : %%ocaml type ratio = {num: int; denom: int};; let add_ratio r1 r2 = {num = r1.num * r2.denom + r2.num * r1.denom; denom = r1.denom * r2.denom};; add_ratio {num=1; denom=3} {num=2; denom=5};; In : %ocaml {num=1; denom=3} --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-197-077c7ab12521> in <module> ----> 1 get_ipython().run_line_magic('ocaml', '{num=1; denom=3}') /usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py in run_line_magic(self, magic_name, line, _stack_depth) 2324 kwargs['local_ns'] = sys._getframe(stack_depth).f_locals 2325 with self.builtin_trap: -> 2326 result = fn(*args, **kwargs) 2327 return result 2328 /usr/local/lib/python3.6/dist-packages/ocaml/__init__.py in ocaml(line) 13 def ocaml(line): 14 with sys_pipes(): ---> 15 return toploop.get(line) 16 17 del ocaml ValueError: ocaml error (Failure\"unknown type ratio\") Of course it fails! But it could be translated to Python dictionaries. ### Exceptions - fail¶ In : exc = %ocaml exception Empty_list Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-207-709df63f312a>\", line 1, in <module> exc = get_ipython().run_line_magic('ocaml', 'exception Empty_list') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2326, in run_line_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 15, in ocaml return toploop.get(line) File \"<string>\", line unknown SyntaxError: ocaml evaluation error on lines 1:11 to 1:20 Error: > 1: let out = (exception Empty_list);; Syntax error: operator expected. ### Polymorphic variants - fail¶ In : %%ocaml Format.printf \"%i%!\" (let value float = 0 in value float);; 0 In : zero = %ocaml let value float = 0 in value float print(zero, type(zero)) 0 <class 'int'> In : variant = %ocaml float print(variant, type(variant)) Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-237-35ef86792a45>\", line 1, in <module> variant = get_ipython().run_line_magic('ocaml', 'float') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2326, in run_line_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 15, in ocaml return toploop.get(line) File \"<string>\", line unknown SyntaxError: unsupported type Tvariant ### Optional arguments - fail¶ It would be difficult to implement them correctly along side the (awesome) partial application closure feature... In : %%ocaml let bump ?(step = 1) x = x + step;; Format.printf \"\\n%i%!\" (bump 41);; Format.printf \"\\n%i%!\" (bump ~step:12 30);; 42 42 In : bump = %ocaml let bump ?(step = 1) x = x + step in bump Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-241-9255dc0fa695>\", line 1, in <module> bump = get_ipython().run_line_magic('ocaml', 'let bump ?(step = 1) x = x + step in bump') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2326, in run_line_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 15, in ocaml return toploop.get(line) File \"<string>\", line unknown SyntaxError: optional arguments are not supported ### Recursive list?¶ In : %%ocaml let rec list1 = 0 :: list2 and list2 = 1 :: list1 in Format.printf \"%i -> %i -> %i -> %i ...%!\" (List.hd list1) (List.hd list2) (List.hd (List.tl list2)) (List.hd (List.tl list1));; 0 -> 1 -> 0 -> 1 ... In : # don't run if False: list1, list2 = %ocaml let rec list1 = 0 :: list2 and list2 = 1 :: list1 in (list1, list2) It fails, but takes 100% CPU and freezes. But in Python we can do it: In : list1 = list2 = list1.append(list2) list2.append(list1) print(list1) print(list2) [0, [1, [...]]] [1, [0, [...]]] ### From standard library¶ What about Sets, mapped to set? What about HashTbl, mapped to dict? And Stack, Queue, etc? TODO: left as an exercise for the reader. ### Map - fail¶ In : %%ocaml module IntPairs = struct type t = int * int let compare (x0,y0) (x1,y1) = match Stdlib.compare x0 x1 with 0 -> Stdlib.compare y0 y1 | c -> c end module PairsMap = Map.Make(IntPairs) let m = PairsMap.(empty |> add (0,1) \"hello\" |> add (1,0) \"world\") (* not an expression, not usable in %ocaml magic *) ### Stack (or any module using a custom type) - fail¶ In : stack = %ocaml Stack.create() --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-10-bbd04f52cfc6> in <module> ----> 1 stack = get_ipython().run_line_magic('ocaml', 'Stack.create()') /usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py in run_line_magic(self, magic_name, line, _stack_depth) 2324 kwargs['local_ns'] = sys._getframe(stack_depth).f_locals 2325 with self.builtin_trap: -> 2326 result = fn(*args, **kwargs) 2327 return result 2328 /usr/local/lib/python3.6/dist-packages/ocaml/__init__.py in ocaml(line) 13 def ocaml(line): 14 with sys_pipes(): ---> 15 return toploop.get(line) 16 17 del ocaml ValueError: ocaml error (Failure\"unknown type t\") ## 😮 Curryed functions!¶ Imagine you define this function in math:$p : (x,y,z) \\mapsto x * y * z$, on$\\mathbb{N}^3 \\to \\mathbb{N}$. Then the Curryed form states that it is equivalent to$p' : x \\mapsto y \\mapsto z \\mapsto x * y * z$, informally defined on$\\mathbb{N} \\to \\mathbb{N} \\to \\mathbb{N} \\to \\mathbb{N}$. So for instance if$x=1$and$y=2$,$p'(x)(y)$is$z \\mapsto 1 * 2 * z$, which is also$z \\mapsto p(1, 2, z)$. In Python function, that would be this function: In : def product3values(x, y, z): return x * y * z But you can't directly use it for partial application: In : x = 1 y = 2 partial_product = product3values(x, y) z = 10 print(f\"With x = {x}, y = {y}, and {partial_product} applied to z = {z}, we got {partial_product(z)}\") --------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-80-3ba473df199e> in <module> 1 x = 1 2 y = 2 ----> 3 partial_product = product3values(x, y) 4 z = 10 5 print(f\"With x = {x}, y = {y}, and {partial_product} applied to z = {z}, we got {partial_product(z)}\") TypeError: product3values() missing 1 required positional argument: 'z' With the Python standard library, it's possible to use functools.partial to obtain partially evaluated functions, which can be viewed as a limited support of Curryed function. In : import functools partial_product = functools.partial(product3values, 1, 2) z = 10 print(f\"With x = {x}, y = {y}, and {partial_product} applied to z = {z}, we got {partial_product(z)}\") With x = 1, y = 2, and functools.partial(<function product3values at 0x7ff25cda0c80>, 1, 2) applied to z = 10, we got 20 But in OCaml, the conventions is to directly write functions in Curry form, rather than tuple form: In : %%ocaml (* this is advised *) let product_curry (x:int) (y:int) (z:int) : int = x * y * z in let x = 1 and y = 2 in let partial_product = product_curry x y in let z = 10 in Format.printf \"With x = %i, y = %i, and partial_product applied to z = %i, we got %i.\" x y z (partial_product z);; With x = 1, y = 2, and partial_product applied to z = 10, we got 20. Indeed, in most situations, the tuple form is just not \"OCaml\"esque, and tedious to use, and does not allow partial application! In : %%ocaml (* this is NOT advised *) let product_curry (xyz : (int * int * int)) : int = let x, y, z = xyz in x * y * z in let x = 1 and y = 2 in let partial_product = product_curry x y in let z = 10 in Format.printf \"With x = %i, y = %i, and partial_product applied to z = %i, we got %i.\" x y z (partial_product z);; Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-89-a59ab8443eec>\", line 1, in <module> get_ipython().run_cell_magic('ocaml', '', '(* this is NOT advised *)\\nlet product_curry (xyz : (int * int * int)) : int =\\n let x, y, z = xyz in\\n x * y * z\\nin\\nlet x = 1 and y = 2 in\\nlet partial_product = product_curry x y in\\nlet z = 10 in\\nFormat.printf \"With x = %i, y = %i, and partial_product applied to z = %i, we got %i.\" x y z (partial_product z);;\\n') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2371, in run_cell_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 30, in ocaml return toploop.eval(cell) File \"<string>\", line unknown SyntaxError: ocaml evaluation error on lines 7:165 to 7:178 Error: 2: let product_curry (xyz : (int * int * int)) : int = 3: let x, y, z = xyz in 4: x * y * z 5: in 6: let x = 1 and y = 2 in > 7: let partial_product = product_curry x y in 8: let z = 10 in 9: Format.printf \"With x = %i, y = %i, and partial_product applied to z = %i, we got %i.\" x y z (partial_product z);; This function has type int * int * int -> int It is applied to too many arguments; maybe you forgot a ;'. Well that was some long explanation, but now comes the magic! If you use %ocaml to get in Python the values returned from OCaml, then functions are Curryed function! In : product_curry = %ocaml let product_curry (x:int) (y:int) (z:int) : int = x * y * z in product_curry The only information we have on this function is the OCaml signature, in its docstring: In : help(product_curry) Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance int -> int -> int -> int So we can't use it as a classical 3-arguments Python function: In : product_curry(1, 2, 10) Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-93-30a4c1f01ec3>\", line 1, in <module> product_curry(1, 2, 10) File \"<string>\", line unknown SyntaxError: (Failure \"expected int, got Tuple\") But we CAN use it as a Curryed function! In : product_curry(1)(2)(10) Out: 20 Which is awesome because now we can do partial evaluation as in OCaml! In : partial_product_1 = product_curry(1) partial_product_1(2)(10) Out: 20 In : partial_product_2 = product_curry(1)(2) partial_product_2_too = partial_product_1(2) partial_product_2(10), partial_product_2_too(10) Out: (20, 20) What's very cool is that these functions docstrings keep showing the signature of the underlying OCaml function, even if they were obtained from pure Python cells! In : help(partial_product_1) help(partial_product_2) help(partial_product_2_too) Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance int -> int -> int Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance int -> int Help on built-in function anonymous_closure: anonymous_closure(...) method of builtins.PyCapsule instance int -> int That's it for this feature, it's cool and interesting. ## Some questions¶ ### Can we share variables between two consecutive full cells?¶ In the %ocaml mode, nothing can be shared from the OCaml side, as it's just an expression, let's check: In : %ocaml let x = 1 in x Out: 1 In : %ocaml x Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-67-269a4d148dbe>\", line 1, in <module> get_ipython().run_line_magic('ocaml', 'x') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2326, in run_line_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 15, in ocaml return toploop.get(line) File \"<string>\", line unknown SyntaxError: ocaml evaluation error on lines 1:11 to 1:12 Error: > 1: let out = (x);; Unbound value x But what about full cell mode, %%ocaml? In : %%ocaml (* See https://en.wikipedia.org/wiki/42_(number) *) let answer_to_life = 42 in Format.printf \"\\n... « The answer to life, the universe, and everything is %i »%!\" answer_to_life;; ... « The answer to life, the universe, and everything is 42 » In : %%ocaml Format.printf \"\\n... « The answer to life, the universe, and everything is %i »%!\" answer_to_life;; Traceback (most recent call last): File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 3343, in run_code exec(code_obj, self.user_global_ns, self.user_ns) File \"<ipython-input-71-0d2d3c7f5c67>\", line 1, in <module> get_ipython().run_cell_magic('ocaml', '', 'Format.printf \"\\\\n... « The answer to life, the universe, and everything is %i »%!\" answer_to_life;;\\n') File \"/usr/local/lib/python3.6/dist-packages/IPython/core/interactiveshell.py\", line 2371, in run_cell_magic result = fn(*args, **kwargs) File \"/usr/local/lib/python3.6/dist-packages/ocaml/__init__.py\", line 30, in ocaml return toploop.eval(cell) File \"<string>\", line unknown SyntaxError: ocaml evaluation error on lines 1:85 to 1:99 Error: > 1: Format.printf \"\\n... « The answer to life, the universe, and everything is %i »%!\" answer_to_life;; Unbound value answer_to_life ==> Answer: no, we cannot share any memory between two consecutive cells. Well, too bad, but it's not so important. ### Is there any documentation of the magic or commands?¶ No. In : ?%ocaml Docstring: <no docstring> File: /usr/local/lib/python3.6/dist-packages/ocaml/__init__.py ### More remarks¶ Note that there blog post says that using the opttoploop could be used to compile the OCaml to a faster version (native code), but do not document about this. Note that with the toploop module, the OCaml code is evaluated by compiling to bytecode which is not optimal, switching to the opttoploop module that generates native code should make it even faster. In : \"opttoploop\" in dir(ocaml) Out: False Also note that the ocaml module is shipped with an example of a tiny module which was written in OCaml and compiled, being made available to Python directly: In : # it doesn't have a docstring, don't try help(<...>) or <...>? ocaml.ocaml.example_module.approx_pi Out: <function PyCapsule.anonymous_closure> In : ocaml.ocaml.example_module.approx_pi(1000000) Out: 3.1415916986605086 ## Final note: a tiny benchmark¶ Let's compare the speed of naive Python and naive OCaml sum of a list/array of floats, for various input size. In : import ocaml import numpy as np In : python_sum = sum ocaml_sum = %ocaml List.fold_left (+.) 0. numpy_sum = np.sum In : print(python_sum( [1.0, 2.0, 3.0, 4.0, 5.0] )) print(ocaml_sum( [1.0, 2.0, 3.0, 4.0, 5.0] )) print(numpy_sum( [1.0, 2.0, 3.0, 4.0, 5.0] )) 15.0 15.0 15.0 Now for a \"large\" array, let's use IPython %timeit magic for very quick benchmarking. Science is about making hypotheses, designing experiments to check them, and conclude. My hypothesis here is that the OCaml version will be between 10 to 50 slower than the Python one (and Numpy version is 50-200 faster than Python). In : sizes = [100, 1000, 10000, 100000, 1000000, 10000000] print(f\"Comparing time of python_sum and ocaml_sun :\") for size in sizes: print(f\"\\n- For size = {size}:\") X = list(np.random.randn(size)) print(\"\\tFor python sum: \", end='') %timeit python_sum(X) assert np.isclose(python_sum(X), ocaml_sum(X)) print(\"\\tFor OCaml sum: \", end='') %timeit ocaml_sum(X) assert np.isclose(python_sum(X), numpy_sum(X)) print(\"\\tFor numpy.sum: \", end='') %timeit numpy_sum(X) Comparing time of python_sum and ocaml_sun : - For size = 10000000: For python sum: 677 ms ± 12.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) For OCaml sum: 2.92 s ± 441 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) For numpy.sum: 632 ms ± 4.41 ms per loop (mean ± std. dev. of 7 runs, 1 loop each) Well that's better than what I expected! It seems that the overhead is constant and not increasing when the size of the input is increasing! It means that if the Python code runs in time$T_1(n)$for inputs of size$n$, then then OCaml binding code runs in less than$T_2(n) \\leq \\alpha T_1(n) + \\beta$, with two constants$\\alpha, \\beta$. In : import matplotlib.pyplot as plt µs = 1 ms = 1000*µs s = 1000*ms X = sizes # TODO: get this automatically? Y_python = [ 7.27*µs, 72.1*µs, 786*µs, 7.55*ms, 68.2*ms, 677*ms ] Y_ocaml = [ 16*µs, 157*µs, 1.8*ms, 24.2*ms, 286*ms, 2.92*s ] Y_numpy = [ 12*µs, 67.7*µs, 615*µs, 6.25*ms, 62.6*ms, 632*ms ] fig = plt.figure(figsize=(14, 10), dpi=300) plt.loglog(X, Y_python, color=\"blue\", marker=\"o\", label=\"naive Python\", lw=4, ms=15) plt.loglog(X, Y_ocaml, color=\"green\", marker=\"d\", label=\"using OCaml\", lw=4, ms=15) plt.loglog(X, Y_numpy, color=\"orange\", marker=\"s\", label=\"using Numpy\", lw=4, ms=15) plt.ylabel(\"Time in micro-seconds\") plt.xlabel(\"Size of input list\") plt.legend() plt.title(\"Tiny benchmark comparing OCaml binding to Python\") plt.show()", null, "Just to check the experimental values of$\\alpha$and$\\beta\\$ in my claim above, let's use numpy.polyfit function:\n\nIn :\nnp.polyfit(Y_python, Y_ocaml, deg=1)\n\nOut:\narray([ 4.31769413, -3617.94315775])\n\nSo the OCaml bidding code runs about 4.5 times slower than the Python one!\n\nIt means that if you're doing a data analysis or some things in Python, and suddenly you think of an easy way to write an elegant and fast OCaml version, it's definitely viable to write it in OCaml, use ocaml_function = %ocaml ... and then use to solve your task! The overhead for using OCaml interpreted functions should not be too large.\n\n## Conclusion: demonstration of Pypi package OCaml for polyglot notebook¶\n\nThis (long) notebook dived in the details of this Pypi ocaml` package allows to embed a real and complete OCaml runtime (with full standard library) in an IPython console or Jupyter notebook running IPython kernel (Python 3). OCaml functions and tiny programs can then be called directly from the IPython/Jupyter console, and results can be printed, or affected to Python variables! It even supports Currying multi-argument functions!\n\nIt's too bad that the package lack documentation, and is not open source, I would have liked to improve it a little bit!\n\nSee also: note, if you really want to use OCaml in a Jupyter notebook, the best solution is OCaml-jupyter kernel! (i opened an issue there to present this to the developer, just for his curiosity)\n\nThat's it for today! See other notebooks" ]

[ null, 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ZbZomELHuzwIHtstkdimZIqli++gAsugMcfT2+GY47JnEa2zTYreXPGmzCuK8x+P/G5CFVgx4uhVV+osmLDTZIkSZIkacOU1WWyEEIHoGfx0xnA3jHGKaXZI8b4anGhbDzQGDgvhPBSjPHRsp1WkiRJkiRJkiRJklQZFcUibnvrNi7936UsKVySWG7X3bsy6LBB1MqrlVimpIpj4UK44Qa46SZYktw/Tb+y7bYwZAgctbIDv5bOhncvg89HQEInOf5K472h/Qio3yr5bEmSJEmSpCyW1WUyYEDxfQR6l7ZItkyM8ZsQwiXAPUAArgEsk0mSJEmSJEmSJEmSVmvq3KmcOvZUnvvqucQyN6q1EXcfczfHbH9MYpmSKo4YYcyYzGlk336bzgw1a0KfPnDhhVCt2gpvxgjf/B3evgAW/5j8cHkNoM2NsM3pEHKSz5ckSZIkScpyWVsmCyG0BFoWP10E/H09t/w7MAyoAewUQmgZY5y8nntKkiRJkiRJkiRJkiqp/5v8f3R9oiuzF89OLPOY7Y7h7mPvZqNaGyWWKani+Phj6NkT/vvf9GY46SS4+WbYfPOVvDnvcxh/LvyQ0oBbdoLdBkF1/w2VJEmSJElalawtkwFti+8j8FWMcfH6bBZjXBRC+JLlBbW2gGUySZIkSZIkSZIkSdKvzFk8h+5PdWf0+6MTy6xZtSaDDx/MGbudQQghsVxJFcO8eTBgAAweDAUF6cyw004wdCgcdNBK3ixcAh8NhA+ugaIlic9GnRbQ7g5oenDy2ZIkSZIkSRVMNpfJmpZ4XFafMpXcp+kqV0mSJEmSJEmSJEmSNkgvf/Myncd05ts53yaWuUezPXiww4O0aNQisUxJFUOM8PDD0KsXfP99OjPUqQNXXQXdu0PVqitZ8ONLMP5smPtx4rORkwc7XQYtL4Xc6snnS5IkSZIkVUDZXCbLL74PQPMy2rPkPvmrXCVJkiRJkiRJkiRJ2qAsKVhCvxf6MfD1gURiIpm5IZe++/fliv2voEpONv/6XlIa3nsPevSAV15Jb4aTT4Ybb4SmK/vK5sUz4N1e8OX9SY+VsfHvMqeR1d0+nXxJkiRJkqQKKps/jf6uxOOGIYT9Yozr/PFYCOEAoFGJl6at82SSJEmSJEmSJEmSpEpj8vTJdBrTiXd/eDexzG0bbsvoDqPZY7M9EsuUVDHMmgX9+sHtt0NRUToztGkDw4bBPvus5M0YMwWyd3vBkpkJTwZUawy73QJbdoIQks+XJEmSJEmq4LK5TPZW8X0kczrZoBDCXjHGwtJuFEKoAty8wstvrud8kiRJkiRJkiRJkqQKrCgWMfStoVzyv0tYUrgksdwzdzuTWw6/hdp5tRPLlJT9iorgvvvg0kthxox0ZmjQAK69Fs46C3JzV7Jgzkcw/myY/nLiswGwzRnQ5kao1jCdfEmSJEmSpEoga8tkMcavQwhvAHuSKZTtDowJIfwlxrhgbfcJIdQC/l58fSx++Y0Y49dlPLIkSZIkSZIkSZIkqYL4bu53dHm0C//98r+JZTap2YS7j72bY7c/NrFMSRXD+PHQrVvmPg0hwJlnZopkjRuvZEHBIph8LXx0ExTlJz4f9VpCuztho32Tz5YkSZIkSapksrZMVuxi4BUyJ5MF4GjgkxDC1cA/YoyzV3VhCKE+8GegD7AJy084KwJ6levUkiRJkiRJkiRJkqSs9a8P/8VZj5/FrMWzEss8usXR3HPsPWxce+PEMiVlv59+gssvh3vugRjXvL487LEHDB8Ou+++igXfPwvjz4X5XyQ6FwC51aFVP9jhIsjNSz5fkiRJkiSpEsrqMlmM8Y0QwgDgSpaXwTYFbgeGhBDeBz4AZgILgZpAY6AV0BqoWnxNyY/bro4xvpHUzyBJkiRJkiRJkiRJyg5zFs+h59M9GfXeqMQya1atyS2H3cJZu59FCCGxXEnZraAARoyAPn1g9ux0ZmjSBG66CU4+GXJyVrJg0Q/w9gXwzd8Tnw2ATY6AdsOh9tbp5EuSJEmSJFVSWV0mA4gxDgghFABXs7wUFoA8oC2wsu9FKvkJ/LISWgT6xRivKcdxJUmSJEmSJEmSJElZ6JVvXqHzmM58M+ebxDLbbdqO0SeMZrtG2yWWKSn7vfIKdO8O77+fTn5ubib/yiuhfv2VLIhF8PkIePcyyJ+T8HRA9aaw+xDY4kSwhCtJkiRJklTmsr5MBhBjvC6E8CJwF7DTspdXd0nxfSi+fQR0jTG+Wm5DSpIkSZIkSZIkSZKyztLCpfR/oT83vnYjcbW/Zi47OSGHPvv1oc/+faiaWzWRTEnZb9o06N0bHnoovRkOOACGDoXWrVexYNZ7MK4rzHwr0bkyArQ4F3a5FvLqpZAvSZIkSZK0YagQZTKAGOPrIYTWwKHAacCBwEaruWQ68BJwL/BsjDGZ3wpIkiRJkiRJkiRJkrLChz99SKdHOvHOD+8klrlNg214sMOD7LX5XollSspuS5fCbbfBVVfB/PnpzLDppjBoEPzpT6s47Ct/Pky6Ej4ZDLEw4emABm2g3Qho3D75bEmSJEmSpA1MhSmTARQXwp4tvhFC2ALYCqgP1AYWALOBL2OM36YzpSRJkiRJkiRJkiQpTTFGho0bRu//9WZxweLEcs/Y9QxuPeJWaufVTixTUnb773+hZ0/4+ON08qtWhQsvhD59oPaq/mma+jhM6A4LU/hTmyq1YOerYbsekFOh/oxJkiRJkiSpwqrQn8IUF8YsjUmSJEmSJEmSJEmSAJg2bxpdHu3Cs188m1hm45qNGXnMSI7f4fjEMiVlt2++gYsugn//O70ZDjsscyLa9tuvYsHCqTChJ0wdk+hcv9jseNj9Nqi1eTr5kiRJkiRJG6gKXSaTJEmSJEmSJEmSJGmZf3/4b8564ix+XvRzYplHtTiKe469h6a1myaWKSl7LV4MN98M110HixalM8OWW8Ktt8Jxx0EIK1lQVACfDoP3+0LB/KTHg5qbQ9thsNmxyWdLkiRJkiTJMpkkSZIkSZIkSZIkqWKbu2Qu5z19Hve/e39imTWq1GDQYYM4u+3ZhJW2NSRtaJ54As47D778Mp386tXh0kuhd2+oUWMVi2aOh3FdYdY7ic4GQMiF7c+H1ldC1drJ50uSJEmSJAmwTCZJkiRJkiRJkiRJqsBe/fZVOo/pzNezv04ss+2mbRndYTTbN94+sUxJ2evzz+H88+HJJ9Ob4fjj4ZZbYKutVrFg6Rx4vw98OhyICU5WrNEe0P5OaNAm+WxJkiRJkiT9imUySZIkSZIkSZIkSVKFs7RwKVe9eBU3vHYDRbEokcyckMPl+15OvwP6UTW3aiKZkrLXggVw3XVw882wdGk6M7RoAbfdBkccsYoFMcKUf8HE82DR94nOBkDVetDmetjmLMjJTT5fkiRJkiRJv1GhymQhhNbAkcBuwOZAPaAGEEq5VYwxblPG40mSJEmSJEmSJEmSEvDxjI/p+EhH3v7+7cQyt6q/FaNPGM3em++dWKak7BQj/OtfcOGFMHVqOjPUqgV9+2ZORKtWbRWL5n8F47vB908lOdpyzf8Mu90KNZqmky9JkiRJkqSVqhBlshDC7sAwoP2Kb63jlnH9JpIkSZIkSZIkSZIkJS3GyO3jb6fXf3uxqGBRYrmntTmNwUcMpk61OollSspOH34IPXrA88+nN8Of/wwDB8Jmm61iQVE+fDQIPhgAhcn9W/mL2ltD29th08OTz5YkSZIkSdIaZX2ZLIRwCjASyGV5eSyucF+qLctiLkmSJEmSJEmSJElScr6f9z2nPXYaT3/+dGKZjWo0YuQxI+mwY4fEMiVlp7lz4aqr4LbboKAgnRlatYKhQ+HAA1ez6KfXYFxXmDM5qbGWy6kKO/aGlldAlRrJ50uSJEmSJGmtZHWZLISwD3A3mSJZLL6F4lsBMBtYkNZ8kiRJkiRJkiRJkqTyN+ajMZz5+JnMXDQzscwjtj2Ce4+9l03qbJJYpqTsEyOMHg29esGPP6YzQ926MGAAnHsuVK26ikVLfoZ3L4UvRiY62y+a7Aft74R6O6WTL0mSJEmSpLWW1WUy4GaWF8kCsBAYCvwD+CDGmNJ3PUmSJEmSJEmSJEmSytu8JfM47+nzuO/d+xLLrF6lOoMOG8Q5bc8hhJBYrqTs8+670L07vPZaejN06QLXXw8bb7yKBTHC1w/B2xfCkp8SnQ2AvIaw60DY+lQIOcnnS5IkSZIkqdSytkwWQmgO7MHyItl3wEExxs9SHUySJEmSJEmSJEmSVO5en/I6ncd05stZXyaWudsmu/HQCQ+xQ+MdEsuUlH1+/hn69oU774SionRm2G03GD4c9txzNYvmfgrjz4Ufn0tsrl/Z6pRMkax6k3TyJUmSJEmStE6ytkwG7F18H8gUyrpZJJMkSZIkSZIkSZKkyi2/MJ+rXrqK61+9nqKYTIsjJ+Rw6T6X0v/A/uTl5iWSKSn7FBbCPffA5ZfDzJnpzNCwYeYkstNPh9zcVSwqXAIf3gCTr4OipYnOB0Dd7aHdnbDxgclnS5IkSZIkab1lc5msaYnHs4HHU5pDkiRJkiRJkiRJkpSAT2Z8QqcxnZgwbUJimVvV34oHOzzIPlvsk1impOzz5pvQvTtMnJhOfghw9tlw9dXQqNFqFv74Aow7G+Z9mthsv8ipBi2vgJ16Q2615PMlSZIkSZJUJrK5TLbsU6cIfBljjGkOI0mSJEmSJEmSJEkqHzFG7pxwJxc9exGLChYllntqm1MZcsQQ6larm1impOwyfTpceincd196M+y1FwwbBrvttppFi6fD2xfD1w8mNtevND0E2t4OdVukky9JkiRJkqQyk81lsuklHmfznJIkSZIkSZIkSZKkdfTD/B84/bHT+c9n/0kss2GNhtz1+7v4w05/SCxTUnYpKIDbb4d+/WDOnHRm2HhjuOkm6NQJcnJWsSgWwRf3wru9YemsROcDoPpGsNut0PwvmePTJEmSJEmSVOFlc0lrQvF9ADZPcxBJkiRJkiRJkiRJUtkb+/FYznz8TGYsnJFY5uHbHM69x93LpnU2TSxTUnZ56SXo0QMmTUonPzcXevaE/v2hXr3VLJw9GcZ3hZ9eS2y2X9m2K7S5HvIapJMvSZIkSZKkcpG1ZbIY4/shhE+A7YEGIYR2Mcbxac8lSZIkSZIkSZIkSVo/85fO5/ynz+eed+5JLLN6leoMPHQg3dp1I3i6jrRB+u476NUL/va39Gb43e9g6FBo2XI1iwoWwgdXw0c3QyxIbLZf1G8N7UZAk72Sz5YkSZIkSVK5y9oyWbEBwEPFj/sDv09xFkmSJEmSJEmSJEnSenpjyht0HtOZL2Z9kVjmrk13ZfQJo9mpyU6JZUrKHkuXwuDBMGAALFiQzgybbQaDBsGJJ8Jq+6zTnoLx3WDBV4nN9ovcmtD6StjhfMipmny+JEmSJEmSEpGT9gCrE2P8G/AwEIAjQwj9Ux5JkiRJkiRJkiRJkrQO8gvz6fdCP/a9b9/EimSBwGX7XsabZ7xpkUzaQD3zDLRuDZdckk6RLC8PLr8cPv4YTjppNUWyhdPg1ZPgxaPSKZJtejQcPRl26mWRTJIkSZIkqZLL9pPJALqQKb39GegXQtgZuCLG+HG6Y0mSJEmSJEmSJEmS1sanMz+l0yOdGD9tfGKZzes158EOD7Jf8/0Sy5SUPb7+Gi64AMaOTW+GI4+EIUOgRYvVLCoqhM/ugPevgPy5ic32ixqbwu63weYnrOHINEmSJEmSJFUWWV0mCyH0K374MfAlsDVwPHB8CGESMAGYDiwu7d4xxgFlNKYkSZIkSZIkSZIkaSVijIyYOIKLnr2IhfkLE8s9eZeTue2I26hXvV5imZKyw6JFMHAgXH89LC71X5OUja22ypTIfv/7NfSzfn4HxnWFn5Mr2v4i5ECL7rDL1VC1bvL5kiRJkiRJSk1Wl8mAK4FY4nkEln3MtjPQej32tkwmSZIkSZIkSZIkSeXkx/k/cvpjp/PkZ08mltmgegPuOuYu/rjTHxPLlJQdYoTHHoPzz8+cSpaG6tXh8suhV6/M41XKnwfv94NPb4NYlNh8v2i4O7QfkbmXJEmSJEnSBifby2QrE9e8ZLVCGewhSZIkSZIkSZIkSVqFxz55jDMeO4OfFv6UWOahWx/KfcfdR7O6zRLLlJQdPv0UzjsPnn46vRlOOAEGDYItt1zDwiljYWIPWDg1galWUKUO7HINtOgGObnJ50uSJEmSJCkrVIQyWVjzEkmSJEmSJEmSJElS2uYvnc+Fz1zIyLdHJpZZLbcaNx16E93bdycn5CSWKyl98+fDtddmSlz5+enMsP32cNttcNhha1i44FuY0AO+eyyRuX5j8z/A7kOgpoVbSZIkSZKkDV22l8l+l/YAkiRJkiRJkiRJkqQ1e3Pqm3Qe05nPf/48scw2TdswusNoWm7UMrFMSemLEf7v/+Cii+C779KZoXZt6NcvcyJaXt5qFhYVwCdDYFJ/KFiQ2Hy/qNUc2g6HZkcnny1JkiRJkqSslNVlshjjS2nPIEmSJEmSJEmSJElatfzCfK595VquefkaCmNhIpmBQO99enPVgVdRrUq1RDIlZYcPPoAePeDFF9OboWNHuOkm2HTTNSyc8RaM6wqz30tkrl8JubDDRdC6H1SplXy+JEmSJEmSslZWl8kkSZIkSZIkSZIkSdnrs5mf0WlMJ8Z9Ny6xzC3qbcGDHR5k/+b7J5YpKX1z5sCVV8LQoVCYTG/1N3beOZO//5r++Vk6G967HD67E4gJTLaCxntB+xFQv3Xy2ZIkSZIkScp6lskkSZIkSZIkSZIkSaUSY2Tk2yO54JkLWJi/MLHczjt3ZuiRQ6lXvV5imZLSVVQEo0bBJZfA9OnpzFCvHlxzDZx9NlRZ3V/axAjf/APevgAW/5DYfL+oWh92vRG2OQNCTvL5kiRJkiRJqhAsk0mSJEmSJEmSJEmS1tr0BdM547EzePzTxxPLbFC9AXf+/k5OanlSYpmS0vf229C9O7zxRnoznH46XHcdbLTRGhbO+wLGnws/PJvIXL/R/K+w2y1QY+N08iVJkiRJklRhWCaTJEmSJEmSJEmSJK2VJz59gtMfO53pC5I7HuiQrQ/h/uPup1ndZollSkrXzJlwxRVw112Zw77S0LYtDB8O7duvYWHhUvhoIEy+BgoXJzLbr9TeFtrdDpscmny2JEmSJEmSKqQKWSYLIdQB9iy+bQE0AOoA84BZwDfAm8BbMcZ5ac0pSZIkSZIkSZIkSZXBgqULuOjZixgxcURimdVyq3HDITfQc4+e5IScxHIlpaewEEaOzBTJfv45nRkaNYIbboDTToOcNf3TM/1lGHc2zP0okdl+JScPdroUWl4GudWTz5ckSZIkSVKFVaHKZCGENsAFwElA3lpcsiSE8A9gcIzxvfKcTZIkSZIkSZIkSZIqo3HfjaPTI5347OfPEsvceeOdeeiEh2i1UavEMiWl6/XXoXt3eOeddPJzcuCcc2DAAGjYcA2Ll8yEd3rBl/clMttvbHQgtLsD6u2QTr4kSZIkSZIqtArx9W0hhCohhOuA8UAnoBoQim8rvaT4Vh04GZgQQrg2hFChynOSJEmSJEmSJEmSlJaCogIGvDSAve/ZO7EiWSDQa+9ejDtjnEUyaQPxww9w6qmwzz7pFcn23RfefhuGDVtDkSxG+PIBeGKHdIpk1RrDng/Awc9bJJMkSZIkSdI6y/pyVXEB7FHgCJaXx2KJx6sqlC1bB5ALXArsEkI4LsZYWB6zSpIkSZIkSZIkSVJl8PnPn9N5TGfenPpmYpmb192cUR1GceCWByaWKSk9+fkwfDj07w9z56YzQ9OmMHAgdOwIYXV/fQIw52MYfw5MfzGJ0X5r69Ng15ugWqN08iVJkiRJklRpZH2ZDBgBHFn8eFmJLACvA88B7wEzgAVALaAxsAtwELDPCtcdWbzfGQnNLkmSJEmSJEmSJEkVRoyRe965h/OfPp8F+QsSy+3YuiPDjhpG/er1E8uUlJ4XXoAePWDy5HTyq1SB88+Hvn2hbt01LC5cDJOvgw9vgKL8JMb7tbo7QvsRsNF+yWdLkiRJkiSpUsrqMlkIYR+gC8tPGAvAU8CFMcZPVnPpI0D/EML2wCDgKJYXyrqEEO6JMb5RfpNLkiRJkiRJkiRJUsXy04KfOOPxM3jsk8cSy6xfvT53HH0Hf27158QyJaVnyhS4+GL4v/9Lb4aDD4ahQ2HHHddi8Q//g3HnwPzPy32u38itDq36wg4XQ25e8vmSJEmSJEmqtLK6TAZcWXwfyJTBrokx9lvbi4sLZ78PIVwF9GV5oexK4PAynVSSJEmSJEmSJEmSKqgnP32S0x87nR8X/JhY5kFbHcT9x93P5vU2TyxTUjqWLIFbboFrroGFC9OZYfPN4dZb4YQTIIQ1LF70I7x9IXzzcCKz/cYmh0Pb4VBnm3TyJUmSJEmSVKllbZkshFAXOIDlp5KNLU2RrKQYY/8QQiugQ/FLB4YQ6sQY55XBqJIkSZIkSZIkSZJUIS1YuoCLn72YOyfemVhmXm4eNxx8A+fteR45ISexXEnpeOopOO88+OyzdPLz8qB3b7jsMqhZcw2LYxF8PhLevRTyZycx3q9Vbwq7D4YtTlqLxpskSZIkSZK0brK2TAbsy/L5ItB/Pffrz/IyWZXi/Z9azz0lSZIkSZIkSZIkqUIa/914Oo3pxKczP00ss/VGrXnohIdovXHrxDIlpePLL+GCC+Cxx9Kb4fe/z5xGtu22a7F41vsw/myY8Ua5z/VbAVqcA7tcC3n1U8iXJEmSJEnShiSby2Sblng8Lcb4wfpsFmP8IITwHdCs+KVmq1svSZIkSZIkSZIkSZVRQVEB179yPQNeHkBBUUEimYHAhXtdyDUHXUP1KtUTyZSUjoUL4cYbM7clS9KZYZttYPDgTJlsjQoWwKSr4ONbIBaW92i/VX8XaD8CGu+RfLYkSZIkSZI2SNlcJmtcfB+BaWW05/csL5E1KqM9JUmSJEmSJEmSJKlC+OLnL+g8pjNvTE3u5J3N6m7GqONH8butfpdYpqTkxQhjx2ZOI/vmm3RmqFED+vSBCy+E6mvTW/3uCZjQHRakMHCVWtB6AGzfE3Ky+c93JEmSJEmSVNlk86dRC0o8rldGe9Yt8XhhGe0pSZIkSZIkSZIkSVktxsh9797HeU+fx/yl8xPL/UurvzD8qOE0qNEgsUxJyfvkE+jZE559Nr0ZTjwRbr4ZtthiLRYvnAoTz4Mpj5T7XCu12XGw+21Qa22GlSRJkiRJkspWNpfJphffB2DLEEL9GOPsdd0shFAf2IrMSWcl91c5CiFsCUwCahe/9E2MccvUBpIkSZIkSZIkSZI2MD8t+ImznjiLsR+PTSyzXrV63H707fy19V8Ty5SUvHnz4OqrYfBgyM9PZ4Ydd4ShQ+Hgg9dicVEhfDoM3u8DBckVa39RczPYfShsfnzy2ZIkSZIkSVKxbC6TvVN8H4GqwGnALeux32nF+yzb853VrFUZCCEE4B6WF8kkSZIkSZIkSZIkJeipz56iy6Nd+HHBj4llHrjlgTxw/ANsUc8Td6TKKkb429/g4ovh++/TmaFOHbjySujRA6pWXeNymDkBxnWFWW+X92i/FXJgu/Ng56ugap3k8yVJkiRJkqQSsrZMFmP8NITwBbA1mdPJrgoh/C/G+H5p9wohtAauIlMiC8CXMcZPy3RgrczZwEHAj8DGKc8iSZIkSZIkSZIkbTAW5i+k17O9uH3C7Yll5uXmcd1B13HBXheQE3ISy5WUrPffzxS4Xn45vRk6d4Ybb4RNNlmLxflz4b0+8NlwiEXlPttvNGwH7UdAw12Tz5YkSZIkSZJWIts/wR9BpvwVgVrAiyGE40uzQQjhWOAFoGaJve4o2zG1ohBCc+Cm4qc90pxFkiRJkiRJkiRJ2pBMmDaB3UbslmiRrNVGrRh/5ngu2vsii2RSJTV7NvTsCbvuml6RbJdd4JVXYNSotSiSxQjf/gue2BE+HZp8kaxqXWg7DA57wyKZJEmSJEmSskq2f4p/G/BV8eMI1Af+HUJ4OYRwaghhi5VdFELYovj9F4ExQMMSb38JDC2/kVXsHqA2MDbG+M+0h5EkSZIkSZIkSZIqu8KiQq59+Vr2umcvPpn5SWK5F+55IePPHM/OG++cWKak5BQVwb33wnbbwdChmedJq18fhg+HiRNh333X4oL5X8NLv4dXT4RF08p5upXY4iQ4+iPYrhvk5CafL0mSJEmSJK1GlbQHWJ0Y49Lik8VeJlMki2ROF9un+EYIYS4wE1hA5vSyRkDdEtuEEtf9DBwXY8xP6EfIWiGEbYD2wGZAHjAL+Bh4Pca4eD337gocDMwGzl2/SSVJkiRJkiRJkiStyZezvqTzmM68PuX1xDKb1WnGA8c/wMFbH5xYpqRkjR8P3bvDuHHp5IcAZ5wB114LTZqsxQVF+fDxrTDpSihcVN7j/VatraDd7bDpEclnS5IkSZIkSWspq8tkADHGySGEw4F/As3JFMMgUw4DqFd8W+nlLC+SfQ2cGGP8sPymXTchhGZkil17FN+3BeqUWPJNjHHLMso6HugL7LaKJfNDCPcDV8UYZ6zD/lsAA4uf9ooxfr8uc0qSJEmSJEmSJElasxgj9797Pz2f7sn8pfMTy/1Tyz9xx9F30KBGg8QyJSVnxgy4/HK4+26Icc3ry8Mee8CwYdC27Vpe8NPrMP5smD2pXOdaqVAFduwFrfpAlZrJ50uSJEmSJEmlkPVlMoAY44QQQmvgeqALsOyTt9V9ZBmKbwuAe4ErYozJ/fZkDUII+wAXkSmQbZpAXjXgHqDjGpbWBroDfwoh/DHG+HIpo0aSKcI9H2O8u/STSpIkSZIkSZIkSVobMxbOoOsTXXnko0cSy6xbrS63H3U7f239V0IIa75AUoVSWAgjRkCfPjBrVjozNGkCN94Ip5wCOTlrccHSWfDupfD5XeU+20o12Rfa3Qn1W6aTL0mSJEmSJJVShSiTARQXwXqEEPoAfwUOIFPE2hwo+fFhETAFeBN4CfhbjHFOwuOujXZAhySCQgg5wD+A41Z4qxD4FpgDbMWvT3hrAjwVQjgkxvjGWuacARwGLATOWt+5JUmSJEmSJEmSJK3c058/TZdHu/DD/B8Syzyg+QE8cPwDNK/fPLFMScl59VXo0QPefTed/Jwc6N4drroK6tdfiwtihK8fhncuhMXTy3u838prALsOhK27QFib1pskSZIkSZKUHSpMmWyZ4mLYHcU3AEII9cicqDU/S4tjpTWfzM9TVnrx2yLZncDVMcZp8Evh7DhgMLBF8ZqawP+FEFqt6b9rCGEzYFDx034xxi/KaHZJkiRJkiRJkiRJxRbmL+SS/17CsPHDEsusmlOVaw+6lgv3upDcnNzEciUl4/vvoXdvGD06vRn23x+GDoWdd17LC+Z+BhPOhR/+V65zrdKWnWG3m6H6RunkS5IkSZIkSeuhwpXJVqa46FRRS2TzgInAeGBc8f1WwAtlsXkIoRFwxQovXxZjvKHkCzHGImBMCGEc8CqwZfFbmwEXAv3XEDUSqEtm/sHrN7UkSZIkSZIkSZKkFb39/dt0fKQjH8/4OLHMlk1aMvqE0bRp2iaxTEnJyM+H227LnAQ2b146M2y6Kdx8M/z5zxDCWlxQuAQ+vBEmXwdFS8p9vt+osx20uwOaHpR8tiRJkiRJklRGKkWZrIJ6HHgW+Li4yPWLEMJWZZjTG6hT4vnLwI2rWhxj/C6EcAZQ8uu7Lggh3BZjnLmya0IIpwFHAPnA6THGwvUfW5IkSZIkSZIkSRJAYVEhN712E/1e7EdBUUFiuefvcT7XH3I91atUTyxTUjL+9z/o2RM++iid/KpV4YILoE8fqFNnzesB+PFFGH82zP2kPEdbuZw8aHk57HQp5FZLPl+SJEmSJEkqQ5bJUhJj/KK8M0IIOUCXFV6+MsYYV3ddjPG5EMIrwH7FL9UBTgLuWElGM+CW4qc3xhgnrd/UkiRJkiRJkiRJkpb5atZXnDz2ZF799tXEMjetsykPHP8Ah2x9SGKZkpLx7bdw0UXwr3+lN8Ohh2ZORNthh7W8YPFP8M7F8NWocp1rlTY+KHMaWd3t0smXJEmSJEmSyphlssptb6BJiedfAi+u5bX3sLxMBnA8KymTAT2BesBC4PMQwp/XsG+tEmsWxBgfX8t5JEmSJEmSJEmSpA1GjJFR742ix1M9mLd0XmK5J7U8iTuOvoOGNRomlimp/C1eDIMGwbXXwqJF6czQvDnceiscfzyEsBYXxCL48j54pzcs/bm8x/utak1gt1tgy45rObAkSZIkSZJUMWR1mSyEsC/wUomXDokxvrAO+xwE/Lf4aQT2iDFOLIMRs93RKzz/75pOJSu5doXnB4YQasUYF6zwerXi+5rA/Wuxb2Pgb8WPvwEsk0mSJEmSJEmSJEklzFw4k65PdOXfH/07scy61eoy/KjhdGzdkWBpQqpUnnwSzjsPvvginfxq1eDSS6F3b6hZcy0vmvMhjDsbfnqlXGdbpW3OhDY3QDWLtZIkSZIkSap8srpMBnQFlv2mYty6FMkAYozPhxDeAXYr3u9MYEMok7VZ4fnra3thjHFaCOFrYMvil/KAnYDxZTGYJEmSJEmSJEmSpN969otnOXXsqXw///vEMvdvvj+jjh9F8/rNE8uUVP6++ALOPx+eeCK9GY47Dm65Bbbeei0vKFgEk6+BjwZCUX65zrZS9VpB+zuhyT7JZ0uSJEmSJEkJyUl7gFUJIeQAR5E5SSwCD63nlqOK7yNw7HruVVHsuMLzD0t5/YrrV9yPGOP5McawpluJS74p8fqWpZxHkiRJkiRJkiRJqpQW5S+i51M9OXz04YkVyarmVOWGg2/g+ZOft0gmVSILFkCfPrDTTukVyVq0gP/8B8aOLUWRbNoz8J9WMPm65ItkuTUyJ5Ed+bZFMkmSJEmSJFV62XwyWWugQfHjCDy5nvs9CQwmczLZxiGE7WOMn6znnlkrhFAD2GKFl6eUcpsV12+/7hNJkiRJkiRJkiRJWpl3vn+Hjo905KMZHyWWuVOTnRjdYTS7brJrYpmSyleM8O9/w4UXwpTS/nVAGalZE/r2hQsugGrV1vKiRd/DxAvg23+U62yrtOlR0HYY1N4qnXxJkiRJkiQpYdlcJit5CtbsGOOX67NZjPGLEMJsoH7xSy2BSlsmAxqTKc4tkw9ML+Ue363wfKP1mkiSJEmSJEmSJEnSLwqLCrn59Zvp+0Jf8hM8hadn+57ccMgN1KhaI7FMSeXro4+gRw947rn0ZvjTn2DgQNh887W8oKgQPh8B710G+XPLdbaVqrEp7D4ENv8DhLDm9ZIkSZIkSVIlkc1lsqbF95HflprW1VSWl8maldGe2ar2Cs8XxhhjKfdYsIY9UxVC2AhoUsrLtimPWSRJkiRJkiRJkqTS+Hr215w85mRe+faVxDI3qb0J9x9/P4dtc1himZLK19y5MGAADBkCBQXpzNCyJQwdCr/7XSkumvUujOsKM8eV11irEWC77rDLNVC1bgr5kiRJkiRJUrqyuUxWs8TjFUtN66rkPllVjCoHK/58i9dhj0Vr2DNt5wL90x5CkiRJkiRJkiRJWlsxRka/P5pu/+nGvKXzEsv9405/5M6j76RRzUaJZUoqPzHCQw9Br17www/pzFC3Llx1FXTrBlWrruVF+fNhUn/4ZAjEwnKdb6Ua7AbtR0CjtslnS5IkSZIkSVkim8tkc0o8LqvfaDQs8XhhGe2Zraqv8HzpOuyxZIXnNdZxFmKMYV2vlSRJkiRJkiRJkiqDnxf9zNlPnM0/P/xnYpl18uow7KhhdN65MyH4KzupMnj3XejRA159Nb0ZTjkFbrgBmjYtxUVTH4UJPWDhlHKba5Wq1Iadr4HtukFONv+pjCRJkiRJklT+svkTsp+K7wOweQihRoxxxZOy1loIoSbQHIgr7F9ZrXgSWd467FFtDXtKkiRJkiRJkiRJWgv/+/J/nDL2FKbNm5ZY5r5b7Muo40exVYOtEsuUVH5+/hn69YM77oCionRm2G03GDYM9tqrFBctmAITe2TKZGnY/ATYfQjU3CydfEmSJEmSJCnLZHOZ7OMSj/OAw4D1+WTxcJYXqiLwxXrsVRHMX+H5iieVrY0VTyJbcc+03Q6U9msbt2H9/nckSZIkSZIkSZIkrbVF+Yu47LnLGPLWkMQyq+RU4erfXU2vvXuRm5ObWK6k8lFUBPfeC5ddBjNmpDNDw4Zw3XVwxhmQu7b/rBQVwCe3waR+ULCgXOdbqZpbQLvh0Oz3yWdLkiRJkiRJWSxry2QxxvdDCNOBJmROJ+vL+pWA+pApkQVgNjBufWfMcisWv2qGEEKMMa509crVWsOeqYoxTgeml+aaEEI5TSNJkiRJkiRJkiT92rs/vEvHRzry4U8fJpa5Q+MdeOiEh9htk90Sy5RUfsaNg+7dYfz4dPJDgK5d4ZproFGjUlw4YxyM7wqz3i2v0VYt5MIOF0DrK6HKin/2IEmSJEmSJCkn7QHWYCyZ8hfAriGEW9Zlk+Lrdi1+GoGxpSxVVUQzyPysy1QFNirlHs1WeF6q4pYkSZIkSZIkSZK0ISosKuSm126i/cj2iRbJurfrzsSzJlokkyqB6dPh9NNhjz3SK5LtuSdMmAB33FGKItnSOTC+Gzy7ZzpFskZ7whETYdeBFskkSZIkSZKkVcjak8mKXQucSqYIFYDzQgiNge4xxrlrujiEUBcYDvyV5aeSLQWuKa+Bs0WMcVEI4VugeYmXtwB+LMU2W6zw/OP1HkySJEmSJEmSJEmqxL6Z/Q2njD2Fl755KbHMprWbcv9x93P4tocnlimpfBQUZMpbffvCnDnpzLDRRnDTTdC5M+Ss7VcUxwjf/h9MPB8W/1Ce461c1XrQ5gbY9iwI2f69ypIkSZIkSVK6srpMFmOcEkK4HujP8jJYR+DYEMIo4D/AhBjjjGXXFJfN2gJHAZ2Buiw/3SwCN8YYv0rup0jVx/y6TLYTUJrvLNtxJftJkiRJkiRJkiRJWkGMkYcmPUS3/3Rj7pI1fi9mmTlhxxMY8fsRNK7ZOLFMSeXj5Zehe3eYNCmd/Nxc6NEDrrwS6tUrxYXzv8ycRvb90+U12uo1/wvsdgvUaJpOviRJkiRJklTBZHWZDCDGeFUIoRXwB5YXyuoC3YpvhBAisBCoyfLiGPy6RBaA/4sx9k9o9GzwLlDy6wf3Bh5YmwtDCJsAW5Z4KR/4sKwGkyRJkiRJkiRJkiqLWYtmcc6T5/CPyf9ILLN2Xm2GHjmUU3Y5hRDCmi+QlLWmTYNeveDhh9Ob4cADYehQaNWqFBcVLoWPb4YProbCxeU12qrV3gba3Q6bHJZ8tiRJkiRJklSBZX2ZrNhfgIHAeWSKYcuEEve1V7gmsrxEBjAIuLQcZ8xGTwCXlHh+SAghxBjjqi4oYcVPW1+IMc4vu9EkSZIkSZIkSZKkiu+5L5/jlLGn8N287xLL3GfzfRjVYRRbN9g6sUxJZW/pUhgyBAYMgPkp/Ta+WTMYNAhOOglK1Uud/iqM7wpzUvhO2pyqsOMl0PJyqFIj+XxJkiRJkiSpgstJe4C1EWMsiDFeABwJvEWmIFby1LEVb5RY8ypwWIyxV4yxMNHB0/c6MKPE862BA9fy2tNXeP5oWQwkSZIkSZIkSZIkVQaLCxZz4TMXcsiDhyRWJKuSU4VrD7qWl059ySKZVME9+yzsvDP07p1OkaxqVbjsMvj4Y/jTn0pRJFsyE946A/63XzpFso32hyPfg12utkgmSZIkSZIkraOKcjIZADHGZ4BnQgjtyJyctR+wDdAQqAPMA34GPgNeAZ6OMb6T0ripizEWhRDuBy4u8XL/EMKLqzudLIRwMJn/tsvMA/6vfKaUJEmSJEmSJEmSKpb3fniPTmM68cH0DxLL3L7R9jx0wkPsvunuiWVKKnvffAMXXgiPPJLeDEcckTkRbbvtSnFRjPDVg/DORbBkxprXl7VqjWDXm2GrU0p5hJokSZIkSZKkFVWoMtkyMcbxwPi056ggbgTOBmoXPz8AuAS4YWWLQwjNgLtXeHlIjDGFT4MlSZIkSZIkSZKk7FEUi7jljVu44vkrWFq4NLHcbu26cdOhN1Gzas3EMqVstnQpfPABTJyYuX3+OSxcCIsXZ97Ly4Pq1aFmTdh2W9h998ytVavMe2lYtAgGDoTrr8/MmYattoLBg+GYY0rZx5r7CYw/B358obxGW72tu0Cbm6B643TyJUmSJEmSpEqmQpbJKosQwj5AjZW8tcsKz6uHEA5ZxTbTYowfriojxjgjhHAdcF2Jl68PIWwBXBNjnFY8Sw5wLDAE2KLk/sCg1f8kkiRJkiRJkiRJUuX27ZxvOWXsKbz49YuJZTat3ZR7j72XI1scmVimlI3y8+Gxx+C//82Ux95/P1MaWxvPPbf8cV4e7Lxzplh26KFw7LFQtWr5zLxMjPD443D++fDVV+WbtSrVq8Nll0GvXlBjZX+hsCqFi2Hy9fDhDVCUXIH2F3V3gHZ3wsYHJJ8tSZIkSZIkVWIhxpj2DBusEMLXQPP13OaBGOOpa8jJAR4Ffr/CW4XAN8AcYCug/grvLwIOjTG+tp4zZo0QQkvgg2XPP/jgA1q2bJniRJIkSZIkSZIkScp2D096mHOfPJc5S+Yklnn8Dscz8piRNK7pSTzacE2dCiNHwl13wQ8/lP3+m2wCZ56ZuW22Wdnv/9lncN558NRTZb/32urQAW65BbbcspQX/vBc5jSyeZ+Vx1irl1MNWvWBHXtBbrXk8yVJkiRJkqRyNnnyZFq1alXypVYxxslJ5eckFaT0xBiLgBOBv6/wVi6wNbArvy2SzQSOqkxFMkmSJEmSJEmSJKk0Zi2axV///Vc6PtIxsSJZ7bza3HPsPTxy0iMWybRBijFzmtgf/pApQA0YUD5FMoDvv8/sv+WWmbznnsvkr68FC+Dyy6FVq/SKZNttB08/DY88Usoi2eLp8HoneP6QdIpkTQ+Foz/IlMkskkmSJEmSJEnlokraA6yLEEIgU4DaEWgI1CNTjBsVY/w6xdGyVoxxMfCXEMK/gD5Am1UsXQA8AFwVY5ye0HhlLoRwKnDqSt6qmewkkiRJkiRJkiRJqoie/+p5Thl7ClPnTk0sc6/N9uLBDg+yTcNtEsuUssknn8Dpp8NrCX/laWFhpnT1yCOwzz5w772ZMlZpxQj//CdcdFHmVLU01KoF/frB+edDXl4pLoxF8MXd8M4lkD+7nKZbjeobw263QvM/QwjJ50uSJEmSJEkbkApVJgsh7AJcBBwH1F7JkleBr1dyXW9gh+Kn38YYryynEUslxrhlCpn/Bv4dQtgW2ANoBuQBs4GPgNeKi2cV3ZbAAWkPIUmSJEmSJEmSpIplScESrnj+Cga9MSixzCo5Veh/QH8u3fdSquRUqF/hSmWisBAGD4Y+fWBxyr+tfu012GUXuPZaOO88yM1du+smT4YePeCFF8p3vtX5y19g4EBo1qyUF86eBOPOhhmvl8tcqxdg267Q5nrIq59CviRJkiRJkrThqRC/iQgh5AG3Amcve2kly+JqtvgBuKF4TQwh3L+hn2AWY/wc+DztOcrR18BLK3m9JtAu2VEkSZIkSZIkSZJUEUz6cRIdH+nIpOmTEsvcrtF2jO4wmnbN/BWWNkyffgpdusDrafSYVmHx4szpYo88suZTyubMgauugttuy5Ti0tC6NQwdCgeU9utWCxbCBwPgo0EQC8plttWqvzO0HwGN90w+W5IkSZIkSdqA5aQ9wJqEEGqSKQWdTelLZMs8DPxUfH0AOpbZgMpKMcb7Y4wHrngDuqQ9myRJkiRJkiRJkrJLUSziljduoe3ItokWyc5pew5vn/W2RTJtkGKEYcMyp4BlU5GspGWnlA0blpm3pKIiGDUKtt8ebr01nSJZvXqZEtvbb69Dkey7/8CTLeHDG5MvkuXWhF0HwhETLJJJkiRJkiRJKagIJ5P9DdiD5aWxCIwFngWmAE+saYMYY0EIYQxwVvFLRwLXlvmkkiRJkiRJkiRJkiqUKXOmcOqjp/L8V88nlrlRrY2499h7OXq7oxPLlLJJjNC7N9x8c9qTrNnixdCjB3z7Ldx4I4SQKW917w5vvJHeXKedBtdfDxttVMoLF06DiefBlH+Vy1xr1OwYaDsUajVPJ1+SJEmSJElSdpfJQgjHAMewvEj2GfCHGOMHJdbA2p1O9jiZMlkA2ocQasQYF5XtxJIkSZIkSZIkSZIqir9/8HfOefIcZi+enVjmcdsfx8hjRtKkVpPEMqVsUlgIZ58Nd9+d9iSlM3Ag/PAD1KgBI0f+9qSypOy+OwwfDnvsUcoLiwrhs9vhvSugYF65zLZaNZplSmSbHZ9p5EmSJEmSJElKTVaXyYC+xfcB+AE4MMb4/TruNb7E41xgR+Dt9ZhNkiRJkiRJkiRJUgU0e/Fsuv2nGw9PejixzFpVazHkiCGctutpy74wU9rgxFgxi2TLPPhgetmNGmVOIjvtNMjNLeXFP78N47rCzxPKZbbVCjmwXU/YeQBUrZN8viRJkiRJkqTfyNoyWQhhY2B3lp861nc9imTEGKeHEH4Cln3F3/ZYJpMkSZIkSZIkSZI2KC9+/SInjzmZKXOnJJa552Z78mCHB9m24baJZUrZJkbo3bviFsnSkpOTKeBdfTU0bFjKi/Pnwft94dOhEIvKZb7VatgW2o+Ahrslny1JkiRJkiRplbK2TAbsQ+ZEMoB84O9lsOcMlpfJGpfBfpIkSZIkSZIkSZIqgCUFS+jzfB8GvTGI+Mv3WZav3JBLvwP6cfl+l1MlJ5t/NSuVv+HD4eab056iYtl7bxg2DHbdtZQXxghTx8CEnrDou3KZbbWq1IFdroMW50BOaY9RkyRJkiRJklTesvk3Fk2L7yPweYxxQRnsObfE49plsJ8kSZIkSZIkSZKkLPfB9A/o+EhH3v/x/cQyWzRswegTRtO+WfvEMqVs9ckn0KtX2lNUHE2bwk03QadOEMKa1//Kgm9gfHeY9kS5zLZGW5wIuw2Gmpumky9JkiRJkiRpjbK5TFavxOO5q1xVOrVKPF5URntKkiRJkiRJkiRJykJFsYjb3rqNS/93KUsKlySW23X3rgw6bBC18mqtebFUyRUWwmmnweLFaU+S/apUgfPOg379oG7dUl5clA8fD4ZJV0LhwnKYbg1qbQlth0Ozo5LPliRJkiRJklQq2Vwmm1Xicb1VriqdpiUezyyjPSVJkiRJkiRJkiRlmalzp3Lq2FN57qvnEsvcqNZG3H3M3Ryz/TGJZUrZbsgQeP31tKfIfgcfDLfdBjvttA4X//QGjO8KsyeV+VxrFKrAjhdDq75QpWby+ZIkSZIkSZJKLZvLZD8W3wdgqxBCXoxx6bpuFkJoATQu8dKU9RlOkiRJkiRJkiRJUnb6v8n/R9cnujJ78ezEMo/Z7hjuPvZuNqq1UWKZUrb75BO44oq0p8hum28Ot9wCf/gDhFDKi5fOgncvg8/vAmJ5jLd6jfeG9iOgfqvksyVJkiRJkiSts2wuk00o8TgPOAh4ej3261ji8VLgzfXYS5IkSZIkSZIkSVKWmbN4Dt2f6s7o90cnllmzak0GHz6YM3Y7g1DqJohUecUIp58OixenPUl2ysuDXr3gssugVq1SXhwjfPM3ePsCWDy9XOZbrbwG0OZG2OZ0CDnJ50uSJEmSJElaL1lbJosxTgkhfAjsWPzSJaxjmSyEsAnQg+VfxfVqjNGPrCVJkiRJkiRJkqRK4qWvX+LksSfz7ZxvE8vco9kePNjhQVo0apFYplRRPP88vPZa2lNkp6OPhsGDYdtt1+HieZ/D+HPhh/+W9VhrZ8tOsNsgqO4pjJIkSZIkSVJFle1fETUSWPb1ffuHEK4o7QYhhDrAv4AGJfYaXCbTSZIkSZIkSZIkSUrVkoIlXPLfS/jdA79LrEiWG3K58oArefW0Vy2SSatw++1pT5B9tt4aHn8cnnhiHYpkhUtg0tXwZKt0imR1WsBB/4O9H7RIJkmSJEmSJFVwWXsyWbHbgfOA5mSKYANCCJsCl8cY56zp4hDC4WSKY9ux/FSy8THGJ8tnXEmSJEmSJEmSJElJmTx9Mh0f6ch7P76XWOa2DbdldIfR7LHZHollShXN1Knw6KNpT5E9atSAyy+Hiy+G6tXXYYMfX4LxZ8Pcj8t8tjXKyYOdLoOWl0LuugwvSZIkSZIkKdtkdZksxpgfQvgL8DxQnUyh7Gzg5BDC48DE4qWBTFns6BDCbsC2wEHANiXeC8DPwF8S/SEkSZIkSZIkSZIklamiWMTQt4Zyyf8uYUnhksRyz9rtLAYdPojaebUTy5QqopEjobAw7Smywx/+AIMGQfPm63Dx4hnwbi/48v6yHmvtbPw7aHcH1N0+nXxJkiRJkiRJ5SKry2QAMca3Qgh/Bv5OplAGUAv4U/FtmQCcv8JzWF4kmwP8Mcb4VbkOLEmSJEmSJEmSJKncfDf3O7o82oX/fvnfxDKb1GzC3cfezbHbH5tYplRR5efDXXelPUX6dtgBhg6FQw5Zh4tjzBTI3u0FS2aW9WhrVq0x7HYLbNkJQljzekmSJEmSJEkVStaXyQBijI+HENqTKZS1JFMQ++XtEo9LFshiidcmA3+IMX5a3rMqO4QQTgVOXclbNZOdRJIkSZIkSZIkSWXln5P/SdcnujJr8azEMo9ucTT3HHsPG9feOLFMqSJ77DH44Ye0p0hP9epwzTXQowfk5a3DBnM+gvFnw/SXy3y2tbLNGdDmRqjWMJ18SZIkSZIkSeWuQpTJAGKMk0MIbYATgfOA9iwvj61o2esfAAOBh2KMReU+pLLJlsABaQ8hSZIkSZIkSZKk9Tdn8Rx6Pt2TUe+NSiyzZtWa3HLYLZy1+1kET+aR1tp/kzs0MCudeCJcdNE6XFiwCCZfCx/dBEX5ZT7XGtVrCe3uhI32TT5bkiRJkiRJUqIqTJkMIMZYSOZ0sr+HEBoC+wI7Ao2A+sBCYAbwFfBCjHFaSqMqfV8DL63k9ZpAu2RHkSRJkiRJkiRJ0rp65ZtX6DymM9/M+SaxzHabtmP0CaPZrtF2iWVKlcXEiWlPkK6PP16Hi75/FsafC/O/KPN51ii3OrTqBztcBLnrcpSaJEmSJEmSpIqmQpXJSoox/gw8VnyTfiXGeD9w/4qvhxBakjmxTpIkSZIkSZIkSVlsaeFS+r/Qnxtfu5FITCQzJ+TQZ78+9Nm/D1VzqyaSKVUmS5fC+++nPUW63nsv898hb216WYt+gLcvgG/+Xu5zrdQmR0C74VB763TyJUmSJEmSJKWiwpbJJEmSJEmSJEmSJFVOH/70IZ0e6cQ7P7yTWOY2DbbhwQ4PstfmeyWWKVU2H3yQKVJtyJYuhcmTYdddV7MoFsHnI+DdyyB/TmKz/aJ6U9h9CGxxIoSQfL4kSZIkSZKkVFkmkyRJkiRJkiRJkpQVimIRw8cNp/f/erO4YHFiuWfsega3HnErtfNqJ5YpVUYTJ6Y9QXaYOHE1ZbJZ78G4rjDzrURnygjQ4lzY5VrIq5dCviRJkiRJkqRsUGnLZCGEqkBDYFaMcQP/7jNJkiRJkiRJkiQpu02bN40uj3bh2S+eTSyzcc3G3H3M3Ry3w3GJZUqVmWWyjAkT4IwzVngxfz5MuhI+GQyxMPmhGrSBdiOgcfvksyVJkiRJkiRllUpXJgsh/BG4CGgL5BS/9iFwFzAsxhhTHE+SJEmSJEmSJEnSCv794b8564mz+HnRz4llHtXiKO459h6a1m6aWKZUqcUifpo6k8Z10h4kfV983ojiP1fImPo4TOgOC79NfpgqtWDnq2G7HpBT6f5ERJIkSZIkSdI6yOpPCkMIJwE3Fz+NwGExxk9Ws34QcP6ypyXeagkMBv4QQjgqxriw7KeVJEmSJEmSJEmSVBpzl8yl51M9eeC9BxLLrFGlBoMOG8TZbc8mhLDmCyStnSUz+fdfN4K/pj1I+o6+ZzrQBBZOhQk9YeqYdAbZ7HjY/TaotXk6+ZIkSZIkSZKyUlaXyYBOwGbFj19bQ5Hsz8AFxU9j8S0U31P8eD9gNHBCuUwrSZIkSZIkSZIkaa28+u2rdB7Tma9nf51YZttN2zK6w2i2b7x9YpmSNjz5Swvg48Hwfl8omJ/8ADU3h7bDYLNjk8+WJEmSJEmSlPWytkwWMl8DuD/Ly2D/Ws3aKsB1xU+XlcgWAB8AjYFtSrx+XAjhyBjjU+U0uiRJkiRJkiRJkqRVWFq4lKtevIobXruBoliUSGZOyOHyfS+n3wH9qJpbNZFMSRuuoSccBm9/kHxwyIXtz4fWV0LV2snnS5IkSZIkSaoQsrZMBmwP1C1+HIFnVrP2CGBLlhfPngQ6xhjnAoQQOgB/Z/nP2xOwTCZJkiRJkiRJkiQl6KOfPqLTmE68/f3biWVu3WBrHuzwIHtvvndimZI2bNtvnEKRrFF7aD8CGrRJPluSJEmSJElShZKT9gCrsW2Jx4uBT1az9k/F9wFYCJyyrEgGEGMcA9xY/H4ADg4h1P3NLpIkSZIkSZIkSZLKXIyR4eOGs9tduyVaJDutzWm82/Vdi2SSKq+qdaHtcDj0dYtkkiRJkiRJktZKNp9MtnnxfQS+jTHG1aw9mOWnkv0rxvjzStbcBfQpfpwLtAFeLoM5JUmSJEmSJEmSJK3C9/O+57THTuPpz59OLLNRjUaMPGYkHXbskFimJCVuiz/B7rdCjU3SnkSSJEmSJElSBZLNZbLaJR7PWdWiEMJ2QFOWl8keW9m6GOPUEMI0YNPil1pgmUySJEmSJEmSJEkqN2M+GsOZj5/JzEUzE8s8YtsjuPfYe9mkjuUKSZVU7a2h7e2w6eFpTyJJkiRJkiSpAsrmMlneWq7bq/g+AEXAS6tZW7JMVn/dxpIkSZIkSZIkSZK0OvOWzOO8p8/jvnfvSyyzepXqDDpsEOe0PYcQQmK5kpSYnKqwY29oeQVUqZH2NJIkSZIkSZIqqGwuk80r8bjhatYdWHwfgY9ijD+vZm1RicfV1nEuSZIkSZIkSZIkSavw2rev0XlMZ76a/VVimbtvsjujTxjNDo13SCxTkhLVZD9ofyfU2yntSSRJkiRJkiRVcNlcJvup+D4AzUMINWKMi0ouCJmvFDyCTJEM4OU17Fm/xOOFZTGkJEmSJEmSJEmSJMgvzOeql67i+levpygWrfmCMpATcrhs38vod0A/8nLzEsmUpETlNYRdB8LWp0LISXsaSZIkSZIkSZVANpfJ3i++j2Tm/D3wzxXWHApsXGLdi2vYc5MSj39a5SpJkiRJkiRJkiRJa+2TGZ/QaUwnJkybkFjmVvW34sEOD7LPFvsklilJidrqlEyRrHqTtCeRJEmSJEmSVIlkc5nsQ+B7oCmZ08muCyE8H2OcCRBCqANcX2L9UuDZVW0WQmgB1Cnx0hdlPrEkSZIkSZIkSZK0AYkxcseEO7j42YtZVLAosdxT25zKkCOGULda3cQyJSkxdbeHdnfCxgemPYkkSZIkSZKkSihry2QxxhhCeAC4lMypY1sDk0MI/wbyyZxUttWy5cAjMcY5q9lyv5LbA5PLfmpJkiRJkiRJkiRpw/DD/B847dHTeOrzpxLLbFijISOPGckJO56QWKYkJSanGrS8AnbqDbnV0p5GkiRJkiRJUiWVtWWyYtcDp5A5nQxgI+Ds4seBTCkMMqeSXbWGvf5QfB+ByTHGeWU4p7JMCOFU4NSVvFUz2UkkSZIkSZIkSZIqn7Efj+XMx89kxsIZiWUevs3h3HvcvWxaZ9PEMiWtnSlToF9vuO+YtCepwJoeAm1vh7ot0p5EkiRJkiRJUiWX1WWyGOO8EMJRwHNAQ5aXxyh+HIAi4OwY46er2ieEsAlwSInrny+fiZVFtgQOSHsISZIkSZIkSZKkymTeknlc8MwF3PPOPYllVq9SnYGHDqRbu26EEBLLlbRm+fkweDBcdRXUyAEsk5Ve9Y1gt1uh+V/Af+MkSZIkSZIkJSCry2QAMcb3Qgg7Af3JnC62UfFbS4GXgKtjjK+uYZueQNVlWwKPl8esyipfk/nfx4pqAu2SHUWSJEmSJEmSJKnie2PKG3Qa04kvZ32ZWOauTXfloRMeYscmOyaWKWntvPIKnHMOTJ6ceV6jTrrzVEjbdoU210Neg7QnkSRJkiRJkrQByfoyGUCMcTrQDegWQqgH1ABmxBgL1nKLZ4E3SzxfWclIlUiM8X7g/hVfDyG0BD5Ieh5JkiRJkiRJkqSKKr8wn6tfvpprX7mWoliUSGYgcOm+l3LlgVeSl5uXSKaktTN9OvTuDQ88kPYkFVj91tBuBDTZK+1JJEmSJEmSJG2AKkSZrKQY4xxgTimveaGcxpEkSZIkSZIkSZIqrU9nfkqnRzoxftr4xDKb12vOgx0eZL/m+yWWKWnNCgth5Ei47DKYPTvtaSqo3JrQ+krY4XzIqZr2NJIkSZIkSZI2UBWuTCZJkiRJkiRJkiSpfMUYGTFxBBc9exEL8xcmlnvKLqdw25G3Ubda3cQyJa3ZxIlw7rkwblzak1Rgmx4NbYdB7S3TnkSSJEmSJEnSBs4ymSRJkiRJkiRJkqRf/Dj/R05/7HSe/OzJxDIbVG/AXcfcxR93+mNimZLWbPZs6NsXbr8diorSnqaCqrEp7H4bbH4ChJD2NJIkSZIkSZJU8ctkIYSmwGHLnscYR6U4jiRJkiRJkiRJklRhPfbJY5zx2Bn8tPCnxDIP3fpQ7jvuPprVbZZYpqTVixEefhguugh+/DHtaSqokAMtusMuV0NVT1uUJEmSJEmSlD0qfJkMaAncD8Ti55bJJEmSJEmSJEmSpFKYv3Q+Fz5zISPfHplYZrXcatx06E10b9+dnJCTWK6k1fvoIzj3XHjxxbQnqcDq7wx73gsNd097EkmSJEmSJEn6jcpQJlsmsLxQJkmSJEw+r4cAAQAASURBVEmSJEmSJGktvDn1TTqP6cznP3+eWGabpm0Y3WE0LTdqmVimpNVbsACuuQYGDYL8/LSnqeAOfAZqNk17CkmSJEmSJElaqcpUJpMkSZIkSZIkSZK0lvIL87n2lWu55uVrKIyFiWQGAr336c2A3w0gLzcvkUxJa/bYY9CzJ3zzTdqTVBI5uWlPIEmSJEmSJEmrZJlMkiRJkiRJkiRJ2sB8NvMzOo3pxLjvxiWWuUW9LXiww4Ps33z/xDIlrd7XX2dKZI8/nvYkkiRJkiRJkqSkWCaTJEmSJEmSJEmSNhAxRka+PZILnrmAhfkLE8vtvHNnhh45lHrV6yWWKWnVliyBQYPgmmtg0aK0p5EkSZIkSZIkJckymSRJkiRJkiRJkrQBmL5gOqc/djpPfPpEYpkNqjfgzt/fyUktT0osU9LqPf88nHsufPJJ2pNIkiRJkiRJktJgmUySJEmSJEmSJEmq5J749AlOf+x0pi+YnljmIVsfwv3H3U+zus0Sy5S0at9/DxdfDA8/nPYkkiRJkiRJkqQ0WSaTJEmSJEmSJEmSKqkFSxdw4TMXctfbdyWWWS23GjcccgM99+hJTshJLFfSyhUUwB13QJ8+MHdu2tNIkiRJkiRJktJmmUySJEmSJEmSJEmqhMZ9N45Oj3Tis58/Syxzl413YfQJo2m1UavEMiWt2ltvwTnnwDvvpD2JJEmSJEmSJClb+FWAkiRJkiRJkiRJUiVSUFTAgJcGsPc9eydWJAsEeu3di7fOeMsimZQFfv4Zzj4b9trLIpkkSZIkSZIk6dcqw8lk04AH0h5CkiRJkiRJkiRJStvnP39O5zGdeXPqm4llbl53c0Z1GMWBWx6YWKaklSsqglGjoFcvmDEj7WkkSZIkSZIkSdmowpfJYowfAV3SnkOSJEmSJEmSJElKS4yRe965h/OfPp8F+QsSy+3YuiPDjhpG/er1E8uUtHKTJsG558Krr6aTv8MO6eRKkiRJkiRJkkonJ+0BJEmSJEmSJEmSJK276Qumc/w/jufMx89MrEhWv3p9/v6HvzP6hNEWyaSUzZ+fOYls113TKZLVrAk33QTPP598tiRJkiRJkiSp9Cr8yWSSJEmSJEmSJEnShurJT5/ktMdOY/qC6YllHrTVQTxw/ANsVnezxDIl/VaM8MgjcN558N136cxwwgkweDBsvjmwOJ0ZJEmSJEmSJEmlY5lMkiRJkiRJkiRJqmAWLF3Axc9ezJ0T70wsMy83jxsOvoHz9jyPnJCTWK6k3/r8c+jRA55+Op38rbeGoUPhqKPSyZckSZIkSZIkrbsKXSYLIWwObAE0AOoA84BZwDcxxqlpziZJkiRJkiRJkiSVh/HfjafTmE58OvPTxDJbb9Sah054iNYbt04sU9JvLV4MN94I118PS5Ykn5+XB5demrnVqJF8viRJkiRJkiRp/VW4MlkI4XfAWcB+wCarWfc98BIwMsb4YjLTSZIkSZIkSZIkSeWjoKiA61+5nqteuorCWJhIZiBw0V4Xcc1B11CtSrVEMiWt3DPPQLdu8MUX6eQfcggMHw7bbZdOviRJkiRJkiSpbFSYMlkIoRXwANBm2UtruGRT4M/An0MIbwOnxhgnl9+EyiYhhFOBU1fyVs1kJ5EkSZIkSZIkSVp/X/z8BZ3HdOaNqW8klrlZ3c0YdfwofrfV7xLLlPRb330H558P//pXOvmbbAKDB8OJJ0JY02/pJUmSJEmSJElZr0KUyUIIpwB3AnlkSmSx+AYrL5XFEo8DsDswIYTQNcY4qjxnVdbYEjgg7SEkSZIkSZIkSZLWR4yRe9+5l/OfOZ/5S+cnlvuXVn9h+FHDaVCjQWKZkn4tPx+GDoX+/WF+cv/3/0VuLvTsCVdeCXXrJp8vSZIkSZIkSSofWV8mCyF0AO4GclleIltWIJsCvAfMABYAtYDGwC7A5sVrlhXLqgH3hBDmxBgfTWZ6pehr4KWVvF4TaJfsKJIkSZIkSZIkSaX304KfOOuJsxj78djEMutVq8cdR9/BX1r/JbFMSb/12mtwzjkwaVI6+XvtBXfcAbvskk6+JEmSJEmSJKn8ZHWZLITQCLiP5UWyACwChgD3xhg/X8212wCnAz2BGsXX5wL3hxC2jTHOLOfxlaIY4/3A/Su+HkJoCXyQ9DySJEmSJEmSJEml8dRnT9Hl0S78uODHxDIP3PJAHjj+Abaot0VimZJ+bcYM6N0b7rsvnfyGDeGmm6BLF8jJSWcGSZIkSZIkSVL5yvaPf/sBdVleJJsE7BRjvHx1RTKAGOMXMcbLgZbF1y07zawu0Kf8RpYkSZIkSZIkSZLWzcL8hXR7shtHPXxUYkWyvNw8bj70Zp47+TmLZFJKiopg5EjYfvv0imRnnAGffAKnn26RTJIkSZIkSZIqs6w9mSyEEIC/sLxI9i2wf4xxTmn2iTF+E0I4EHgH2KJ4r47ABWU5ryRJkiRJkiRJkrQ+JkybQKdHOvHJzE8Sy2y1USseOuEhdt5458QyJf3aO+/AOefAW2+lk7/LLnDHHbDXXuu50cIpZTKPJEmSJEmSJKl8ZfP3ibUHGpMpf0XgotIWyZaJMc4GLmb56WSNQgjty2JISZIkSZIkSZIkaX0UFBVw7cvXstc9eyVaJLtwzwsZf+Z4i2RSSubOhfPOg7Zt0ymS1a4Nt94KEyasZ5GsqAA+GgTP7ltms0mSJEmSJEmSyk/WnkwGtCjxeD7w6Hru9xgwD6hT/Hw7YNx67ilJkiRJkiRJkiStsy9nfUnnMZ15fcrriWU2q9OMB45/gIO3PjixTEnLxQj/+AdceCF8/306M/zpTzBoEDRrtp4bzRgH47vCrHfLYixJkiRJkiRJUgKyuUy2UfF9BL6OMRasz2YxxvwQwtdA6xX2lyRJkiRJkiRJkhIVY+T+d++n59M9mb90fmK5f2r5J+44+g4a1GiQWKak5T75BLp1g+eeSye/RQsYPhwOPXQ9N8qfC+/1gU+HkfmVviRJkiRJkiSposjmMlluiceFZbRnyX1yymhPSZIkSZIkSZIkaa3NWDiDsx4/izEfj0kss161egw/ajh/bf1XQgiJ5UrKWLgQrrsObroJ8vOTz69eHa64Anr1gmrV1mOjGGHqGJjQAxZNK7P5JEmSJEmSJEnJyeYy2fTi+wA0DyGEGOM6f6VZyPxWrHmJl35an+EkSZIkSZIkSZKk0nr686fp8mgXfpj/Q2KZBzQ/gFEdRrFFvS0Sy5S03BNPQI8e8PXX6eQfdRQMHQpbb72eGy34FiZ0h+8eL5O5JEmSJEmSJEnpyObTub4q8bg+cPB67ncw0GAV+0uSJEmSJEmSJEnlZmH+Qnr8pwdHPnRkYkWyqjlVuemQm3ju5Ocskkkp+OYb6NABjjkmnSLZZpvBI49kymzrVSQrKoCPboEnd7JIJkmSJEmSJEmVQDafTPYGMA+oTeZ0sptDCO1ijPml3SiEUBUYWOKl+cDrZTKlJEmSJEmSJEmStBpvf/82HR/pyMczPk4ss2WTlow+YTRtmrZJLFNSxtKlcOutMGAALFyYfH6VKnDhhdC3L9SuvZ6bzRwP486CWe+WxWiSJEmSJEmSpCyQtSeTFZfGHiNTJItAa+CxEEKpPu4OIdQExgC7LNsaGBtjLCjDcSVJkiRJkiRJkqRfKSwq5PpXrmePu/dItEh2/h7nM+GsCRbJpBS8+CK0aQOXXppOkWz//eHdd+HGG9ezSJY/Fyb0hGf2sEgmSZIkSZIkSZVMNp9MBtAXOBGoSqZUdhjwUQihH/CPGOMqP34vLpGdBAwAmpEpkQVgKdC/nOeWJEmSJEmSJEnSBuyrWV9x8tiTefXbVxPL3LTOpjxw/AMcsvUhiWVKyvjxR7j4Yhg9Op38Jk3g5puhc2cIYT02ihGmjoEJPWDRtDKbT5IkSZIkSZKUPbK6TBZj/DqEcClwC8vLYM2Au4HbQgjjgfeBGcACoBbQiMwpZO2Amiw/2Yzi+0tijF8n+GNIkiRJkiRJkiRpAxFjZNR7o+jxVA/mLZ2XWO5JLU/ijqPvoGGNhollSoLCQhgxAi6/HObMST4/BDj7bLj2WmjQYD03W/AtTOgO3z1eJrNJkiRJkiRJkrJTVpfJAGKMg0MIjYArWF4KC2SKYwcU31Zm2fetxRKPr44x3lZes0qSJEmSJEmSJGnDNXPhTLo+0ZV/f/TvxDLrVqvL8KOG07F1R8J6HUckqbTGj4dzzoGJE9PJ3313uOMOaNduPTcqKoBPboNJ/aBgQZnMJkmSJEmSJEnKXllfJgOIMfYNIYwD7gI2ZnmpbJmSvxkreQpZKL79CJwZY3yivGeVJEmSJEmSJEnShueZz5+hy6Nd+H7+94ll7t98f0YdP4rm9ZsnlikJZs2CK66AO++EuOJvrhNQr17mJLKzz4bc3PXcbOZ4GHcWzHq3LEaTJEmSJEmSJFUAFaJMBhBjfDyEsDXQGTgd2A1Y2Ufjy4plhcBE4G7goRjjokQGlSRJkiRJkiRJ0gZjUf4iLvnfJQwdNzSxzKo5VbnmoGu4aK+LyM1Z3yaJpLUVI4weDRdfDNOnpzNDp04wcCA0bbqeG+XPhff6wKfD+O13uUqSJEmSJEmSKrMKUyYDKC6E3QXcFUKoBbQFmgMNgNrAfGAW8A0wIca4IK1ZJUmSJEmSJEmSVLm98/07dHykIx/N+CixzJ2a7MToDqPZdZNdE8uUBJMnw7nnwssvp5O/445w++1w4IHruVGMMHUsTOgBi74rg8kkSZIkSZIkSRVN1pbJQgi5QK0SLy2KMeYve1JcFHsp8cEkSZIkSZIkSZK0QSssKmTg6wPp90I/8ovy13xBGenZvic3HHIDNarWSCxT2tAtWAADBsAtt0BBQfL5NWpA//5wwQWQl7eemy34NlMi++6xMplNkiRJkiRJklQxZW2ZDDgFGFni+aHA8ynNIkmSJEmSJEmSJPH17K85eczJvPLtK4llblpnU+4/7n4O3ebQxDKlDV2M8Oij0LMnTJmSzgzHHQdDhkDz5uu5UVEBfDoU3u8LBQvKZDZJkiRJkiRJUsWVzWWyjYFQ/Hh2jNEimSRJkiRJkiRJklIRY2T0+6Pp9p9uzFs6L7HcP+70R+48+k4a1WyUWKa0ofvyy0yJ7Mkn08nfcku47TY45pgy2GzmBBh3Fsx6pww2kyRJkiRJkiRVBtlcJptffB+Bb9IcRJIkSZIkSZIkSRuunxf9zNlPnM0/P/xnYpl18uow7KhhdN65MyGENV8gab0tWQIDB8K118LixcnnV60KvXvD5ZdDzZrruVn+XHivL3w2DGJRmcwnSZIkSZIkSaocsrlM9n3aA0iSJEmSJEmSJGnD9t8v/supj57KtHnTEsvcd4t9ebDDg2xZf8vEMqUN3f/+B926waefppN/0EEwfDjssMN6bhQjTB0LE3rAou/KYjRJkiRJkiRJUiWTk/YAq/FR8X0ANk9zEEmSJEmSJEmSJG1YFuUv4vynz+ew0YclViSrklOF6w++nhdPedEimZSQadPgz3+GQw9Np0jWtCk8/HCmzLbeRbIF38LLx8MrJ6RQJAuwVZeEMyVJkiRJkiRJ6yJrTyaLMU4OIUwGWgINQgh7xBjfSnsuSZIkSZIkSZIkVW7v/vAuHR/pyIc/fZhY5o6Nd2T0CaPZbZPdEsuUNmQFBZmTwPr2hXnzks/PyYHu3WHAAKhXbz03KyqAT4fC+32hYEGZzFcq9VtD+7ug9jbw1X3J50uSJEmSJEmSSiWbTyYDuKvE46tSm0KSJEmSJEmSJEmVXmFRITe9dhPtR7ZPtEjWo30PJp410SKZlJA33oC2beH889Mpku2xB0yYAEOGlEGRbOYEeKY9vH1h8kWy3BrQ5kY4YiI03jPZbEmSJEmSJEnSOsvak8mK3Q6cBOwDHBpCuDnGeHHKM0mSJEmSJEmSJKmS+Wb2N5wy9hRe+ualxDKb1m7K/cfdz+HbHp5YprQhmzkTLr0U7r47nfwGDeCGG+CMMzInk62X/LnwXl/4bBjEojKZr1Q2OQLa3Q61t1r+WrVGcML05GfJRtUapT2BJEmSJEmSJK1SVpfJYoyFIYRjgMeAfYELQgjtgX4xxhdTHU5ZLYRwKnDqSt6qmewkkiRJkiRJkiQpm8UYeWjSQ3T7TzfmLpmbWO4JO57AiN+PoHHNxollShuqoiK4/37o3TtTKEtDly5w443QpEkZbDZlDEzoAYu+K4PNSql6U9h9CGxxIoTw6/dCDlQvix9QkiRJkiRJklSesrpMFkLoV/zwJaAFsDGZU8qeCyH8CEwAvgLmAvml2TvGOKAMR1X22RI4IO0hJEmSJEmSJElS9pq1aBbnPHkO/5j8j8Qya+fVZuiRQzlll1MIKxYxJJW599+Hc86B119PJ79VK7jjDth33zLYbMEUmNgDpj5aBpuVVoAWZ8Mu10Fe/RTyJUmSJEmSJEllJavLZMCVQCzxPALLfqvWFDh6Pfa2TFa5fU2mhLiimkC7ZEeRJEmSJEmSJEnZ5rkvn+OUsafw3bzkTvbZZ/N9GNVhFFs32DqxTGlDNW8e9O8Pt90GhYXJ59eqBVddBT17QtWq67lZUQF8Ogze7wMFC8pkvlKp3xrajYAmeyWfLUmSJEmSJEkqc9leJluZuOYlqxXKYA9luRjj/cD9K74eQmgJfJD0PJIkSZIkSZIkKTssLljM5c9dzq1v3ppYZpWcKlx14FVcss8l5ObkJpYrbYhihH/+Ey64AKZNS2eGP/4Rbr0VNtusDDb7eSK8dRbMersMNiul3BrQ+krY4QLIWd9GnCRJkiRJkiQpW1SEMllY8xJJkiRJkiRJkiRp9d774T06jenEB9OT+9657Rttz0MnPMTum+6eWKa0ofrsM+jeHZ59Np38bbaBYcPgiCPKYLP8efB+X/h0KMSiMtiwlDY5AtrdDrW3Sj5bkiRJkiRJklSusr1M9ru0B5AkSZIkSZIkSVLFVhSLuOWNW7ji+StYWrg0sdxu7bpx06E3UbNqzcQypQ3RokVwww2Z29Lk/i/+i2rV4LLL4JJLoHr1MthwyliY0B0WfVcGm5VS9aaw+xDY4kQIfu+rJEmSJEmSJFVGWV0mizG+lPYMkiRJkiRJkiRJqri+nfMtp4w9hRe/fjGxzKa1m3LvsfdyZIsjE8uUNlRPPZU5jezLL9PJP/xwGDoUWrQog80WTIGJPWDqo2WwWWkFaHE27HId5NVPIV+SJEmSJEmSlJSsLpNJkiRJkiRJkiRJ6+rhSQ9z7pPnMmfJnMQyj9/heEYeM5LGNRsnliltiKZMgQsugH//O538Zs1g8GD4wx/K4ACvogL4dBi83wcKFpTFeKVTvzW0GwFN9ko+W5IkSZIkSZKUOMtkkiRJkiRJkiRJqlRmLZrFuf85l79/8PfEMmvn1WbIEUPo0qYLYb2bJZJWJT8fhgyBK6+EBSn0rnJz4fzzoX9/qFOnDDb8eSK8dRbMersMNiul3BrQuj/scCHkVE0+X5IkSZIkSZKUCstkkiRJkiRJkiRJqjSe/+p5Thl7ClPnTk0sc+/N9+bBDg+ydYOtE8uUNkSvvALnnAOTJ6eTv88+cMcd0Lp1GWyWPw/e7wufDoVYVAYbltImR0C74VDbf7ckSZIkSZIkaUNjmUySJEmSJEmSJEkV3pKCJVzx/BUMemNQYplVcqrQ/4D+XLrvpVTJ8dduUnmZPh1694YHHkgnv3FjGDgQTj4ZcnLKYMMpY2FiD1iYXOn1F9U3ht2HwBYngacoSpIkSZIkSdIGKat/qxVCqAGcWOKlN2KMn63DPtsBe5Z46W8xxvz1nU+SJEmSJEmSJEnpm/TjJDo+0pFJ0ycllrldo+0Y3WE07Zq1SyxT2tAUFsLIkXDZZTB7djoznHUWXHcdNGpUBpstmJIpkU19tAw2Wwfbng1troe8+unkS5IkSZIkSZKyQlaXyYC/AncVP14KbL2O+8wv3qdq8fN84G/rN5okSZIkSZIkSZLSVBSLGPzmYC577jKWFi5NLPectucw8NCB1MqrlVimtKF5+2045xwYNy6d/DZt4I47YM8917h0zYoK4NNh8H5fKJhfBhuWUr1W0H4ENNk7+WxJkiRJkiRJUtbJ9jLZqUAAIvCvGOP367JJjHFaCOER4M8l9rVMJkmSJEmSJEmSVEFNmTOFUx89lee/ej6xzI1rbcy9x93LUS2OSixT2tDMng19+8Ltt0NRUfL5devC/7N3n+FR1fn7x98nIfTebUhTugIK9t776m+bigoWIIAgiCBSBEVBkKJIEbvgrqu79t57AQWkiYoKCEhRegsp5/8guIv+kSIz50yS9+u6cs1kOPO5P3lgHuR4z3fw4PwiW7FE3E1f9Tl82h5WT0vAsD2UXgqa3QwNe0Baxq6vlyRJkiRJkiQVCSlbJguCoAJwJPlFMoAn9nLk4/yvTHZ8EASlwjDcvJczJUmSJEmSJEmSFLHHZz9O5ouZrNmyJrLMCxpcwH3n3Ue1MtUiy5SKkjCEf/wDrr8eli+PZ4eLL4YRI2CffRIwLHs9zBwAX98NYQytuH3OgFbjoGzd6LMlSZIkSZIkSSktZctkQHMgfdvzEHhvL+e9u21OABTfNv/jvZwpSZIkSZIkSZKkiKzZsobOL3XmH7P+EVlmmYwy3HXmXVzZ4kqCIIgsVypKvvwSOneGt9+OJ79BAxg7Fk45JUEDFz8Ln3WBTYsTNHAPlKwBh90Ftf4K/s6SJEmSJEmSJO1AKpfJDt7u+aIwDNfuzbAwDNcGQfADUGvbSw2wTCZJkiRJkiRJklQgvP3921zxzBX8sO6HyDKP3P9IJl04ifqV60eWKRUlmzbB4MFw552QnR19fsmS0L9//mloJUokYODGH+DzrrD4mQQM+wPqd4TmQ6B4xXjyJUmSJEmSJEkFQiqXySpuewyBnxI0cyX/K5NVTtBMSZIkSZIkSZIkJUlWThb93urHiI9HEBJGkpkepHPzCTfT57g+FEtL5dtpUsH13HPQtSssXBhP/rnnwt13Q506CRiWlwtf3wMz+0HOhgQM3EMVmkLre6Ha0dFnS5IkSZIkSZIKnFS++5W23fMgQTO3n5OIz5aTJEmSJEmSJElSksxeMZtLn7qUmctnRpZ5UOWDmHzRZFrv1zqyTKkoWbAgv0T2/PPx5NeqlV8iO/98CBJxF3rV5zClQ/5j1NJLQbOboWEPSMuIPl+SJEmSJEmSVCClcpnsl9PIAqBmgmbW2O756gTNlCRJkiRJkiRJUgLlhXnc9cld9HmzD1m5WZHldjisAyNOH0GZ4mUiy5SKiq1bYcQIuPVW2Lw5+vxixaBnT+jXD8ok4j/x7PUwcwB8fTeEeQkYuIf2OQNajYOydaPPliRJkiRJkiQVaKlcJlux3fN9giCoFYbhoj86LAiCWsB+QLiD+ZIkSZIkSZIkSUoBi9ctpu0zbXnz+zcjy6xepjoPnP8A5x58bmSZUlHy1lvQuTPMmxdP/oknwtix0LhxggYufhY+6wKbFido4B4oWQNajoYD/5ago9UkSZIkSZIkSUVNKpfJPuV/xS+AS4EhezGvzbbHYNvcqXsxS5IkSZIkSZIkSQn2xJwn6PBCB9ZsWRNZ5nkHn8f9599P9TLVI8uUioply/JPA3vssXjyq1fPPw3t0ksT1Lva+AN83hUWP5OAYX9A/Q7QfCgUrxhPviRJkiRJkiSpUEjZMlkYhiuCIJgFNCO/ANYrCIJHwjBcuqezgiDYD7iB/BJZAHwVhuEPCV1YkiRJkiRJkiRJf8jaLWvp8nIXJs+cHFlm6YzSjD5jNFe3vJrA032khMrNhfHjoW9fWLcu+vwggE6dYPBgqFgxAQPzcuHre2BmP8jZkICBe6hCE2g9EaodHX22JEmSJEmSJKnQSdky2TYTgXvIL4FVAF4JguDUMAxX7O6AIAhqAK9sez/bZk1M9KKSJEmSJEmSJEnac+8ueJfLn7mcRWsXRZZ5xH5HMOnCSRxU5aDIMqWiYsoU6NgRpk+PJ//ww2HCBDjssAQNXPU5TOmQ/xi19JLQ9GZo2APSi0efL0mSJEmSJEkqlNLiXmAX7gN+uXMYAk2B2UEQXBEEQcbO3hgEQUYQBG2BWUDjbe8HWAyMS866kiRJkiRJkiRJ2h1ZOVn0fr03Jz1yUmRFsvQgnYEnDOSDKz+wSCYl2KpV+SWyI4+Mp0hWsWL+aWiffJKgIln2Bvi8O7zaOp4iWc3T4Zw50ORGi2SSJEmSJEmSpIRK6ZPJwjDMDoLgYuAtoDj5hbCqwIPA8CAI3gI+A1YAG4CyQHXgcOBkoAoQbHtfAGwBLg7DcGvEP4okSZIkSZIkSZK2mbNiDpc+dSlfLP8issz6lesz+cLJHLH/EZFlSkVBGMIjj8ANN8BPP8WzwxVXwLBhUL16ggYufg4+6wKbfkjQwD1Qsga0HA0H/g2CIPp8SZIkSZIkSVKhl9JlMoAwDD8OgqAd8DCQwf+KYVWBv2z72pFf/rL+y/VZwBVhGH6U1IUlSZIkSZIkSZK0Q3lhHmM+HUPvN3qTlZsVWW77lu0ZccYIyhYvG1mmVBTMng2ZmfDBB/HkN26cfxrZ8ccnaOCmxfBZV1j8dIIG7qH6HaD5ECheKZ58SZIkSZIkSVKRkPJlMoAwDB8PguBb4AngQPILYr/Y0cexhdtdEwDfAn8Lw3BaUheVJEmSJEmSJEnSDi1Zt4R2z7bj9e9ejyyzWulq3H/+/Zzf4PzIMqWiYMMGGDQIRo2C3Nzo80uXhoED4brrICMjAQPzcuGbsfBFX8jZkICBe6hCE2h9L1Q7JvpsSZIkSZIkSVKRUyDKZABhGE4NgqAB0BboBjTayeW/FMxmAXcBk8IwzE7uhpIkSZIkSZIkSdqRJ+c8SYcXOrB6y+rIMs89+FzuP+9+apStEVmmVNiFITz1VH6Ja/HieHa46KL8ElutWgkauGoaTOkAqz5L0MA9kF4Smt4MDXtAevHo8yVJkiRJkiRJRVKBKZMBhGG4FZgITAyCYD/gOKAeUBkoB6wHVgHfAO+HYfhjXLtKkiRJkiRJkiQVdWu3rKXrK1159ItHI8ssnVGakaePpP1h7QmCYNdvkLRbvv0WunSBV16JJ79OHbjnHjj77AQNzN4AMwfA13dBmJegoXug5unQahyUqxd9tiRJkiRJkiSpSCtQZbLthWG4BHg87j0kSZIkSZIkSZL0/3t/4ftc9vRlLFy7MLLMVvu2YvJFkzm4ysGRZUqF3ZYtMGwY3H47ZGVFn1+8OPTuDX36QKlSCRq6+Dn4rAts+iFBA/dAyerQ8i448G9g4VWSJEmSJEmSFIMCWyaTJEmSJEmSJElS6tmau5Wb376ZOz68g5Awksy0II1+x/Wj3/H9yEjPiCRTKgpeew06d4b58+PJP/VUGDsWDk5UP3TTYvisKyx+OkED91D99tB8KBSvFE++JEmSJEmSJElYJpMkSZIkSZIkSVKCzF05lzZPtWH6sumRZdarVI9JF07iqAOOiixTKuyWLIHu3eHJJ+PJ32cfGD0a/vKXBB3elZcL34yFL/pCzoYEDNxDFZpA63uh2jHRZ0uSJEmSJEmS9BuWySRJkiRJkiRJkrRX8sI8xk4ZS683erElZ0tkuVe3uJpRZ46ibPGykWVKhVlODowZAwMGwIYYOldpadC1KwwaBOXLJ2joqmkwpQOs+ixBA/dAekloOgAaXg/pxaPPlyRJkiRJkiRpByyTSZIkSZIkSZIk6Q9bun4p7Z5tx2vfvhZZZtXSVbn/vPu5oOEFkWVKhd2HH0KnTjBzZjz5Rx0F48ZB8+YJGpi9AWYOgK/vgjAvQUP3QM3TodU4KFcv+mxJkiRJkiRJknYiljJZEATH//a1MAzf253rEmVHeZIkSZIkSZIkSdp9/577bzq80IFVm1dFlnn2QWfzwPkPULNszcgypcLsp5+gd2948MF48itXhmHDoF27/JPJEmLxc/BZF9j0Q4IG7oGS1aHlaDjw7xAE0edLkiRJkiRJkrQLcZ1M9g4Qbvd9yI53+e11ifJ7eSokgiBoC7TdwT+VjnYTSZIkSZIkSZIKn3VZ6+j6clce+eKRyDJLFSvFyDNG0uGwDgQWNKS9lpeXXyDr3RtWRdcH/ZWrroKhQ6Fq1QQN3LQEPu8KPzyVoIF7qH57aD4UileKJ1+SJEmSJEmSpN0Qd6Fqd+/0eUdQe6o2cELcS0iSJEmSJEmSVNh8sOgDLnv6MhasWRBZ5uH7Hs7kCyfToGqDyDKlwmzGDMjMhE8+iSf/kENg/Hg4+ugEDczLhW/GwRd9IWd9gobugQqNofVEqHZM9NmSJEmSJEmSJO2hOMtkFsmUTAuAd3fwemmgVbSrSJIkSZIkSZJU8G3N3crAdwZyx4d3kBfmRZKZFqRx07E3MeCEAWSkZ0SSKRVm69bBgAEwZkz+yWRRK1sWbr0VunSBYom6U71qOkxpD6s+S9DAPZBeEpoOgIbXQ3rx6PMlSZIkSZIkSfoD4iqTDUrwddKvhGH4MPDwb18PgqAJMDvqfSRJkiRJkiRJKsi+XPklbZ5uw7Qfp0WWWbdSXSZdOImjD0jU0UVS0RWG8K9/QY8e8OOP8ezwt7/BiBGw334JGpi9AWbdDF+NhogKrr9S8zRoNR7K1Ys+W5IkSZIkSZKkvRBLmSwMw90qie3udZIkSZIkSZIkSUq8MAwZN3UcPV/vyZacLZHlXtn8SkafOZpyJcpFlikVVl99BZ07w5tvxpNfvz6MHQunn57AoYufh886w6YfEjh0N5WsDi1Hw4F/hyCIPl+SJEmSJEmSpL0U18lkkiRJkiRJkiRJSmE/rv+RK5+7klfmvxJZZpVSVbjvvPu4sNGFkWVKhdXmzXD77TBsGGzdGn1+iRLQty/ccAOULJmgoZuWwOdd4YenEjRwD9W7BlrcAcUrxZMvSZIkSZIkSVICWCaTJEmSJEmSJEnSrzz15VO0f749P2/+ObLMM+ufyYPnP8g+5faJLFMqrF58Ea69Fr7/Pp78s86CMWOgXr0EDczLhW/GwRd9IWd9gobugQqNodW9UP3Y6LMlSZIkSZIkSUowy2SSJEmSJEmSJEkCYH3Werq90o2HZjwUWWbJYiUZcfoIMg/PJAiCyHKlwmjRIujWDZ55Jp78/feHu+6CCy+EhP3nvGo6TGkPqz5L0MA9kF4SmvaHhj0hvXj0+ZIkSZIkSZIkJYFlMkmSJEmSJEmSJPHhog+57OnL+H5NdEcZHbbPYUy+aDINqzaMLFMqjLZuhVGj4JZbYNOm6POLFYPu3WHAAChbNkFDszfArJvhq9EQ5iVo6B6oeRq0Ggfl6kefLUmSJEmSJElSElkmkyRJkiRJkiRJKsKyc7MZ9O4ghnwwhLyIChtpQRp9ju3DgBMGUNzTfqS98u670KkTzJ0bT/5xx8G4cdC0aQKHLn4ePusMm35I4NDdVLI6tBwFB16cwOPVJEmSJEmSJElKHQW2TBYEQXGgPFAK2OO/4odhuCjhS0mSJEmSJEmSJBUg836aR5un2vD5j59HllmnYh0mXTiJY2odE1mmVBgtXw433ACTJsWTX60a3HknXHZZAjtXm5bA513hh6cSNHAP1bsGmg+FEpXjyZckSZIkSZIkKQIFpkwWBEFV4BLgLKAFUG0vxoUUoJ9dkiRJkiRJkiQpkcIwZPxn4+n5Wk8252yOLLdd83aMPnM05UuUjyxTKmxyc+Hee+Gmm2Dt2ujzgwA6dIDbboPKiepc5eXCN+Pgi76Qsz5BQ/dAhcbQ6l6ofmz02ZIkSZIkSZIkRSzlC1VBEATAjUBf8k8hgz9wEpkkSZIkSZIkSZJg2YZlXPnslbw8/+XIMiuXqsx9593HRY0uiixTKow++wwyM/Mf49CyJYwfD61bJ3Do6hnwaXtYNTWBQ3dTWgloNgAa9oT04tHnS5IkSZIkSZIUg5QukwVBkA78A/gz/yuQhdu+LJRJkiRJkiRJkiTtgWfmPcM1z1/DT5t+iizzjHpn8OAFD7JvuX0jy5QKm9WroV+//CJXGEafX7483H47dOwI6ekJGpq9AWYNhK9GQ5iboKF7oOZp0GoclKsffbYkSZIkSZIkSTFK6TIZcD3wl23PfymQBcAKYDbwM7ApntUkSZIkSZIkSZIKhvVZ6+n+ancemP5AZJkli5Vk+GnD6dyqM0HgZwRKf0QYwuTJ0LMnrFgRzw5t2sDw4VCzZgKHLnkBpnaGTYsSOHQ3lagGh42GAy8GfzdJkiRJkiRJkoqglC2TBUFQAujLr0tkbwH9wjD8JM7dJEmSJEmSJEmSCoqPf/iYNk+34bvV30WW2aJmCx676DEaVWsUWaZU2MydC506wbvvxpPfsCGMGwcnnZTAoZuWwOfd4If/JHDoHqh3DTQfCiUqx5MvSZIkSZIkSVIKSNkyGXAiUI78MlkIPAX8LQzDvDiXkiRJkiRJkiRJKgiyc7O59b1bue3928iL6PZKQMCNx97IwBMHUjy9eCSZUmGzcSPceiuMGAE5OdHnlyoFAwZAjx5QPFH/Geflwjfj4YubIGd9gobugQqNodW9UP3Y6LMlSZIkSZIkSUoxqVwmq7/tMQDygG4WySRJkiRJkiRJknbt65+/ps1TbZi6dGpkmQdWOJBJF07iuAOPiyxTKkzCEJ59Frp2hR9+iGeHCy6A0aOhdu0EDl09Az5tD6ui+330X2kloGl/aHQDWHCVJEmSJEmSJAlI7TJZ+W2PIfB1GIZL41xGkiRJkiRJkiQp1YVhyL2f38v1r13PpuxNkeVecegV3H3W3ZQvUX7XF0v6/3z3XX6J7MUX48mvXRvuvhvOOy+BQ7M3wKyB8NVoCHMTOHg31TwVWo2HcvV3fa0kSZIkSZIkSUVIKpfJVm/3fF1sW0iSJEmSJEmSJBUAyzcs56rnruLFb6Jro1QuVZl7z72XPzf+c2SZUmGSlQXDh8Ntt8GWLdHnZ2TADTdA375QunQCBy95AaZ2hk2LEjh0N5WoBi1HQe1LIAiiz5ckSZIkSZIkKcWlcpls1nbPa8S2hSRJkiRJkiRJUop77qvnuPq5q1m5aWVkmafVPY2H//Qw+5bbN7JMqTB54w3o3Bm+/jqe/JNPhrFjoWHDBA7dtAQ+7wY//CeBQ/dAvauh+R1QonI8+ZIkSZIkSZIkFQCpXCb7BFgJVANqBUFQKwzDGD66TpIkSZIkSZIkKTVt2LqBHq/24L5p90WWWSK9BMNOG0aX1l1IC9Iiy5UKi6VL4frr4fHH48mvWRNGjoS//z2BB3fl5cI34+GLmyBnfYKG7oHyjaD1vVD9uOizJUmSJEmSJEkqYFK2TBaGYW4QBKOA27e9dD3QLcaVJEmSJEmSJEmSUsYniz/hsqcvY/6q+ZFlNq/ZnMkXTqZJ9SaRZUqFRU5O/klg/fvD+hj6Vmlp+Seh3XorVKiQwMGrZ8Cn7WHV1AQO3U1pJaBpf2h0A6QXjz5fkiRJkiRJkqQCKGXLZNvcCVwItAI6BUHwThiGT8e8kyRJkiRJkiRJUmyyc7O57f3bGPzeYHLD3EgyAwJ6HdOLW066heIWNqQ99sknkJkJM2bEk9+6NYwfDy1bJnBozkaYeTN8NRoi+l30KzVOgdYToFz96LMlSZIkSZIkSSrAUrpMFoZhThAEZwOvA82BfwVBMBQYHoZhDJ/XJ0mSJEmSJEmSFJ9vfv6GNk+3YcqSKZFlHljhQB698FGOP/D4yDKlwuLnn6FPH7jvvnjyK1WCoUPh6qvzTyZLmCUvwtROsGlRAofuphLVoOUoqH0JBEH0+ZIkSZIkSZIkFXApXSYDCMPw5yAIjgZGA9cAfYHrgiB4HZgGrAS2/IG5jyZyT0mSJEmSJEmSpGQJw5D7pt1H91e7syl7U2S5lx1yGWPOGkOFkhUiy5QKg7w8ePhh6NUrv1AWh7ZtYdgwqFYtgUM3LYXPu8EP/07g0D1Q72pofgeUqBxPviRJkiRJkiRJhUDKl8kAwjDcEgTBc8AJQAOgLPCnbV9/lGUySZIkSZIkSZKU8lZsXMFVz13FC1+/EFlmpZKVmHDuBP7a5K+RZUqFxcyZ0KkTfPhhPPlNm8K4cXDccQkcmpcL8yfAjD6Qsz6Bg3dT+UbQ+l6onsgfSpIkSZIkSZKkoinly2RBEFQBHgNO2/ZS+NtL9mBcuO36386QJEmSJEmSJElKOc9/9TxXPXcVKzetjCzz1Lqn8vAFD7Nf+f0iy5QKg/XrYeBAuOsuyM2NPr9MGRg0CLp2hYyMBA5ePQOmdICfpyRw6G5KKwFN+0GjXpBePPp8SZIkSZIkSZIKoZQukwVBUBF4F2jEr0tge1Ig+9XIBKwlSZIkSZIkSZKUVBu3bqTHqz2YOG1iZJkl0ktwx6l3cO0R15IWpEWWKxV0YQj//jdcdx0sXRrPDn/+M4waBfvvn8ChORth1kCYNwrCGNpxNU6BVuOh/EHRZ0uSJEmSJEmSVIildJkMGA40Jr9E9supYmuA14DZwM/ApriWkyRJkiRJkiRJSrQpS6bQ5qk2fLPqm8gyD61xKJMvmkzT6k0jy5QKg2++gS5d4LXX4smvVw/uuQfOPDPBg5e8CJ91ho0LEzx4N5SoCi1HQe1LIfCzQiVJkiRJkiRJSrSULZMFQVANuJz/lchC4GZgWBiGWXHuJkmSJEmSJEmSlGg5eTnc9t5t3PrereRGdApQQEDPo3ty60m3UqJYiUgypcJg82YYOjT/a+vW6PNLlIAbb8z/KlkygYM3LYXPu8EP/07g0D1Q7ypofgeUqBJPviRJkiRJkiRJRUDKlsmAE4EM/ncq2c1hGA6OdSNJkiRJkiRJkqQkmL9qPm2easOnSz6NLLNWhVo8+qdHOaH2CZFlSoXBK6/kn0b27bfx5J9+ev5pZAcdlMChebkwfwJ8cRNkr0vg4N1UviG0vheqHx99tiRJkiRJkiRJRUwql8lqb3sMgC3AyPhWkSRJkiRJkiRJSrwwDHlg+gNc98p1bMzeGFnupc0u5Z6z76FiyYqRZUoF3Q8/QPfu8J//xJO/334wejT83/9BECRw8OovYEp7+HlKAofuprQS0LQfNLoB0j0dUZIkSZIkSZKkKKRymSx322MIfB2G4aY4l5EkSZIkSZIkSUqkFRtXcM3z1/DcV89FllmxZEUmnDOBvzX9W2SZUkGXnQ133QUDB8LG6Dqf/5WeDtddBzffDOXKJXBwzkaYNRDmjYIwd5eXJ1yNU6DVeCifyCPWJEmSJEmSJEnSrqRymWzxds+zY9tCkiRJkiRJkiQpwV78+kWufO5KVmxcEVnmyXVO5pE/PcL+5fePLFMq6D74ADIzYfbsePKPPhrGj4dDDknw4CUvwWedYOPCBA/eDSWqQstRUPvSBB+xJkmSJEmSJEmSdkcql8nmbHsMgAPiXESSJEmSJEmSJCkRNm7dSM/XejLh8wmRZZZIL8GQU4bQ7chupAVpkeVKBdnKldCrFzz8cDz5VarA8OFwxRWQlsj/bDcthWnXwaInEzh0D9S7CprfASWqxJMvSZIkSZIkSZJSt0wWhuGcIAhmAM2BakEQtAzDcFq8W0mSJEmSJEmSJP0xU5dM5dKnLuWbVd9EltmsejMeu+gxmtVoFlmmVJDl5cF990GfPrB6dTw7tG8Pt9+eXyhLmLxcmH8vfNEHstclcPBuKt8QWt8L1Y+PPluSJEmSJEmSJP1KypbJthkJPLrt+WDg7Bh3kSRJkiRJkiRJ2mM5eTkMeX8Ig94dRG6YG0lmQMD1R13P4JMHU6JYiUgypYJu2jTIzIQpU+LJb94cxo+HI49M8ODVX8CUDvDzpwkevBvSSkDTftDoBkj3d5EkSZIkSZIkSakgpctkYRhODoLgdKANcEYQBKPCMOwe916SJEmSJEmSJEm749tV33LZ05fx8eKPI8s8oPwBPPKnRzipzkmRZUoF2dq10L8/jB2bfzJZ1MqVg8GDoVMnKJbIu7c5G2HWIJg3EiIqsv5KjZOh1QQof1D02ZIkSZIkSZIk6XeldJlsm7bAOqAT0DUIgsOBm8MwfCvWrSRJkiRJkiRJkn5HGIY8OP1Bur3SjY3ZGyPLvaTZJYw9eywVS1aMLFMqqMIQ/vlP6NEDli+PZ4eLL4YRI2CffRI8eMlL8Fkn2LgwwYN3Q4mq0HIk1G4DQRB9viRJkiRJkiRJ2qmULpMFQfDgdt8uAGoDRwOvB0GwBpgGrAS27OHoMAzDqxKwoiRJkiRJkiRJ0q+s3LiS9i+055l5z0SWWaFEBcafM56Lm10cWaZUkM2bl38S2Ntvx5N/8MEwbhycckqCB29aCtOug0VPJnjwbqp7JbQYBiWqxJMvSZIkSZIkSZJ2KaXLZOSfShZu930I/PLxdZWAk//AzGDbHMtkkiRJkiRJkiQpoV765iWufPZKlm+M7pijk2qfxMN/ephaFWpFlikVVJs2wW23wfDhkJ0dfX7JktCvH/TsCSVKJHBwXi7Mvxe+6APZ6xI4eDeVbwitJkCNE6LPliRJkiRJkiRJeyTVy2Q7Eu76EkmSJEmSJEmSpOhsyt7EDa/dwLjPxkWWWTy9OLeffDvdj+pOWpAWWa5UUD3/PFx7LSxcGE/+OefAmDFQp06CB6/+AqZ0gJ8/TfDg3ZBWApr0hca9ID2R7ThJkiRJkiRJkpQsBaFMFuz6EkmSJEmSJEmSpHh8tvQz2jzVhq9+/iqyzKbVm/LYRY9xSI1DIsuUCqoFC6BbN3juuXjya9WCu++G88+HIJF3PnM2wqxBMG8khLkJHLybapwMrcZD+YOjz5YkSZIkSZIkSX9YqpfJEv25fJIkSZIkSZIkSQmRk5fDHR/cwcB3B5KTlxNZbo8je3DbKbdRsljJyDKlgmjrVhgxAm69FTZvjj6/WDHo2RP69YMyZRI8fMlL8Fln2LggwYN3Q4mq0HIk1G6T4HacJEmSJEmSJEmKQkqXycIwXBj3DpIkSZIkSZIkSb/13ervuOzpy/joh48iy9yv3H488qdHOKXuKZFlSgXVW29B584wb148+SecAOPGQePGCR68+Uf4vBssejLBg3dT3SuhxTAoUSWefEmSJEmSJEmStNdSukwm/VFBELQF2u7gn0pHu4kkSZIkSZIkqTAJw5CHZzxM11e6smHrhshy/97074w7exyVSlWKLFMqiJYtyz8N7LHH4smvXj3/NLRLL03woV1hHsy/F2bcCNnrEjh4N5VvCK0mQI0Tos+WJEmSJEmSJEkJZZlMhVVtwLtZkiRJkiRJkqSE+WnTT7R/vj1Pz3s6sswKJSow7pxxXNLsksgypYIoNxfGj4e+fWFdDF2rIIBOnWDwYKhYMcHDV8+EKe3h508TPHg3pBWHJv2gcS9ILxF9viRJkiRJkiRJSjjLZCqsFgDv7uD10kCraFeRJEmSJEmSJBV0r8x/hXbPtmPZhmWRZZ5w4Ak8euGj1KpQK7JMqSCaMgUyM2HatHjyDz88v8h2+OEJHpyzEWbdAvNGQJib4OG7ocbJ0Go8lD84+mxJkiRJkiRJkpQ0lslUKIVh+DDw8G9fD4KgCTA76n0kSZIkSZIkSQXTpuxN9Hq9F2Onjo0sMyMtg9tOvo0eR/UgPS09slypoFm9Gvr0gYkTIQyjz69QAYYMgfbtIT3R/6kufRmmdoKNCxI8eDeUqAItRkKdy/KPXJMkSZIkSZIkSYWKZTJJkiRJkiRJkqQdmPbjNC596lLm/TQvsswm1Zrw2EWPcWjNQyPLlAqaMIRHH4UbboCVK+PZ4fLLYdgwqFEjwYM3/wifXweLnkjw4N1Utx00HwYlq8aTL0mSJEmSJEmSks4ymSRJkiRJkiRJ0nZy83IZ9uEwBrwzgJy8nMhyrzviOoacOoSSxUpGlikVNLNnQ6dO8P778eQ3bgzjxsEJJyR4cJgH8++FGTdC9roED98N5RtAq3uhRqJ/MEmSJEmSJEmSlGosk0mSJEmSJEmSJG3z/ervufyZy/lg0QeRZe5Xbj8e/tPDnFr31MgypYJmwwYYNAhGjYLc3OjzS5eGm2+G666D4sUTPHz1TJjSAX7+JMGDd0NacWjSFxr3hvQS0edLkiRJkiRJkqTIWSaTJEmSJEmSJElFXhiGPPrFo1z78rWs37o+sty/Nvkr488ZT+VSlSPLlAqSMISnn4Zu3WDx4nh2uPBCGD0aatVK8OCcjTDrFpg3AsIYGnI1ToJWE6D8wdFnS5IkSZIkSZKk2FgmkyRJkiRJkiRJRdrPm36mwwsd+M+X/4kss3yJ8ow9eyyXNruUIAgiy5UKkm+/hWuvhZdfjie/Th0YMwbOOScJw5e+DFM7wcYFSRi+CyWqQIuRUOcy8PePJEmSJEmSJElFjmUySZIkSZIkSZJUZL06/1XaPduOHzf8GFnm8Qcez6N/epQDKx4YWaZUkGzZAsOGwe23Q1ZW9PnFi0OvXtCnD5QuneDhm3+Ez6+DRU8kePBuqtsOmg+DklXjyZckSZIkSZIkSbGzTCZJkiRJkiRJkoqczdmb6f1Gb8ZMGRNZZkZaBoNPHsz1R11Pelp6ZLlSQfLaa9ClC3zzTTz5p54K99wDDRokeHCYB/PvhRk3Qva6BA/fDeUbQKsJUOPE6LMlSZIkSZIkSVJKsUwmSZIkSZIkSZKKlGk/TqPNU2348qcvI8tsXK0xky+cTIt9WkSWKRUkS5ZAjx7wREwHdu2zD4waBX/9KwRBgoevmQWftoefP0nw4N2QVhya9IXGvSG9RPT5kiRJkiRJkiQp5VgmkyRJkiRJkiRJRUJuXi7DPxrOgLcHkJ2XHVlutyO6MeSUIZTKKBVZplRQ5OTAmDEwYABs2BB9floadO0KgwZB+fIJHp6zCWbfAl+OgDAnwcN3Q42ToNX4/FPJJEmSJEmSJEmStrFMJkmSJEmSJEmSCr0FaxZw+dOX8/6i9yPL3Lfcvjx8wcOcVu+0yDKlguTDD6FTJ5g5M578o46CceOgefMkDF/6CkzNhI0LkjB8F0pUgRYjoc5lSThmTZIkSZIkSZIkFXSWySRJkiRJkiRJUqEVhiGTZk6iy0tdWL91fWS5f278ZyacM4EqpatElikVFD/9BL17w4MPxpNfuTLccQdceWX+yWQJtflH+Lw7LPpXggfvprptoflwKFk1nnxJkiRJkiRJkpTyLJNJkiRJkiRJkqRCadXmVXR8oSNPzn0yssxyxctxz9n3cNkhlxF4IpD0K3l5+QWy3r1h1ap4drjqKhg6FKomumsV5sH8iTDjRshem+Dhu6F8A2g1AWqcGH22JEmSJEmSJEkqUCyTSZIkSZIkSZKkQuf1b1+n7bNtWbp+aWSZx9Y6lkkXTqJ2xdqRZUoFxYwZkJkJn3wST/4hh8D48XD00UkYvmYWTOkAP32chOG7kFYcmtwEjW+E9BLR50uSJEmSJEmSpALHMpkkSZIkSZIkSSo0Nmdvps+bfbjr07siy8xIy+CWk27hhqNvID0tPbJcqSBYtw4GDIAxY/JPJota2bJwyy1w7bVQLNF3RnM2wexb4MsREOYkePhuqH4itJ6QfyqZJEmSJEmSJEnSbiqQZbIgCBoCBwAVgFJAsKczwjB8NNF7SZIkSZIkSZKk+MxYNoNLn7qUuSvnRpbZqGojJl80mZb7tIwsUyoIwhCeeAK6d4cff4xnh7/+FUaOhP32S8Lwpa/A1E6w8fskDN+FElWgxQioczkEe3ybVJIkSZIkSZIkFXEFpkwWBMEZQHvgdKB0AkZaJpMkSZIkSZIkqRDIzctlxMcj6PdWP7LzsiPLvbb1tdxx6h2UyigVWaZUEHz9NXTuDG+8EU9+/fowdiycfnoShm9eBp9fB4v+lYThu6FuW2g+HEpWjSdfkiRJkiRJkiQVeClfJguCoCLwMHDeLy/txbhw2/vDvdtKkiRJkiRJkiSlgoVrFnL5M5fz3sL3Isvcp+w+PHTBQ5xR/4zIMqWCYPNmuP12GDYMtm6NPr9ECbjpJujVC0qWTPDwMA/mT4QZN0L22gQP3w3lDobW90KNE6PPliRJkiRJkiRJhUpKl8mCICgNvAoczv9KYL8Uwv7QyAStJkmSJEmSJEmSYhSGIY/NeozOL3VmXda6yHIvanQRE8+dSJXSVSLLlAqCl16CLl3g++/jyT/zTLjnHqhXLwnD18yCKR3gp4+TMHwX0opDk5ug8Y2QXiL6fEmSJEmSJEmSVOikdJkM6AO04tclsi3Aa8AMYAWwMa7lJEmSJEmSJElS9FZvXk3mi5n8a86/IsssW7wsY84awxWHXkEQ+Nl10i8WLYLrroOnn44nf//94a674MILIeH/aeZsgtm3wpd3QpiT4OG7ofqJ0HoClG8QfbYkSZIkSZIkSSq0UrZMFgRBceA6fn0S2X1A7zAM18S0liRJkiRJkiRJitGb373JFc9cwZL1SyLLPOaAY3j0wkepW6luZJlSqsvOhlGjYNAg2LQp+vxixaB7dxgwAMqWTULA0ldgaifYGMNRayWqQIsRUOfyJDTkJEmSJEmSJElSUZeyZTLgWKAM/zuV7OEwDDvEu5IkSZIkSZIkSYrDlpwt3PTmTYz6ZFRkmcXSijHoxEH0PqY36WnpkeVKqe699yAzE+bOjSf/2GNh/Hho2jQJwzcvg2ndYeHjSRi+G+q2hebDoWTVePIlSZIkSZIkSVKhl8plsvrbHgMgD+gb4y6SJEmSJEmSJCkmXyz7gjZPt2H2itmRZTas2pDJF07msH0PiyxTSnXLl0OvXvDoo/HkV6sGw4fD5ck4sCvMg/n3wYzekL02wcN3Q7mDofUEqHFS9NmSJEmSJEmSJKlISeUyWZVtjyEwPwzDZXEuI0mSJEmSJEmSopUX5jHy45H0fasvW3O3RpbbuVVnhp02jNIZpSPLlFJZbi5MnAg33QRr1kSfHwTQoQPcdhtUrpyEgDWzYUp7+OnjJAzfhbTi0LgPNLkR0ktGny9JkiRJkiRJkoqcVC6Tbd7u+erYtpAkSZIkSZIkSZFbtHYRVzxzBe8seCeyzJpla/Lg+Q9y1kFnRZYppbrPPoPMzPzHOLRsCePHQ+vWSRieswlm3wpf3glhThICdqH6CdBqAlRoGH22JEmSJEmSJEkqslK5TDZ/u+dVfvcqSZIkSZIkSZJUqPxj1j/o9GIn1matjSzzwoYXMvG8iVQtXTWyTCmVrVkDffvmF7nCMPr88uXh9tuhY0dIT09CwNJXYWombPw+CcN3oUQVaHEn1Lki/9g1SZIkSZIkSZKkCKVymew9YCtQHKgTBEGlMAw9oUySJEmSJEmSpEJq9ebVdHqpE4/PfjyyzLLFy3L3mXfTtnlbAksdEmEIjz0G118PK1bEs8Oll8Kdd0LNmkkYvnkZTOsOC6P7PfMrda7IL5KVtLgqSZIkSZIkSZLikbJlsjAM1wVB8A+gLZAGXAbcHetSkiRJkiRJkiQpKd76/i2ueOYKFq9bHFnm0QcczaQLJ1G3Ut3IMqVUNncudOoE774bT37DhjBuHJx0UhKGh3kw/z6Y0Ruyozv18L/KHQytJ0CNZPxwkiRJkiRJkiRJuy8t7gV24SZg1bbn/YMgqB3jLpIkSZIkSZIkKcG25Gzh+lev55RHT4msSFYsrRi3nnQr77Z91yKZBGzcCDfeCIceGk+RrFQpGDIEvvgiSUWyNbPh9eNgasfoi2RpxaHpzXD2FxbJJEmSJEmSJElSSkjZk8kAwjBcFgTBhcDLQBXgzSAI/hyG4fSYV5MkSZIkSZIkSXtp1vJZXPrUpcxaMSuyzIOrHMxjFz3G4fseHlmmlKrCEJ59Frp1g0WL4tnh/PPhrrugdu0kDM/ZBLNvhS/vhDAnCQG7UP0EaDUBKjSMPluSJEmSJEmSJOl3pHSZDCAMw/eDIDgeeAKoC3waBMG/t33/GbAiDMOtce4oSZIkSZIkSZJ2X16Yx+hPRtPnzT5szY3uT/yZh2cy/LThlCleJrJMKVV9/z107QovvBBP/oEHwt1355fJkmLpq/BZJ9jwXZICdqJ4ZWg5AupcAUEQfb4kSZIkSZIkSdJOpHSZLAiC3N+8FJK/89+2ff1y3Z6ODsMwTOmfXZIkSZIkSZKk5796niAIOPfgc+NeJWF+WPsDbZ9ty1vfvxVZZo0yNXjwggc5+6CzI8uUUlVWFtx5JwweDFu2RJ+fkQE9e0K/flC6dBICNi+DaT1g4T+TMHw31LkCWgyHktXiyZckSZIkSZIkSdqFVC9Ubd8SC7d79CP8JEmSJEmSJEmF2satG7n25WsJgoCT65xM6YxktC6i9fjsx8l8MZM1W9ZElnlBgwu477z7qFbGYof05pvQqRN8/XU8+SedBGPHQqNGSRge5sG398P03pC9JgkBu1DuIGg1AWqeHH22JEmSJEmSJEnSHkiLe4Hd8EuJLNjua29nSZIkSZIkSZKU0ga/N5iFaxeyYM0CBr83OO519sqaLWu49KlLufg/F0dWJCuTUYb7z7ufp//2tEUyFXk//giXXAKnnhpPkaxGDXjssfwyW1KKZGtmw+vHwZQO0RfJ0jKg6QA4e6ZFMkmSJEmSJEmSVCCk+slk72EBTJIkSZIkSZJUxMxdOZc7P77zv9/f+dGdXHbIZTSqlowWRnK9/f3bXPHMFfyw7ofIMo/c/0gmXziZepXrRZYppaKcHBg3Dvr1g/Xro89PS4POneHWW6FChSQE5GyG2bfCl8MhzElCwC5UPx5a3QsVGkafLUmSJEmSJEmS9AeldJksDMMT495BkiRJkiRJkqQohWFI5ouZ5OT9rxiRnZdN5ouZvH3F2wRBEON2uy8rJ4t+b/VjxMcjCCP63Lj0IJ2bT7iZPsf1oVhaSt8CkZLuk08gMxNmzIgnv3VrGD8eWrZMUsDSV+GzTrDhuyQF7ETxytDiTqjbFgrI72RJkiRJkiRJkqRfeCdVkiRJkiRJkqQU8ugXj/Lewvf+v9ffXfguk2ZO4vJDL49hqz0za/ks2jzdhpnLZ0aWeVDlg5h80WRa79c6skwpFf38M/TpA/fdF09+pUowZAhcc03+yWQJt3k5TOsOC/+ZhOG7oc7l+UWyktXiyZckSZIkSZIkSdpLybiFI0mSJEmSJEmS/oBVm1fR8/Wev/vvPV/ryarNqyLcaM/khXmM+ngUre5rFWmRrONhHZneYbpFMhVpeXnw0EPQsGF8RbK2bWHePOjQIQlFsjAP5k+EFxrGUyQrdxCc/CYc9YhFMkmSJEmSJEmSVKB5MpkkSZIkSZIkSSmizxt9+GnTT7/77ys3reSmN29iwrkTItxq9yxet5i2z7Tlze/fjCyzepnqPHD+A5x78LmRZUqpaOZM6NQJPvwwnvymTWHcODjuuCQFrJkNUzrATx8lKWAn0jKgcR9o0gfSS0afL0mSJEmSJEmSlGCeTCZJkiRJkiRJUgr4ZPEnTJw2cZfXTfx8Ip8u/jSCjXbfv2b/i2bjm0VaJDvv4POYlTnLIpmKtPXr4frroWXLeIpkZcrAnXfCtGlJKpLlbIYZN8HLLeIpklU/Hs6aCYcMskgmSZIkSZIkSZIKDU8mkyRJkiRJkiQpZjl5OXR8oeNuXRsS0vHFjky9ZirF0uL9M//aLWvp8nIXJs+cHFlm6YzSjD5jNFe3vJogCCLLlVJJGMK//w3XXQdLl8azw//9H4waBQcckKSAH1+DqZmw4bskBexE8crQ4k6o2xb8PSNJkiRJkiRJkgoZy2SSJEmSJEmSJMXsnin38MXyL3b7+hnLZjB2yli6HdktiVvt3LsL3uXyZy5n0dpFkWUesd8RTLpwEgdVOSiyTCnVzJ8PXbrAq6/Gk1+3LtxzD5x1VpICNi+HaT1g4T+SFLALdS7PL5KVrBZPviRJkiRJkiRJUpLFUiYLguDB37wUhmF41W5clyg7zJMkSZIkSZIkKWpL1i2h/9v99/h9/d/uz1+a/IV9y+2bhK1+X1ZOFgPeHsDwj4YTEkaSmR6k0//4/vQ9vm/sp7FJcdmyBYYOzf/Kyoo+v3hx6NMHeveGUqWSEBDmwbcPwPRekL0mCQG7UO4gaDUBap4cfbYkSZIkSZIkSVKE4rrj2hb+e4c52PZ8R+Wu7a9LlJ3lSZIkSZIkSZIUqe6vdmfD1g17/L71W9fT/dXu/OvP/0rCVjs2Z8UcLn3q0j06RW1v1a9cn8kXTuaI/Y+ILFNKNa+8kn8a2bffxpN/+un5p5EdlKxDAdfMgakdYOWHSQrYibQMaNwHmvSB9JLR50uSJEmSJEmSJEUsLe4FJEmSJEmSJEkqql6d/ypPzn3yD7//iTlP8Nq3ryVwox3LC/O465O7OGziYZEWydq3bM/0DtMtkqnIWrwY/vxnOOuseIpk++4LTzyRX2ZLSpEsZzN80Rdebh5Pkaz68XDWF3DIIItkkiRJkiRJkiSpyIjrZDLIPyEskddJkiRJkiRJklRgbM7eTOeXOu/1nM4vdWZW5ixKFktOEWLJuiW0fbYtb3z3RlLm70i10tV44PwHOK/BeZFlSqkkOxvuvhtuvhk2bow+Pz0dunWDgQOhXLkkhfz4OkztCBu+S1LAThSvDC2GQ922EPjZm5IkSZIkSZIkqWiJq0xWJ8HXSZIkSZIkSZJUoAz9YCjfrt77o4bmr5rP0A+GMvDEgXu/1G88OedJOrzQgdVbVid89u859+Bzuf+8+6lRtkZkmVIq+eADyMyE2bPjyT/6aBg/Hg45JEkBm5fDtB6w8B9JCtiF2pdByxFQslo8+ZIkSZIkSZIkSTGLpUwWhuHCRF4nSZIkSZIkSVJB8vXPXzP0w6EJmzfkgyFc0uwSDq5ycELmrd2ylmtfvpZJMyclZN7uKJ1RmpGnj6T9Ye0JgiCyXClVrFwJvXvDQw/Fk1+lCgwbBm3bQloyDusK8+DbB2B6L8hek4SAXShbH1pPgJqnRJ8tSZIkSZIkSZKUQuI6mUySJEmSJEmSpCIpDEM6vdiJrblbEzZza+5WOr/UmdfavLbXRaz3F77PZU9fxsK10X3eW+v9WjPpwkkJK8NJBUleHtx/P9x4I6yO7hDAX7nmGhgyJL9QlhRr5sDUDrDywyQF7ERaBjS+EZrcBOklo8+XJEmSJEmSJElKMcn4XEFJkiRJkiRJkvQ7Hp/9OG9+/2bC577x3Rv8a86//vD7t+Zupc8bfTjh4RMiK5KlBWkMOH4AH7T7wCKZiqTp0+Goo6BDh3iKZIceCh9/DBMnJqlIlrMZvugLLzePp0hW7Tg46ws45BaLZJIkSZIkSZIkSdt4MpkkSZIkSZIkSRFZu2UtPV7rkbT53V/tzln1z6JCyQp79L65K+fS5qk2TF82PUmb/f/qVarH5Ismc+T+R0aWKaWKtWuhf38YOzb/ZLKolSsHgwdDp05QLFl3C398HaZmwoZvkxSwE8UrQYs7oW5bCPxsTUmSJEmSJEmSpO1590SSJEmSJEmSpIj0e6sfyzYsS9r8ZRuW0f/t/rt9fV6Yx5hPx3DYxMMiLZJd3eJqZnScYZFMRU4Ywj/+AQ0bwpgx8RTJ/v53mDcPunZNUpFsywr48FJ4+/R4imS1L4Nz50G9Ky2SSZIkSZIkSZIk7YAnk0mSJEmSJEmSFIHPl37OuM/GJT1n7NSxtG3elpb7tNzpdUvXL6Xds+147dvXkr7TL6qWrsr9593PBQ0viCxTShXz5kHnzvDWW/HkH3xw/klop56apIAwD759EGb0gq2rkxSyE2XrQ+sJUPOU6LMlSZIkSZIkSZIKED+OT5IkSZIkSZKkJMvNy6Xjix3JC5N/DFFemEfHFzqSm5f7u9f8e+6/aTa+WaRFsrMPOptZmbMskqnI2bQJ+vaFQw6Jp0hWsiQMHgwzZyaxSLZ2LrxxAky5JvoiWVoGNO0P58yySCZJkiRJkiRJkrQbPJlMkiRJkiRJkqQku/fze/ls6WeR5U1dOpWJn08ks1Xmr15fl7WOri935ZEvHolsl1LFSjHyjJF0OKwDQRBEliulguefh2uvhYUL48k/5xwYMwbq1ElSQM5mmHMbfDkM8rKTFLIT1Y6D1vdChUbRZ0uSJEmSJEmSJBVQlskkSZIkSZIkSUqiZRuWcdObN0We2+fNPlzU6CJqlK0BwPsL3+fyZy5nwZoFke1w+L6HM/nCyTSo2iCyTCkVLFwIXbvCc8/Fk3/AAXD33XDBBZC0DuePr8PUTNjwbZICdqJ4JWgxHOq2gyAt+nxJkiRJkiRJkqQCzLsrkiRJkiRJkiQlUc/XerI2a23kuWuz1tLz9Z5szd3KTW/exAkPnxBZkSwtSKP/8f356MqPLJKpSNm6FYYOhUaN4imSFSsGvXvDl1/Cn/6UpCLZlhXwURt4+/R4imS128C586DeVRbJJEmSJEmSJEmS/gBPJpMkSZIkSZIkKUne+v4tHpv1WGz5k2dO5tPFn/LNqm8iy6xbqS6TLpzE0QccHVmmlArefhs6dYJ58+LJP+EEGDcOGjdOUkCYB98+CDN6wdbVSQrZibL1ofV4qHlq9NmSJEmSJEmSJEmFiGUySZIkSZIkSZKSICsni8wXM+NeI9Ii2ZXNr2T0maMpV6JcZJlS3JYtg5494bGYeqPVq8Odd0KbNkk6iQxg7VyY0gFWfpCkgJ1Iy4BGvaHJTVCsVPT5kiRJkiRJkiRJhYxlMkmSJEmSJEmSkmD4R8P5+uev414jElVKVeH+8+/nTw3/FPcqUmRyc2HCBOjbF9aujT4/CCAzEwYPhkqVkhSSsxnm3AZfDoO87CSF7ES1Y6H1vVAhWcetSZIkSZIkSZIkFT2WySRJkiRJkiRJSrDvVn/Hbe/fFvcakTiz/pk8eP6D7FNun7hXkSIzZUp+kWvatHjyDz8cxo/Pf0yaZW/AlI6w4dskhvyO4pWgxXCo2w6CtOjzJUmSJEmSJEmSCjHLZCqUgiBoC7TdwT+VjnYTSZIkSZIkSUVNGIZ0eakLW3K2xL1KUpUqVoo7T7+TzMMzCYIg7nWkSKxeDTfdBPfeC2EYfX6FCjBkCLRvD+npSQrZsgKm9YAFjyUpYBdqt4GWI6Bk9XjyJUmSJEmSJEmSCjnLZCqsagMnxL2EJEmSJEmSpKLnqS+f4uX5L8e9RlIdts9hTL5oMg2rNox7FSkSYQiTJkHPnrByZTw7XHYZDB8ONWokKSDMg28fhBm9YOvqJIXsRNn60Ho81Dw1+mxJkiRJkiRJkqQixDKZCqsFwLs7eL000CraVSRJkiRJkiQVFeuz1tPtlW5xr5E0aUEafY7tw4ATBlA8vXjc60iRmD0bOnWC99+PJ79xYxg3Dk5I5kforZ0LUzrCyhh+yLQMaNQbmtwExUpFny9JkiRJkiRJklTEWCZToRSG4cPAw799PQiCJsDsqPeRJEmSJEmSVDQMfGcgS9YviXuNpKhTsQ6TLpzEMbWOiXsVKRIbNsAtt8CoUZCTE31+6dJw881w3XVQPFndzZzNMOd2+PIOyMtOUshOVDsWWt8LFRpHny1JkiRJkiRJklREFcgyWRAEAdACaARUBioAacCjYRguiHE1SZIkSZIkSVIRNXP5TO769K6410iKds3bMfrM0ZQvUT7uVaSkC0N4+mno1g0WL45nhwsvhNGjoVatJIYsewOmZMKG+UkM+R3FK0GL4VC3HQRp0edLkiRJkiRJkiQVYQWqTBYEwaHA9cAFQNkdXPIBsGAH7+sFNNz27aIwDAcmaUVJkiRJkiRJUhGUF+bR8YWO5Ia5ca+SUJVLVea+8+7jokYXxb2KFIlvv4Vrr4WXX44nv04dGDMGzjkniSFbVsC062HB5CSG7ETtS6HlSChZPZ58SZIkSZIkSZKkIq5AlMmCICgOjAI6/vLSDi4LdzJiGTB02zVhEAQPe4KZJEmSJEmSJClRHpz+IB8v/jjuNRLqjHpn8OAFD7JvuX3jXkVKuqwsGDYMbr8dtmyJPj8jA3r3hj59oHTpJIWEefDdQzD9Bti6OkkhO1G2HrQaD/ucFn22JEmSJEmSJEmS/ivly2RBEJQG3gRak18i+21pLGTH5bLt/QMYDlTb9v2lwG0JXFOSJEmSJEmSVESt3LiS3m/0jnuNhClZrCTDTxtO51adCYJd/fldKvhefx06d4Zvvokn/5RTYOxYaNAgiSFr58KUjrDy/SSG/I60DGjUC5r0hWKlos+XJEmSJEmSJEnSr6TFvcBu+CdwxHbfh8DTQCZwLrsukhGGYc629/zirEQuKEmSJEmSJEkqunq90YtVm1fFvUZCtKjZgmntp9GldReLZCr0liyBv/0NTj89niJZzZrwz3/ml9mSViTL3QJf9IeXm8dTJKt2LJw5HQ4dbJFMkiRJkiRJkiQpRaT0yWRBEJwHnMf/TiP7Bvi/MAxnb3cN/P+nle3I80B78stnrYMgKBWG4ebEbixJkiRJkiRJKkreX/g+D894OO419lpAwI3H3sjAEwdSPL143OtISZWTA2PGwIABsGFD9PlpaXDttTBoEFSokMSgZW/AlEzYMD+JIb8joyK0GA71roSgIHy2pSRJkiRJkiRJUtGR0mUyoP+2xwBYBpwYhuGPf3DW1O2epwONgGl7sZskSZIkSZIkqQjLzs0m88XMuNfYaxlpGbza5lVOqnNS3KtISffRR5CZCTNnxpN/5JEwfjw0b57EkC0rYVoPWDA5iSE7UftSaDECStWIJ1+SJEmSJEmSJEk7lbIfBRgEQQ3gMPJPHQuB/ntRJCMMwxXAyu1earB3G0qSJEmSJEmSirJRn4xizso5ca+x17Lzsvls6WdxryEl1U8/wdVXwzHHxFMkq1QJJk6EDz9MYpEszINvH4AXGsZTJCtbD056DY6ebJFMkiRJkiRJkiQphaVsmQw4hvwTyQIgB3g8ATN/2u551QTMkyRJkiRJkiQVQQvXLGTQu4PiXiNhBr47kEVrF8W9hpRweXlw//3QoAE88EA8O1x5JXz1FVxzDaQl687c2i/hjRPh06th66okhfyOtAxo0hfOngX7nBZttiRJkiRJkiRJkvZYKpfJam57DIH5YRhuTMDMdds9L5uAeZIkSZIkSZKkIqjbK93YlL0p7jUSZlP2Jrq90i3uNaSE+uILOPbY/BLXqoj7VQDNmsEHH+SX2KpVS1JI7haYOQBePhRWvp+kkJ2odgycOR0OHQzFSkWfL0mSJEmSJEmSpD2WymWyCts9X/e7V+2ZMts935ygmZIkSZIkSZKkIuT5r57n2a+ejXuNhHtm3jO88PULca8h7bV166B7d2jZEj7+OPr8smVh5EiYNg2OOSaJQcvehBebwexbIS87iUE7kFERWt8Hp74HFZtEmy1JkiRJkiRJkqS9UizuBXZi9XbPK/zuVXum5nbPf07QTEmSJEmSJElSEbFx60auffnauNdImmtfvpaT65xM6YzSca8i7bEwhCeeyC+S/fhjPDv85S/5RbL9909iyJaVMO16WDApiSE7UftSaDECStWIJ1+SJEmSJEmSJEl7JZVPJlu+7TEA6gRBUHxvhgVBcBBQdbuXftibeZIkSZIkSZKkomfwe4NZuHZh3GskzYI1Cxj83uC415D22NdfwxlnwN//Hk+RrH59eOWV/DJb0opkYQjfPggvNIynSFa2Hpz0Ghw92SKZJEmSJEmSJElSAZbKZbLPtnteHDh5L+ddut3zrcAnezlPkiRJkiRJklSEzF05lzs/vjPuNZLuzo/uZO7KuXGvIe2WzZthwABo1gxefz36/BIlYNAgmDUrv8yWNGu/hDdPhE+vgq2rkhi0A0ExaHITnD0L9jkt2mxJkiRJkiRJkiQlXLG4F/g9YRj+EATBXKDRtpd6A6/8kVlBEOwDXAuE2176IAzDLXu/pSRJkiRJkiRJhU9AEPcK0i699BJ06QLffx9P/plnwj33QL16SQzJ3QJzboe5QyEvO4lBv6PaMdDqXqjYJPpsSZIkSZIkSZIkJUUqn0wGcB/894718UEQ9N3TAUEQlAP+DVTabtbohGwnSZIkSZIkSSoyGldrTM+jesa9RtL1PLonjao12vWFUkwWLYKLLoJzzomnSLb//vCf/+SX2ZJaJFv2Jrx0CMy+NfoiWUZFaD0RTn3PIpkkSZIkSZIkSVIhk+plsnHAgm3PA+CWIAjGBkFQYXfeHATBGcAU4EjyTyULgalhGL6YhF0lSZIkSZIkSYVc/xP6c2CFA+NeI2lqV6xNv+P7xb2GtEPZ2TB8ODRqBE8/HX1+ejr07AlffplfZguSdYDflpXw0eXw1qmw/pskhezEgZfAufOg/jUQpPqtREmSJEmSJEmSJO2pYnEvsDNhGGYHQXAx8BZQkvxCWUfg8iAIngc+33ZpQH5R7JwgCFoC9YGTgXrb/VsArAIujvSHkCRJkiRJkiQVGqUzSjPmrDGc//j5ca+SFGPOGkPpjNJxryH9f957Dzp1gjlz4sk/9lgYNw6aNUtiSBjCdw/B9Btg66okBv2OsnWh1XjY5/TosyVJkiRJkiRJkhSZlC6TAYRh+GkQBH8HHie/UAZQBvjbtq9fBMB1v/ke/lckWwv8OQzD75O6sCRJkiRJkiSpUDuvwXlc0OACnv3q2bhXSag/NfwT5x58btxrSL+yYgXccAM8+mg8+VWrwp13wuWXJ/EkMoC1X8LUjrDivSSG/I6gGDTuBU36QbFS0edLkiRJkiRJkiQpUmlxL7A7wjB8HmgNzOV/J43995+3+wr4dYnsl9fmAEeEYfhORCtLkiRJkiRJkgqxu8+6u1Cd4FU6ozR3nXlX3GtI/5WbC+PHQ4MG8RTJggA6dICvvoIrrkhikSx3C8wcAC8fGk+RrNoxcNYMOPQ2i2SSJEmSJEmSJElFRIEokwGEYTgHaA5cAkzZ9nLwmy9+8/oc4Arg0DAMv45sWUmSJEmSJElSoVarQi0ubnJx3GskzMATBlKrQq2415AA+PxzOOoo6NQJ1qyJPr9FC/j4Y5gwASpXTmLQsrfgpUNg9q2Ql53EoB3IqAitJ8Kp70HFJtFmS5IkSZIkSZIkKVbF4l5gT4RhmAs8DjweBEFl4FigEVAFqAhsAn4CvgfeDsNwaUyrSpIkSZIkSZIKqTVb1nD9q9fz4IwH414lIZpWb8p1R14X9xoSa9ZAv34wbhyEYfT55cvDbbdBZiakpycxaMtKmN4Tvo/hyDWAAy+BliOhVI148iVJkiRJkiRJkhSrAlUm214YhquA57Z9SZIkSZIkSZKUdM9/9TwdX+zI0vWF57PMxp8znoz0jLjXUBEWhvDYY3D99bBiRTw7XHIJjBgBNWsmMSQM4buH84tkW1clMeh3lK0LrcbDPqdHny1JkiRJkiRJkqSUUWDLZJIkSZIkSZIkReXnTT/T9ZWu/GPWP+JeJaHaNW/HsbWOjXsNFWFffgmdOsE778ST36BB/kloJ5+c5KC182BqB1jxXpKDdiAoBo1ugKb9oVip6PMlSZIkSZIkSZKUUiyTSZIkSZIkSZK0E/+e+286v9SZFRtjOjIpSSqXqsyw04bFvYaKqI0bYfBguPNOyMmJPr9UKejfP/80tOLFkxiUuwXmDIG5QyAvO4lBv6Pq0dD6XqjYNPpsSZIkSZIkSZIkpSTLZJIkSZIkSZIk7cDyDcvp8nIX/j3333GvkhTDTh1G1dJV415DRdCzz0LXrrBoUTz5550Hd98NtWsnOWjZWzC1I6z/JslBO5BREVrcAfWuhiAt+nxJkiRJkiRJkiSlLMtkkiRJkiRJkiRtJwxD/jn7n3R9uSs/b/457nWS4ugDjqZdi3Zxr6Ei5vvvoVs3eP75ePIPPDC/RHb++UkO2rISpveE7x9NctDvOPBiaDkSStWMJ1+SJEmSJEmSJEkprUCVyYIgSAcOB1oAtYDyQCkg2MNRYRiGVyV4PUmSJEmSJElSAbdk3RIyX8zk+a9jartEID1IZ/w540nztCJFJCsLRoyAwYNh8+bo8zMyoGdP6NsXypRJYlAYwncP5xfJtq5KYtDvKFMHWo2Hfc+IPluSJEmSJEmSJEkFRoEokwVBUAHoB1wGVNvbcUAIWCaTJEmSJEmSJAH5p5E9PONhur/anbVZa+NeJ6muO/I6DqlxSNxrqIh4803o3Bm++iqe/JNOgrFjoVGjJAetnQdTO8KKd5MctANBMWh0AzTtB8VKR58vSZIkSZIkSZKkAiXly2RBEBwFPE1+iWz7E8jCeDaSJEmSJEmSJBUmi9Yu4prnr+G1b1+Le5Wk27/8/gw8cWDca6gI+PFHuP56+Oc/48mvUQNGjoSLL4Yg2PX1f1juFpgzBOYOhbytSQz6HVWPhtb3QsWm0WdLkiRJkiRJkiSpQErpMlkQBE2AV4Gy214K+V+hLJm3/iRJkiRJkiRJhVxemMfEzydyw+s3sGHrhrjXicRdZ95F2eJld32h9Afl5MC4cdC/P6xbF31+Wlr+SWi33AIVKyY5bPnbMKUjrP86yUE7kFERWtwB9a6GIC36fEmSJEmSJEmSJBVYKV0mA8aRXyT75RSyAHgNeBaYBfwMbIpnNUmSJEmSJElSQfXtqm+55vlreHvB23GvEpmzDzqbCxteGPcaKsQ+/RQyM2H69HjyW7WC8ePhsMOSHLTlJ5jeE75/JMlBv+PAi6HlSChVM558SZIkSZIkSZIkFWgpWyYLgqAecBz/O41sNfB/YRi+E+dekiRJkiRJkqSCKzcvl3um3MNNb93Epuyi81llJYuVZMxZYwiCIO5VVAitWgV9+sB990EY7vr6RKtYEYYOhauvhvT0JAaFYX6BbHpPyPo5iUG/o0wdaDUe9j0j+mxJkiRJkiRJkiQVGilbJgOO2fYYkF8o62CRTJIkSZIkSZL0R33101dc+dyVfPTDR3GvErl+x/WjbqW6ca+hQiYvDx55BHr1gp9+imeHtm3hjjugevUkB62dB1M7wop3kxy0A0ExaHQDNO0HxUpHny9JkiRJkiRJkqRCJZXLZDW3e74a+E9ci0iSJEmSJEmSCq6cvBxGfjySAW8PICs3K9LsUsVKsTlnc6SZv9WgSgN6Ht0z1h1U+MyaBZmZ8OGH8eQ3aQLjx8NxxyU5KHcLzBkKc4dA3tYkh+1A1aOh9b1QsWn02ZIkSZIkSZIkSSqUUrlMlrvtMQS+C8MwjHMZSZIkSZIkSVLBM3vFbK589kqmLp0aaW6ZjDIMO20YB1c5mNMmnRZp9m+NP2c8JYqViHUHFR7r18OgQTB6NOTm7vLyhCtTBgYOhG7dICMjyWHL34YpHWH910kO2oGMCtD8Dqh/DQRp0edLkiRJkiRJkiSp0ErlMtmi7Z6XjG0LSZIkSZIkSVKBk52bzdAPhnLre7eSnZcdafapdU/lvvPuo3bF2gBc2uxSHpv1WKQ7/KLNIW04qc5JsWSrcAlD+M9/4LrrYMmSeHb4v/+DUaPggAOSHLTlJ5jeE75/JMlBv+PAv0PLUVCqZjz5kiRJkiRJkiRJKtRSuUz2EfmnkgVA7SAIioVhmBPzTpIkSZIkSZKkFDf9x+m0e7YdXyz/ItLc8iXKM/L0kVzZ4kqCIPjv6yNOH8ELX7/A2qy1ke5TsWRF7jztzkgzVTjNnw9dusCrr8aTX7cu3HMPnHVWkoPCML9ANr0nZP2c5LAdKFMHWo2Dfc+MPluSJEmSJEmSJElFRlrcC/yeMAyXAG9s+7YMcHaM60iSJEmSJEmSUlxWThb93upHq/taRV4kO/ugs5nTaQ5XtbzqV0UygBpla3D7KbdHug/A7SffTo2yNSLPVeGxZQsMGgRNm8ZTJCteHAYMgNmzIyiSrfsK3jwJPmkXfZEsKAaNb4RzZlskkyRJkiRJkiRJUtKl8slkAL2BE8nf844gCN4Mw3BjvCtJkiRJkiRJklLNlCVTaPdsO+aunBtpbqWSlbjrzLtoc0ib/69Etr0Oh3XgoRkP8dnSzyLZq9W+rWh/WPtIslQ4vfJK/mlk334bT/7pp+efRnbQQUkOys2COUNg7hDI25rksB2oehS0vhcqNos+W5IkSZIkSZIkSUVSyp5MBhCG4Qyg07ZvDwZeCIKgenwbSZIkSZIkSZJSyebszfR6vRdHPXBU5EWyCxteyNzOc7ns0Mt2WiQDSE9LZ8I5E0gLkv9n+bQgjQnnTiA9LT3pWSp8Fi+Gv/wl/ySwOIpk++4LTzyRX2ZLepFs+Tvw0iEwe1D0RbKMCtBqApz2gUUySZIkSZIkSZIkRSqly2QAYRg+ALQBNgMnAHOCIBgYBEGzYFd35yVJkiRJkiRJhdYHiz7g0AmHMvyj4eSFeZHlVitdjSf+/AT/+et/qFm25m6/77B9D6PT4Z12feFe6tyqMy33aZn0HBUu2dkwciQ0agT//nf0+enp0L07fPllfpktqXeAtvwEH7eFN0+C9V8nMeh3HPh3OHceHNQBIiiYSpIkSZIkSZIkSdsLwjCMe4fdEgRBXeB5oBHwy9LZwCpgyx6OC8MwrJfA9VRABEHQBJj9y/ezZ8+mSZMmMW4kSZIkSZIkaU9t3LqRPm/24Z4p9xAS7d+4L256MXedeRfVylT7Q+9fu2UtDcc2ZNmGZQneLF/NsjWZ13keFUpWSMp8FU4ffACdOsGsWfHkH300jBsHhx6a5KAwhO8fhenXQ9bPSQ7bgTJ1oNU42PfM6LMlSZIkSZIkSZKUMubMmUPTpk23f6lpGIZzosovFlXQ3giC4BhgJNCQ/CLZL59HWRzY/Y99/Z+C0aCTJEmSJEmSJP3KW9+/xdXPXc33a76PNLdm2ZpMOGcCFzS8YK/mVChZgZGnj+SSpy5J0Ga/NuqMURbJtNtWroTeveGhh+LJr1IFhg2Dtm0hLdkHdK37CqZ0hBXvJDloB4Ji0KgnNO0PxUpHny9JkiRJkiRJkiRtJ9m35vZaEARdgHeAw/lfiSzciy9JkiRJkiRJUgGzLmsdHV/oyCmPnhJ5keyKQ69gbqe5e10k+8Xfm/6dU+qckpBZ2zu17qn8rcnfEj5XhU9eHkycCA0axFcku+Ya+OoruPLKJBfJcrNg1iB46ZB4imRVj4KzpkHzIRbJJEmSJEmSJEmSlBJS+mSyIAjOAe4iv0T2Sxnsl0LZVmAtsCme7SRJkiRJkiRJUXhl/iu0f749P6z7IdLc/cvvz8RzJ3LWQWcldG4QBIw7ZxzNxjdja+7WhMwsnl6csWePJQiCXV+sIm36dMjMhE8/jSf/0ENh/Hg46qgIwpa/A1M6wPqvIwj7jYwK0PwOqH8NBCn/2Y6SJEmSJEmSJEkqQlK6TAaM5n9FsgBYAYwEngO+DsMwL77VJEmSJEmSJEnJtHrzanq81oOHZzwceXaHwzow7LRhlC9RPinzD65yMDcecyO3vHdLQub1ObYPB1c5OCGzVDitXQv9+8PYsfknk0WtXDm49Vbo3BmKJfvu1JafYMYN8N3DSQ76HQf+HVqOglI148mXJEmSJEmSJEmSdiJly2RBEBwJ1CO/SAYwEzglDMOf49tKkiRJkiRJkhSF5756jo4vdOTHDT9Gmlu7Ym3uP+9+Tql7StKz+hzXh8dmPca3q7/dqzn1K9fnxmNvTNBWKmzCEB5/HHr0gGXL4tnh73+HESNg332THBSG8P2jMP16yIrhdlKZ2tBqHOyb2NMMJUmSJEmSJEmSpERKi3uBnWi57THY9ni1RTJJkiRJkiRJKtx+2vQTl/znEi54/ILIi2TXtr6WWZmzIimSAZQsVpKxZ4/d6zljzx5LyWIlE7CRCpt58+DUU+GSS+Ipkh10ELz2GvzznxEUydZ9BW+eDJ+0jb5IFhSDxr3hnDkWySRJkiRJkiRJkpTyUvZkMqDCds+XhGH4WWybSJIkSZIkSZKS7sk5T9L5pc6s3LQy0tyDKh/EA+c/wHEHHhdpLsAZ9c/gL43/wpNzn/xD7/9rk79yer3TE7yVCrpNm+C222D4cMjOjj6/ZEno2xduuAFKlEhyWG4WzB0Kc26HvK1JDtuBKkfCEROhYrPosyVJkiRJkiRJkqQ/IJXLZL/83wIhsDTORSRJkiRJkiRJybNswzK6vNSF/3z5n0hz04I0ehzZg0EnDaJ0RulIs7c36oxRvDz/ZTZs3bBH7ytXvByjzhiVpK1UUL3wAlx7LSxYEE/+2WfDmDFQt24EYcvfgakd808li1pGBWg+FOq3hyAt+nxJkiRJkiRJkiTpD0rlMtkP2z0vH9sWkiRJkiRJkqSkCMOQx2Y9RrdXurFq86pIsxtXa8yD5z/IEfsfEWnujuxXfj9uPelWur/afY/ed+tJt7JvuX2TtJUKmoULoVs3ePbZePIPOADuvhsuuACCIMlhW36CGTfAdw8nOeh31PobHDYKSu0TT74kSZIkSZIkSZK0F1L5oxI/ADYAAVAvCAILZZIkSZIkSZJUSCxZt4TzHz+fy56+LNIiWXqQTt/j+jKt/bSUKJL9okvrLjSv2Xy3r29eszmdW3dO3kIqMLZuhaFDoVGjeIpkxYpBr14wdy786U9JLpKFIXz3CLzYMJ4iWZnacOJLcOzjFskkSZIkSZIkSZJUYKVsmSwMw43Ak9u+LQZcHuM6kiRJkiRJkqQECMOQB6Y9QONxjXnh6xcizT60xqFMvWYqg08eTIliJSLN3pViacUYf854AnbdxAkImHDOBIqlFYtgM6Wyd96B5s2hTx/YvDn6/OOPhxkz4I47oGzZJIet+xreOgU+aQtZPyc57DeCdGjcG86ZA/ueFW22JEmSJEmSJEmSlGApWybbpj/wyx3BQUEQNIhzGUmSJEmSJEnSH7dwzULOmHwGVz9/Neuy1kWWm5GWwS0n3sKUa6bQYp8WkeXuqSP3P5JrWl6zy+vaH9Y+pU5VU/SWL4fLLoOTToIvv4w+v1o1ePTR/DJbkyZJDsvNglm3wEvNYPnbSQ7bgSpHwpnToPlQKFY6+nxJkiRJkiRJkiQpwVK6TBaG4VLgfGAtUAl4OwiC0+LdSpIkSZIkSZK0J/LCPMZNHUfT8U15/bvXI80+fN/DmdZhGv1P6E/x9OKRZv8RQ04dQrXS1X7336uVrsaQU4ZEuJFSSW4ujB0LDRrA5MnR5wcBdOoEX32VX2YLdn2Q3t5Z/i68fCjMuhnytiY57DcyKkCr8XD6h1DpkGizJUmSJEmSJEmSpCQqFvcCOxMEQS1gCfBXYCJQG3glCIKPgCeBz4GVwJY9nR2G4aLEbSpJkiRJkiRJ2pH5q+Zz9XNX8+7CdyPNLZFegltOuoUeR/WgWFpK/yn8VyqXqszw04bT9tm2O/z3O0+/k0qlKkW7lFLC1KmQmQmffx5P/mGHwfjx0KpVBGFZP8P0G+C7hyII24Faf4PDRkGpfeLJlyRJkiRJkiRJkpIo1e+gLwDC7b4PgQA4etvXHxWS+j+7JEmSJEmSJBVYuXm53P3p3fR9qy+bczZHmn3U/kfx4AUP0rBqw0hzE+XyQy/noRkP/X8FvBMOPIHLDrkspq0Ul9WroW9fmDABwnDX1ydahQpw++3QoQOkpyc5LAzh+0kw/XrI+inJYTtQpja0Ggf7nhV9tiRJkiRJkiRJkhSRglKoCvhfqSzc7jVJkiRJkiRJUoqZ99M8rnz2Sj5e/HGkuaWKleL2U27n2tbXkp6W7NZL8gRBwLhzxnHohEPJycsBICMtg/HnjCcI/NN4URGGMGkS9OwJK1fGs8Nll8Hw4VCjRgRh676GqR1h+dsRhP1GkA4Nr4dmN0Ox0tHnS5IkSZIkSZIkSREqKGUysDwmSZIkSZIkSSktJy+HER+N4OZ3biYrNyvS7BNrn8j9591Pvcr1Is1NlsbVGtPzqJ4M/XAoAD2P7kmjao1i3kpRmTMHOnWC996LJ79RIxg3Dk48MYKw3CyYewfMuQ3ytkYQ+BtVjoDWE6HSIdFnS5IkSZIkSZIkSTFI9TLZI3EvIEmSJEmSJEnatVnLZ9Hu2XZ8/uPnkeaWLV6W4acNp/1h7UkL0iLNTrb+J/Tnn7P/SRAE9Du+X9zrKAIbNsAtt8CoUZCTE31+6dIwYAB07w7Fi0cQuPxdmNoB1n0VQdhvZJSH5kOhfgcoZL87JEmSJEmSJEmSpJ1J6TJZGIbt4t5BkiRJkiRJkvT7tuZuZegHQxn83mCy87IjzT693ulMPHciB1Y8MNLcqJTOKM2Ys8YQBAGlM0rHvY6SKAzhmWegWzf44Yd4dvjTn2D0aDgwiv+csn6G6TfAdw9FELYDtf4Kh42GUvvEky9JkiRJkiRJkiTFKKXLZJIkSZIkSZKk1DXtx2m0e7YdM5fPjDS3QokKjDxjJO2atyMIgkizo3Zeg/PiXkFJ9t13cO218NJL8eTXrg1jxsC550YQFobw/SSYfj1k/RRB4G+UORAOHwf7nR19tiRJkiRJkiRJkpQiLJNJkiRJkiRJkvZIVk4Wt7x7C3d8eAe5YW6k2ecefC4TzpnAfuX3izRXSrSsLBg2DG6/HbZsiT4/IwN69YKbboLSURx8t+5rmJoJy9+KIOw3gnRoeD00GwDFykSfL0mSJEmSJEmSJKUQy2SSJEmSJEmSpN326eJPafdsO7786ctIcyuXqszdZ97NJc0uKfSnkanwe/116NwZvvkmnvxTToGxY6FBgwjCcrNg7jCYcxvkZUUQ+BtVjoDWE6HSIdFnS5IkSZIkSZIkSSnIMpkkSZIkSZIkaZc2ZW9iwNsDGPXJKPLCvEiz/6/R/zH27LHUKFsj0lwp0ZYuhR494F//iie/Zk0YNQr+9jeIpJO54j2Y0gHWzYsg7DcyykPzoVCvPaSlR58vSZIkSZIkSZIkpSjLZJIkSZIkSZKknXp/4ftc+dyVzF81P9LcaqWrMe6ccfy58Z8jzZUSLScH7rkHBgyA9eujz09Lgy5d4JZboEKFCAKzfobpveC7ByMI24Faf4XDRkOpfeLJlyRJkiRJkiRJklKYZTJJkiRJkiRJ0g5t2LqBPm/04Z6p90SefUmzS7jrzLuoWrpq5NlSIn38MWRmwhdfxJN/xBEwfjy0aBFBWBjCgskwrQdk/RRB4G+UORAOHwf7nR19tiRJkiRJkiRJklRAxFImC4Lgrd+8FIZheMpuXJcoO8yTJEmSJEmSJOV787s3ufr5q1mwZkGkufuU3YcJ507g/AbnR5orJdrPP8ONN8L998eTX6kS3HEHXHVV/slkSbfua5iaCcuTdWtnJ4J0aHg9NBsAxcpEny9JkiRJkiRJkiQVIHGdTHYiEG57Hmz3fGfXJcrO8iRJkiRJkiSpSFu7ZS03vH4D9027L/Lsds3bMfKMkVQsWTHybClR8vLgoYegd+/8QlkcrrwShg6FatUiCMvNgrnDYM5tkJcVQeBvVDkCWt8LlQ6NPluSJEmSJEmSJEkqgOIqk0mSJEmSJEmSUszL37xM+xfas3jd4khzDyh/APeddx9n1D8j0lwp0b74AjIz4eOP48lv1gzGj4djjokocMV7MKUDrJsXUeB2MsrDoUOgfgdIS48+X5IkSZIkSZIkSSqg4iyTBb/zfGfXSZIkSZIkSZISbNXmVXR/tTuPfvFo5NkdD+vIHafdQfkS5SPPlhJl3Tq4+WYYMwZyc6PPL1sWBg2Ca6+FjIwIArN+hum94LsHIwjbgVp/gZajofS+8eRLkiRJkiRJkiRJBVgsZbIwDNMSeZ0kSZIkSZIk6Y95Zt4zZL6YybINyyLNrVOxDveffz8n1zk50lwpkcIQnnwSuneHpUvj2eEvf4GRI2H//SMIC0NYMBmm9YCsnyII/I0yB8LhY2G/c6LPliRJkiRJkiRJkgqJOE8mIwiCAduehsCkMAwXxLiOJEmSJEmSJBUZKzeupOsrXXl89uOR5gYEdD2iK7edfBtlipeJNFtKpK+/hi5d4PXX48mvXx/uuQfOOCOiwHXfwNSOsPytiAK3E6RDwx7Q7GYo5u8NSZIkSZIkSZIkaW/EWiYDBpJfJAP4EFgQ2yaSJEmSJEmSVASEYcgTc56gy8td+GlTtCcLHVzlYB48/0GOqXVMpLlSIm3eDEOGwB13wNat0eeXKAE33QS9ekHJkhEE5mbB3GEw5zbIy4og8DeqHAGt74VKh0afLUmSJEmSJEmSJBVCcZfJAAL+VyiTJEmSJEmSJCXJsg3L6PRiJ56e93SkuWlBGj2P6snAEwdSKqNUpNlSIr38cv5pZN99F0/+GWfkn0ZWv35EgSvegykdYd2XEQVuJ6M8HDoE6neAtPTo8yVJkiRJkiRJkqRCKhXKZBbJJEmSJEmSJCmJwjBk0sxJXPfKdazesjrS7CbVmvDgBQ/Ser/WkeZKifTDD3DddfDUU/Hk77cf3HUXXHQRBEEEgVmrYEYv+PaBCMJ2oNZfoOVoKL1vPPmSJEmSJEmSJElSIZYKZTJJkiRJkiRJUpIsXreYDi904KVvXoo0Nz1Ip8+xfeh3fD9KFCsRabaUKNnZMHo0DBoEGzdGn5+eDt27w4ABUK5cBIFhCAseg2k9IGtlBIG/UeZAOHws7HdO9NmSJEmSJEmSJElSEWGZTJIkSZIkSZIKoTAMeWD6A1z/2vWsy1oXaXbzms158PwHabFPi0hzpUR67z3o1AnmzIkn/9hjYdw4aNYsosB138DUTFj+ZkSB2wnSoWEPaHYzFCsTfb4kSZIkSZIkSZJUhFgmkyRJkiRJkqRCZsGaBVz93NW8+X20pZCMtAxuPuFmeh3Ti4z0jEizpURZsQJ69YJHHoknv2pVGD4cLr8c0tIiCMzNgi+Hw+zBkJcVQeBvVGkNrSdCpUOjz5YkSZIkSZIkSZKKIMtkkiRJkiRJklRI5IV5jJ86nt5v9GZj9sZIs1vt24qHLniIJtWbRJorJUpuLtx3H/TpA2vWRJ8fBNC+Pdx+O1SuHFHoivdhSgdY92VEgdspVg6aD4H6HSEtPfp8SZIkSZIkSZIkqYiyTCZJkiRJkiRJhcD8VfO56rmreG/he5Hmlkgvwa0n3Ur3o7pTLM0/Oatg+vxzyMyEqVPjyW/RAsaPhyOOiCgwaxXM6AXfPhBR4G8c8Gc47C4ovW88+ZIkSZIkSZIkSVIR5p19SZIkSZIkSSrAcvNyuevTu+j3Vj8252yONPuYA47hgfMfoEHVBpHmSomyZg307w/jxkFeXvT55cvD4MH5RbZiUdyxCUNY8BhM6wFZKyMI/I3StaDVWNjv3OizJUmSJEmSJEmSJAGWySRJkiRJkiSpwJq7ci5XPnslny75NNLc0hmlGXLKELq07kJakBZptpQIYQj/+Adcfz0sXx7PDpdcAnfeCfvsE1Hgum9gaiYsfzOiwO0E6dCwOzQbCMXKRJ8vSZIkSZIkSZIk6b9SqUw2IgiC1RFlhWEYnhJRliRJkiRJkiQlVE5eDsM/HM7AdweyNXdrpNkn1T6J+8+/n7qV6kaaKyXKl19Cp07wzjvx5DdokH8S2sknRxSYuxW+HAazB0NeVkSh26nSGlrfC5WaR58tSZIkSZIkSZIk6f+TKmWyADgkwqwwoixJkiRJkiRJSqiZy2fS7tl2TPtxWqS55YqXY/hpw7nmsGs8jUwF0saNMHgwjBgB2dnR55cqBf37Q48eUKJERKEr3ocpHWDdlxEFbqdYOWg+BOp3hLT06PMlSZIkSZIkSZIk7VCqlMkkSZIkSZIkSTuxNXcrt79/O7e9fxs5eTmRZp9R7wwmnjeRWhVqRZorJcqzz0LXrrBoUTz5554Ld98NdepEFJi1Cmb0hm/vjyjwNw74Mxx2F5TeN558SZIkSZIkSZIkSb8rlcpkQdwLSJIkSZIkSVIq+nzp57R7th2zVsyKNLdiyYqMOmMUVxx6BUHgn3BV8CxYkF8ie/75ePJr1YIxY+D88yMKDENY8A+Y1h2yVkYUup3StaDVWNjv3OizJUmSJEmSJEmSJO2WVCmThcCdwNy4F9GeC4IgAzgLOGzbV12gClAJyAKWAp8B/wKeD8MwjGlVSZIkSZIkqUDZkrOFQe8MYvhHw8kNcyPNPr/B+Yw/Zzz7lvNkIRU8WVkwYgQMHgybN0efn5EBPXtC375QpkxEoevnw9RMWPZGRIHbCdKhYXdoNhCKRfUDS/p/7N13mNXlnf//1xl6UbE3LLH3Bmq6phijsaRusrtJNlIsCIq9994bqAhiks1m07OWGLsxURMVrNh77yLSy8zn98e4359rEAaYuc8wPB7XxeXMmXPu5xuuTP6YmffcAAAAAAAAC6O9LJMlyY1VVd1W7yFYKCsnufoTPtYlyQYf/vm3JHfXarXvVlX1eqnhAAAAAGBx9PeX/54B1wzIE+88UbS7fI/lc8kul+QHm/3AbWQslm67LRkyJHnyyfr0d9wxufTSZOONCwUbZyWPn5NMOCVpmlko+hHLb5dsNypZdqvybQAAAAAAAGCBtadlMhZv7yW5I803kD2f5I0kE5Msk2TLJIOSbJ7ks0lurdVq21RVNaNOswIAAABAuzVt9rQce9uxufAfF6ZKVbT9vU2+l0t2uSQr9165aBdaw+uvN98G9stf1qe/8srNt6H9278lxfYw3/pbcu8+yQePFwp+ROelkq3OSNbbN2noVL4PAAAAAAAALBTLZLSG15KsWFVV0yd8/I5arXZpkj8k2T3JxkkGJLm00HwAAAAAsFi444U7MvCagXl24rNFuyv1WimX7nppvrPJd4p2oTXMmZNcdlly7LHJBx+U7zc0NN+EdsopSZ8+haIz30sePCJ5dkyh4Mes8d2k34VJz9Xr0wcAAAAAAAAWmmUyFtk8lsg++pw5tVrtjDQvkyXJl2KZDAAAAACSJJNnTs5Rtx6VkfeNLN7+4RY/zIU7X5jley5fvA2L6p57kv32Sx54oD79bbdtXmTr169QsKqSF36Z3H9QMvPtQtGP6Llmsu3IZPXdyrcBAAAAAACAVmGZbAlVq9XWTbJdkr5JuiaZmOSJJHdXVTWjjbIf/Z2wS7dRAwAAAAAWKzc/e3MGXzs4L056sWh3taVWy6jdRmW3DSyFsPh5773k6KOTK65o3q8qrU+f5IwzksGDk06dCkUnP5Pct1/yxi2Fgh9R65RsODzZ/MSkS+/yfQAAAAAAAKDVWCZrB2q12uppXuza/sP/9k+y1Eee8mJVVWu3UuubSY5Lss0nPGVKrVb7aZKTq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[ "# #42d4f5 Color Information\n\nIn a RGB color space, hex #42d4f5 is composed of 25.9% red, 83.1% green and 96.1% blue. Whereas in a CMYK color space, it is composed of 73.1% cyan, 13.5% magenta, 0% yellow and 3.9% black. It has a hue angle of 191.1 degrees, a saturation of 89.9% and a lightness of 61%. #42d4f5 color hex could be obtained by blending #84ffff with #00a9eb. Closest websafe color is: #33ccff.\n\n• R 26\n• G 83\n• B 96\nRGB color chart\n• C 73\n• M 13\n• Y 0\n• K 4\nCMYK color chart\n\n#42d4f5 color description : Bright cyan.\n\n# #42d4f5 Color Conversion\n\nThe hexadecimal color #42d4f5 has RGB values of R:66, G:212, B:245 and CMYK values of C:0.73, M:0.13, Y:0, K:0.04. Its decimal value is 4379893.\n\nHex triplet RGB Decimal 42d4f5 `#42d4f5` 66, 212, 245 `rgb(66,212,245)` 25.9, 83.1, 96.1 `rgb(25.9%,83.1%,96.1%)` 73, 13, 0, 4 191.1°, 89.9, 61 `hsl(191.1,89.9%,61%)` 191.1°, 73.1, 96.1 33ccff `#33ccff`\nCIE-LAB 78.946, -27.604, -27.235 42.267, 54.834, 94.738 0.22, 0.286, 54.834 78.946, 38.778, 224.614 78.946, -52.027, -39.844 74.05, -27.701, -24.019 01000010, 11010100, 11110101\n\n# Color Schemes with #42d4f5\n\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #f56342\n``#f56342` `rgb(245,99,66)``\nComplementary Color\n• #42f5bd\n``#42f5bd` `rgb(66,245,189)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #427bf5\n``#427bf5` `rgb(66,123,245)``\nAnalogous Color\n• #f5bd42\n``#f5bd42` `rgb(245,189,66)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #f5427b\n``#f5427b` `rgb(245,66,123)``\nSplit Complementary Color\n• #d4f542\n``#d4f542` `rgb(212,245,66)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #f542d4\n``#f542d4` `rgb(245,66,212)``\n• #42f563\n``#42f563` `rgb(66,245,99)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #f542d4\n``#f542d4` `rgb(245,66,212)``\n• #f56342\n``#f56342` `rgb(245,99,66)``\n• #0cb8df\n``#0cb8df` `rgb(12,184,223)``\n• #12c9f2\n``#12c9f2` `rgb(18,201,242)``\n• #2acef4\n``#2acef4` `rgb(42,206,244)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n``#5adaf6` `rgb(90,218,246)``\n• #72dff8\n``#72dff8` `rgb(114,223,248)``\n• #8be5f9\n``#8be5f9` `rgb(139,229,249)``\nMonochromatic Color\n\n# Alternatives to #42d4f5\n\nBelow, you can see some colors close to #42d4f5. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #42f5e9\n``#42f5e9` `rgb(66,245,233)``\n• #42f2f5\n``#42f2f5` `rgb(66,242,245)``\n• #42e3f5\n``#42e3f5` `rgb(66,227,245)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #42c5f5\n``#42c5f5` `rgb(66,197,245)``\n• #42b6f5\n``#42b6f5` `rgb(66,182,245)``\n• #42a7f5\n``#42a7f5` `rgb(66,167,245)``\nSimilar Colors\n\n# #42d4f5 Preview\n\nThis text has a font color of #42d4f5.\n\n``<span style=\"color:#42d4f5;\">Text here</span>``\n#42d4f5 background color\n\nThis paragraph has a background color of #42d4f5.\n\n``<p style=\"background-color:#42d4f5;\">Content here</p>``\n#42d4f5 border color\n\nThis element has a border color of #42d4f5.\n\n``<div style=\"border:1px solid #42d4f5;\">Content here</div>``\nCSS codes\n``.text {color:#42d4f5;}``\n``.background {background-color:#42d4f5;}``\n``.border {border:1px solid #42d4f5;}``\n\n# Shades and Tints of #42d4f5\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, #010d10 is the darkest color, while #fcfeff is the lightest one.\n\n• #010d10\n``#010d10` `rgb(1,13,16)``\n• #021d23\n``#021d23` `rgb(2,29,35)``\n• #032c35\n``#032c35` `rgb(3,44,53)``\n• #043b48\n``#043b48` `rgb(4,59,72)``\n• #054b5a\n``#054b5a` `rgb(5,75,90)``\n• #065a6d\n``#065a6d` `rgb(6,90,109)``\n• #076980\n``#076980` `rgb(7,105,128)``\n• #087992\n``#087992` `rgb(8,121,146)``\n• #0988a5\n``#0988a5` `rgb(9,136,165)``\n• #0a98b8\n``#0a98b8` `rgb(10,152,184)``\n• #0ba7ca\n``#0ba7ca` `rgb(11,167,202)``\n• #0cb6dd\n``#0cb6dd` `rgb(12,182,221)``\n• #0dc6ef\n``#0dc6ef` `rgb(13,198,239)``\n• #1dccf3\n``#1dccf3` `rgb(29,204,243)``\n• #2fd0f4\n``#2fd0f4` `rgb(47,208,244)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n• #55d8f6\n``#55d8f6` `rgb(85,216,246)``\n• #67dcf7\n``#67dcf7` `rgb(103,220,247)``\n• #7ae1f8\n``#7ae1f8` `rgb(122,225,248)``\n• #8de5f9\n``#8de5f9` `rgb(141,229,249)``\n• #9fe9fa\n``#9fe9fa` `rgb(159,233,250)``\n• #b2edfb\n``#b2edfb` `rgb(178,237,251)``\n• #c4f2fc\n``#c4f2fc` `rgb(196,242,252)``\n• #d7f6fd\n``#d7f6fd` `rgb(215,246,253)``\n• #eafafe\n``#eafafe` `rgb(234,250,254)``\n• #fcfeff\n``#fcfeff` `rgb(252,254,255)``\nTint Color Variation\n\n# Tones of #42d4f5\n\nA tone is produced by adding gray to any pure hue. In this case, #969fa1 is the less saturated color, while #3ad9fd is the most saturated one.\n\n• #969fa1\n``#969fa1` `rgb(150,159,161)``\n• #8fa4a8\n``#8fa4a8` `rgb(143,164,168)``\n• #87a9b0\n``#87a9b0` `rgb(135,169,176)``\n``#7fadb8` `rgb(127,173,184)``\n• #78b2bf\n``#78b2bf` `rgb(120,178,191)``\n• #70b7c7\n``#70b7c7` `rgb(112,183,199)``\n• #68bccf\n``#68bccf` `rgb(104,188,207)``\n• #61c1d6\n``#61c1d6` `rgb(97,193,214)``\n• #59c6de\n``#59c6de` `rgb(89,198,222)``\n• #51cae6\n``#51cae6` `rgb(81,202,230)``\n• #4acfed\n``#4acfed` `rgb(74,207,237)``\n• #42d4f5\n``#42d4f5` `rgb(66,212,245)``\n``#3ad9fd` `rgb(58,217,253)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #42d4f5 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" ]

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[ "", null, "", null, "", null, "SEARCH HOME", null, "Math Central Quandaries & Queries", null, "", null, "Question from Franco: Hi There ! I am an intellectually very curious person with university degrees in the humanities field , but with a fairly poor mathematical background dating back to my High School days ( 50 years ago) , where I did Algebra, Trigonometry, etc. I have now found a new interest in the CAUSAL aspect of reality , as opposed to the equally valid, but widely different ( although complementary )aspect dealt with in Philosophy and I ' d like to tackle Physics, with the ambition to gain some insight also into its more recent challenging developments, such as the Theory of of Relativity and Quantum Mechanics. I have read a lot about them in non-mathematical terms and I believe I have a basic grasp of their conceptual signification ( which for me, as in anything, is essential, even in Maths , at least as far as a mathematically unaided abstract thinking allows me !). I would like now to sharpen my mathematical tools, at least well enough to get me through some college level work. I am now honing my skills with the C.O.W. ( Calculus on the Web ) site, but I am am keeping my options open with other educational, sites, such as yours, which I have recently discovered. I have completed the pre-calculus level in a few months and I am now about to enter the « forbidden » land of Calculus, which I never did before. So far, by racking my brains, I have been able to get through, but in this case, I have hit a brick-wall and this is why I'd like to get your help. I have read Professor Steve La Rocque's answer to a student regarding simultaneous equations . It is very well laid out, but I still have a problem regarding the following set of equations in relation to the equation of a circle. We are investigating the circle passing through (3,1), (-2,0) and (-3,-4). I have to substitute these points into the generic equation x^2+y^2+Dx+Ey=F 3 D + E - F = -10 -2 D - F = -4 -3 D - 4 E - F = -25 Although I have been able to solve correctly other drills on the same topic, on this one, with THREE equations, I have hit a brick-wall and I can't get out of the thicket even even by following Prof. Larocque's step-by-step explanation, Simply put, I cannot come up with the right values for D, E, F. Can somebody lay out the sequence with the solution , so that I can work my way backward and see where I was making the mistake.? Thank you so much ! Franco", null, "Franco,\n\nThere are many ways to approach this problem but what I see is that the second equation only involves D and F so I would like another equation with only D and F as variables. To do so I multiply both sides of the first equation by 4 and then add the resulting equation to the third equation.\n\nFirst equation times four:\n\n12D + 4E - 4F = - 40\n\nThird equation:\n\n-3D - 4E - F = - 25\n\nSum:\n\n9D - 5F = - 65                (*)\n\nNow I compare this equation to the second given equation and see that I can eliminate F by multiplying both sides of the second equation by 5.\n\nSecond equation times 5:\n\n-10 D - 5F = -20\n\nEquation (*):\n\n9D - 5F = - 65\n\nSubtract:\n\n-19 D = 45\nD = - 45/19\n\nSubstitute this value for D into equation (*) to find F. Finally substitute the values of D and F into any of the given equations and solve for E.\n\nI hope this helps,\nPenny", null, "", null, "", null, "", null, "", null, "Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences." ]

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[ "# Find the Expression for the Resistors Connected in Series and Write the Two Characteristics of It. - Science and Technology 1\n\nFind the expression for the resistors connected in series and write the two characteristics of it. (Draw figure).\n\n#### Solution\n\nExpression for the resistors in series:", null, "R1, R2 and R3 are the three resistors connected in series between points C and D as shown in the figure above. I is the current and V is the PD across points\n\nC and D.\n\nRs is the effective resistance in a circuit, and V1, V2 and V3 are the potentials across the three resistors such that\nV = V1 + V2 + V3 ---- (1)\n\nUsing Ohm’s law, the total potential difference\nV = I Rs\nand V1 = IR1, V2 = IR2 and V3 = IR3\n\nSubstituting these values in Equation 1, we get\n\nIRs = IR1 + IR2 + IR3\n∴ Rs = R1 + R2 + R3\nFor n number of resistors connected in series,\nRs = R1 + R2 + R3 + R4 + ----- + Rn\n\nCharacteristics of a series combination of resistors:\na) The same current flows through each resistor.\nb) The effective resistance of the combination is greater than any of the resistances in the combination.\nc) The effective resistance of the combination is equal to the sum of individual resistors.\n\nConcept: System of Resistors - Resistors in Series\nIs there an error in this question or solution?" ]

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[ "src/HOL/Tools/Sledgehammer/sledgehammer_run.ML\n author blanchet Wed Dec 12 21:48:29 2012 +0100 (2012-12-12 ago) changeset 50510 7e4f2f8d9b50 parent 50201 c26369c9eda6 child 50557 31313171deb5 permissions -rw-r--r--\nexport a pair of ML functions\n``` 1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_run.ML\n```\n``` 2 Author: Fabian Immler, TU Muenchen\n```\n``` 3 Author: Makarius\n```\n``` 4 Author: Jasmin Blanchette, TU Muenchen\n```\n``` 5\n```\n``` 6 Sledgehammer's heart.\n```\n``` 7 *)\n```\n``` 8\n```\n``` 9 signature SLEDGEHAMMER_RUN =\n```\n``` 10 sig\n```\n``` 11 type fact_override = Sledgehammer_Fact.fact_override\n```\n``` 12 type minimize_command = Sledgehammer_Reconstruct.minimize_command\n```\n``` 13 type mode = Sledgehammer_Provers.mode\n```\n``` 14 type params = Sledgehammer_Provers.params\n```\n``` 15\n```\n``` 16 val someN : string\n```\n``` 17 val noneN : string\n```\n``` 18 val timeoutN : string\n```\n``` 19 val unknownN : string\n```\n``` 20 val run_sledgehammer :\n```\n``` 21 params -> mode -> int -> fact_override\n```\n``` 22 -> ((string * string list) list -> string -> minimize_command)\n```\n``` 23 -> Proof.state -> bool * (string * Proof.state)\n```\n``` 24 end;\n```\n``` 25\n```\n``` 26 structure Sledgehammer_Run : SLEDGEHAMMER_RUN =\n```\n``` 27 struct\n```\n``` 28\n```\n``` 29 open ATP_Util\n```\n``` 30 open ATP_Problem_Generate\n```\n``` 31 open ATP_Proof_Reconstruct\n```\n``` 32 open Sledgehammer_Util\n```\n``` 33 open Sledgehammer_Fact\n```\n``` 34 open Sledgehammer_Provers\n```\n``` 35 open Sledgehammer_Minimize\n```\n``` 36 open Sledgehammer_MaSh\n```\n``` 37\n```\n``` 38 val someN = \"some\"\n```\n``` 39 val noneN = \"none\"\n```\n``` 40 val timeoutN = \"timeout\"\n```\n``` 41 val unknownN = \"unknown\"\n```\n``` 42\n```\n``` 43 val ordered_outcome_codes = [someN, unknownN, timeoutN, noneN]\n```\n``` 44\n```\n``` 45 fun max_outcome_code codes =\n```\n``` 46 NONE\n```\n``` 47 |> fold (fn candidate =>\n```\n``` 48 fn accum as SOME _ => accum\n```\n``` 49 | NONE => if member (op =) codes candidate then SOME candidate\n```\n``` 50 else NONE)\n```\n``` 51 ordered_outcome_codes\n```\n``` 52 |> the_default unknownN\n```\n``` 53\n```\n``` 54 fun prover_description ctxt ({verbose, blocking, ...} : params) name num_facts i\n```\n``` 55 n goal =\n```\n``` 56 (quote name,\n```\n``` 57 (if verbose then\n```\n``` 58 \" with \" ^ string_of_int num_facts ^ \" fact\" ^ plural_s num_facts\n```\n``` 59 else\n```\n``` 60 \"\") ^\n```\n``` 61 \" on \" ^ (if n = 1 then \"goal\" else \"subgoal \" ^ string_of_int i) ^\n```\n``` 62 (if blocking then \".\"\n```\n``` 63 else \"\\n\" ^ Syntax.string_of_term ctxt (Thm.term_of (Thm.cprem_of goal i))))\n```\n``` 64\n```\n``` 65 fun launch_prover (params as {debug, verbose, blocking, max_facts, slice,\n```\n``` 66 timeout, expect, ...})\n```\n``` 67 mode minimize_command only learn\n```\n``` 68 {state, goal, subgoal, subgoal_count, facts} name =\n```\n``` 69 let\n```\n``` 70 val ctxt = Proof.context_of state\n```\n``` 71 val hard_timeout = Time.+ (timeout, timeout)\n```\n``` 72 val birth_time = Time.now ()\n```\n``` 73 val death_time = Time.+ (birth_time, hard_timeout)\n```\n``` 74 val max_facts =\n```\n``` 75 max_facts |> the_default (default_max_facts_for_prover ctxt slice name)\n```\n``` 76 val num_facts = length facts |> not only ? Integer.min max_facts\n```\n``` 77 fun desc () =\n```\n``` 78 prover_description ctxt params name num_facts subgoal subgoal_count goal\n```\n``` 79 val problem =\n```\n``` 80 {state = state, goal = goal, subgoal = subgoal,\n```\n``` 81 subgoal_count = subgoal_count,\n```\n``` 82 facts = facts\n```\n``` 83 |> not (Sledgehammer_Provers.is_ho_atp ctxt name)\n```\n``` 84 ? filter_out (curry (op =) Induction o snd o snd o fst\n```\n``` 85 o untranslated_fact)\n```\n``` 86 |> take num_facts}\n```\n``` 87 fun print_used_facts used_facts =\n```\n``` 88 tag_list 1 facts\n```\n``` 89 |> map (fn (j, fact) => fact |> untranslated_fact |> apsnd (K j))\n```\n``` 90 |> filter_used_facts false used_facts\n```\n``` 91 |> map (fn ((name, _), j) => name ^ \"@\" ^ string_of_int j)\n```\n``` 92 |> commas\n```\n``` 93 |> enclose (\"Fact\" ^ plural_s (length facts) ^ \" in \" ^ quote name ^\n```\n``` 94 \" proof (of \" ^ string_of_int (length facts) ^ \"): \") \".\"\n```\n``` 95 |> Output.urgent_message\n```\n``` 96 fun really_go () =\n```\n``` 97 problem\n```\n``` 98 |> get_minimizing_prover ctxt mode learn name params minimize_command\n```\n``` 99 |> verbose ? tap (fn {outcome = NONE, used_facts as _ :: _, ...} =>\n```\n``` 100 print_used_facts used_facts\n```\n``` 101 | _ => ())\n```\n``` 102 |> (fn {outcome, preplay, message, message_tail, ...} =>\n```\n``` 103 (if outcome = SOME ATP_Proof.TimedOut then timeoutN\n```\n``` 104 else if is_some outcome then noneN\n```\n``` 105 else someN, fn () => message (preplay ()) ^ message_tail))\n```\n``` 106 fun go () =\n```\n``` 107 let\n```\n``` 108 val (outcome_code, message) =\n```\n``` 109 if debug then\n```\n``` 110 really_go ()\n```\n``` 111 else\n```\n``` 112 (really_go ()\n```\n``` 113 handle ERROR msg => (unknownN, fn () => \"Error: \" ^ msg ^ \"\\n\")\n```\n``` 114 | exn =>\n```\n``` 115 if Exn.is_interrupt exn then\n```\n``` 116 reraise exn\n```\n``` 117 else\n```\n``` 118 (unknownN, fn () => \"Internal error:\\n\" ^\n```\n``` 119 ML_Compiler.exn_message exn ^ \"\\n\"))\n```\n``` 120 val _ =\n```\n``` 121 (* The \"expect\" argument is deliberately ignored if the prover is\n```\n``` 122 missing so that the \"Metis_Examples\" can be processed on any\n```\n``` 123 machine. *)\n```\n``` 124 if expect = \"\" orelse outcome_code = expect orelse\n```\n``` 125 not (is_prover_installed ctxt name) then\n```\n``` 126 ()\n```\n``` 127 else if blocking then\n```\n``` 128 error (\"Unexpected outcome: \" ^ quote outcome_code ^ \".\")\n```\n``` 129 else\n```\n``` 130 warning (\"Unexpected outcome: \" ^ quote outcome_code ^ \".\");\n```\n``` 131 in (outcome_code, message) end\n```\n``` 132 in\n```\n``` 133 if mode = Auto_Try then\n```\n``` 134 let val (outcome_code, message) = TimeLimit.timeLimit timeout go () in\n```\n``` 135 (outcome_code,\n```\n``` 136 state\n```\n``` 137 |> outcome_code = someN\n```\n``` 138 ? Proof.goal_message (fn () =>\n```\n``` 139 [Pretty.str \"\",\n```\n``` 140 Pretty.mark Markup.intensify (Pretty.str (message ()))]\n```\n``` 141 |> Pretty.chunks))\n```\n``` 142 end\n```\n``` 143 else if blocking then\n```\n``` 144 let\n```\n``` 145 val (outcome_code, message) = TimeLimit.timeLimit hard_timeout go ()\n```\n``` 146 in\n```\n``` 147 (if outcome_code = someN orelse mode = Normal then\n```\n``` 148 quote name ^ \": \" ^ message ()\n```\n``` 149 else\n```\n``` 150 \"\")\n```\n``` 151 |> Async_Manager.break_into_chunks\n```\n``` 152 |> List.app Output.urgent_message;\n```\n``` 153 (outcome_code, state)\n```\n``` 154 end\n```\n``` 155 else\n```\n``` 156 (Async_Manager.launch SledgehammerN birth_time death_time (desc ())\n```\n``` 157 ((fn (outcome_code, message) =>\n```\n``` 158 (verbose orelse outcome_code = someN,\n```\n``` 159 message ())) o go);\n```\n``` 160 (unknownN, state))\n```\n``` 161 end\n```\n``` 162\n```\n``` 163 fun class_of_smt_solver ctxt name =\n```\n``` 164 ctxt |> select_smt_solver name\n```\n``` 165 |> SMT_Config.solver_class_of |> SMT_Utils.string_of_class\n```\n``` 166\n```\n``` 167 val auto_try_max_facts_divisor = 2 (* FUDGE *)\n```\n``` 168\n```\n``` 169 fun run_sledgehammer (params as {debug, verbose, blocking, provers, max_facts,\n```\n``` 170 slice, ...})\n```\n``` 171 mode i (fact_override as {only, ...}) minimize_command state =\n```\n``` 172 if null provers then\n```\n``` 173 error \"No prover is set.\"\n```\n``` 174 else case subgoal_count state of\n```\n``` 175 0 => (Output.urgent_message \"No subgoal!\"; (false, (noneN, state)))\n```\n``` 176 | n =>\n```\n``` 177 let\n```\n``` 178 val _ = Proof.assert_backward state\n```\n``` 179 val print = if mode = Normal then Output.urgent_message else K ()\n```\n``` 180 val state =\n```\n``` 181 state |> Proof.map_context (Config.put SMT_Config.verbose debug)\n```\n``` 182 val ctxt = Proof.context_of state\n```\n``` 183 val {facts = chained, goal, ...} = Proof.goal state\n```\n``` 184 val (_, hyp_ts, concl_t) = strip_subgoal ctxt goal i\n```\n``` 185 val ho_atp = exists (Sledgehammer_Provers.is_ho_atp ctxt) provers\n```\n``` 186 val reserved = reserved_isar_keyword_table ()\n```\n``` 187 val css = clasimpset_rule_table_of ctxt\n```\n``` 188 val all_facts =\n```\n``` 189 nearly_all_facts ctxt ho_atp fact_override reserved css chained hyp_ts\n```\n``` 190 concl_t\n```\n``` 191 val _ = () |> not blocking ? kill_provers\n```\n``` 192 val _ = case find_first (not o is_prover_supported ctxt) provers of\n```\n``` 193 SOME name => error (\"No such prover: \" ^ name ^ \".\")\n```\n``` 194 | NONE => ()\n```\n``` 195 val _ = print \"Sledgehammering...\"\n```\n``` 196 val (smts, (ueq_atps, full_atps)) =\n```\n``` 197 provers |> List.partition (is_smt_prover ctxt)\n```\n``` 198 ||> List.partition (is_unit_equational_atp ctxt)\n```\n``` 199 fun launch_provers state get_facts translate provers =\n```\n``` 200 let\n```\n``` 201 val facts = get_facts ()\n```\n``` 202 val num_facts = length facts\n```\n``` 203 val facts = facts ~~ (0 upto num_facts - 1)\n```\n``` 204 |> map (translate num_facts)\n```\n``` 205 val problem =\n```\n``` 206 {state = state, goal = goal, subgoal = i, subgoal_count = n,\n```\n``` 207 facts = facts}\n```\n``` 208 fun learn prover =\n```\n``` 209 mash_learn_proof ctxt params prover (prop_of goal) all_facts\n```\n``` 210 val launch = launch_prover params mode minimize_command only learn\n```\n``` 211 in\n```\n``` 212 if mode = Auto_Try orelse mode = Try then\n```\n``` 213 (unknownN, state)\n```\n``` 214 |> fold (fn prover => fn accum as (outcome_code, _) =>\n```\n``` 215 if outcome_code = someN then accum\n```\n``` 216 else launch problem prover)\n```\n``` 217 provers\n```\n``` 218 else\n```\n``` 219 provers\n```\n``` 220 |> (if blocking then Par_List.map else map)\n```\n``` 221 (launch problem #> fst)\n```\n``` 222 |> max_outcome_code |> rpair state\n```\n``` 223 end\n```\n``` 224 fun get_facts label is_appropriate_prop provers =\n```\n``` 225 let\n```\n``` 226 val max_max_facts =\n```\n``` 227 case max_facts of\n```\n``` 228 SOME n => n\n```\n``` 229 | NONE =>\n```\n``` 230 0 |> fold (Integer.max o default_max_facts_for_prover ctxt slice)\n```\n``` 231 provers\n```\n``` 232 |> mode = Auto_Try ? (fn n => n div auto_try_max_facts_divisor)\n```\n``` 233 in\n```\n``` 234 all_facts\n```\n``` 235 |> (case is_appropriate_prop of\n```\n``` 236 SOME is_app => filter (is_app o prop_of o snd)\n```\n``` 237 | NONE => I)\n```\n``` 238 |> relevant_facts ctxt params (hd provers) max_max_facts fact_override\n```\n``` 239 hyp_ts concl_t\n```\n``` 240 |> map (apfst (apfst (fn name => name ())))\n```\n``` 241 |> tap (fn facts =>\n```\n``` 242 if verbose then\n```\n``` 243 label ^ plural_s (length provers) ^ \": \" ^\n```\n``` 244 (if null facts then\n```\n``` 245 \"Found no relevant facts.\"\n```\n``` 246 else\n```\n``` 247 \"Including (up to) \" ^ string_of_int (length facts) ^\n```\n``` 248 \" relevant fact\" ^ plural_s (length facts) ^ \":\\n\" ^\n```\n``` 249 (facts |> map (fst o fst) |> space_implode \" \") ^ \".\")\n```\n``` 250 |> print\n```\n``` 251 else\n```\n``` 252 ())\n```\n``` 253 end\n```\n``` 254 fun launch_atps label is_appropriate_prop atps accum =\n```\n``` 255 if null atps then\n```\n``` 256 accum\n```\n``` 257 else if is_some is_appropriate_prop andalso\n```\n``` 258 not (the is_appropriate_prop concl_t) then\n```\n``` 259 (if verbose orelse length atps = length provers then\n```\n``` 260 \"Goal outside the scope of \" ^\n```\n``` 261 space_implode \" \" (serial_commas \"and\" (map quote atps)) ^ \".\"\n```\n``` 262 |> Output.urgent_message\n```\n``` 263 else\n```\n``` 264 ();\n```\n``` 265 accum)\n```\n``` 266 else\n```\n``` 267 launch_provers state (get_facts label is_appropriate_prop o K atps)\n```\n``` 268 (K (Untranslated_Fact o fst)) atps\n```\n``` 269 fun launch_smts accum =\n```\n``` 270 if null smts then\n```\n``` 271 accum\n```\n``` 272 else\n```\n``` 273 let\n```\n``` 274 val facts = get_facts \"SMT solver\" NONE smts\n```\n``` 275 val weight = SMT_Weighted_Fact oo weight_smt_fact ctxt\n```\n``` 276 in\n```\n``` 277 smts |> map (`(class_of_smt_solver ctxt))\n```\n``` 278 |> AList.group (op =)\n```\n``` 279 |> map (snd #> launch_provers state (K facts) weight #> fst)\n```\n``` 280 |> max_outcome_code |> rpair state\n```\n``` 281 end\n```\n``` 282 val launch_full_atps = launch_atps \"ATP\" NONE full_atps\n```\n``` 283 val launch_ueq_atps =\n```\n``` 284 launch_atps \"Unit equational provers\" (SOME is_unit_equality) ueq_atps\n```\n``` 285 fun launch_atps_and_smt_solvers () =\n```\n``` 286 [launch_full_atps, launch_smts, launch_ueq_atps]\n```\n``` 287 |> Par_List.map (fn f => ignore (f (unknownN, state)))\n```\n``` 288 handle ERROR msg => (print (\"Error: \" ^ msg); error msg)\n```\n``` 289 fun maybe f (accum as (outcome_code, _)) =\n```\n``` 290 accum |> (mode = Normal orelse outcome_code <> someN) ? f\n```\n``` 291 in\n```\n``` 292 (unknownN, state)\n```\n``` 293 |> (if blocking then\n```\n``` 294 launch_full_atps\n```\n``` 295 #> mode <> Auto_Try ? (maybe launch_ueq_atps #> maybe launch_smts)\n```\n``` 296 else\n```\n``` 297 (fn p => Future.fork (tap launch_atps_and_smt_solvers) |> K p))\n```\n``` 298 handle TimeLimit.TimeOut =>\n```\n``` 299 (print \"Sledgehammer ran out of time.\"; (unknownN, state))\n```\n``` 300 end\n```\n``` 301 |> `(fn (outcome_code, _) => outcome_code = someN)\n```\n``` 302\n```\n``` 303 end;\n```" ]

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[ "Welcome to Itron North America\n\n×\n\nForecasting\n\n# The Logit Function: A Tool for New Things", null, "With emerging technologies such as electric vehicles and photovoltaics, developing a forecast is challenging due to the lack of history. For many, using a Bass Diffusion Model is the solution. While this model is widely used for forecasting new product sales, it is rarely seen in the electric industry due to the infrequency of new technologies.\n\nThe Bass Diffusion Model is shown below:", null, "Where:\n• “q” is the Coefficient of Imitation. The Coefficient of Imitation is the likelihood that someone will start using the product because of internal influence such as “word-of-mouth.”\n• “P” is the Coefficient of Innovation. The Coefficient of Innovation is the likelihood that someone will start using the product because of external influences such as media coverage.\n• “m” is the Market Potential. The Market Potential is the theoretical total number who will use the product.\n\nWhile the formula may be intimidating, the result is simple. The equation creates an S-shaped forecast with the parameterization controlling the speed of adoption and technology saturation.", null, "While MetrixND doesn’t have a function called “Bass Diffusion,” that doesn’t mean that you can’t create it in a transformation variable. The picture above was created using the following parameters from a microwave oven adoption model (http://www.bus.iastate.edu/zjiang/research/vbm_ijrm.pdf).\n• p = 0.00071\n• q = 0.3444\n• m = 1\n\nHowever, MetrixND provides a similar result in using the “Logit” function. This function creates an S-shaped curved through two data points using the syntax below.\n\nLOGIT (Year1, Period1, Value1, Year2, Period2, Value2)\n\nIn this function, the S-shaped curve goes through Value1 in Year1, Period1 and Value2 in Year2, Period2 where the numerical values for Value1 and Value2 are greater than 0.0 and less than 1.0. The logit function is defined by the equation below.", null, "Once again, if the formula is too intimidating, just look at the results. Using the following parameterization, the result is almost identical to the Bass Diffusion Model shown above.", null, "Using a Bass Diffusion Model or Logit function creates S-shaped curves that replicate real-world technology adoption patterns.\n\nEither of these curves may be used in a regression model to calibrate the shape to historical adoption patterns. By exploring different curve parameterizations, a regression model can be created that fits the historic technology adoption and projects the future adoption along a classic adoption curve.\n\nBelow are the Bass and Logit curves applied to historic photovoltaic adoption from 2008 through 2016 for one service territory. Both trends fit the historic data and present an adoption patterns that accelerates in the future. The slight difference in the forecast results from the variation in the mathematical equations.", null, "The next time you forecast a new technology such as electric vehicles or photovoltaics, consider using the Logit function." ]

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[ "# What is the difference between implicit and explicit type conversion in C#?\n\nThe following is the difference between implicit and explicit type conversion −\n\n## Implicit Type Conversion\n\nThese conversions are performed by C# in a type-safe manner.\n\nTo understand the concept, let us implicitly convert int to long.\n\nint val1 = 11000;\nint val2 = 35600;\nlong sum;\n\nsum = val1 + val2;\n\nAbove, we have two integer variable and when we sum it in a long variable, it won’t show an error. Since the compiler does the implicit conversion on its own.\n\nLet us print the values now.\n\n## Example\n\nusing System;\nusing System.IO;\n\nnamespace Demo {\nclass Program {\nstatic void Main(string[] args) {\nint val1 =34567;\nint val2 =56743;\nlong sum;\n\nsum = val1 + val2;\n\nConsole.WriteLine(\"Sum= \" + sum);\n\n}\n}\n}\n\n## Explicit Type Conversion\n\nThese conversions are done explicitly by users using the pre-defined functions.\n\nLet us see an example to typecast double to int −\n\n## Example\n\nusing System;\n\nnamespace Program {\nclass Demo {\nstatic void Main(string[] args) {\ndouble d = 1234.89;\nint i;\n\n// cast double to int.\ni = (int)d;\nConsole.WriteLine(i);\n}" ]

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[ "# 6以内分解和组合的图\n\n6的分解:6=1+56=2+46=3+3合成:1+5=62+4=63+3=6\n\n1 2 3 4 5 6 7 8 9 101+92+83+74+6=105+5\n\n1、请幼儿在9的分解与组合基础上,用上楼梯的方法点数:10能分成9和1、8和2、7和3、6和4、5和5、4和6、3和7、2和8、1和92、幼儿操作,教师在操作板上演示后并巡回指导.3、请个别幼儿当小老师用上楼梯的方法演示10的分\n\n3的分解:3=2+1 3=1+26的分解:6=5+1 6=4+2 6=3+3" ]

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[ "# I'm unable to figure out this error ''too many input arguments\"\n\n1 次查看（过去 30 天）\nnaheeda reshi 2023-5-7\n\nclear all; close all;\nclc;\nt=[0:1:10];\nx=[2:2:20];\nrbw = 75e3;\nFrOffset = [100e3 300e3 500e3 1e6 3e6 10e6];\nPNTarget = [-130 -140 -135 -130 -140 -155];\n[PNMeasure] = phaseNoiseMeasure(t,x,rbw,FrOffset,'on','Phase noise',PNTarget,'Type','Time','Histogram','off')\nplot(FrOffset,PNMeasure);\n##### 2 个评论显示 无隐藏 无\nnaheeda reshi 2023-5-7\nError using phaseNoiseMeasure\nToo many input arguments.\nError in pn_meas (line 8)\n[PNMeasure] = phaseNoiseMeasure(t,x,rbw,FrOffset,'on','Phase\nnoise',PNTarget,'Type','Time','Histogram','off')\ndpb 2023-5-7\n\nt=[0:1:10];\nx=[2:2:20];\nwhos t x\nName Size Bytes Class Attributes t 1x11 88 double x 1x10 80 double\nt=[1:1:10];\nrbw = 75e3;\nFrOffset = [100e3 300e3 500e3 1e6 3e6 10e6];\nPNTarget = [-130 -140 -135 -130 -140 -155];\n[PNMeasure] = phaseNoiseMeasure(t,x,rbw,FrOffset,'on','Phase noise') % Try the shortest list given as inputs...,PNTarget,'Type','Time','Histogram','off')\nIndex in position 2 exceeds array bounds.\n\nError in phaseNoiseMeasure (line 206)\nPnReal=interp1(PhaseNoisePn(:,1),PhaseNoisePn(:,2),FrOffset);\n[PNMeasure] = phaseNoiseMeasure(t,x,rbw,FrOffset,'on','Phase noise',PNTarget,'Type','Time','Histogram','off')\nplot(FrOffset,PNMeasure);\nGet different error -- first compained that t,x weren't same length so fixed that as shown, then the above.\nI have no idea what the function is trying to do so no real klew about where the interpolation issue might be coming from...\nIn just reading the input description, it seems to meet the syntax definition\n[PNMeasure] = phaseNoiseMeasure(t,x,rbw,FrOffset,'on','Phase noise') % Try the shortest list given as inputs...,PNTarget,'Type','Time','Histogram','off')\nThe first input form you gave erred trying to use griddedinterpolant internally on a dimension mismatch of needing multiple dimensions. So, I cut the input down to the minimal number of inputs given in the documentation and then it aborted as above trying to use interp1. As noted, since I've no klew what the function is trying to do, I don't hve any idea what it's trying to interpolate over, but my initial guess of your specific input problem is that the magnitude of the phase frequencies of the input signal, being just a straight line aren't commensurate with the requested values you've asked for in the otherr inputs and the function just isn't robust-enough to handling nonsensical inputs to catch the issue.\nI couldn't reproduce your initial question error with the input case you provided, however...\nMy suggestion would be to go back to using one of the sample datasets and learn how to use the function with them and the given examples in the doc, then use real-world data (or at least some made up that will have real frequency components in it in the ranges expected by the analysis and results will likely be much better.\n\n### 回答（1 个）\n\nDinesh 2023-6-6\n\nHi Naheeda!\nI tried reproducing the issue on my side. The arrays ‘t’ and ‘x’ should be of the same dimension here ‘t’ is of dimensions 1 * 11 and ‘x’ is of dimensions 1 * 10. So, that must be changed. I am not getting the too many input arguments error as the input arguments for the function phaseNoiseMeasure are correct.\nNow running phaseNoiseMeasure will prompt an interpolation error and this is about not having enough sample points to perform the interpolation operation. So, increase the number of sample points. After using the following ‘x’ and ‘t’ the function will work.\nx = rand (1,100,'double');\nt = linspace (1,2, 100);\nPlease refer to the following MATLAB documentation regarding examples on phase noise profile from time domain signal.\nFor details about ‘linspace’ and ‘rand’ functions refer the following MATLAB documentations\nhope this helps,\nThank you!\n\n### 类别\n\nHelp CenterFile Exchange 中查找有关 Matrix Indexing 的更多信息\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]

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[ "# ML text generating code with Python and Tensorflow\n\nI wanted a simple code review for improvement to increase the efficiency of my text generating model. This model is taken from the official TensorFlow site but is being trained on different datasets. I am using TensorFlow 2.0 (beta1) GPU version and Keras.\n\nI was training this on a Harry Potter book but I found that the output was not the best, despite training it for a couple of hours(when loss stabilized at around 0.0565). Here is the code:-\n\nimport numpy as np\nimport tensorflow as tf\nimport matplotlib.pyplot as plt\nfrom keras.models import Sequential\nfrom keras.layers import Dense\nfrom keras.layers import Dropout\nfrom keras.callbacks import ModelCheckpoint\nfrom keras.layers import LSTM\nfrom keras.utils import np_utils\nimport os\n\nvocab = sorted(set(text))\n\n# Creating a mapping from unique characters to indices\nchar2idx = {u:i for i, u in enumerate(vocab)}\nidx2char = np.array(vocab)\n\ntext_as_int = np.array([char2idx[c] for c in text])\n\n# The maximum length sentence we want for a single input in characters\nseq_length = 200\nexamples_per_epoch = len(text)//(seq_length+1)\n\n# Create training examples / targets\nchar_dataset = tf.data.Dataset.from_tensor_slices(text_as_int)\n\nsequences = char_dataset.batch(seq_length+1, drop_remainder=True)\n\ndef split_input_target(chunk):\ninput_text = chunk[:-1]\ntarget_text = chunk[1:]\nreturn input_text, target_text\n\ndataset = sequences.map(split_input_target)\n\n# Batch size\nBATCH_SIZE = 64 # DEfault is 64\n\n# Buffer size to shuffle the dataset\n# (TF data is designed to work with possibly infinite sequences,\n# so it doesn't attempt to shuffle the entire sequence in memory. Instead,\n# it maintains a buffer in which it shuffles elements).\nBUFFER_SIZE = 10000\n\ndataset = dataset.shuffle(BUFFER_SIZE).batch(BATCH_SIZE, drop_remainder=True)\n\n# Length of the vocabulary in chars\nvocab_size = len(vocab)\n\n# The embedding dimension\nembedding_dim = 256\n\n# Number of RNN units\nrnn_units = 960 # 32 multiple\n\ndef build_model(vocab_size, embedding_dim, rnn_units, batch_size):\nmodel = tf.keras.Sequential([\ntf.keras.layers.Embedding(vocab_size, embedding_dim,\nbatch_input_shape=[batch_size, None]),\ntf.keras.layers.LSTM(rnn_units,\nreturn_sequences=True,\nstateful=True,\nrecurrent_initializer='glorot_uniform'),\ntf.keras.layers.Dropout(0.5),\ntf.keras.layers.Dense(vocab_size)\n])\nreturn model\n\nmodel = build_model(\nvocab_size = len(vocab),\nembedding_dim=embedding_dim,\nrnn_units=rnn_units,\nbatch_size=BATCH_SIZE)\n\ndef loss(labels, logits):\nreturn tf.keras.losses.sparse_categorical_crossentropy(labels, logits, from_logits=True)\n\n# Directory where the checkpoints will be saved\ncheckpoint_dir = '/home/awesome_ruler/Documents/Atom projects/HarryPotter/CheckPoints'\n\ncheckpoint_prefix = os.path.join(checkpoint_dir, \"ckpt_{epoch}\")\n\ncheckpoint_callback=tf.keras.callbacks.ModelCheckpoint(\nfilepath=checkpoint_prefix,\nsave_weights_only=True)\n\nEPOCHS=350\nhistory = model.fit(dataset, epochs=EPOCHS, callbacks=[checkpoint_callback]) # Comment to evaluate the model\n\ncheckpoint_dir = 'CheckPoints/ckpt_380'\n\nmodel = build_model(vocab_size, embedding_dim, rnn_units, batch_size=1)\n\nmodel.summary()\n\ndef generate_text(model, start_string):\n# Evaluation step (generating text using the learned model)\n\n# Number of characters to generate\nnum_generate = 1000\n\n# Converting our start string to numbers (vectorizing)\ninput_eval = [char2idx[s] for s in start_string]\ninput_eval = tf.expand_dims(input_eval, 0)\n\n# Empty string to store our results\ntext_generated = []\n\n# Low temperatures results in more predictable text.\n# Higher temperatures results in more surprising text.\n# Experiment to find the best setting.\ntemperature = 0.2\n\n# Here batch size == 1\nmodel.reset_states()\nfor i in range(num_generate):\npredictions = model(input_eval)\n# remove the batch dimension\npredictions = tf.squeeze(predictions, 0)\n\n# using a categorical distribution to predict the character returned by the model\npredictions = predictions / temperature\npredicted_id = tf.random.categorical(predictions, num_samples=1)[-1,0].numpy()\n\n# We pass the predicted character as the next input to the model\n# along with the previous hidden state\ninput_eval = tf.expand_dims([predicted_id], 0)\n\ntext_generated.append(idx2char[predicted_id])\n\nreturn (start_string + ''.join(text_generated))\n\nprint(generate_text(model, start_string=u\"homework\"))\n\n\nSince the original dataset had many more characters, I reduced the Rnn units, keeping it a multiple of 32. Also, I converted the GRU layer to LSTM as it has better memory holding capability(theoretically). Can anyone suggest any other improvements? I would be really glad to know them\n\nAlso, here is some sample output to show you an Idea of how bad the model is (I think the main reason is that the dataset is very small). But is there still something that can be done?\n\nhomework than Privet Drive, which was\ndifficult as there wasn’t much longerulble – he went into the\nliving-room window. Harry was streaming it all right – now, where at last\non to a confused – and we couldn’t remember what I said what’s best is tites,\nbut the reflected here, sixteen minutes later, Dumbledore with the Quidditch Cup, what’s already.’\nHe was engreed. It was a very direction boats as passing the wall, because of it and\nthe fire, flanding in the middle of a ploughed field, halfway\nacross a suspension bridge and at the top of a munched of ‘Hagrid’s arms ... this is what is it?’ Harry whispered.\n‘It’s the black eyes on his cupboard, there’s something you’ve\ngot your owl broomstick, Potter’s obviously spet the only one who’ve got yeh anything ...\n‘Master,’ Harry tried. And there, she were all get still staring at the cart. He\nwas still started looking from the roof of his neck, and fell one\nof them at night and getting pellets were died. He managed to bane\nwhen we arrived.\n\n• So, you want better output because the current is unsatisfactory and you borrowed most of the code? – Mast Mar 31 at 16:58\n• @Mast Basically, I want to get a feel for transfer learning - adapting existing models on a new dataset. Since it is my first time, I want to know what parts of the code are the ones usually targeted my pros when optimizing a specific code for some other dataset. This would help me much in my other projects. Advice about the no. of layers and rnn units is also very helpful and appreciated – neel g Mar 31 at 17:06" ]

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[ "Question f9d12\n\nJun 10, 2016\n\n${\\text{55.3 g mol}}^{- 1}$\n\nExplanation:\n\nThe trick here is to realize that the density of the gaseous element is actually five times that of molecular oxygen, ${\\text{O}}_{2}$.\n\nYour strategy here will be to determine the\n\nYou can use the ideal gas law equation\n\n$\\textcolor{b l u e}{| \\overline{\\underline{\\textcolor{w h i t e}{\\frac{a}{a}} P V = n R T \\textcolor{w h i t e}{\\frac{a}{a}} |}}} \\text{ }$\n\nHere you have\n\n$P$ - the pressure of the gas\n$V$ - the volume it occupies\n$n$ - the number of moles of gas\n$R$ - the universal gas constant, usually given as $0.0821 \\left(\\text{atm\" * \"L\")/(\"mol\" * \"K}\\right)$\n$T$ - the absolute temperature of the gas\n\nto show that the molecular mass of the molecule is five times that of atomic oxygen.\n\nUnder similar conditions for pressure and temperature, equal number of moles of gas occupy the same volume. If you take\n\n$n = \\frac{m}{M} _ M$\n\nto be the number of moles of gas present in a sample, you can say that\n\n$P V = \\frac{m}{M} _ M \\cdot R T$\n\nRearrange to get\n\n$P \\cdot {M}_{M} = \\frac{m}{V} \\cdot R T$\n\nwhich is equivalent to\n\n${\\overbrace{\\frac{m}{V}}}^{\\textcolor{b l u e}{\\text{density}}} = \\frac{P}{R T} \\cdot {M}_{M}$\n\nAs you know, the ratio between the mass of a substance and the volume it occupies gives you that substance's density. Assuming that you're dealing with ideal gases, the same number of moles of ${\\text{X}}_{3}$ and of ${\\text{O}}_{2}$ will occupy the same volume $V$.\n\nNow, you have\n\n${m}_{{O}_{2}} / V = \\frac{P}{R T} \\cdot {M}_{{\\text{M O}}_{2}} \\to$ for oxygen gas\n\nand\n\n${m}_{{X}_{3}} / V = \\frac{P}{R T} \\cdot {M}_{{\\text{M X}}_{3}} \\to$ for the triatomic molecule ${\\text{X}}_{3}$\n\nYou know that\n\n${\\overbrace{{m}_{{X}_{3}} / \\textcolor{red}{\\cancel{\\textcolor{b l a c k}{V}}}}}^{\\textcolor{p u r p \\le}{{\\text{density of X\"_ 3)) = 5 xx overbrace(m_ (O_2)/color(red)(cancel(color(black)(V))))^(color(darkgreen)(\"density of O}}_{2}}}$\n\n$\\textcolor{w h i t e}{a a a a} {m}_{{X}_{3}} = 5 \\times {m}_{{O}_{2}}$\n\nThis means that the difference between these densities lies in the fact that each individual molecule of ${\\text{X}}_{3}$ is five times heavier than a molecule of ${\\text{O}}_{2}$.\n\nTherefore, the molar mass of ${\\text{X}}_{3}$ must be five times bigger than the molar mass of ${\\text{O}}_{2}$.\n\n${M}_{{\\text{M X\"_ 3) = 5 xx M_(\"M O}}_{2}}$\n\nThe molar mass of oxygen gas is approximately equal to ${\\text{32 g mol}}^{- 1}$, which means that you have\n\nM_ (\"M X\"_3) = 5 xx \"32 g mol\"^(-1) = \"160 g mol\"^(-1)\n\nThe molecule is triatomic, which of course means that it contains $3$ atoms of element $\\text{X}$. Therefore, the molar mass of $\\text{X}$ will be\n\nM_\"M X\" = M_(\"M X\"_3)/3 = \"160 g mol\"^(-1)/3 = color(green)(|bar(ul(color(white)(a/a)color(black)(\"55.3 g mol\"^(-1))color(white)(a/a)|)))\n\nI'll leave the answer rounded to three sig figs.\n\nJun 10, 2016\n\nAtomic mass(relative) =55.3 (up to one decimal place)\n\nExplanation:\n\nFor the sake of convenient discussion the Symbol of the gaseous element is considered as E .\n\nSince it is tri-atomic one its molecular formula will be written as ${E}_{3}$\n\nIf its Relative atomic mass is a then its Relative molecular mass will be 3a .\n\nNow by the given condition\n\nUnder the same condition of temperature and pressure\n\n$\\left(\\text{The density of \"E_3\" gas\")/(\"The density of \" O_2 \" gas }\\right) = 5$\n\nHence we can write Mass per unit voume in place of density to represent the ratio.\n\n$\\left(\\text{The Mass of unit volume of \" E_3 \" gas\")/(\" The Mass of unit volume of \" O_2 \" gas }\\right) = 5$\n\nAgain by Avogadro's Law It is known that under the same condition of temperature and pressure equal volume of all gases contain same number of molecules. Here we consider that under the same condition of temperature and pressure unit volume of all gases contain n molecules.\n\nSo the relation becomes\n\n$\\left(\\text{The Mass of n molecules of \" E_3 \" gas\")/(\" The Mass of n molecules of \" O_2 \" gas }\\right) = 5$\n\n$= \\left(\\text{The Mass of 1 molecule of \" E_3 \" gas\")/(\" The Mass of 1 molecules of \" O_2 \" gas }\\right) = 5$\n\nDividing both numerator and denominator by\n\n${\\text{Mass of\" 1/12 \" part of \" }}_{6}^{12} C$ we get\n\nThe ratio\n\n$= \\left(\\left(\\text{The mass of 1 molecule of \" E_3\" gas\")/ ( \"Mass of 1/12th part of \"\"_6^12C\" ) )/((\"The mass of 1 molecule of \"O_2 \" gas \")/( \"Mass of 1/12th part of \" \"\"_6^12C}\\right)\\right) = 5$\n\n$\\implies \\left(\\text{The Relative Molecular mass of \" E_3\" gas\")/(\"The Relative Molecular mass of \"O_2 \" gas }\\right) = 5$\n\nInserting\n\n$\\text{The Relative Molecular mass of \" O_2 \" gas } = 32$\n\n$\\text{ and Relative Molecular mass of } {E}_{3} = 3 a$\n\nwe get\n\n=>(3a)/32\"=5=>color(blue)(a =160/3~~55.3)#\n\nPlease Note that Relative Molecular mass,Relative Atomic mass are unit less quantities\nAs discussed here\nhttp://digipac.ca/chemical/molemass/moles2.htm" ]

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[ "Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета\n Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум", null, "Авторизация", null, "Поиск по указателям", null, "", null, "", null, "", null, "", null, "Ferguson T.S. — Mathematical Statistics. A Decision Theoretic Approach", null, "Обсудите книгу на научном форуме", null, "Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Mathematical Statistics. A Decision Theoretic Approach Автор: Ferguson T.S. Язык:", null, "Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1967 Количество страниц: 196 Добавлена в каталог: 07.12.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID", null, "Предметный указатель", null, "-distribut.ion      101 103", null, "-distribution      10:3 Absolute error loss      47 Acceptance region      258 Action space      1 Action space, terminal      309 Admissible decision rule      54 70 Admissible decision rule,", null, "63 Admissible decision rule, almost      185 Agreeing preference pattern and utility      13 Alternative hypothesis      199 As good as      54 Basu's Theorem      350 Bayes deeision rule      31 37 44 31:3 Bayes deeision rule,", null, "32 38 Bayes deeision rule, admissibility of      60 62 Bayes deeision rule, existence of      67 Bayes deeision rule, extended      50 Bayes deeision rule, generalized      50 Bayes deeision rule, limit of      49 Bayes deeision rule, nonrandomized      43 60 Bayes deeision rule, sequential      313 353 Bayes risk      31 Behavioral and randomized rule      24 25 Behavioral and randomized rule,equivalence of      25 26 Behavioral and randomized rule,relation between invariant      151 192 Behavioral strategy      25 26 Bernoulli trials      318 332 338 360 377 Bernoulli trials, dependent      328 340 Best invariant rule      154 Best invariant rule, not minimax      175 Best test      200 Beta distribution      101 223 Beta-binomial distribution      97 100 104 105 328 Better than      54 Binomial distribution      98 Binomial distribution, Bayes estimates for      52 53 Binomial distribution, Bayes sequential estimates for      318ff Binomial distribution, minimax estimates for      93 95 Bio-assay      123 Bivariate normal distribution      112 Bivariate Poisson distribution      241 Bluffing      3 43 214 Boundary      67 Bounded from below      63 Boundedly complete sufficient statistic      132 Canonical form      266 Cauchy distribution      102 174 236 239 247 298 Chance move      3 Characteristic fundion      99 107 Classification problems      291 Closed from below      64 Closure      64 Compact      84 Complete class of decision rules      55 Complete class of decision rules, essentially      55 Complete class of decision rules, essentially minimal      212 Complete class of decision rules, minimal      55 69 Complete class of decision rules, minimal essentially      55 Complete class theorem      58 87 Complete sufficient statistic      132 Composite hypothesis      206 Confidence ellipsoids      276 Confidence sets      257 Confidence sets, invariant family of      261 Confidence sets, unbiased family of      260 Convex function      76 Convex function, strictly      80 Convex hull      36 65 Convex set      35 Convex set, strictly      75 Correlation coefficient      112 Cost function      310 Covariance matrix      105 106 Critical region      198 Decision function or rule      7 Decision function or rule, behavioral      25 Decision function or rule, best      28 Decision function or rule, equalizer      90 Decision function or rule, invariant      148 341 Decision function or rule, monotone multiple      286 Decision function or rule, nonrandomized      7 Decision function or rule, randomized      24 Decision function or rule, reasonable      29 Decision function or rule, sequential      312 Decision function or rule, terminal      311 Decision problem      7 Decision problem, sequential      315 Decision problemtruncated sequential      315 Diagonal matrix      105 Digamma function      179 Discrimination      295 Dominated family of distributions      116 Double exponential distribution      241 256 378 Dvoretsky — Wald — Wolfowitz theorem      79 142 Equalizer rule      90 Equivalence relation      11 153 Estimation      11 30 46 Estimation of a distribution function      192 348 Estimation of a median      197 350 Exponential distribution      101 180 255 327 349 Exponential family of distributions      126 139 209 217 227 Extended Bayes rule      50 59 87 91 Factorization theorem      115 Fibonacei numbers      339 Fisher — Yates test      252 Fundamental identity      373 Fundamental lemma      201 Fundamental problem of decision theory      28 34 Gambler's ruin      371 378 Game      1 Game, statistical      7 Gamma distribution      52 101 136 181 Gamma function      101 Generalized Bayes rule      50 Geometric distribution      95 99 180 234 327 339 Glivenko — Calltelli lemma      192 Group of trallsformations      143 147 Half-normal distribution      190 Hoelder's inequality      80 128 Hypergeometric distribution      97 99 328 Hypothesis, composite      206 Hypothesis, general linear      264 Hypothesis, null      199 Hypothesis, simple      199 Identifiability      144 Identity transformation      143 Inadmissible decision rule      54 Indicator function      100 Inner product      71 Interior      67 Interval estimate      184 Invariance      30 143 Invariance and convex loss      158 Invariance and sufficiency      157 Invariance in testing hypotheses      242 Invariance of cost      341 Invariance of decision problem      145 341 Invariance of distributions      144 341 Invariance of general linear hypothesis      268 Invariance of loss      145 341 Invariance of prior distribution      162 299 Invariant rules and prior information      152 Inverse probability methods      32 Inverse transformation      143 Jensen's inequality      76 122 331 Laplace transformation      134 Latin square      274 Least favorable distribution      34 39 57 81 90 Least squares      269 Lebesgue integral      7 138 Lebesgue measure      50 Locally best test      235 249 255 Locally best test, one-sided      235 Locally best test, unbiased      237 Location parameter      164 Location parameter, best invariant estimate of      168 186 345 Location parameter, best invariant test for      245 Location parameter, minimax estimate of      171 Location-scale parameter      166 184 Logistic distribution      102 123 215 241 256 200 logit      121 Loss function      1 309 Lower boundary point      64 Lower quantant      63 Lower semicontinuity      84 86 Mann — Whitney test      251 Maximal invariant      243 247 343 Maximum likelihood estimate      123 Mean squared error      11 Minimax decision rule      83 39 57 90 Minimax decision rule,", null, "33 39 Minimax theorem      57 82 85 Minimum", null, "estimate      123 Minimum Bayes risk      31 39 Minimum logit-", null, "estimate      123 Mixed strategy      23 26 Modal interval      51 Moment generating function      37:3 Monotone likelihood ratio      208 259 286 218 307 Move      2 Multinomial distribution      205 Multiple decision problem      10 284 Multiple decision problem, monotone      285 Natural ordering      54 Natural parameter space      128 Necessary and sufficient statistic      132 Negative binomial distribution      96 99 Neyman structure      227 Neyman — Pearson lemma      201 Neyman — Pearson lemma, generalized      204 238 Noneentral", null, ",", null, ", and t-distributions      102 103 Nonnegative definite matrix      80 106 Nonregular families      130 137 259 Nonsingular normal distribution      109 Normal distribution      101 Normal distribution, admissibility of sample mean      141 142 185 Normal distribution, inadmissibility of sample mean      169 Normal distribution, independence of sample mean and variance      115 Normal distribution, invariant estimates for      135 182ff Normal distribution, minimax estimates for      94 176ff Normal distribution, multiple decisions for      288 290 294 303ff Normal distribution, multivariate      107 119 153 169 294 Normal distribution, tests for      207 234 246 249 265ff Normal distribution, unbiased estimates for      48 122 135 Normal form of game      1 Null hypothesis      199 Objectivists      32 Odd or even      2 8 40 42 One-sided t.est      212 286 One-to-one transformation      143 One-way classification      265 273 280 282 Onto transformation      143 Orbit      149 Order statistics      119 153 192 249 252 Orthogonal group      148 153 244 268 Orthogonal matrix      105 Parameter space      1 309 Payoff      11 Personal probability      17 Pitman estimate      188 247 Poisson distribution      99 Poisson distribution, Bayes estimates for      52 326 Poisson distribution, minimax estimates for      96 327 Poisson distribution, unbiased estimates for      136 Poisson distribution, unbiased tests for      233 Positive definite matrix      106 Power function      198 199 235 Preference pattern      12 Prior distribution      31 37 60 Prior distribution, invariant      162 299 Probability of error      10 200 Pseudo-game      214 Quantile      51 Random stopping time      311 Randomized decisions      22 Randomized decisions, space of      22 Rank test      251 Ranking problems      294 Rao — Blackwell theorem      121 125 331 Rao-Blackwellization      124 Regression      265 273 283 Riemann integral      8 133 Riemann — Stieltjes integral, S      170 Risk function      7 312 Risk set      34 63 Risk set, nonrandomized      36 Rule      see Decision function Sample distribution function      192 196 348 Sample space      6 310 Scale parameter      164 178 190 Semicontinuity      84 Separating hyperplane theorem      73 82 87 Sequential probability ratio test      361 Sequential probability ratio test, extended      362 Sequential probability ratio test, optimal property of      365 369 Set estimate      283 Similar test      266 Simple function      8 Simple hypothesis      199 Singular normal distribution      109 Size of a test      200 206 Slippage problems      299ff Spectral theorem      106 Squared error loss      46 Statistical decision problem or game      7 Stopping rule      310 Stopping rule, invariant      341 Strategy      2 Strategy, mixed      23 Subjective probability      17 Subjectivists      32 Sufficiency and invariance      157 Sufficient, sequence      330 Sufficient, statistic      113 Sufficient, statistic, complete class of rules based on      120 Sufficient, statistic, minimal      132 Support of a distribution      61 Supporting hyperplane theorem      73 77 t-distribution      103 t-test      230 232 234 246 263 Terminal action space      309 Terminal decision rule      311 test      198 199 Testing hypotheses      10 198 Three-way classification      274 Tmnsitive group      174 Tramformation      143 Transitive sufficient, sequence      334 Transpose of a vector      71 Two-sided problems      222 Two-sided tests      216 Two-way classification      266 271 281 283 Unbiased estimates      29 48 122 134 Unbiased estimates, sequential      332 Unbiased tests      224ff Uniform distribution      100 Uniform distribution, Bayes estimates for      45 Uniform distribution, best invariant estimate for      181 185 190 191 Uniform distribution, minimax sequential estimate for      346\n1 2", null, "Реклама", null, "", null, "", null, "", null, "", null, "© Электронная библиотека попечительского совета мехмата МГУ, 2004-2022", null, "|", null, "|", null, "О проекте" ]

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[ "Solutions by everydaycalculation.com\n\nReduce 28/30 to lowest terms\n\nThe reduced form of 28/30 is 14/15\n\nSteps to simplifying fractions\n\n1. Find the GCD (or HCF) of numerator and denominator\nGCD of 28 and 30 is 2\n2. Divide both the numerator and denominator by the GCD\n28 ÷ 2/30 ÷ 2\n3. Reduced fraction: 14/15\n\nEquivalent fractions:\n\nMore fractions:" ]

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[ " Electronic Diagrams, Prints and Schematics | Instrumentation Tools\n\n# Electronic Diagrams, Prints and Schematics\n\nTo read and understand an electronic diagram or electronic schematic, the basic symbols and conventions must be understood.\n\nElectronic prints fall into two basic categories, electronic schematics and block diagrams. Electronic schematics represent the most detailed category of electronic drawings. They depict every component in a circuit, the component’s technical information (such as its ratings), and how each component is wired into the circuit.\n\nBlock diagrams are the simplest type of drawing. As the name implies, block diagrams represent any part, component, or system as a simple geometric shape, with each block capable of representing a single component (such as a relay) or an entire system. The intended use of the drawing dictates the level of detail provided by each block. This article will review the basic symbols and conventions used in both types of drawings.\n\n#### Electronic Schematic Drawing Symbology\n\nOf all the different types of electronic drawings, electronic schematics provide the most detail and information about a circuit. Each electronic component in a given circuit will be depicted and in most cases its rating or other applicable component information will be provided. This type of drawing provides the level of information needed to troubleshoot electronic circuits.\n\nElectronic schematics are the most difficult type of drawing to read, because they require a very high level of knowledge as to how each of the electronic components affects, or is affected by, an electrical current. This article reviews only the symbols commonly used in depicting the many components in electronic systems. Once mastered, this knowledge should enable the reader to obtain a functional understanding of most electronic prints and schematics.\n\nFigure 1 and Figure 2 illustrate the most common electronic symbols used on electronic schematics.", null, "Figure 1 : Electronic Symbols", null, "Figure 2 : Electronic Components\n\n#### Examples of Electronic Schematic Diagrams\n\nElectronic schematics use symbols for each component found in an electrical circuit, no matter how small. The schematics do not show placement or scale, merely function and flow. From this, the actual workings of a piece of electronic equipment can be determined. Figure 3 is an example of an electronic schematic diagram.", null, "Figure 3 Example of an Electronic Schematic Diagram\n\nA second type of electronic schematic diagram, the pictorial layout diagram, is actually not so much an electronic schematic as a pictorial of how the electronic circuit actually looks. These drawings show the actual layout of the components on the circuit board. This provides a two-dimensional drawing, usually looking down from the top, detailing the components in their location.\n\nShown in Figure 4 is the schematic for a circuit and the same circuit drawn in pictorial or layout format for comparison. Normally the pictorial layout would be accompanied by a parts list.", null, "Figure 4 A : Circuit Schematic Diagram", null, "Figure 4 B : Printed Circuit Board Layout\n\nFigure 4 Comparison of an Electronic Schematic Diagram and its Pictorial Layout Diagram\n\n#### Reading Electronic Prints, Diagrams and Schematics\n\nTo properly read prints and schematics, the reader must identify the condition of the components shown and also follow the events that occur as the circuit functions. As with electrical systems, the relays and contacts shown are always in the de-energized condition. Modern electronic systems usually contain few, if any, relays or contacts, so these will normally play a minor role.\n\nElectronic schematics are more difficult to read than electrical schematics, especially when solid state devices are used (The Electronic Science Fundamental Handbook discusses electrical schematics in detail). Knowledge of the workings of these devices is necessary to determine current flow. In this section, only the basics will be covered to assist in reading skills.\n\nThe first observation in dealing with a detailed electronic schematic is the source and polarity of power. Generally, power will be shown one of two ways, either as an input transformer, or as a numerical value. When power is supplied by a transformer, polarity marks will aid in determining current flow. In this convention, dots on the primary and secondary indicate current flow into the primary and out of the secondary at a given instant of time. In Figure 5, the current is into the top of the primary and out of the bottom of the secondary.", null, "Figure 5 Transformer Polarity Markings\n\nGenerally, the electrical power source is indicated at the point where it enters a particular schematic. These values are stated numerically with polarity assigned (+15 volts, -15 volts). These markings are usually at the top and bottom of schematics, but not always.\n\nIn the example shown in Figure 6, power is shown at both the top and bottom in a circuit using two power sources. Unless specified as an Alternating Current (AC) power source, the voltages can normally be assumed to be Direct Current (DC).", null, "Figure 6 Schematic Showing Power Supply Connections\n\nIn any circuit, a ground must be established to create a complete current path. Ground is usually depicted by the use of the ground symbol that was shown previously. The direction of current flow can be determined by observing the polarity of the power supplies. When polarities are shown, current flow can be established and ground may not always be shown.\n\nWith the power sources located and the ground point established, operation of the devices can be determined.\n\nThe most common semiconductor devices are the transistor and the diode. They are made from materials like silicone and germanium, and have electrical properties intermediate between conductors and insulators. The semiconductor will be one of two varieties, the PNP or NPN. The designation indicates the direction the electrons move through the device. The direction of the arrow indicates type, as shown in Figure 2. There are, however, many different ways to install a transistor to achieve different operational characteristics. These are too numerous to cover here, so only the most common and basic configuration (the common emitter) will be shown.\n\nEven though transistors contain multiple junctions of p- or n-type material, current flow is generally in the same direction. Using conventional current flow (i.e. from + to -), current will travel through the transistor from most positive to least positive and in the direction of the arrow on the emitter. In Figure 7, the transistor has a positive power supply with ground on the emitter. If the input is also positive, the transistor will conduct.", null, "Figure 7 NPN Transistor-Conducting\n\nIf the input goes negative, as in Figure 8, the conduction of the device stops because the input, or in this case the base junction, controls the transistor condition. Notice that when current flows, it does so in the direction of the arrow.", null, "Figure 8 NPN Transistor Non-conducting\n\nFigure 9 uses a PNP transistor. The same rules apply as above except that this time polarities of power must change to allow current flow.", null, "Figure 9 PNP Transistor\n\nThe same rules that apply to transistors hold true with diodes. However, diodes are simpler than transistors because they have only one junction and conduct in only one direction, as indicated in Figure 10. The diode symbol, like the transistor symbol, shows the direction of conduction by the direction of the arrow, which is from positive to negative.", null, "Figure 10 Diode\n\nAlthough these simple rules will not allow you to read all electronic schematics, they will aid in understanding some of the basic concepts.\n\nAn item that may cause confusion when reading electronic prints or schematics is the markings used to show bistable operation. In most cases, bistables will be indicated by a box or circle, as shown in Figure 11 (A). The lines in or around these bistables not only mark them as bistables, but also indicate how they function.", null, "Figure 11 Bistable Symbols\n\nFigure 11 (B) shows the various conventions used to indicate bistable operation. Commonly, one circuit will interface with other circuits, which requires a method that allows the reader to follow one wire or signal path from the first drawing to the second. This may be done in many ways, but generally the line or conductor to be continued will end at a terminal board. This board will be labeled and numbered with the continuation drawing indicated (a separate drawing may exist for each line). With the next drawing in hand, only the terminal board that matches the previous number needs to be found to continue.\n\nIn cases where terminal boards are not used, the conductor should end with a number (usually a single digit) and also the next drawing number. To assist in locating the continuation, coordinates are provided on some drawings that indicate the location of the continuation on the second drawing. The continuation point on the second drawing will also reference back to the first drawing and the coordinates of the continuation.\n\n#### Block Drawing Symbology\n\nNot all electronics prints are drawn to the level of detail depicting the individual resistors and capacitors, nor is this level of information always necessary. These simpler drawings are called block diagrams. Block diagrams provide a means of representing any type of electronic circuit or system in a simple graphic format.\n\nBlock diagrams are designed to present flow or functional information about the circuit or system, not detailed component data. The symbols shown in Figure 12 are used in block diagrams.", null, "Figure 12 Example\n\nBlocks When block diagrams are used, the basic blocks shown above (Figure 12) can be used for almost anything. Whatever the block represents will be written inside. Note that block diagrams are presented in this article with electronic schematics because block diagrams are commonly found with complex schematic diagrams to help present or summarize their flow or functional information.\n\nThe use of block diagrams is not restricted to electronic circuits. Block diagrams are used extensively to show complex instrument channels and other complex systems when only the flowpath of the signal is important.\n\n#### Examples of Block Diagrams\n\nThe block diagram is the most basic and easiest to understand of all the types of engineering prints. It consists of simple blocks that can represent as much, or as little, as desired. An example of a block diagram is shown in Figure 13.\n\nThis particular block diagram represents an instrumentation channel used to measure the neutron flux, indicate the measured flux, and generate output signals for use by other systems.", null, "Figure 13 Example Block Diagram\n\nEach block represents a stage in the development of a signal that is used to display on the meter at the bottom or to send to systems outside the bounds of the drawing. Notice that not all blocks are equal. Some represent multiple functions, while others represent only a simple stage or single bistable circuit in a larger component. The creator of the block diagram decides the content of each block based on the intended use of the drawing.\n\nEach of the type of drawing reviewed in this and previous modules is not always distinct and separate. In many cases, two or more types of drawings will be combined into a single print. This allows the necessary information to be presented in a clear and concise format.\n\nFigure 14 provides a sample illustration of how the various types of drawings can be combined. In this example, mechanical symbols are used to represent the process system and the valves controlled by the electrical circuit; electrical single line symbols are used to show the solenoid relays and contacts used in the system; and electronic block symbols are used for the controllers, summers, I/P converter, and bistables.", null, "Figure 14 Example of a Combined Drawing, P&ID, Electrical Single Line, and Electronic Block Diagram\n\nFigure 15 illustrates the use of an electronic block diagram combined with an electrical single line diagram. This drawing represents a portion of the generator protection circuitry of a nuclear power generating plant.", null, "Figure 15 Example Combination Diagram of Electrical Single Line, and Block Diagram\n\n#### Examples :\n\nExample 1 To assist in your understanding of reading symbols and schematics, answer the following questions concerning the following figures. The answers to each example are given on the page questions concerning the following the questions.", null, "Figure 16 Example 1\n\nRefer to Figure 16 to answer the following:\n\n1. List the number which corresponds to the listed component\n\n• a. coil or inductor\n• b. PNP transistor\n• c. diode positive\n• d. power supply\n• e. fixed resistor\n• f. capacitor\n• g. NPN transistor\n• h. variable resistor\n• i. negative power supply\n• j. circuit ground\n• k. potentiometer\n\n2. What is the value of R13? (Include units) .\n\n3. With the input to Q1 at -15 volts, will the transistor be conducting or nonconducting? Why?\n\n4. What is the value of C1? (Include units)\n\nAnswers to questions on Figure 16\n\n1. a.10   d. 7   b.2   e.4   c.3   f.9    g.1   j. 11   h.6   k. 5    i.8\n2. 3.3 kilo-ohm, or 3300 ohms.\n3. Nonconducting, because the potential of the base (-15 v) is not positive relative to the emitter (-15 v).\n\n#### Example 2", null, "Figure 17 Example 2\n\nRefer to Figure 17 to answer the following:\n\na. How many resistors are there in the circuit?\n\nb. How many transistors are there? , and are they PNP or NPN transistors?\n\nc. What is CR 4 ?\n\nd. How many power supplies are there feeding the circuit and its components?\n\ne. How many capacitors are in the circuit?\n\nf. Q2 will conduct when the output of U 2 is a positive or negative voltage?\n\nAnswers to questions on Figure 17\n\na. Seven resistors, R11, R13, R14, R20, R12, Rl, RL\n\nb. Two, both are NPN type transistors.\n\nc. Diode\n\nd. Two power supplies, a 1-5 VDC to the U2 amplifier and 24 VDC battery in the circuit.\n\ne. One, C7\n\nf. NPN transistors conduct when their base junction is positive" ]

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[ "Home‎ > ‎How To's‎ > ‎Particles‎ > ‎\n\n### Creating particle species\n\nSpecies are created by using the Species class (defined in scripts/species.py) . For example:\n\n`beam = Species(type=Potassium, charge_state=+1, name=\"Beam ions (K+)\")`\n`plasma_electrons = Species(type=Electron, name=\"Plasma electrons\", color=red)`\n`plasma_ions = Species(type=Hydrogen, charge_state=+1, name=\"Plasma ions\", color=green)`\n\nThe color argument specifies the color of the markers that will be used when plotting particles of the species (defaulting to black). The Species instance can be used to access information about the species. For example:\n\n`beam.sq    # gives the charge of the species`\n`beam.charge   #  also the charge`\n`beam.mass     #  the mass of the species`\n`beam.emitn # normalized emittance`\n`beam.hxrms # time history of Xrms in the z-windows`\n\nThese can be use to set the quantities as well. For example:\n\n`beam.emitn = 1.1e-6`\n\nMore things are available as well. For example\n\n`plasma_electrons.ppzx() # plots the particles in z-x space. The particles will be red.`\n`plasma_ions.getx() # returns a list of all of the plasma ions x positions`\n`plasma_ions.add_uniform_cylinder(...) # creates particles`\n\n### Particle data\n\nThe particle data can be accessed in one of two ways. The arrays can be accessed directly - for example beam.xp will directly access the arrays holding the x coordinates. The data can be obtained indirectly as well, via the \"get\" routines. For example beam.getx(). In serial, beam.getx() will return the same array as beam.xp, but in parallel, beam.getx() will gather the data from all of the processors, whereas beam.xp is only the data for particles in the local domain. The \"get\" routines can be used for down selection of the particles, for instance beam.getz(xl=0.1, xu=0.2) will get the z of particle within (0.1 <= x <= 0.2).\n\nIn addition to the basic particle quantities, further quantities can be added. These are quantities that are saved for each particles and are carried with them. There are a number of quantities that are automatically initialized by Warp. For example, setting\n\n`top.tbirthpid = nextpid()`\n\nwill save the time of birth for each particle. The routine \"nextpid()\" sets up the space for the new quantity. The birth time for each particle can later be retrieved using the species instance - beam.tbirth, or beam.gettbirth(). Other built in quantities include saving additional information about the particle's birth and the data from the previous time step. See the Particles module in top.v for the list of built in quantities that can be setup.\n\nThe species instance allows one to add user defined particle quantities. For instance, a quantity called alpha can be created.\n\n`beam.addpid('alpha')`\n\nThe quantity would need to be setup by the user. For example, it could be passed into the particle creation routines,\n\n`beam.add_uniform_cylinder(..., alpha=1.1)`\n\nor set directly,\n\n`beam.alpha = 1.1`\n\nThe data can be obtained either directly, via beam.alpha, or indirectly, via beam.getalpha().\n\nAn important note is that when a quantity is setup for one species, it will then be available in all species. So, with the example of \"alpha\", one would also have the data plasma_ions.alpha." ]

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[ "Prime Factors of 624\n\nLooking to get a list of the prime factors of 624? In this article we'll give you all of the information you need, including the definition of the prime factors of 624, how to calculate the prime factors of 624 (also known as the prime factorization of 624). As a bonus, we'll also list out the prime factor tree of 624 the product of prime factors of 624, and tell you how many prime factors 624 has.\n\nPrime Factors of 624 Definition\n\nEvery number can be represented as a product of prime numbers. So when we talk aqbout prime factorization of 624, we're talking about the building blocks of the number. A prime factor is a positive integer that can only be divided by 1 and itself. The prime factors of 624 are all of the prime numbers in it that when multipled together will equal 624.\n\nLet's look at how to find all of the prime factors of 624 and list them out.\n\nHow to Find the Prime Factors of 624\n\nYou'll often see the process of finding prime factors of 624 referred to as prime factorization. To get the prime factors of 624 we need to divide 624 by the smallest prime number possible. You then repeat the same process by taking the result and dividing that number by the smallest prime number. Eventually, you end up with the number 1.\n\nThis process creates something called a prime factor tree of 624. The prime numbers used in this tree are the prime factors of 624. Let's look at the prime factor tree for 624:\n\n• 624 ÷ 2 = 312\n• 312 ÷ 2 = 156\n• 156 ÷ 2 = 78\n• 78 ÷ 2 = 39\n• 39 ÷ 3 = 13\n• 13 ÷ 13 = 1\n\nPut simply, all of the prime numbers that you used to divide above are the prime factors of 624 as well. So what we are left with is the answer to your search, the prime factors of 624:\n\n2, 2, 2, 2, 3, and 13\n\nHow Many Prime Factors of 624 Are There?\n\nIf we count up all of the prime factors of 624 used in the prime factor tree above, we can see that 624 has a total of 6 prime factors.\n\nProduct of Prime Factors of 624\n\nThe prime factors shown above (2, 2, 2, 2, 3, and 13) are completely unique to 624. When we multiply all of them together the result will be 624 and this is what we call the product of prime factors of 624. The prime factor products of 624 are listed below:\n\n2 x 2 x 2 x 2 x 3 x 13 = 624\n\nSo there you have it. A complete guide to the factors of 624. You should now have the knowledge and skills to go out and calculate your own factors and factor pairs for any number you like.\n\nFeel free to try the calculator below to check another number or, if you're feeling fancy, grab a pencil and paper and try and do it by hand. Just make sure to pick small numbers!\n\nIf you found this content useful in your research, please do us a great favor and use the tool below to make sure you properly reference us wherever you use it. We really appreciate your support!\n\n• \"Prime Factors of 624\". VisualFractions.com. Accessed on January 27, 2022. http://visualfractions.com/calculator/prime-factors/prime-factors-of-624/.\n\n• \"Prime Factors of 624\". VisualFractions.com, http://visualfractions.com/calculator/prime-factors/prime-factors-of-624/. Accessed 27 January, 2022." ]

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[ "Document Type : Research Paper\n\nAuthors\n\nEnergy Engineering and Physics Department, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran\n\nAbstract\n\nOne of the challenging problems in the Oil & Gas industry is accurate and reliable multiphase flow rate measurement in a three-phase flow. Application of methods with minimized uncertainty is required in the industry. Previous developed correlations for two-phase flow are complex and not capable of three-phase flow. Hence phase behavior identification in different conditions to designing and modeling of three-phase flow is important. Numerous laboratory and theoretical studies have been done to describe the Venturi multiphase flow meter in both horizontal and vertical flow. However, it is not possible to select the measurement devices for all similar conditions. In this study a new venturi model was developed that implemented in Simulink/Matlab for predicting mass flow rate of gas, water and oil. This models is simple and semilinear. Several classified configurations of three phase flow were simulated using Computational Fluid Dynamics (CFD) analysis to get hydrodynamics parameters of the flows to use as inputs of the model. The obtained data, used as test and train data in Least squares support vector machine (LSSVM) algorithm. The pressure drop, mass flow rate of gas, oil and water have been calculated with LSSVM method. Two tuning parameters of LSSVM, namely γ and σ^2, obtained as 1150954 and 0.4384, 53.9199 and 0.18163, 8.8714 and 0.14424, and 10039130.2214 and 0.74742 for pressure drop, mass flow rate of oil, gas mass flow rate, water mass flow rate, respectively. Developed models was found to have an average relative error of 5.81%, 6.31% and 2.58% for gas, oil and water respectively.\n\nGraphical Abstract", null, "Keywords", null, "20.1001.1.22287922.2020.10.1.12.7\n\nMain Subjects\n\n###### ##### References", null, "" ]

[ null, "https://jcarme.sru.ac.ir/data/jcarme/coversheet/841555304815.jpg", null, "https://jcarme.sru.ac.ir/images/dor.png", null, "https://jcarme.sru.ac.ir/lib/captcha/captcha.php", null ]

[ "# ST_X\n\n## Syntax\n\n```ST_X(p)\nX(p)\n```\n\n## Description\n\nReturns the X-coordinate value for the point `p` as a double-precision number.\n\n`ST_X()` and `X()` are synonyms.\n\n## Examples\n\n```SET @pt = 'Point(56.7 53.34)';\n\nSELECT X(GeomFromText(@pt));\n+----------------------+\n| X(GeomFromText(@pt)) |\n+----------------------+\n| 56.7 |\n+----------------------+\n```", null, "" ]

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[ "### What people are saying -Write a review\n\nWe haven't found any reviews in the usual places.\n\n### Contents\n\n PART II 134 The Theodolite 159 Mensuration 179\n Mensuration of Areas 200 Of OHsets 250 Method of surveying Dip for Dif Dist of land 3\n\n### Popular passages\n\nPage 38 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.\nPage 25 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.\nPage 199 - RULE. From half the sum of the three sides subtract each side severally.\nPage 106 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.\nPage 27 - The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc. Thus BA is the versed sine of the arc AG." ]

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[ "Solutions by everydaycalculation.com\n\n36/98 + 5/80 is 337/784.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 98 and 80 is 3920\n2. For the 1st fraction, since 98 × 40 = 3920,\n36/98 = 36 × 40/98 × 40 = 1440/3920\n3. Likewise, for the 2nd fraction, since 80 × 49 = 3920,\n5/80 = 5 × 49/80 × 49 = 245/3920", 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 ]

[ "# 12527 (number)\n\n12,527 (twelve thousand five hundred twenty-seven) is an odd five-digits prime number following 12526 and preceding 12528. In scientific notation, it is written as 1.2527 × 104. The sum of its digits is 17. It has a total of 1 prime factor and 2 positive divisors. There are 12,526 positive integers (up to 12527) that are relatively prime to 12527.\n\n## Basic properties\n\n• Is Prime? Yes\n• Number parity Odd\n• Number length 5\n• Sum of Digits 17\n• Digital Root 8\n\n## Name\n\nShort name 12 thousand 527 twelve thousand five hundred twenty-seven\n\n## Notation\n\nScientific notation 1.2527 × 104 12.527 × 103\n\n## Prime Factorization of 12527\n\nPrime Factorization 12527\n\nPrime number\nDistinct Factors Total Factors Radical ω(n) 1 Total number of distinct prime factors Ω(n) 1 Total number of prime factors rad(n) 12527 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) -1 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) 9.43564 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 12,527 is 12527. Since it has a total of 1 prime factor, 12,527 is a prime number.\n\n## Divisors of 12527\n\n2 divisors\n\n Even divisors 0 2 1 1\nTotal Divisors Sum of Divisors Aliquot Sum τ(n) 2 Total number of the positive divisors of n σ(n) 12528 Sum of all the positive divisors of n s(n) 1 Sum of the proper positive divisors of n A(n) 6264 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 111.924 Returns the nth root of the product of n divisors H(n) 1.99984 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors\n\nThe number 12,527 can be divided by 2 positive divisors (out of which 0 are even, and 2 are odd). The sum of these divisors (counting 12,527) is 12,528, the average is 6,264.\n\n## Other Arithmetic Functions (n = 12527)\n\n1 φ(n) n\nEuler Totient Carmichael Lambda Prime Pi φ(n) 12526 Total number of positive integers not greater than n that are coprime to n λ(n) 12526 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 1499 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 12,526 positive integers (less than 12,527) that are coprime with 12,527. And there are approximately 1,499 prime numbers less than or equal to 12,527.\n\n## Divisibility of 12527\n\n m n mod m 2 3 4 5 6 7 8 9 1 2 3 2 5 4 7 8\n\n12,527 is not divisible by any number less than or equal to 9.\n\n## Classification of 12527\n\n• Arithmetic\n• Prime\n• Deficient\n\n### Expressible via specific sums\n\n• Polite\n• Non-hypotenuse\n\n• Prime Power\n• Square Free\n\n## Base conversion (12527)\n\nBase System Value\n2 Binary 11000011101111\n3 Ternary 122011222\n4 Quaternary 3003233\n5 Quinary 400102\n6 Senary 133555\n8 Octal 30357\n10 Decimal 12527\n12 Duodecimal 72bb\n20 Vigesimal 1b67\n36 Base36 9nz\n\n## Basic calculations (n = 12527)\n\n### Multiplication\n\nn×y\n n×2 25054 37581 50108 62635\n\n### Division\n\nn÷y\n n÷2 6263.5 4175.67 3131.75 2505.4\n\n### Exponentiation\n\nny\n n2 156925729 1965808607183 24625684422181441 308485948756666911407\n\n### Nth Root\n\ny√n\n 2√n 111.924 23.2246 10.5794 6.60039\n\n## 12527 as geometric shapes\n\n### Circle\n\n Diameter 25054 78709.5 4.92997e+08\n\n### Sphere\n\n Volume 8.23436e+12 1.97199e+09 78709.5\n\n### Square\n\nLength = n\n Perimeter 50108 1.56926e+08 17715.9\n\n### Cube\n\nLength = n\n Surface area 9.41554e+08 1.96581e+12 21697.4\n\n### Equilateral Triangle\n\nLength = n\n Perimeter 37581 6.79508e+07 10848.7\n\n### Triangular Pyramid\n\nLength = n\n Surface area 2.71803e+08 2.31673e+11 10228.3" ]

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[ "### Comentarios de la gente -Escribir un comentario\n\nNo encontramos ningún comentario en los lugares habituales.\n\n### Contenido\n\n CHAPTER 9 CHAPTER II 15 Of the Quotient 21\n CHAPTER IV 27 NATUKE AND USE OF LOGARITHMS 49 CHAPTER VII 66\n\n### Pasajes populares\n\nPágina 50 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.\nPágina 49 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers.\nPágina 61 - The fourth term is found by multiplying the second and third terms together and dividing by the first § 14O.\nPágina 50 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.\nPágina 19 - Cxz+, etc.=A'+B'x+C'z2 + , etc., must be satisfied for each and every value given to x, then the coefficients of the like powers of x in the two members are equal each to each.\nPágina 74 - The logarithm of a number in any system is equal to the Naperian logarithm of that number multiplied by the modulus of the system.\nPágina 49 - Corollary. When the base is less than unity, it follows, from art. 3, that the logarithms of all numbers greater than unity are negative, while those of all numbers less than unity are positive. But when, as is almost always...\nPágina 55 - ... place, the characteristic being positive when this figure is to the left of the units' place, negative when it is to the right of the units' place, and zero when it is in the units\nPágina 27 - I have no doubt that he made the difcovery himfelf, without any light from Briggs, and that he thought it was new for all powers in general, as it was indeed for roots and quantities with fractional and irrational exponents.\nPágina 50 - Bee that to divide one number by another, we subtract the log. of the divisor from the log. of the dividend, and the remainder is the log." ]

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[ "# Often asked: What Is A Static Pressure Change Aviation?\n\n## What is meant by static pressure?\n\n: the force per unit area that is exerted by a fluid upon a surface at rest relative to the fluid.\n\n## What happens to static pressure as altitude increases?\n\nstatic pressure decreases with increase of altitude; static pressure at a given altitude will vary from day to day.\n\n## What is static pressure in Bernoulli’s equation?\n\nThe equation states that the static pressure ps in the flow plus the dynamic pressure, one half of the density r times the velocity V squared, is equal to a constant throughout the flow. We call this constant the total pressure pt of the flow.\n\n## Is static pressure the same as atmospheric pressure?\n\nWhat is the difference between static pressure and atmospheric pressure? Atmospheric pressure is the total pressure of the air including static pressure and also dynamic/velocity pressure, or the pressure caused by air moving. Therefore, atmospheric pressure is the sum of the dynamic and static pressure.\n\nYou might be interested:  Question: The First Crm Conference Was Hosted By Nasa In 1979 As A Result Of Which Two Aviation Accidents?\n\n## How do I calculate static pressure?\n\nAdd total elbow equivalents to the length of straight duct to arrive at the total system duct length. Multiply the static pressure for 100 feet of duct by the percentage of 100 feet that you have. This will be the static pressure caused by the ductwork.\n\n## What is ideal static pressure in HVAC?\n\nAn instrument called a “manometer” is used to measure pressure and ideally the static pressure should be. 82”. When your system static pressure is proper all is good, but when it’s high is when the problems start to happen.\n\n## What is the difference between dynamic and static pressure?\n\nStatic pressure is the pressure you have if the fluid isn’t moving or if you are moving with the fluid. Dynamic pressure is the pressure of a fluid that results from its motion. It is the difference between the total pressure and static pressure.\n\n## Why does static pressure decrease as velocity increases?\n\nWell, conservation of mass says the flow has to move faster to get the same amount of fluid through, so the velocity increases. Since we’re not adding/removing energy, then this increase must come from some of that energy that was going into making the fluid’s pressure. Meaning, in the end, your pressure decreases.\n\n## Does temperature affect static pressure?\n\n4 Answers. Yes, temperature affects dynamic pressure by affecting air density: it reduces with increasing temperature.\n\n## What is static pressure of the liquid?\n\nStatic pressure, or hydrostatic pressure as it is sometimes called, is the pressure exerted by a fluid at rest. Since the fluid is not moving, static pressure is the result of the fluid’s weight or the force of gravity acting on the particles in the fluid. There are two different ways to measure static pressure.\n\nYou might be interested:  Quick Answer: What Is An Aviation Del Controller?\n\n## What is static pressure used for?\n\nStatic pressure in design and operation of aircraft An aircraft’s airspeed indicator is operated by the static pressure system and the pitot pressure system. The static pressure system is open to the exterior of the aircraft to sense the pressure of the atmosphere at the altitude at which the aircraft is flying.\n\n## What does negative static pressure mean?\n\nWhen gauge static pressure is negative, it means it is below operating pressure, but it is positive.\n\n## Is stagnation pressure higher than static pressure?\n\nThe ‘ stagnation pressure ‘ is the pressure that the fluid would obtain if brought to rest without loss of mechanical energy. The ‘total pressure ‘ is the sum of the static pressure, the dynamic pressure, and the gravitational potential energy per unit volume.\n\n## What causes static pressure?\n\nHigh static pressure is often caused by blockages in ducts, improper duct sizing, closed dampers, and kinked flex ducts while low static pressure is caused by leaking ductwork, separated duct connections, missing filters, or low fan speeds, he said.\n\n## Can total pressure be less than static pressure?\n\nBecause Total Pressure is the sum of static and dynamic pressure, the static pressure normally cannot be higher than the total." ]

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[ "", null, "The Exciting Universe Of Music Theory\npresents\n\nmore than you ever wanted to know about...\n\n# Scale 1635: \"Sygimic\"", null, "### Bracelet Diagram\n\nThe bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The \"i\" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.\n\n### Tonnetz Diagram\n\nTonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).\n\nZeitler\nSygimic\nDozenal\nKAQian\n\n## Analysis\n\n#### Cardinality\n\nCardinality is the count of how many pitches are in the scale.\n\n6 (hexatonic)\n\n#### Pitch Class Set\n\nThe tones in this scale, expressed as numbers from 0 to 11\n\n{0,1,5,6,9,10}\n\n#### Forte Number\n\nA code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.\n\n6-Z19\n\n#### Rotational Symmetry\n\nSome scales have rotational symmetry, sometimes known as \"limited transposition\". If there are any rotational symmetries, these are the intervals of periodicity.\n\nnone\n\n#### Reflection Axes\n\nIf a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.\n\nnone\n\n#### Palindromicity\n\nA palindromic scale has the same pattern of intervals both ascending and descending.\n\nno\n\n#### Chirality\n\nA chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.\n\nyes\nenantiomorph: 2253\n\n#### Hemitonia\n\nA hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.\n\n3 (trihemitonic)\n\n#### Cohemitonia\n\nA cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.\n\n0 (ancohemitonic)\n\n#### Imperfections\n\nAn imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.\n\n3\n\n#### Modes\n\nModes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.\n\n5\n\n#### Prime Form\n\nDescribes if this scale is in prime form, using the Starr/Rahn algorithm.\n\nno\nprime: 411\n\n#### Generator\n\nIndicates if the scale can be constructed using a generator, and an origin.\n\nnone\n\n#### Deep Scale\n\nA deep scale is one where the interval vector has 6 different digits, an indicator of maximum hierarchization.\n\nno\n\n#### Interval Structure\n\nDefines the scale as the sequence of intervals between one tone and the next.\n\n[1, 4, 1, 3, 1, 2]\n\n#### Interval Vector\n\nDescribes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.\n\n<3, 1, 3, 4, 3, 1>\n\n#### Proportional Saturation Vector\n\nFirst described by Michael Buchler (2001), this is a vector showing the prominence of intervals relative to the maximum and minimum possible for the scale's cardinality. A saturation of 0 means the interval is present minimally, a saturation of 1 means it is the maximum possible.\n\n<0.6, 0.167, 0.6, 0.5, 0.6, 0.333>\n\n#### Interval Spectrum\n\nThe same as the Interval Vector, but expressed in a syntax used by Howard Hanson.\n\np3m4n3sd3t\n\n#### Distribution Spectra\n\nDescribes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.\n\n<1> = {1,2,3,4}\n<2> = {3,4,5}\n<3> = {4,5,6,7,8}\n<4> = {7,8,9}\n<5> = {8,9,10,11}\n\n#### Spectra Variation\n\nDetermined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.\n\n2.333\n\n#### Maximally Even\n\nA scale is maximally even if the tones are optimally spaced apart from each other.\n\nno\n\n#### Maximal Area Set\n\nA scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.\n\nno\n\n#### Interior Area\n\nArea of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.\n\n2.116\n\n#### Polygon Perimeter\n\nPerimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.\n\n5.699\n\n#### Myhill Property\n\nA scale has Myhill Property if the Distribution Spectra have exactly two specific intervals for every generic interval.\n\nno\n\n#### Balanced\n\nA scale is balanced if the distribution of its tones would satisfy the \"centrifuge problem\", ie are placed such that it would balance on its centre point.\n\nno\n\n#### Ridge Tones\n\nRidge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.\n\nnone\n\n#### Propriety\n\nAlso known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either \"Proper\", \"Strictly Proper\", or \"Improper\".\n\nImproper\n\n#### Heteromorphic Profile\n\nDefined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.\n\n(8, 18, 62)\n\n#### Coherence Quotient\n\nThe Coherence Quotient is a score between 0 and 1, indicating the proportion of coherence failures (ambiguity or contradiction) in the scale, against the maximum possible for a cardinality. A high coherence quotient indicates a less complex scale, whereas a quotient of 0 indicates a maximally complex scale.\n\n0.6\n\n#### Sameness Quotient\n\nThe Sameness Quotient is a score between 0 and 1, indicating the proportion of differences in the heteromorphic profile, against the maximum possible for a cardinality. A higher quotient indicates a less complex scale, whereas a quotient of 0 indicates a scale with maximum complexity.\n\n0.173\n\n## Generator\n\nThis scale has no generator.\n\nThese are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.\n\n* Pitches are shown with C as the root\n\nF♯{6,10,1}231.5\na♯m{10,1,5}231.5\n\nAbove is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.\n\nDiameter 3 2 no C♯+, f♯m F, f♯°, F♯, a♯m\n\nAlso known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.\n\nThere are 2 ways that this hexatonic scale can be split into two common triads.\n\n Major: {5, 9, 0}Major: {6, 10, 1} Diminished: {6, 9, 0}Minor: {10, 1, 5}\n\n## Modes\n\nModes are the rotational transformation of this scale. Scale 1635 can be rotated to make 5 other scales. The 1st mode is itself.\n\n 2nd mode:Scale 2865", null, "Solimic 3rd mode:Scale 435", null, "Raga Purna Pancama 4th mode:Scale 2265", null, "Raga Rasamanjari 5th mode:Scale 795", null, "Aeologimic 6th mode:Scale 2445", null, "Zadimic\n\n## Prime\n\nThe prime form of this scale is Scale 411\n\n Scale 411", null, "Lygimic\n\n## Complement\n\nThe hexatonic modal family [1635, 2865, 435, 2265, 795, 2445] (Forte: 6-Z19) is the complement of the hexatonic modal family [615, 825, 915, 2355, 2505, 3225] (Forte: 6-Z44)\n\n## Inverse\n\nThe inverse of a scale is a reflection using the root as its axis. The inverse of 1635 is 2253\n\n Scale 2253", null, "Raga Amarasenapriya\n\n## Enantiomorph\n\nOnly scales that are chiral will have an enantiomorph. Scale 1635 is chiral, and its enantiomorph is scale 2253\n\n Scale 2253", null, "Raga Amarasenapriya\n\n## Transformations:\n\nIn the abbreviation, the subscript number after \"T\" is the number of semitones of tranposition, \"M\" means the pitch class is multiplied by 5, and \"I\" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b\n\nAbbrev Operation Result Abbrev Operation Result\nT0 <1,0> 1635       T0I <11,0> 2253\nT1 <1,1> 3270      T1I <11,1> 411\nT2 <1,2> 2445      T2I <11,2> 822\nT3 <1,3> 795      T3I <11,3> 1644\nT4 <1,4> 1590      T4I <11,4> 3288\nT5 <1,5> 3180      T5I <11,5> 2481\nT6 <1,6> 2265      T6I <11,6> 867\nT7 <1,7> 435      T7I <11,7> 1734\nT8 <1,8> 870      T8I <11,8> 3468\nT9 <1,9> 1740      T9I <11,9> 2841\nT10 <1,10> 3480      T10I <11,10> 1587\nT11 <1,11> 2865      T11I <11,11> 3174\nAbbrev Operation Result Abbrev Operation Result\nT0M <5,0> 615      T0MI <7,0> 3273\nT1M <5,1> 1230      T1MI <7,1> 2451\nT2M <5,2> 2460      T2MI <7,2> 807\nT3M <5,3> 825      T3MI <7,3> 1614\nT4M <5,4> 1650      T4MI <7,4> 3228\nT5M <5,5> 3300      T5MI <7,5> 2361\nT6M <5,6> 2505      T6MI <7,6> 627\nT7M <5,7> 915      T7MI <7,7> 1254\nT8M <5,8> 1830      T8MI <7,8> 2508\nT9M <5,9> 3660      T9MI <7,9> 921\nT10M <5,10> 3225      T10MI <7,10> 1842\nT11M <5,11> 2355      T11MI <7,11> 3684\n\nThe transformations that map this set to itself are: T0\n\n## Nearby Scales:\n\nThese are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.\n\n Scale 1633", null, "KAPian Scale 1637", null, "Syptimic Scale 1639", null, "Aeolothian Scale 1643", null, "Locrian Natural 6 Scale 1651", null, "Asian Scale 1603", null, "JUXian Scale 1619", null, "Prometheus Neapolitan Scale 1571", null, "Lagitonic Scale 1699", null, "Raga Rasavali Scale 1763", null, "Katalian Scale 1891", null, "Thalian Scale 1123", null, "Iwato Scale 1379", null, "Kycrimic Scale 611", null, "Anchihoye Scale 2659", null, "Katynimic Scale 3683", null, "Dycrian\n\nThis scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow and Lilypond, graph visualization by Graphviz, audio by TiMIDIty and FFMPEG. All other diagrams and visualizations are © Ian Ring. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.\n\nPitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO\n\nTons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy, and George Howlett for assistance with the Carnatic ragas." ]

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[ "# Adaptive multi-step differential transformation method to solve ODE systems\n\n## Authors\n\n• AHMET GOKDOGAN Gümüşhane University, Department of Mathematical Engineering, 29100, Gümüşhane, Turkey\n• MEHMET MERDAN Gümüşhane University, Department of Mathematical Engineering, 29100, Gümüşhane, Turkey\n\n## Keywords:\n\nThe differential transform method, adaptive, Runge-Kutta method, chaotic systems.\n\n## Abstract\n\nIn this paper, it is given a fast algorithm to solve chaotic differential systems using the multi-step differential transforms method (MsDTM). The approach is applied to a number of chaotic nonlinear differential equations and numerical results are given. Performance analyses reveal that the proposed approach is an efficiency tool to solve using fewer time step to the considered equation systems.\n\n## References\n\nREFERENCES\n\nAbdel-Halim Hassan, I. H. 2002. On solving some eigenvalue problems by using a differential Transformation. Applied Mathematics and Computation127: 1–22.\n\nArikoğlu, A. & Özkol, I. 2005. Solution of boundary value problems for integro-differential equations by using differential transform method. Applied Mathematics and Computation 168: 1145–1158.\n\nArnodo, A., Coullet, P. & Tresser, C. 1981. Possible new strange attractors with spiral structure. Communications in Mathematical Physics 79(4):573–579.\n\nAyaz, F. 2004. Solutions of the system of differential equations by differential transform Method. Applied Mathematics and Computation 147: 547–567.\n\nChang, S. H. & Chang, I. L. 2008. A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Applied Mathematics and Computation195: 799–808.\n\nChen, C. L. & Liu, Y.C. 1998. Solution of two point boundary value problems using the differential transformation method.Journal of Optimization Theory and Applications 99: 23–35.\n\nChen, C. K. & Ho, S. H. 1999a. Transverse vibration of a rotating twisted Timoshenko beam under axial loading using differential transform.International journal of mechanical sciences 41: 1339-1356.\n\nChen, C. K. & Ho, S. H. 1999b. Solving partial differential equations by two-dimensional differential transform method. Applied Mathematics and Computation 106: 171–179.\n\nCoullet, P., Tresser, C. & Arnodo, A. 1979. Transition to stochasticity for a class of forced oscillators.Physics Letters A 72:268-270.\n\nEbaid, A. E. H. 2010. Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method, Communications in Nonlinear Science and Numerical Simulation.15: 1921–1927.\n\nEl-Shahed, M. 2008. Application of differential transform method to non-linear oscillatory Systems.Communications in Nonlinear Science and Numerical Simulation13: 1714–1720.\n\nErtürk, V. S. & Momani, S. 2007. Comparing numerical methods for solving fourth-order boundary value problems. Applied Mathematics and Computation 188 (2): 1963- 1968.\n\nGenesio, R. & Tesi, A. 1992. Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems.Automatica 28: 531-548.\n\nGökdoğan, A., Merdan, M. & Yıldırım, A. 2012a. Adaptivemulti-step differential transformation method for solving nonlinear differential equations. Mathematical and Computer Modelling 55: 761-769.\n\nGökdoğan, A., Merdan, M. & Yildirim, A. 2012b. A multistage differential transformation method for approximate solution of Hantavirusinfection model. Communications in Nonlinear Science and Numerical Simulation17(1): 1-8.\n\nHo, S. H. & Chen, C. K. 1998. Analysis of general elastically end restrained non-uniform beams using differential transform. Applied Mathematical Modelling 22: 219–234.\n\nJang, M. J., Chen, C. L. & Liu, Y. C. 1997. Analysis of the response of a strongly nonlinear damped system using a differential transformation technique. Applied Mathematics and Computation 88: 137-151.\n\nJang, M. J., Chen, C. L. & Liy, Y. C. 2000a. On solving the initial-value problems using the differential transformation method. Applied Mathematics and Computation 115: 145–160.\n\nJang, M. J., Chen, C. L. & Liu, Y. C. 2000b. On solving the initial value problems using the differential transformation method.Applied Mathematics and Computation 115: 145–160.\n\nJang, M. J., Chen, C. L. & Liu, Y. C. 2001. Two-dimensional differential transform for partial differential equations. Applied Mathematics and Computation 121: 261–70.\n\nJordan, D. W. & Smith, P. 1999. Nonlinear Ordinary Differential Equations. Oxford University Press.\n\nKöksal, M. & Herdem, S. 2002. Analysis of nonlinear circuits by using differential Taylor Transform.Computers & Electrical Engineering 28: 513–525.\n\nLorenz, E. 1963. Deterministicnonperiodic flow. Journalof the Atmospheric Sciences 20: 130-141.\n\nMerdan, M. & Gökdoğan, A. 2011. Solution Of Nonlinear Oscillators With Fractional Nonlinearities By Using The Modified Differential Transformation Method. Mathematical and Computational Applications 16(3): 761–772.\n\nMerdan, M., Gökdoğan, A & Ertürk, V. S. 2011a. On Solving Coullet System by Differential Transformation Method. Çankaya University Journal of Science and Engineering 8 (1): 111-121.\n\nMerdan, M., Gökdoğan, A & Ertürk, V. S. 2011b. A numeric-analytic method for approximating three-species food chain models. International Journal of the Physical Sciences 6(2): 1822-1833.\n\nMomani, S. & Ertürk, V. S. 2008. Solutions of non-linear oscillators by the modified differential transform method. Computers & Mathematics with Applications 55(4): 833- 842.\n\nOdibat, Z. M., Bertelle, C., Aziz-Alaoui, M. A. & Duchamp, G. H. E. 2010. A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers & Mathematics with Applications 59:1462-1472.\n\nOlek, S. 1994. An accurate solution to the multispecies Genesio equations. SIAM Review 36(3): 480-488.\n\nRavi, A. S. V. K. & Aruna, K. 2008. Solution of singular two-point boundary value problems using differential transformation method.Physics Letters A 372: 4671–4673.\n\nRavi, A. S. V. K. & Aruna, K. 2009a. Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations. Chaos Solitons & Fractals 41: 2277-2281.\n\nRavi, A. S. V. K. & Aruna, K. 2009b. Differential transform method for solving the linear and nonlinear Klein–Gordon equation. Computer Physics Communications 180: 708–711.\n\nYildirim, A., Merdan, M. & Gökdoğan, A. 2012. Chaotic systems via multi-step differential transformation method. Canadian Journal of Physics 90:1–16.\n\nZhou, J. K. 1986. Differential Transformation and its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China." ]

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[ "# What is the Greatest Common Factor of 40 and 52?\n\nGreatest common factor (GCF) of 40 and 52 is 4.\n\nGCF(40,52) = 4\n\nWe will now calculate the prime factors of 40 and 52, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40 and 52.\n\nGCF Calculator and\nand\n\n## How to find the GCF of 40 and 52?\n\nWe will first find the prime factorization of 40 and 52. After we will calculate the factors of 40 and 52 and find the biggest common factor number .\n\n### Step-1: Prime Factorization of 40\n\nPrime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:\n\n40 = 23 × 51\n\n### Step-2: Prime Factorization of 52\n\nPrime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:\n\n52 = 22 × 131\n\n### Step-3: Factors of 40\n\nList of positive integer factors of 40 that divides 40 without a remainder.\n\n1, 2, 4, 5, 8, 10, 20\n\n### Step-4: Factors of 52\n\nList of positive integer factors of 52 that divides 40 without a remainder.\n\n1, 2, 4, 13, 26\n\n#### Final Step: Biggest Common Factor Number\n\nWe found the factors and prime factorization of 40 and 52. The biggest common factor number is the GCF number.\nSo the greatest common factor 40 and 52 is 4.\n\nAlso check out the Least Common Multiple of 40 and 52" ]

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[ "# Anekāntavāda And Syādvāda: Logical Analysis Of Saptabhaṅgī-Naya\n\nMalliṣeṇa distinguishes a pramāṇa from a durnaya and a naya. According to him, a pramāṇa is always true and for which we assign the truth-value T, but a durnaya is always false for which we assign the truth-value F. The truth value of a naya (incomplete judgement) is different from the truth-value T or the truth-value F hence it is intermediate between these two truth-values. This gives rise to a third intermediate truth value I.\n\nAccording to Vadi Devasuri's Pramāṇa-naya-Tattvālokālaṁkāra, (3 loc cit.) the above seven predications can be interpreted as follows:\n\nThe first predication consists of an affirmative statement. This may mean that an object exists in some respects. The expression 'in some respect' is to be taken in the context of various factors like space, time, substance and mode. For instance, the substance of an object X could be related to the material of which it is made. The space relates to the spatial location of X. The time of existence of X is the present time at which it exists. The mode of X describes its configuration.\n\nLet us represent, the first affirmative predication by a proposition P which takes a truth-value T.\n\nThe second predication consists of a negative statement that 'in some respect' an object X is non-existent. Here the word 'may be' (syād) or 'in some respects' is crucial in respect of assigning the truth-value to this predication. To elucidate that the object X may not exist with reference to either space, time, substance or mode we note that on account of restraint 'in some respects' we shall consider the connective of negation (˥) as a 'complete' negation and not as a 'diametrical' negation in the sense of Reichenbach. Let us represent the second predication by the proposition ˥P which takes the truth-value I, as shown by the following truth-table:\n\n(Reichenbach 4 loc. cit.)\n\nTruth-Table No. 1\n\n P ˥P T I I I F T\n\nThe third predication consists of affirmative and negative statements conjunctively made one after another. Since the affirmative proposition P and negative proposition ˥P are taken conjunctively one after another we assign the truth-value T to the non-simultaneous conjunction of the affirmative proposition P and the negative proposition ˥P. We denote this non-simultaneous conjunction of P and ˥P by the notation (P° ˥P).\n\nThe fourth predication consists of affirmative and negative statements made simultaneously. Since an object X is incapable of being expressed in terms of existence and non-existence at the same time, even allowing Syād, it is termed 'indescribable'. Hence we assign to the fourth predication which is the simultaneous conjunction of the affirmative proposition P and the negative proposition ˥P, the indeterminate truth-value I and denote the statement corresponding to the fourth predication as (P ˄ ˥) P.\n\nThe fifth predication consists in an affirmative statement conjoined with an indescribable statement at the same time. We denote this fifth predication by P ˄ (P ˄ ˥P).\n\nReferring to the column for simultaneous conjunction in the truth-table that follows:\n\nTruth-Table No. 2\n\n A B A ° B A ˄ B A ˅ B T T T T T T I T I T T F T I T I T T I T I I T I I I F F F I F T T I T F I F F I F F F F F\n\nWe see that since P takes the truth-value T by the first predication and (P ˄ ˥P) is assigned the truth-value I by the fourth predication, the proposition P ˄ (P ˄ ˥P) takes the truth-value I.\n\nThe sixth predication consists of a negative statement conjoined with an indescribable statement at the same time. We denote this sixth predication by (˥P) ˄ (P ˄ ˥P). Referring to the column for the simultaneous conjunction (˄) in the table given above, we see that since ˥P takes the truth-value I by the predication and (P ˄ ˥P) is assigned the truth-value I by the fourth predication we see that the proposition ˥P ˄ (P ˄ ˥P) takes the truth-value I.\n\nThe seventh or the last predication consists of an affirmative and negative statements made non-simultaneously conjoined simulta­neously with affirmative and the negative statement conjoined simultaneously. This statement is denoted by (P° ˥P) ˄ (P ˄ ˥P). Referring to the columns for the connectives for simultaneous conjunction and for non-simultaneous conjunction in the truth-table No. 2 and noting that P takes the truth-value T by the first predication and ˥P takes the truth-value I by the second predication. We see that (P° ˥P) takes the truth-value T (third predication) and (P ˄ ˥P) takes the truth-value I (fourth predication). The seventh predication thus takes the truth-value I according to the same truth-table.\n\nHence, we see that the pramāṇa saptabhaṅgī of the Jainas is a table of seven statements which are derived from a true statement by the operations of negation, non-simultaneous and simultaneous conjunctions that are denoted by ˥, °, ˄ respectively.\n\nLet us consider P as a true statement then the pramāṇa saptabhaṅgī can be represented as follows:\n\n(1) P (assertion of P)\n\n(2) Not P ('complete' negation of P) denoted by ˥P\n\n(3) P and non-simultaneously not P (non-simultaneous conjunction of P and ˥P) denoted by P° ˥P\n\n(4) P and simultaneously not P (simultaneous conjunction of P and ˥P) denoted by (P ˄ ˥P)\n\n(5) P and simultaneously (P and simultaneously not P) denoted by P ˄ (P ˄ ˥P)\n\n(6) Not P and simultaneously (P and simultaneously not P) denoted by ˥P ˄ (P ˄ ˥P)\n\n(7) (P and non-simultaneously not P) and simultaneously (P and simultaneously not P) denoted by (P° ˥P) ˄ (P ˄ ˥P)\n\nPictorially we can depict the pramāṇa saptabhaṅgī as follows with the truth-values to the right:\n\n OBJECT X P (T) ˥P (I) P° ˥P (T) P ˄ ˥P (I) P ˄ (P ˄ ˥P) (I) ˥P ˄ (P ˄ ˥P) (I) (P° ˥P) ˄ (P ˄ ˥P) (I)\n\nAn object X can be viewed from any one of these seven standpoints. However, since the totality of all these seven possibilities comprises the pramāṇa saptabhaṅgī (Complete judgement of the phenomenal world in terms of seven possibilities), the disjunction, denoted by ˅, of these seven predication should lead to a tautology. We can represent this disjunction as follows:\n\n(P ˅ 1 P) ˅ (P° ˥P) ˅ (P ˄ ˥P) ˅\n[P ˄ (P ˄ ˥P)] ˅ [(˥P) ˄ (P ˄ ˥P)] ˅\n[(P° ˥P) ˄ (P ˄ ˥P)].\n\nAs we have noted earlier, the seven predications, conjoined by the disjunction above, take the truth-value T, I, T, I, I, I respectively. Referring to the column for the disjunction in the truth-value No. 2 and noting that the disjunction is associative as can be easily checked using the same truth-table, we see that the disjunction of all these seven predications is indeed a tautology taking the truth-value T.\n\nFootnotes\n1:\n\n2:\n\nSources\nJain Vishwa Bharati Institute\nLadnun - 341 306 (Rajasthan) General Editor:\nSreechand Rampuria\nEdited by:\nRai Ashwini Kumar\nT.M. Dak\nAnil Dutta Mishra\n\nFirst Edition:1996\n\nPrinted by:\nPawan Printers\nJ-9, Naveen Shahdara, Delhi-110032", null, "" ]

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[ "# Traffic Stop Disposition: Classification Using F# and KNN\n\nI have already looked at the summary statistics of the traffic stop data I received from the town here.  My next stop was to try and do a machine learning exercise with the data.  One of the more interesting questions I want to answer is what factors into weather a person gets a warning or a ticket (called disposition)?  Of all of the factors that may be involved, the dataset that I have is fairly limited:", null, "Using dispositionId as the result variable, there is StopDateTime and Location (Latitude/Longitude).  Fortunately, DateTime can be decomposed into several input variables.  For this exercise, I wanted to use the following:\n\n• TimeOfDay\n• DayOfWeek\n• DayOfMonth\n• MonthOfYear\n• Location (Latitude:Longitude)\n\nAnd the resulting variable being disposition.  To make it easier for analysis, I limited the analysis set to finalDisposition as either “verbal warning” or “citation”  I decided to do a K-Nearest Neighbor because it is regarded as an easy machine learning algorithm to learn and the question does seem to be a classification problem.\n\nMy first step was to decide weather to write or borrow the KNN algorithm.  After looking at what kind of code would be needed to write my own and then looking at some other libraries, I decided to use Accord.Net.\n\nMy next first step was to get the data via the web service I spun up here.\n\n2.\n3. open FSharp.Data\n4. open Microsoft.FSharp.Data.TypeProviders\n5. open Accord.MachineLearning\n6.\n8. type MachineLearningEngine =\n\nMy next first step was to filter the data to only verbal warnings (7) or citations (15).\n\n1.   static member BaseDataSet =\n3.             |> Seq.filter(funx -> x.DispositionId = 7 || x.DispositionId = 15)\n4.           |> Seq.map(fun x -> x.Id, x.StopDateTime, x.Latitude, x.Longitude, x.DispositionId)\n5.           |> Seq.map(fun (a,b,c,d,e) -> a, b, System.Math.Round(c,3), System.Math.Round(d,3), e)\n6.           |> Seq.map(fun (a,b,c,d,e) -> a, b, c.ToString() + \":\" + d.ToString(), e)\n7.           |> Seq.map(fun (a,b,c,d) -> a,b,c, match d with\n8.                                               |7 -> 0\n9.                                               |15 -> 1\n10.                                               |_ -> 1)\n11.           |> Seq.map(fun (a,b,c,d) -> a, b.Hour, b.DayOfWeek.GetHashCode(), b.Day, b.Month, c, d)\n12.           |> Seq.toList\n\nYou will notice that I had to transform the dispositionIds from 7 and 15 to 1 and 0.  The reason why is that the KNN method in Accord.Net assumes that the values match the index position in the array.  I had to dig into the source code of Accord.Net to figure that one out.\n\nMy next step was to divide the dataset in half: one half being the training sample and the other the validation sample:\n\n1. static member TrainingSample =\n2.     let midNumber = MachineLearningEngine.NumberOfRecords/ 2\n3.     MachineLearningEngine.BaseDataSet\n4.         |> Seq.filter(fun (a,b,c,d,e,f,g) -> a < midNumber)\n5.         |> Seq.toList\n6.\n7. static member ValidationSample =\n8.     let midNumber = MachineLearningEngine.NumberOfRecords/ 2\n9.     MachineLearningEngine.BaseDataSet\n10.         |> Seq.filter(fun (a,b,c,d,e,f,g) -> a > midNumber)\n11.         |> Seq.toList\n\nThe next step was to actually run the KKN.  Before I could do that though, I had to create the distance function.  Since this was my 1st time, I dropped the geocoordinates and focused only on the time of day derivatives.\n\n1. static member RunKNN inputs outputs input =\n2.     let distanceFunction (a:int,b:int,c:int,d:int) (e:int,f:int,g:int,h:int) =\n3.       let b1 = b * 4\n4.       let f1 = f * 4\n5.       let d1 = d * 2\n6.       let h1 = h * 2\n7.       float((pown(a-e) 2) + (pown(b1-f1) 2) + (pown(c-g) 2) + (pown(d1-h1) 2))\n8.\n9.     let distanceDelegate =\n10.           System.Func<(int * int * int * int),(int * int * int * int),float>(distanceFunction)\n11.\n12.     let knn = new KNearestNeighbors<int*int*int*int>(10,2,inputs,outputs,distanceDelegate)\n13.     knn.Compute(input)\n\nYou will notice I  tried to normalize the values so that they all had the same basis.  They are not exact, but they are close.  You will also notice that I had to create a delegate from for the distanceFunction (thanks to Mimo on SO).  This is because Accord.NET was written in C# with C# consumers in mind and F# has a couple of places where the interfaces are not as seemless as one would hope.\n\nIn any event, once the KKN function was written, I wrote a function that to the validation sample, made a guess via KKN, and then reported the result:\n\n1. static member GetValidationsViaKKN  =\n2.     let inputs = MachineLearningEngine.TrainingInputClass\n3.     let outputs = MachineLearningEngine.TrainingOutputClass\n4.     let validations = MachineLearningEngine.ValidationClass\n5.\n6.     validations\n7.         |> Seq.map(fun (a,b,c,d,e) -> e, MachineLearningEngine.RunKNN inputs outputs (a,b,c,d))\n8.         |> Seq.toList\n9.\n10. static member GetSuccessPercentageOfValidations =\n11.     let validations = MachineLearningEngine.GetValidationsViaKKN\n12.     let matches = validations\n13.                     |> Seq.map(fun (a,b) -> match (a=b) with\n14.                                                 | true -> 1\n15.                                                 | false -> 0)\n16.\n17.     let recordCount =  validations |> Seq.length\n18.     let numberCorrect = matches |> Seq.sum\n19.     let successPercentage = double(numberCorrect) / double(recordCount)\n20.     recordCount, numberCorrect, successPercentage\n\nI then hopped over to my UI console app and looked that the success percentage.\n\n1. private static void GetSuccessPercentageOfValidations()\n2. {\n3.     var output = MachineLearningEngine.GetSuccessPercentageOfValidations;\n4.     Console.WriteLine(output.Item1.ToString() + \":\" + output.Item2.ToString() + \":\" + output.Item3.ToString());\n5. }", null, "So there are 12,837 records in the validation sample and the classifier guessed the correct disposition 9,001 times – a success percentage of 70%\n\nSo it looks like there is something there.  However, it is not clear that this is a good classifier without further tests – specifically seeing if the how to most common case results when pushing though the classifier.  Also, I would assume to make this a true ‘machine learning’ algorithm I would have to feed the results back to the distance function to see if I can alter it to get the success percentage higher.\n\nOne quick note about methodology – I used unit tests pretty extensively to understand how the KKN works.  I created a series of tests with some sample data to see who the function reacted.\n\n1. [TestMethod]\n2. public void TestKKN_ReturnsExpected()\n3. {\n4.\n5.     Tuple<int, int, int, int>[] inputs = {\n6.         new Tuple<int, int, int, int>(1, 0, 15, 1),\n7.         new Tuple<int,int,int,int>(1,0,11,1)};\n8.     int[] outputs = { 1, 1 };\n9.\n10.     var input = new Tuple<int, int, int, int>(1, 1, 1, 1);\n11.\n12.     var output = MachineLearningEngine.RunKNN(inputs, outputs, input);\n13.\n14. }\n\nThis was a big help to get me up and running (walking, really..)…" ]

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[ "Filters\n\n71,996 Hits in 4.5 sec\n\n### Bounded real lemmas for fractional order systems\n\nShu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang\n2015 International Journal of Automation and Computing\nThis paper derives the bounded real lemmas corresponding to L∞ norm and H∞ norm (L-BR and H-BR) of fractional order systems.  ...  From this advantage, we further address the synthesis problem of H∞ control for fractional order systems in the form of LMI.  ...  Zeng Liao for their suggestive help on this research, and Dr. Xi Zhou for pointing out some mistakes in the previous version of this paper.  ...\n\n### Reduced-order H∞ filtering for commensurate fractional-order systems\n\nJun Shen, James Lam, Ping Li\n2013 52nd IEEE Conference on Decision and Control\nBased on the bounded real lemma for commensurate fractional-order systems, a sufficient condition is established in terms of linear matrix inequalities (LMls) under which the stability as well as the H  ...  This paper is concerned with the reduced-order H= filtering problem of commensurate fractional-order systems.  ...  Fortunately, the bounded real lemma for commensurate fractional-order systems was established in .  ...\n\n### Robust Nonfragile Controllers Design for Fractional Order Large-Scale Uncertain Systems with a Commensurate Order1<α<2\n\nJianyu Lin\n2015 Mathematical Problems in Engineering\nBased on the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale uncertain systems in both cases of additive and multiplicative  ...  The paper concerns the problem of stabilization of large-scale fractional order uncertain systems with a commensurate order1<α<2under controller gain uncertainties.  ...  The idea is mainly based on the geometric analysis of a fractional system stability domain. Based on Lemma 5, the stability domain for a fractional order 1 < < 2 is convex.  ...\n\n### A universal framework of GKYP lemma for singular fractional order systems [article]\n\nYuman Li, Yiheng Wei, Yuquan Chen, Yong Wang\n2019 arXiv   pre-print\nThen the bounded real lemma in the sense of L is derived for different frequency ranges.  ...  In this paper, a universal framework of finite frequency band GKYP lemma for singular fractional order systems is established.  ...  L ∞ BOUNDED REAL LEMMAS FOR THE SFOS In this section, the L ∞ bound real lemmas for the SFOS in different frequency ranges will be derived.  ...\n\n### Robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties\n\nSulan Li\nThis paper investigates the problems of robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties.  ...  Firstly, some sufficient conditions of the robust asymptotical stable for such fractional-order uncertain systems are derived. Secondly, the robust stabilizing state-feedback controller is designed.  ...  The significance of fractional-order representation is that it is more adequate to describe real world systems than those of integer-order models .  ...\n\n### New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems\n\nOmar Kahouli, Assaad Jmal, Omar Naifar, Abdelhameed M. Nagy, Abdellatif Ben Makhlouf\n2022 Mathematics\nIn this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven.  ...  In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced.  ...  In this paper, we present a Barbalat-like lemma for the class of Katugampola fractional-order systems.  ...\n\n### Stability for Caputo Fractional Differential Systems\n\nSung Kyu Choi, Bowon Kang, Namjip Koo\n2014 Abstract and Applied Analysis\nWe introduce the notion ofh-stability for fractional differential systems.  ...  Then we investigate the boundedness andh-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method.  ...  obtained some results about stability of solutions for fractional-order dynamic systems using fractional Lyapunov direct method and fractional comparison principle.  ...\n\n### Robust stability bounds of uncertain fractional-order systems\n\nYingDong Ma, Jun-Guo Lu, WeiDong Chen, YangQuan Chen\n2014 Fractional Calculus and Applied Analysis\nAbstractThis paper considers the robust stability bound problem of uncertain fractional-order systems.  ...  The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically  ...  Acknowledgements This work was partially supported by the National Natural Science Foundation of China under Grants 60974002, 61221003 and 61374030, and the Research Foundation for the Doctoral Program  ...\n\n### Analysis of a Fractional-Order Couple Model with Acceleration in Feelings\n\nIlknur Koca, Nuri Ozalp\n2013 The Scientific World Journal\nA fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model.  ...  By using stability analysis on fractional-order system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points.  ...  Now, with an application of Lemma 8 to (37) combining with (33), upper bounds for a fractional-order nonlinear system are obtained.  ...\n\n### A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems\n\nHongxing Wang, Aijing Liu\n2018 Journal of Function Spaces\nWe derive a sufficient condition for the system with the fractional-order α satisfying 1≤α<2 in terms of linear matrix inequalities (LMIs).  ...  The condition of the proposed stability criterion for fractional-order system is easy to be verified. An illustrative example is given to show that our result is effective.  ...  study the robust stability and stabilization of fractional-order linear systems with positive real uncertainty.  ...\n\n### SYNTHESIS OF COMPLETE ORTHONORMAL FRACTIONAL BASIS FUNCTIONS WITH PRESCRIBED POLES\n\nHüseyin Akçay\n2007 IFAC Proceedings Volumes\nThis presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.  ...  For a range of noninteger differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are shown to be complete in the space of functions which are  ...  This means that the system defined by (4) with for all maps bounded energy inputs to bounded energy outputs .  ...\n\n### Synthesis of Complete Orthonormal Fractional Basis Functions With Prescribed Poles\n\nH. Akcay\n2008 IEEE Transactions on Signal Processing\nThis presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.  ...  For a range of noninteger differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are shown to be complete in the space of functions which are  ...  This means that the system defined by (4) with for all maps bounded energy inputs to bounded energy outputs .  ...\n\n### On bounded real lemma for fractional systems\n\nMathieu Moze, Jocelyn Sabatier, Alain Oustaloup\n2008 IFAC Proceedings Volumes\nProspects of this study are in the fields covered by the usual bounded real lemma such as ∞ H control, thus aiming at straightforward extension to fractional systems.  ...  Its formulation is similar to the well known bounded real lemma whereas it does not guarantee stability.  ...  Theorem 2 is an extension of the bounded real lemma for fractional systems. It enables computation of a fractional system L 2 -gain from its state-space \"like\" representation.  ...\n\n### Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems\n\nLin Wang, Chunzhi Yang\n2016 Discrete Dynamics in Nature and Society\nSynchronization problem for a class of uncertain fractional order chaotic systems is studied.  ...  Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order.  ...  This result is given to use for stability analysis of fractional order nonlinear systems, especially for Mittag-Leffler stability analysis of fractional order nonlinear systems. Lemma 6.  ...\n\n### Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics\n\nJ. E. Macías-Díaz\n2017 Discrete Dynamics in Nature and Society\nPositive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered  ...  Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions.  ...  For example, it would be interesting to determine whether theorems on the existence and the uniqueness of positive and bounded solutions for more general discrete fractional systems can be established.  ...\n« Previous Showing results 1 — 15 out of 71,996 results" ]

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[ "/ / Article\n\nResearch Article | Open Access\n\nVolume 2016 |Article ID 1037849 | https://doi.org/10.1155/2016/1037849\n\nM. I. Wanas, Nabil L. Youssef, W. El Hanafy, S. N. Osman, \"Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry\", Advances in Mathematical Physics, vol. 2016, Article ID 1037849, 8 pages, 2016. https://doi.org/10.1155/2016/1037849\n\n# Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry\n\nAccepted11 Oct 2016\nPublished28 Nov 2016\n\n#### Abstract\n\nThe importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.\n\n#### 1. Introduction\n\nIn the second decade of the twentieth century, Einstein constructed a successful theory for gravity, the general theory of relativity (GR) . Although an action principle has been used afterwards to derive the equations of the theory, Einstein has used the geometrization philosophy in constructing his theory. Among other principles of this philosophy is that laws of nature are just differential identities in the chosen geometry. The geometry used by Einstein at that time was Riemannian geometry, in which second Bianchi identity is a differential one. This identity can be written in its contracted form aswhere is the Einstein tensor and the semicolon denotes the covariant differentiation using Christoffel symbols (the “dot” in the left hand side of (1) means that when we lower the upper index, it occupies the place of the “dot”). Einstein has considered identity (1) as a geometric representation of the law of conservation of matter and energy which is written aswhere is a symmetric second-order tensor describing the material-energy distribution. The comma in (2) denotes partial differentiation with respect to . In order for (2) to represent a tensor, Einstein has replaced this comma by a semicolon and wrote the field equations of his theory aswhere is a conversion constant. This shows the importance of differential identities in constructing GR.\n\nIn the third decade of the twentieth century, Einstein [2, 3] used another type of geometry, absolute parallelism (AP-) geometry, in his attempt to construct a field theory unifying gravity and electromagnetism. It is characterized by a nonsymmetric linear connection, the Weitzenböck connection, with vanishing curvature. After long discussions and correspondence between A. Einstein and E. Cartan for more than three years, Einstein stopped using AP-geometry claiming that his attempt is not a successful one. This geometry has been neglected for about two decades until McCrea and Mikhail have reconsidered it to treat continuous creation of matter and to build a steady state world model .\n\nIn the sixties of the past century, Dolan and McCrea (1963, private communication to the first author in 1973) have developed a variational method to get fundamental identities in Riemannian geometry, without using an action principle. Unfortunately, this method is not published although it is shown to be of importance when applied in geometries other than the Riemannian one.\n\nIn the seventies of the twentieth century, two important results have been obtained by developing AP-geometry in a certain direction [7, 8]. The first is the use of the dual connection (the transposed Weitzenböck connection) which has simultaneously nonvanishing torsion and nonvanishing curvature. The second result is a differential identity, in AP-geometry, obtained by developing the Dolan-McCrea method to suit AP-space with its dual connection. The identity obtained can be written in the formwhere the stroke “” and the “−” sign are used to denote covariant differentiation using the dual connection and is a second-order nonsymmetric tensor defined in the context of AP-geometry by where is the Hamiltonian derivative of the Lagrangian density with respect to the building blocks (BB) of AP-geometry and is the determinant of (more details about AP-geometry are given in the next section).\n\nIt is to be noted that identity (4) is a generalization of the Bianchi identity (1) to AP-geometry. Einstein tensor is uniquely defined in Riemannian geometry while is not uniquely defined in the AP-geometry. The latter depends on the choice of the Lagrangian density which has many forms in AP-geometry. Several field theories have been constructed [7, 9, 10], using the geometrization philosophy and the identity (4). Many successful applications have been obtained within these theories .\n\nIn the last decade of the twentieth century, another important result has been obtained as a consequence of another development in AP-geometry. It has been discovered that AP-geometry admits a hidden parameter . It was the Bazanski approach that when applied to AP-geometry has led to the above mentioned hidden parameter. The generalization of this hidden parameter has given rise to a modified version of AP-geometry called parameterized absolute parallelism (PAP-) geometry [20, 21].\n\nIn the past ten years or so, AP-geometry has gained a lot of attention in constructing field equations for what is called theories and their applications (c.f. ). The scalar is a torsion scalar characterizing the teleparallel equivalent of GR. It has been shown that many other scalars can be defined in AP-geometry and its different versions. These scalars have been used to construct several field theories with GR limits [7, 9, 10, 2527].\n\nIt is the aim of the present work to find out differential identities in PAP-geometry and to study their relations to similar identities in AP-geometry (4) and in Riemannian geometry (1). For this reason, we give a brief review of PAP-geometry in the next section. In Section 3, we apply a modified version of the Dolan-McCrea variational method in PAP-geometry to get the general form of the identities admitted. In Section 4, we present the interrelationships between the identities in Riemannian geometry, AP-geometry, and PAP-geometry. We discuss the results obtained and give some concluding remarks in Section 5.\n\n#### 2. Brief Review of PAP-Geometry\n\nIn the present section, we are going to give basic mathematical machinery and formulae of PAP-geometry necessary for the present work. For more details, the reader is referred to [20, 21] and the references therein.\n\nAs mentioned in Section 1, it has been shown that the conventional AP-geometry admits a hidden jumping parameter. This parameter has been discovered when using the Bazanski approach to derive path and path deviation equations. The importance of this parameter is that, among other things, its value jumps by a step of one half, which has been tempted to show its relation to some quantum phenomena when used in application. This parameter has no explicit appearance in the conventional AP-geometry. This motivates authors to give the parameter an explicit appearance in a modified version of AP-geometry known in the literature as PAP-geometry.\n\nAn AP-space is a pair , where is a smooth manifold and are independent global vector fields    on . For more details, see . An AP-space admitted at least four natural (“natural” means that the geometric object under consideration is constructed from the building blocks only) linear connections: the Weitzenböck connectionits dual (or transposed) connectionthe symmetric part of (6)and the Levi-Civita connectionassociated with the metric .\n\nIt is to be noted that all these linear connections have nonvanishing curvature except for (6). Among these connections, the only connection that has simultaneously nonvanishing torsion and nonvanishing curvature is the dual connection (7). In order to generalize these connections and to give an explicit appearance of the above mentioned jumping parameter, these connections have been linearly combined to give the object (, , , and are parameters):Imposing the general coordinate transformation of a linear connection on (10), using (6)–(9), the above 4 parameters reduce to one parameter , which leads towhere is the contortion of AP-geometry. Connection (11) will be called the parameterized canonical connection. It is nonsymmetric with nonvanishing curvature; that is, it is of Riemann-Cartan type. Moreover, it is a metric connection .\n\nThe parameter is a dimensionless parameter. For some geometric and physical reasons , this parameter is suggested to have the formwhere is a natural number taking the value ; is the fine structure constant; and is a dimensionless parameter to be fixed by experiment or observation for the system under consideration. The explicit appearance of the parameter in (11) gives rise to the following advantages to PAP-geometry:(1)In the case of , (11) reduces to the Weitzenböck connection (6) of the conventional AP-geometry.(2)In the case of , connection (11) reduces to the Levi-Civita connection (9).(3)Between the limits and , there is a discrete spectrum of spaces (due to the presence of in (12)), each of which has simultaneously nonvanishing curvature and torsion.\n\nIn what follows, we will decorate the tensors containing the parameter by a star. Also, these tensors will retain the same name, as in the conventional AP-geometry, preceded by the adjective “parameterized.” For example, the parameterized contortion is given byThe torsion of the parameterized connection (11) is given bywhere is the torsion of the AP-geometry. Also, the parameterized basic form can be obtained by contraction of (13) or (14):It is to be noted that starred objects have the same symmetry properties as the corresponding unstarred objects defined in the conventional AP-geometry.\n\nNow, since the parameterized canonical connection is nonsymmetric, one can define two other linear connections: the parameterized dual (transposed) connectionand the parameterized symmetric connectionConsequently, using (11), (16), and (17), we can define, respectively, the covariant derivatives:for any arbitrary vector .\n\nIt is of importance to note that the BB of PAP-geometry are the same as those of AP-geometry. In other words, the parameter has no effect on the BB of the geometry.\n\n#### 3. Dolan-McCrea Variational Method in PAP-Geometry\n\nWe are going to apply the Dolan-McCrea variational method to obtain differential identities in PAP-geometry. This method is an alternative to the least action method. It was originally suggested in 1963 to derive Bianchi and other identities in the context of Riemannian geometry. It has been generalized to AP-geometry and used to derive identity (4). Here, we generalize this method to PAP-geometry, giving some details since it is not widely known.\n\nSince, as stated above, the BB of PAP-geometry are the same as those of AP-geometry, let us define the Lagrangian functionconstructed from the BB of PAP, , and its first and second derivatives. Consequently, we can write the scalar density as follows:where is a scalar lagrangian density and . Now, let us assume that the following integral, defined over some arbitrary -dimensional domain ,is invariant under the infinitesimal transformationwhere is an infinitesimal parameter and are 1-forms defined on . Let be the -space such that the -space region is enclosed within . Thus,whereAssuming that and vanish at all points of , thenwhere is the value of at . Now, can be written, using Taylor expansion, in the formUsing (26) and (27) and by integration by parts, it can be shown, after some manipulation, that (26) can be written aswhere is the Hamiltonian derivative defined byConsider a new set of coordinates related to the -coordinate system by the transformationwhere is a vector field vanishing at all points of and is independent of . We can writeSince is a vector, its transformation law isSubstituting from (32) into the above equation, we getSubstituting from (32) again into the above equation givesFinally, this equation can be written asSubstituting from (36) into (30), we getConsequently, we can writeThen, the Jacobian expressions of the above matrices can be given assince the difference between and would be of order as shown by (36).\n\nNow, we express in terms of in two different ways:(i)Using the vector transformation law:(ii)Using Taylor expansion:We have dropped the bar in the second term on the right hand side of this equation as the difference would be of order . Comparing (40) and (41) and using (22), we getwhereand the double stroke operator “” is defined by (18).\n\nNow, we treat the Lagrangian density in the two different ways mentioned above.\n\n(a) Using Taylor expansion,also, we have dropped the bar in the second term on the right hand side of this equation as the difference would be of order .\n\nThe Lagrangian density in (44) means\n\n(b) Using scalar transformation,then, using (20) and (39), we getComparing (44) and (47), we have\n\nBy (46), we getApplying Gauss’s theorem to convert the volume integral on (-space) to a surface integral over (-space), the integral vanishes as vanishes at all points of . Now, we can writewhere is a unit vector normal to .\n\nSo, (50) shows thatSubstituting from (42) into (45), we getUsing (25),then, we can write (52) asComparing (26), (28), and (55) implies thatSubstituting from (43) into (56), we writeLetThe integral identity (57) then becomes\n\nNow, the integral of the first term can be treated as follows:Thus, the integral identity (59) readssince and is an arbitrary vector field. Using the fundamental lemma of the calculus of variation , the expression in the brackets vanishes identically. Hence, we haveUsing (11), (18), and (58), after some manipulations, identity (62) can be written asThis is the differential identity characterizing PAP-geometry.\n\n#### 4. Relation between Differential Identities\n\nThe three differential identities, (1) of Riemannian geometry, (4) of AP-geometry, and (63) of PAP-geometry, are to be related. This idea comes from the fact that the general linear connection (11) reduces to the Weitzenböck connection (6) of the AP-space for and to the Live-Civita connection (9) of the Riemannian space for . Note that the three identities mentioned are derivatives in which linear connections are used. The following two results relate these identities.\n\nTheorem 1. If is a tensor of order 2 on a PAP-space , then one has the identityConsequently, if (the Riemannian case) or is symmetric, one gets\n\nProof. Using the definition of the parameterized dual connection , we haveAs is skew-symmetric in the first pair of indices, the last term on the right vanishes. Hence, we getNow, consider the last term on the right of the above identity:from which (64) follows.\nFinally, it is clear that if , then . On the other hand, if is symmetric, then the term vanishes since is skew-symmetric in and .\n\nTheorem 2. If is a tensor of order 2 on a PAP-space , then one has the identityConsequently, if (the AP case) or is symmetric, one gets\n\nThe above two theorems imply the following result.\n\nCorollary 3. (a) For a symmetric tensor , one has from (64) and (69)(b) In the Riemannian case, the tensor defined by (5) (using the Ricci scalar in the Lagrangian function) coincides with the Einstein tensor; then,and, consequently, for any symmetric tensor defined by (5), one hasin AP- and PAP-spaces, respectively.\n\n#### 5. Discussion and Concluding Remarks\n\nIn the present work, we have used the Dolan-McCrea variational method to derive possible differential identities in PAP-geometry. The importance of this work for physical applications can be discussed in the following points:(1)It is well known that the field equations of GR can be obtained using either one of the following approaches:(a)The Einstein approach, in which the geometrization philosophy plays the main role in constructing the field equations of the theory. One of the principles of this philosophy is that “laws of nature are just differential identities in an appropriate geometry.” Einstein has used this principle to write his field equations. In other words, he has used the second Bianchi identity of Riemannian geometry to construct the field equations of his theory.(b)Hilbert approach, in which the standard method of theoretical physics, the action principle, has been used to derive the field equations of the theory.It is to be noted that the first approach is capable of constructing a complete theory, not only the field equations of the theory. This will be discussed in the following point.(2)Einstein geometrization philosophy can be summarized as follows :“To understand nature, one has to start with geometry and end with physics.”In applying this philosophy, one has to consider its main principles:(a)There is a one-to-one correspondence between geometric objects and physical quantities.(b)Curves (paths) in the chosen geometry are trajectories of test particles.(c)Differential identities represent laws of nature.In view of the above principles, Einstein has used Riemannian geometry to construct a full theory for gravity, GR, in which the metric and the curvature tensors represent the gravitational potential and strength, respectively. He has also used the geodesic equations to represent motion in gravitational fields. Finally, he has used Bianchi identity to write the field equations of GR.The above mentioned philosophy can be applied to any geometric structure other than the Riemannian one. It has been applied successfully in the context of conventional AP-geometry (cf. [7, 9, 10]), using the differential identity (4).PAP-geometry is more general than both Riemannian and conventional AP-geometry. It is shown in Section 2 that PAP-geometry reduces to AP-geometry for and to Riemannian geometry for . In other words, the latter two geometries are special cases of the PAP-geometry. The importance of the parameter has been investigated in many papers (cf. [35, 36]). The value of this parameter is extracted from the results of three different experiments [35, 37, 38]. The value obtained () shows that space-time near the Earth is neither Riemannian () nor conventional AP ().(3)To use PAP-geometry as a medium for constructing field theories, the above three principles are to be considered. The curves (paths) of the geometry have been derived and used to describe the motion of spinning particles [37, 39]. Geometric objects have been used to represent physical quantities via the constructed field theories [25, 26].The present work is done as a step to complete the use of the geometrization philosophy in PAP-geometry. The general form of the differential identity characterizing this geometry is obtained in Section 3. This will help in attributing physical properties to geometric objects, especially conservation. This will be discussed in the next point.(4)The results obtained from the two theorems given in Section 4 are of special importance. It is clear from (71), (72), and (73) that any symmetric tensor defined by (5) is subject to the differential identity of type (72). This result is independent of the values of the parameter .Now, for any symmetric tensor defined by (5) in PAP-geometry, we haveDue to the structure of the parameterized connection (11), the tensor can always be written in the formwhere is Einstein tensor defined in terms of (9) as usual and is a second-order symmetric tensor which vanishes when . Consequently, identity (74) can be written asAs the first term vanishes, due to Bianchi identity, then we get the identityThis implies that the physical entity represented by is conserved in any field theory constructed in PAP-geometry. Identity (77) is thus an identity of PAP-geometry, independent of any such field theory. The tensor is usually used as a geometric representation of a material-energy distribution in any field theory constructed in PAP-geometry [25, 26].(5)Finally, the following properties are guaranteed in any field theory constructed in the context of PAP-geometry:(a)The theory of GR, with all its consequences, can be obtained upon taking .(b)As the parameterized connection (11) is metric, the motion along curves of PAP-geometry preserves the gravitational potential.(c)One can always define a geometric material-energy tensor in terms of the BB of the geometry.(d)Conservation is not violated in any of such theories.\n\n#### Competing Interests\n\nThe authors declare that they have no competing interests.\n\n1. A. Einstein, “The field equations of general relativity,” Sitzungsberichte der Preussischen Akademie der Wissenschaften—Physikalisch—mathematische Klasse, pp. 844–847, 1915. View at: Google Scholar\n2. A. 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View at: Publisher Site | Google Scholar\n12. R. S. de Souza and R. Opher, “Origin of intense magnetic fields near black holes due to non-minimal gravitational-electromagnetic coupling,” Physics Letters B, vol. 705, no. 4, pp. 292–293, 2011. View at: Publisher Site | Google Scholar\n13. A. Mazumder and D. Ray, “Charged spherically symmetric solution in Mikhail-Wanas field theory,” International Journal of Theoretical Physics, vol. 29, no. 4, pp. 431–434, 1990. View at: Publisher Site | Google Scholar\n14. F. I. Mikhail, M. I. Wanas, and A. M. Eid, “Theoretical interpretation of cosmic magnetic fields,” Astrophysics and Space Science, vol. 228, no. 1-2, pp. 221–237, 1995. View at: Publisher Site | Google Scholar\n15. M. I. Wanas, “A generalized field theory: charged spherical symmetric solution,” International Journal of Theoretical Physics, vol. 24, no. 6, pp. 639–651, 1985. View at: Publisher Site | Google Scholar | MathSciNet\n16. M. I. Wanas, “On the relation between mass and charge: a pure geometric approach,” International Journal of Geometric Methods in Modern Physics, vol. 4, no. 3, pp. 373–388, 2007. View at: Publisher Site | Google Scholar | MathSciNet\n17. M. I. Wanas and S. A. Ammar, “A pure geometric approach to stellar structure,” Central European Journal of Physics, vol. 11, no. 7, pp. 936–948, 2013. View at: Publisher Site | Google Scholar\n18. M. I. Wanas, M. Melek, and M. E. Kahil, “New path equations in absolute parallelism geometry,” Astrophysics and Space Science, vol. 228, no. 1-2, pp. 273–276, 1995. View at: Publisher Site | Google Scholar\n19. S. Bazanski, “Hamilton-Jacobi formalism for geodesics and geodesic deviations,” Journal of Mathematical Physics, vol. 30, no. 5, pp. 1018–1029, 1989. View at: Publisher Site | Google Scholar | MathSciNet\n20. M. I. Wanas, “Motion of spinning particles in gravitational fields,” Astrophysics and Space Science, vol. 258, no. 1-2, pp. 237–248, 1997/98. View at: Publisher Site | Google Scholar | MathSciNet\n21. M. I. Wanas, “Parameterized absolute parallelism: a geometry for physical applications,” Turkish Journal of Physics, vol. 24, no. 3, pp. 473–488, 2000. View at: Google Scholar\n22. G. G. L. Nashed, “Kerr-NUT black hole thermodynamics in f(T) gravity theories,” European Physical Journal Plus, vol. 130, no. 7, article 124, 2015. View at: Publisher Site | Google Scholar\n23. G. G. L. Nashed, “A spherically symmetric null tetrads in non-minimal torsion-matter coupling extension of f(T) gravity,” Astrophysics and Space Science, vol. 357, no. 2, pp. 1–11, 2015. View at: Publisher Site | Google Scholar\n24. G. G. L. Nashed and W. El Hanafy, “A built-in inflation in the f(T)-cosmology,” European Physical Journal C, vol. 74, no. 10, article 3099, pp. 1–13, 2014. View at: Publisher Site | Google Scholar\n25. M. I. Wanas and M. M. Kamal, “A field theory with curvature and anticurvature,” Advances in High Energy Physics, vol. 2014, Article ID 687103, 15 pages, 2014. View at: Publisher Site | Google Scholar\n26. M. I. Wanas, N. L. Youssef, and W. S. El-Hanafy, “Pure geometric field theory: description of gravity and material distribution,” https://arxiv.org/abs/1404.2485. View at: Google Scholar\n27. M. I. Wanas, N. L. Youssef, and A. M. Sid-Ahmed, “Teleparallel Lagrange geometry and a unified field theory,” Classical and Quantum Gravity, vol. 27, no. 4, Article ID 045005, 2010. View at: Publisher Site | Google Scholar\n28. F. I. Mikhail, “Tetrad vector fields and generalizing the theory of relativity,” Ain Shams Science Bulletin, vol. 6, pp. 87–111, 1962. View at: Google Scholar\n29. M. I. Wanas, “Absolute parallelism geometry: developments, applications and problems,” Studii si Cercetari Stiintifice: Matematica University Bacau, vol. 10, pp. 297–309, 2001. View at: Google Scholar\n30. N. L. Youssef and W. A. Elsayed, “A global approach to absolute parallelism geometry,” Reports on Mathematical Physics, vol. 72, no. 1, pp. 1–23, 2013. View at: Publisher Site | Google Scholar | MathSciNet\n31. N. L. Youssef and A. M. Sid-Ahmed, “Linear connections and curvature tensors in the geometry of parallelizable manifolds,” Reports on Mathematical Physics, vol. 60, no. 1, pp. 39–53, 2007. View at: Publisher Site | Google Scholar | MathSciNet\n32. N. L. Youssef and A. M. Sid-Ahmed, “Extended absolute parallelism geometry,” International Journal of Geometric Methods in Modern Physics, vol. 5, no. 7, pp. 1109–1135, 2008. View at: Publisher Site | Google Scholar | MathSciNet\n33. B. Van Brunt, The Calculus of Variation, Springer, New York, NY, USA, 2004.\n34. M. I. Wanas, “The accelerating expansion of the universe and torsion energy,” International Journal of Modern Physics A, vol. 22, no. 31, pp. 5709–5716, 2007. View at: Publisher Site | Google Scholar | MathSciNet\n35. A. A. Sousa and J. M. Maluf, “Gravitomagnetic effect and spin-torsion coupling,” General Relativity and Gravitation, vol. 36, no. 5, pp. 967–982, 2004. View at: Publisher Site | Google Scholar | MathSciNet\n36. M. I. Wanas, “The other side of gravity and geometry: antigravity and anticurvature,” Advances in High Energy Physics, vol. 2012, Article ID 752613, 10 pages, 2012. View at: Publisher Site | Google Scholar | MathSciNet\n37. M. I. Wanas, M. Melek, and M. E. Kahil, “Quantum interference of thermal neutrons and spin-torsion interaction,” Gravitation and Cosmology, vol. 6, pp. 319–322, 2000. View at: Google Scholar\n38. Y. Mao, M. Tegmark, A. H. Guth, and S. Cabi, “Constraining torsion with gravity probe B,” Physical Review D, vol. 76, no. 10, Article ID 104029, 2007. View at: Publisher Site | Google Scholar\n39. M. I. Wanas, M. Melek, and M. E. Kahil, “SN1987A: temporal models,” in Proceedings of the IAU Symposium, vol. 205, pp. 396–397, 2001. View at: Google Scholar\n\n#### More related articles\n\nWe are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions." ]

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[ "## Unitary representations of Lie supergroups (Sigiswald Barbier, Ghent University)\n\nAbstract:\n\nUnderstanding all unitary irreducible representations of a Lie group is an important goal in representation theory. Likewise we also want to understand all unitary irreducible representations of a Lie supergroup. Unfortunately, the standard definition of unitarity in the super sense has the disadvantage that a lot of a Lie supergroups do not have any unitary representations at all. Therefore people have been proposing alternative definitions of unitarity. In this talk we will take a look at some of these alternatives.\n\n## A new family of QRKHS in the Clifford-Appell case (Kamal Diki, Politecnico di Milano)\n\nAbstract:\n\nWe will use the classical Fueter mapping theorem in order to construct a special system of Clifford-Appell polynomials in the quaternionic setting. We will discuss various properties of such polynomials and study their algebraic behaviour with respect to the well-known Cauchy-Kowalevski product. Then, based on this system we can introduce a new family of quaternionic reproducing kernel Hilbert spaces in this framework. As particular examples we will treat further results on the Hardy and Fock spaces and their related operators such as creation, annihilation, shift and backward shift operators. Finally, if time allows we will discuss some connections and applications of this new approach to the recent theory of quaternionic slice polyanalytic functions and Schur analysis. This talk is based on recent works that are in collaboration with Daniel Alpay, Fabrizio Colombo, Soeren Krausshar and Irene Sabadini.\n\n## Radon type transforms in the Clifford setting (Teppo Mertens, Ghent University)\n\nAbstract:\n\nThe Radon transform is an integral transform with many applications in both pure and applied mathematics. The Szegö-Radon transform, an integral transform of monogenic functions over the unit sphere, is its counterpart in the Clifford setting. It can moreover be generalized to the framework of complex analysis by replacing the monogenic functions by their holomorphic extensions. This gives rise to several Radon type transforms over the Lie sphere, of which we will give an overview. Afterwards, we will discuss how to invert these transforms by means of so-called dual Radon transforms.\n\n## Generalizing the Deligne category via cobordisms, Khovanov's and Sazdanovic's approach (Alexis Langlois-Rémillard, Ghent University)\n\nAbstract:\n\nThe Deligne category is Deligne's answer to the following question: \"If we were to define the symmetric group outside the non-negative integer, what would its representation theory look like?\" Following this idea, he constructed a category that \"interpolates\" between the categories of finite-dimensional representations of all the symmetric groups for any element of an arbitrary characteristic 0 field. When specialized to non-negative integer, it is equivalent, up to quotient, to the category of finite-dimensional representations of the symmetric group. In general, the Deligne category admits a diagrammatic construction via partition diagrams, which was used extensively by Comes and Ostrik to study its blocks. Thickening partition diagrams gives an equivalence between the partition category generated by partition diagrams and the 2D cobordisms up to two additional relations. In a recent work, Khovanov and Sazdanovic have given a multi-parameters generalization of the Deligne category starting from cobordism categories by using the extra information given by the genus of the surfaces involved. This talk presents their interesting construction image by image.\n\n## A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra D(2,1;ɑ) (Sam Claerebout, Ghent University)\n\nAbstract:\n\nWe construct two infinite-dimensional irreducible representations for D(2,1;ɑ): a Schrödinger model and a Fock model. Further, we also introduce an intertwining isomorphism. These representations are similar to the minimal representations constructed for the orthosymplectic Lie supergroup and for Hermitian Lie groups of tube type. The intertwining isomorphism is the analogue of the Segal-Bargmann transform for the orthosymplectic Lie supergroup and for Hermitian Lie groups of tube type.\n\n## Inverse Source Problems in Fractional Dual-Phase-Lag heat conduction (Frederick Maes, Ghent University)\n\nAbstract:\n\nNon-classical thermal models based on a non-Fourier type law have attracted a lot of interest in the past few decades. In this talk I will discuss the fractional dual-phase-lag heat equation and uniqueness in an associated inverse source problem. First an introduction to the modeling part and fractional calculus will be given. Next I will state and discuss our main uniqueness results of determining a space dependent source given the final time observation. Finally, a possible relaxation of the assumptions will be investigated in two modified models.\nThis talk is based on joint work with Marian Slodicka.\n\n## Clifford invariants of symmetric Lie algebra pairs (Kieran Calvert, University of Manchester)\n\nAbstract:\n\nKostant proved that if g is a semisimple Lie algebra then the Clifford invariants Cl(g)g is isomorphic to a Clifford algebra on the primitive subspace related to g. We prove the analog of Kostants theorem for symmetric pairs (g; k), where g decomposes as p + k. The Clifford invariants Cl(p)k are used in Dirac cohomology. In this talk we describe the structure of Cl(p)as a graded algebra.\n\n## PBW-type bases for simple osp(1|2n)-modules (Asmus Bisbo, Ghent University)\n\nAbstract:\n\nThe Lie superalgebra osp(1|2n) describes the interactions of parabosonic particles, relevant in several areas of theoretical physics. We construct polynomial PBW-type bases for an important class of simple osp(1|2n)-modules know as parabosonic Fock spaces. We present two complementary expressions for the basis elements. Firstly, they are written as polynomials in the odd generators of osp(1|2n) acting on the lowest weight vector. Secondly, they are written as monomials in the generators of the u(n) subalgebra of osp(1|2n) acting on the u(n)-highest weight vectors. Matrix elements corresponding to this basis will also be discussed.\n\n## Distributed order fractional wave equations with irregular coefficients (Srđan Lazendić, Ghent University)\n\nAbstract:\n\nIn this talk, we derive and analyze fractional wave equations describing wave propagation in one-dimension viscoelastic media, modeled by distributed-order fractional constitutive stress-strain relation. More precisely, we consider the system of\nequations which consists of the equation of motion of the one-dimensional deformable-body, the constitutive equation of distributed order fractional type, which describes the mechanical properties of the linear viscoelastic body, and the strain for small local deformations. The system is equivalent to the integrodifferential wave-type equation. First, we show that that the fundamental solution to the generalized Cauchy problem for the distributed order wave equation exists and it is unique. In particular, the fundamental solutions corresponding to four thermodynamically acceptable classes of linear fractional constitutive models and power-type distributed-order models will be discussed. Those results regarding homogeneous materials are obtained in .\n\nFurther, we are interested in obtaining similar results for the cases when viscoelastic material/media are heterogeneous. This implies that the coefficients appearing in equations become non-smooth functions depending on space (or even time) which could also be irregular, such as Dirac delta distribution. We shall concentrate on existence and uniqueness results of weak and very weak solutions. Finally, since the fractional order derivatives are difficult to handle numerically in their original form, we will motivate why the obtained mathematical model, which combines the Laplace transform together with the variational methods, is perfectly suitable for further practical applications.\n\nJoint work with: Sanja Konjik and Ljubica Oparnica.\n\n S. Konjik, S. Lazendic and Lj. Oparnica, Distributed-order fractional constitutive stress-strain relation with irregular coefficients in wave propagation modeling, 2021, Submitted.\n\n## The Dirac delta distribution and inversion formulas for the Radon transform in superspace\n\nAbstract:\n\nIn this talk, we obtain a plane wave decomposition for the delta distribution in superspace, provided that the superdimension is not odd and negative. This decomposition allows for explicit inversion formulas for the super Radon transform in these cases. Moreover, we prove a more general Radon inversion formula valid for all possible integer values of the superdimension. The proof of this result comes along with the study of fractional powers of the super Laplacian, their fundamental solutions, and the plane wave decompositions of super Riesz kernels.\n\n## Finslerian Geometry - Anisotropic Frameworks for Dynamical Systems\n\nAbstract:\n\nIn this presentation we will discuss the basic notions of Finslerian geometry and how it relates to Riemannian geometry. We will then create a Finsler framework to describe certain 2nd order ODES through the means of Finsler geodesics and their invariants. Finally, we will end the presentation by applying the presented framework to an existing ODE.\n\n## Trueskill, step by step\n\nAbstract:\n\nIn 2005 Microsoft Research presented a new Bayesian rating system called TrueskillTM which was then quickly put to use in the online gaming platform Xbox Live®. Compared to the previously used Elo system, Trueskill brings about many advantages in terms of convergence, flexibility, and ranking, and satisfies the demand of a unified framework that could easily be adapted to the games that the online platform currently supports, as well as games that will only be developed in future. In this seminar, I will explain the general idea of the algorithm but also consider a simple example and see, step by step, which operations are used and what their interpretation is from a Bayesian point of view." ]

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[ "# Galois theory for polynomials in several variables\n\nI feel a bit ashamed to ask the following question here.\n\nWhat is (actually, is there) Galois theory for polynomials in $n$-variables for $n\\geq2$?\n\nI am preparing a large audience talk on Lie theory, and decided to start talking about symmetries and take Galois theory as a \"baby\" example. I know that Lie groups are somehow to differential equations what discrete groups are to algebraic equations. But I nevertheless would expect Lie (or algebraic) groups to appear naturally as higher dimensional analogs of Galois groups.\n\nNamely, the Galois group $G_P$ of a polynomial $P(x)$ in one variable can be defined as the symmetry group of the equation $P(x)=0$ (very shortly, the subgroup of permutations of the solutions/roots that preserves any algebraic equation satisfied by them).\n\nThen one of the great results of Galois theory is that $P(x)=0$ is solvable by radicals if and only if the group $G_P$ is solvable (meaning that its derived series reaches $\\{1\\}$).\n\nI was wondering what is the analog of the story in higher dimension (i.e. for equations of the form $P(x_1,\\dots,x_n)=0$. I would naively expect algebraic group to show up...\n\nI googled the main key words and found this presentation: on the last slide it is written that\n\nthe task at hand is to develop a Galois theory of polynomials in two variables\n\nThis convinced me to anyway ask the question\n\nEDIT: the first \"idea\" I had\n\nI first thought about the following strategy. Consider $P(x,y)=0$ as an polynomial equation in one variable $x$ with coefficients in the field $k(y)$ of rational functions in $y$, and consider its Galois group. But then we could do the opposite...what would happen?\n\n• Take the étale fundamental group of the corresponding scheme? Nov 17 '11 at 23:49\n• That doesn't seem like the correct generalization to me. The Galois group of $f(T)$ is the quotient of the etale fundamental group of Spec $k$ by the etale fundamental group of Spec $k[T]/(f(T))$. In particular, we would like to define it as the automorphism group of something. The Galois group of a polynomial, though, is not the automorphism group of $k[T]/f(T)$ but of $k[T_1,T_2,...,T_n]/f(T_1),etc.,etc.$. One could take the limit of the automorphism groups of $X$, some subset of $X \\times X$, some subset of $X\\times X\\times X$, et cetera... Nov 18 '11 at 2:07\n• I don't understand why I see on this question a vote to close. I like this question, and vote NOT to close, and whoever has cast a vote is being very rude by not saying why. Nov 18 '11 at 4:08\n• @Theo I voted to close as not a real question. I have nothing further to add. Nov 18 '11 at 10:20\n• I should also mention that the étale fundamental group can indeed be seen as a generalization of the (absolute) Galois group for objects of dimension >0 (although this may not be the generalization you're looking for). Nov 18 '11 at 14:14\n\n(This should really be a comment I think, but I'm not highly rated enough to leave one, so please bear with me)\n\nA Galois Theoretic condition for a polynomial in two variables to be solvable by radicals is found in the following paper: http://arxiv.org/abs/math/0305226. It seems to indicate that something similar can be done for higher variables. Perhaps I'll ask Jochen next time I see him about this.\n\n• Thank you for the link. I'll have a look as soon as possible. Dec 9 '11 at 8:58\n\nThis will not answer the question but is more than a comment in addition it may be very naive! (This is a hard question not a soft question!!!)\n\nI wonder if given the Galois group <-> étale fundamental group link works for dimension 1, should there not be a link '2-Galois thingie'<->étale 2-type, and hence a link with Grothendieck's Pursuing Stacks and his letters to Breen in 1975. The sought after model might be a profinite (?) crossed module. These are able to be seen as automorphism 2-groups of groupoids, so although they are automorphism things, there is a gap to bridge before the link would work well. I have also met a similar idea when working with orbifolds, and related ideas but have not any definite reply to the particular question, rather more an addition to the question! (I hope this helps... or inspires someone to think 'outside the box'.)\n\nThere would be then a similar idea for polynomials in n-variable and models for n-types??? (This may be all rubbish but it is nice to dream sometimes!)\n\n• I don't think that increasing the number of variables means that we have to use higher category theory. Nov 18 '11 at 8:40\n• @Martin May be not, but the possibility is there. Again it is sometimes not a question of \"have to\" but maybe \"might\". NB. In fact I did not mention higher category theory as the models for 2-types are quite standard simplicial things and those are \"classical\" (due to Whitehead 1950 or Reidemeister 1930s, and Peiffer 1940s). :-) The automorphism 2-group of group is very simply the inner automorphism morphism from G to Aut(G), so is not per se higher category theory Nov 18 '11 at 10:02\n• David Corfield kindly reminded me of this n-cat café posting:golem.ph.utexas.edu/category/2009/12/… Kim has a lot more to say on this area, but it seems that it is a very deep and hard area. In his talk at the INI that David pointed out to me, he mentioned Pursuing Stacks and the anabelian theory mentioned therein, so perhaps (more by chace than by good knowledge) I was nearer the mark than I thought! Nov 20 '11 at 16:35" ]

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[ "Statistics and Time Series.\n\n# Check your regression analysis for these 7 Assumptions.\n\nEconometricus.com: A Quantitative Research Consulting Firm.\n\nAt Econometricus.com we help clients to get statistical data straight and accurate as much as possible. No matter whether our client is a lawyer supporting a case for economic damages, or  a graduate student writing a paper contesting the counterpart’s mishandling of data. Econometricus.com will provide technical support for a cogent understanding of the data being used as evidence in litigation or academic processes.\n\nBefore you submit your paper for which you successfully run several simple or multiple regression analysis, we at econometricus.com can help you out checking everything is sound.\n\nThese are the 7 assumptions your work must comply with wherever you run the Method of Least Squares:\nThe overall objective of checking the 7 assumptions is to gauge how close or far your estimates are from the population data. In other words, we will tell you how “accurate” your betas are.\n\nAssumption 1:\n\nYour model must be linear in the parameters (Note that if your data is not linear in the variables we can linearize it for you).\n\nAssumption 2:\n\nYour X’s values must be fixed and independent of the error term.\n\nAssumption 3:\n\nZero mean value of the error term.\n\nAssumption 4:\n\nHomoscedasticity. Your regression must not suffer heteroscedasticity.\n\nAssumption 5:\n\nNo autocorrelation between disturbances. This means no correlation between error terms.\n\nAssumption 6:\n\nThe number of observations must exceed the number of parameter to estimate. You can do that by yourself.\n\nAssumption 7:\n\nNature of the X variable. Neither outliers nor negative variance in variable X." ]

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[ "# Tricks to Solve Simple Interest Questions\n\nUpdated : Oct 1, 2020, 10:00\nBy : Neha Joshi\n\nTo make the chapter easy for you all, we are providing you with some Important Short Tricks to solve Simple Interest Questions which will surely make the chapter easy for you all.\n\nImportant Short Tricks to solve Simple Interest Questions:\n\nInterest is the money paid by the borrower to the lender for the use of money lent.\nThe sum lent is called the Principal. Interest is usually calculated at the rate of so many rupees for every Rs.100 of the money lent for a year. This is called the rate of per cent per annum.\n‘Per annum’ means for a year. The words ‘per annum’ are sometimes omitted. Thus, 6 p.c. means that Rs.6 is the interest in Rs.100 in one year.\nThe sum of the principal and interest is called the amount. The interest is usually paid yearly, half-yearly or quarterly as agreed upon.\nInterest is of two kinds, Simple and Compound. When interest is calculated on the original principal for any length of time it is called simple interest. Compound interest is defined in the next chapter.\n\nTo find Simple Interest, multiply the principal by the number of years and by the rate per cent and divide the result by 100.\n\nThis may be remembered in the symbolic form\n\nWhere I = Interest, p = principle, t = number of years, r = % rate\n\nEx. 1. Find the simple interest on Rs.400 for 5 years at 6 per cent.\n\nSolution:\n\nInterest for a number of days\n\nWhen the time is given in days or in years and days, 365 days are reckoned to a year. But when the time is given in months and days, 12 months are reckoned to a year and 30 days to the month. The day on which the money is paid back should be include be but not the day of which it is borrowed, ie, in counting, the first day is omitted.\n\nEx. 2. Find the simple interest on Rs.306. 25 from March 3rd to July 27th at  per annum.\n\nSolution:\n\nInterest = Rs.\n\n=  = Rs. 4.59\n\nTo find the principal:\n\nSince I =\n\nEx.3. What sum of money will produce Rs.143 interest in 3(1/4)  years at 2.50 p.c. simple interest?\n\nSolution:\n\nLet the required sum be Rs. P. Then\n\nRs P =\n\nTo find rate %:-\n\nSince I =\n\nEx. 4. A sum of Rs.468.75 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs500. Find the rate of interest per cent annum.\n\nSolution:\n\nHere, P =Rs468.75, t =  or\n\nI = Rs.(500-468.75) = Rs.31.25\n\nrate p.c. =\n\nTo find Time:-\n\nSince, I = P t r / 100\n\nEx. 5. In what time will Rs.8500 amount to Rs.15767.50 at  per cent per annum?\n\nSolution:\n\nHere , interest = Rs.15767.50 – Rs.8500 =Rs.7267.50\n\nMiscellaneous Examples of Simple Interest:\n\nEx.6: The simple interest on a sum of money is 1/9th of the principal, and the number of years is equal to the rate per cent per annum. Find the rate per cent.\n\nSolution:\n\nLet principal = P, time = t year, rate = t\n\nThen,\n\nHence, rate =  %\n\nDirect formula:\n\nRate = time =  %\n\nEx. 7: The rate of interest for the first 2 yrs is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum. To fetch interest of 1520 in six years, money did he deposit?\n\nSolution\n\nLet his deposit be = Rs 100\n\nInterest for first 2 yrs = Rs 6\n\nInterest for next 3 yrs = Rs 24\n\nInterest for the last year = Rs 10\n\nTotal interest = Rs 40\n\nWhen interest is Rs 40, deposited amount is Rs 100\n\nwhen interest is Rs 1520, deposited amount =  = Rs 3800\n\nDirect formula:\n\nPrinciple = Interest*100/r1t1+r2t2+r3t3 =  =Rs 3800\n\nEx.8: A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?\n\nSolution:\n\nLet the sum be Rs 100\n\nAfter 10 years it becomes Rs 200\n\nInterest = 200 - 100 = 100\n\nThen, rate =  =\n\nDirect formula:\n\nTime × Rate = 100 (Multiple numbers of principal – 1)\n\nOr, Rate =\n\nUsing the above formula rate =\n\nEx.9: A sum was put at a certain rate for 2 yrs. Had it been put at a 3% higher rate, it would have fetched Rs 300 more. Find the sum.\n\nSolution:\n\nLet the sum be Rs x and the original rate be y% per annum. Then, new rate = (y+3) % per annum\n\nxy +3x – xy =15,000 or, x =5000\n\nThus, the sum =Rs 5000\n\nDirect Methods:\n\n=\n\nThanks\n\nPrep Smart. Stay Safe. Go Gradeup.\n\nOct 1CTET & Teaching\n\nPosted by:", null, "Postgraduate in Biophysics, Writer and Art Enthusiast\nMember since Aug 2019", null, "GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor,Sector 125, Noida,Uttar Pradesh [email protected]" ]

[ null, "https://gs-post-images.grdp.co/2018/12/screenshot-2018-12-21-at-3-img1545387500435-75.png-rs-high-webp.png", null, "https://gs-post-images.grdp.co/2018/12/screenshot-2018-12-21-at-3-img1545387500435-75.png-rs-high-webp.png", null ]

[ "Aims: We propose a novel nomogram, which graphically expresses the numerical relationship between type 2 diabetes (T2D) and disease-related risk factors.\n\nMethods: Data of 8999 patients from the 2013-2014 Korean National Health and Nutrition Examination Survey were analyzed. Multiple logistic regression analysis was performed to assess risk factors for T2D and a nomogram was constructed based on screened risk factors. A receiver operating curve (ROC) and calibration plot were created to evaluate the accuracy of the nomogram.\n\nResults: The risk factor with the greatest impact on the incidence of T2D was age over 60 years (OR=9.458), followed by presence of dyslipidemia and cardiovascular disease (OR=8.981), family history of T2D (OR=2.916), abdominal obesity (OR=1.759), hypertension (OR=1.747), male gender (OR=1.549), current-smoking status (OR=1.523), lower education level (OR=1.417), and lower income (OR=1.300). The area under the ROC curve (AUC) showed statistically significant determination (AUC=0.826). The equation of the calibration plot was drawn along the ideal line; coefficient of determination was 0.864.\n\nConclusion: Our proposed nomogram could accurately predict the incidence risk of T2D from nationwide data. The novel nomogram can be a useful tool for screening patients with T2D incidence in a Korean population.\n\nDisclosure\n\nS. Chung: None. J. Moon: None. J. Yoon: None. K. Won: None." ]

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[ "# NP-completeness of triangle removal problem\n\nTriangle removal problem states that, given an undirected graph G, can you pick a subset S of vertices such that removing S will remove all triangles from the old graph and |S| <= k. I was trying to use reduce from vertex cover problem, but every construction I attempted has failed. Here's what I've done:\n\n1) Add extra edges to the graph such that every pair of distinct vertices is connected by an edge (In other words, create a complete graph Kn)\n\n2) Create a subgraph of G, but only composed of vertices with degree at least 2 from the original graph\n\nI found a counter example for each construction, and I can't fully grasp the starting point. The goal is that I want to build some graph out of an old graph such that the every triangle should use at least one vertex in S(solution returned by black box for \"triangle removal problem\"), but it has to be a vertex cover for the old graph at the same time. How should I approach this?\n\nEdit: Current attempt - for every existing edge (u,v) in E in a graph, add a new vertex w and add two new edges (u,w) and (w,v) so that it forms a triangle\n\nYour current attempt (at the time of writing this answer at least) is on the right track, it just needs one more step.\n\nTo help understand one way of relating the problems to each other, consider the following alternative way of defining a vertex cover; a vertex cover is a set of vertices whose removal leaves a disconnected graph.\n\nSo Vertex Cover is the problem of selecting vertices to remove that gets rid of all edges, whereas your problem is selecting vertices to get rid of triangles.\n\nThus to convert Vertex Cover to Triangle Removal we need to turn edges in the original graph intro triangles in the new graph (or at least, one sensible way - there could be many reductions).\n\nHence your construction of adding a vertex for every edge in the graph and making a triangle is heading in the right direction, the only problem is that we could remove the new vertices, and that may mess up our answer (it certainly makes it harder to argue about what the vertex cover should be in the original graph). What we need is a way of preventing the added vertices being selected for removal. To do this, instead of adding a single new vertex, add $k+1$ new vertices!\n\nMore precisely (but not completely precisely), given $G$ we construct $G'$ as follows:\n\n• For every vertex $v \\in V(G)$, there is a vertex $v' \\in V(G')$\n• For every edge $uv \\in E(G)$, there is an edge $u'v' \\in E(G')$.\n• For every edge $uv \\in E(G)$, there are $k+1$ vertices $\\{w_{1},\\ldots,w_{k+1}\\} \\subseteq V(G')$ with the edges $u'w_{i}$ and $v'w_{i}$ in $E(G')$ for all $i$.\n\nI won't go through the full proof that this works, but the general gist is that if we want to get rid of all the triangles attached to $u'v'$, it doesn't really help to take any of the $w_{i}$ vertices as there are too many of them, we eventually have to take at least one of $u'$ or $v'$, but once we take one of those, it deals with all the triangles, so any answer that takes a $w_{i}$ vertex must also take $u'$ or $v'$ (or both) and can be replaced by a smaller solution that takes only $u'$ or $v'$ (or both), so we only have to consider solutions of that form, but then we're basically done - as each edge has triangles, one of the two \"original\" vertices must be in the triangle removing solution for each edge, and hence is also a vertex cover.\n\nReally you can make the same argument with your construction, but the additional vertices force things and make the argument clearer (you don't have to deal with arguing for alternative solutions and vertex swapping etc. etc.)\n\n• Thanks for the brilliant explanation. Especially for the first part how you think about reduction process helped me a lot – Ted Nov 13 '17 at 3:10" ]

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[ "# Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem\n\nJames H. Bramble, Joseph E. Pasciak, Dimitar Trenev\n\nResearch output: Contribution to journalArticlepeer-review\n\n29 Scopus citations\n\n## Abstract\n\nWe consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.\nOriginal language English (US) 2079-2079 1 Mathematics of Computation 79 272 https://doi.org/10.1090/s0025-5718-10-02355-0 Published - 2010 Yes\n\n## Fingerprint\n\nDive into the research topics of 'Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem'. Together they form a unique fingerprint." ]

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[ "# dBV, dBu, and dBm\n\nI’ve always have a little trouble remembering the relationship between dBm and the more common signal measurements of dBu and dBV.  The other day I was looking at a transfer function, and I was given results in dBm - the impetus for this post.\n\nFirst, I should make sure we’re all on the same page.  What is a decibel (dB)?  The decibel is a relative measurement.  For voltage we calculate dB as 20log10(Voltage/Reference), where the reference can be absolute (like with dBu and dBV) or relative (plain old dB).  For an amplifier that outputs a signal twice as large as the input, 20log10(2/1) = 6 .02 dB.  If we ran a signal through this amplifier twice, our output is 4 times as large as the input, or 20log10(4/1) = 12.04dB.  This is the value of a dB scale - we can add gain values in dB instead of multiplying them: 22=4, while 6.02+6.02=12.04.\n\nBefore going on I should point out that dBm is not an appropriate measure for a transfer function.  Straight dB is the way to go, as a linear transfer function should produce an output relative to the input - not relative to an absolute value like dBm, dBu, or dBV.  Let’s say I put 0.5 volts into a system, and I get 0.25 volts back out: 20*log10(0.25/0.5) = -6 dB.\n\nSo then dBV, dBu, and dBm are all absolute measurements and each has a defined reference value:\n\n• dBV - 1 Volt\n• dBu - 0.775 Volts\n• dBm - 1 Milliwatt\n\ndBV is straight ahead and simple to work with - this is the measure I use most frequently.  The dBV value of any voltage is 20*log10(V/1), so 1 Volt is 0 dBV, 2 Volts is 6 dBV, and 0.5 Volts is -6 dBV.\n\nLet’s skip to dBm for a second.  This has a reference of 1 milliwatt, a unit of power.  Power is related to voltage by the equation P = VV/R, where R is the resistance the power is dissipated through.  For instance, if I drive 1 Volt into 1000 Ohms of resistance, 1V1V/1000Ohms = 0.001 Watts = 1 mW.  If I increase the voltage by 6 dB (a factor of 2) to 2 Volts, now I’m dissipating 2V2V/1000Ohms = 4 mW.  This is important - doubling the voltage does not lead to a doubling of power, since the power is related to the square of the voltage.  We actually have to use a different formula for dB of power, 10log10(Power/Reference).  With this formula, if we put in our 4mW and 1mW from above, we still get 6 dB of gain.  Math works!\n\nBack to dBu.  dBu is referenced to 0.775 Volts - an odd number to use as a reference.  However, if you calculate the power dissipating by 0dBu through 600Ohms (a long-standing common value for transmission lines), you wind up with exactly 1mW of power, 0dBm.  So 0dBu = 0dBm, if and only if the load is 600 Ohms.  At any other load impedance this relationship changes.\n\nSo back to that transfer function in dBm.  In order to get a relative dB measurement I needed two things: the source voltage and the load impedance.  Knowing the load impedance allows you to calculate the voltage output from the system: V = sqrt(PR).  This is still an absolute measurement, so you need to know what the input signal was to calculate the dB out: 20log10(Output/Input)." ]

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[ "# And, Or, and Not functions in Power Apps\n\nBoolean logic functions, commonly used to manipulate the results of comparisons and tests.\n\n## Description\n\nThe And function returns true if all of its arguments are true.\n\nThe Or function returns true if any of its arguments are true.\n\nThe Not function returns true if its argument is false; it returns false if its argument is true.\n\nThese functions work the same way as they do in Excel. You can also use operators to perform these same operations, using either Visual Basic or JavaScript syntax:\n\nFunction notation Visual Basic operator notation JavaScript operator notation\nAnd( x, y ) x And y x && y\nOr( x, y ) x Or y x || y\nNot( x ) Not x ! x\n\nThese functions work with logical values. You can't pass them a number or a string directly; instead, you must make a comparison or a test. For example, this logical formula x > 1 evaluates to the Boolean value true if x is greater than 1. If x is less than 1, the formula evaluates to false.\n\n## Syntax\n\nAnd( LogicalFormula1, LogicalFormula2 [, LogicalFormula3, ... ] )\nOr( LogicalFormula1, LogicalFormula2 [, LogicalFormula3, ... ] )\nNot( LogicalFormula )\n\n• LogicalFormula(s) - Required. Logical formulas to evaluate and operate on.\n\n## Examples\n\nThe examples in this section use these global variables:\n\n• a = false\n• b = true\n• x = 10\n• y = 100\n• s = \"Hello World\"\n\nTo create these global variables in an app, insert a Button control, and set its OnSelect property to this formula:\n\n``````Set( a, false ); Set( b, true ); Set( x, 10 ); Set( y, 100 ); Set( s, \"Hello World\" )\n``````\n\nSelect the button (by clicking it while you hold down the Alt key), and then set the Text property of a Label control to a formula in the first column of the next table.\n\nFormula Description Result\nAnd( a, b ) Tests the values of a and b. One of the arguments is false, so the function returns false. false\na And b Same as the previous example, using Visual Basic notation. false\na && b Same as the previous example, using JavaScript notation. false\nOr( a, b ) Tests the values of a and b. One of the arguments is true, so the function returns true. true\na Or b Same as the previous example, using Visual Basic notation. true\na || b Same as the previous example, using JavaScript notation. true\nNot( a ) Tests the value of a. The argument is false, so the function returns the opposite result. true\nNot a Same as the previous example, using Visual Basic notation. true\n! a Same as the previous example, using JavaScript notation. true\nLen( s ) < 20 And Not IsBlank( s ) Tests whether the length of s is less than 20 and whether it isn't a blank value. The length is less than 20, and the value isn't blank. Therefore, the result is true. true\nOr( Len( s ) < 10, x < 100, y < 100 ) Tests whether the length of s is less than 10, whether x is less than 100, and whether y is less than 100. The first and third arguments are false, but the second one is true. Therefore, the function returns true. true\nNot IsBlank( s ) Tests whether s is blank, which returns false. Not returns the opposite of this result, which is true. true" ]

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[ "# Estimating Option-Implied Probability Distributions for Asset Pricing\n\nBy Ken Deeley, MathWorks\n\nForecasting the performance of an asset and quantifying the uncertainty associated with such a forecast is a difficult task: one that is frequently made more difficult by a shortage of observed market data.\n\nRecently, there has been interest from central banks in using observed option price data for creating forecasts, particularly during periods of financial uncertainty , . Call and put options on an asset are influenced by how the market believes that asset will perform in the future. This article describes a workflow in which MATLAB® is used to create a forecast for the performance of an asset, starting with relatively scarce option price data observed from the market.  The main steps in this workflow are:\n\n• Computing implied volatility from market data\n• Creating additional data points using SABR interpolation\n• Estimating implied probability densities\n• Simulating future asset prices\n• Presenting the forecast uncertainty in a fan chart\n\nThe fan chart conveys information in an accessible graphical form that enables financial professionals to communicate their forecasted projection and uncertainties to a nonspecialist audience (Figure 1).\n\n## Computing Implied Volatility from Market Data\n\nA key challenge facing analysts is gaining insight from a small amount of available market data. One technique for creating additional data points is interpolation in (K, σ)-space, where K is the strike price and σ is the asset volatility. To use this technique, we first must compute the implied volatility from the market data.\n\nWe assume, at a minimum, that we can observe strike-call price pairs (or strike-put price pairs) for a given asset, and that we also know the underlying asset price, risk-free rate, and expiry time for the option. We store this data in a MATLAB table using the following notation (Figure 2).\n\n• K – strike price (\\$)\n• C – call price (\\$)\n• P – put price (\\$)\n• T – expiry time of the option (years)\n• rf – risk-free rate (decimal number in the range [0, 1])\n• S – underlying asset price (\\$)\nFigure 2. Observed market data in a MATLAB table. This hypothetical data has six observations relating to options with a given expiry time and eight distinct expiry times, giving 48 observations in total.\n\nWhen we are interpolating in (K, σ)-space, the asset volatility, σ, is measured as a decimal number in the range [0, 1]. We begin by analyzing the call price data separately by computing the Black-Scholes implied volatilities using the Financial Toolbox™ function `blsimpv`:\n\n` D.sigmaCall = blsimpv(D.S, D.K, D.rf, D.T, D.C, [], [], [], {'call'}); `\n\nA plot of the results shows that for this data set, the highest volatilities are associated with the end points of the data corresponding to expiry time T=0.25 (Figure 3). The plot also shows that volatility increases as the strike price moves away from some central value, which appears to be close to the underlying asset price S = 100.\n\nSeveral approaches can be used to generate additional points in (K, σ)-space. Simpler methods include fitting quadratic functions to the data for each expiry time, or using the `interp1` function to construct cubic spline interpolants. We choose to use SABR interpolation to create additional data points, since this technique can often give more accurate results at the endpoints of the data set.\n\nThe SABR model is a four-parameter stochastic volatility model used by financial professionals to fit volatility smiles, named for the shape of the resulting curves. Fitting the volatility smile is a two-step process in MATLAB. First, we calibrate the SABR model using the `lsqnonlin` solver from Optimization Toolbox™. This calibration minimizes the norm of the difference between the observed data and the candidate SABR smile, resulting in a vector of optimal parameters for the SABR model. Second, we use the optimal parameters together with the Financial Instruments Toolbox™ function `blackvolbysabr` to interpolate across the required range of strike prices.\n\nThe SABR technique works well even for fitting the awkward data corresponding to the expiry time T = 0.25 (Figure 4).\n\n## Estimating Implied Probability Densities\n\nAfter interpolation in (K, σ)-space, we obtain enough data points to estimate the implied strike price density functions at each expiry time. To do this we use a computational finance principle developed by Breeden and Litzenberger , which states that the probability density function f(K) of the value of an asset at time T is proportional to the second partial derivative of the asset call price C = C(K).\n\nWe first transform the data to the original domain ((K, C)-space) for each expiry time using the `blsprice` function:\n\n```T0 = unique(D.T);\nS = D.S(1);\nrf = D.rf(1);\nfor k = 1:numel(T0)\nnewC(:, k) = blsprice(S, fineK, rf, T0(k), sigmaCallSABR(:, k));\nend\n```\n\nHere, `fineK` is a vector defining the range of strike prices used for the interpolation and `sigmaCallSABR` is the matrix created using SABR interpolation in which the columns contain the interpolated volatility smiles for each expiry time.`\n\nWe then compute the numerical partial derivatives with respect to the strike price. This can be done efficiently in MATLAB using the `diff` function.\n\n```dK = diff(sampleK);\nCdash = diff(newC) ./ repmat(dK, 1, size(newC, 2));\nCddash = diff(Cdash) ./ repmat(d2K, 1, size(Cdash, 2));\n```\n\nWe also use logical indexing to remove spurious negative values that appear as unwanted artifacts of this process. The resulting curves for each expiry time show that as the expiry time increases, the functions become less complete (Figure 5). We will need to extrapolate these functions before we can use them to estimate implied probability densities, since they do not define complete functions over the range of strike prices of interest.\n\nTo extend the definitions of these functions over the complete strike price domain we create a linear interpolant using the `fit` function from Curve-Fitting Toolbox™. It is then easy to extrapolate from this interpolant to cover the range of interest.\n\n```for k = 1:numel(T0)\npdfFitsCall{k} = fit(pdfK, approxCallPDFs(:, k), 'linear');\nend\n```\n\nHere, `pdfK` is a vector defining the required range of strike prices and `approxCallPDFs` is a matrix storing the approximations to the implied densities for each expiry time in its columns. By extrapolating and normalizing the area under each function to ensure that we have valid probability density functions, we obtain the implied densities (Figure 6). Note that the distribution modes gradually move upwards as the time to expiry increases, and there appears to be a trend towards increasing volatility over time.\n\n## Simulating Future Asset Prices\n\nNow that we have complete probability distributions for the asset prices at all future times we can randomly sample from each distribution to create a forecast matrix. We need to randomly sample (with replacement) from a given range of asset prices according to the probability distributions defined in the previous step. This simulation is straightforward to implement using the `randsample` function from Statistics and Machine Learning Toolbox™.\n\n```nSamples = 1e3;\npriceSimCall = NaN(numel(T0), nSamples);\nfor k = 1:numel(T0)\npriceSimCall(k, :) =\nrandsample(fitKCall{k}, nSamples, true, fitValsCall{k});\nend\n```\n\nThe MATLAB code above preallocates a matrix named `priceSimCall` in which each row represents a future time and each column represents a random asset price drawn from the corresponding probability distribution. The loop iterates over each future time, and each iteration creates a row of the `priceSimCall` matrix by randomly sampling from the appropriate distribution. The first input argument to `randsample` is `fitKCall{k}`, a vector that contains the asset strike prices from which to draw the random samples. The second input argument, `nSamples`, is the number of samples required, and the third (`true`) specifies that we want to sample with replacement. The fourth input argument `fitValsCall{k}` is the probability distribution used by the `randsample` function when drawing the random samples. Note that the independent computations performed in this application using sequential `for`-loops can be parallelized using the `parfor` construct. For larger data sets, parallelization allows the application to scale readily as long as multiple processing cores are available for computation.\n\n## Creating a Fan Chart\n\nFan charts are commonly used to plot the projected future evolution of a time series together with the uncertainties associated with the forecasted values. Financial Toolbox provides a `fanplot` function for creating fan charts. This function requires two inputs: the historical data and the forecast data. We define the historical data as simply a point at time T = 0 with corresponding asset price S = 100, although if we had historical data for the asset prices then we could incorporate them here.\n\n` historical = [0, S]; `\n\nThe forecast data comprises the expiry times together with the results from the simulation performed in the previous step.\n\n` forecastCall = [T0, priceSimCall]; `\n\nWe then create the fan chart with a call to the `fanplot` function.\n\n` fanplot(historical, forecastCall) `\n\nThe central line in the fan chart represents the median trajectory, and the edges of each band represent different quantiles of the forecast simulation matrix (Figure 7), with bands closest to the central line indicating the more likely outcomes. In our example, there is an upward trend in the projected asset price, and as we would expect, the forecast uncertainty increases with time.\n\n## Assumptions and Further Improvements\n\nTo improve the accuracy of the final forecast, we could incorporate more data points. We could also modify the workflow to fit probability distributions rather than using extrapolation to complete the definition of the implied density functions, although this could introduce unwanted distributional assumptions. It is a good idea to repeat the process using the put price data. Averaging the forecasts created from the call and put price data results in the fan chart shown in Figure 1. Such averaging tends to smooth out small fluctuations, and counter bias caused by working with only one type of price data.\n\nNote that the entire workflow can be automated using a MATLAB script that computes implied volatility, creates additional data points through interpolation, estimates the implied probability densities, and simulates future asset prices before generating a fan chart to show the results.\n\nPublished 2015 - 92950v00\n\n### References\n\n1. “Option-implied probability distributions for future inflation,” Smith, T., Quarterly Bulletin of the Bank of England, 2012 Q3\n2. “The Information Content of Option Prices During the Financial Crisis,” ECB Monthly Bulletin, February 2011\n3. “Managing Smile Risk”, Hagan, P. S. et al, WILMOTT Magazine\n4. “Prices of state-contingent claims implicit in options prices,” Breeden, D. T. and Litzenberger, R. H. (1978), Journal of Business, Vol. 51, pages 621–51." ]

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[ "# Tag Info\n\nAccepted\n\n### Why has statistics-based AI become more popular than other forms of AI?\n\nThe availability of large data sets. In symbolic/rule-based AI, the 'knowledge' has to be hand-coded, usually by experts. This is expensive and limited to small-scale problems only. In statistical AI/...\n\n### How much statistics is involved in AI?\n\nMany people without a formal/solid background in statistics (e.g. without knowing exactly what the central limit theorem (CLT) states) are doing research on machine learning, which is a very big and ...\nAccepted\n\n### Why is Standard Deviation based on L2 Variance and not L1 Variance\n\nI've found the answer, the L2 is Standard Deviation, and the L1 is Mean Deviation. Standard deviation describes the variation better and the values are always different on different sets of X while ...\nAccepted\n\n### What does it mean when a model \"statistically outperforms\" another?\n\nMost model-fitting is stochastic, so you get different parameters every time you train, and you usually can't say that one algorithm will always give you a better-performing model. However, since you ...\n\n### What is the difference between model and data distributions?\n\nYes. In Machine Learning we consider that the samples in your training set are sampled from an underlying distribution called the data generating distribution. Generative models classify the samples ...\nAccepted\n\n### How does $\\mathbb{E}$ suddenly change to $\\mathbb{E}_{\\pi'}$ in this equation?\n\nAlso, in general, in the conditional expectation, which distribution do we compute the expectation with respect to? From what I have seen, in $\\mathbb{E}[X|Y]$, we always calculate the expected value ...\n\n### What is Bayes' theorem?\n\nBayes' theorem relates conditional probabilities: $$P(A \\mid B) = \\frac{P(B \\mid A) P(A)}{P(B)}$$\n\n### How much statistics is involved in AI?\n\nI work in NLP, and use very little statistics. Actually, almost nothing I do can be classed as 'serious' statistics. So yes, AI is a wide area, and in my company there is a group that does machine ...\nAccepted\n\n### Research paths/areas for improving the performance of CNNs when faced with limited data\n\nSome research areas that come to mind which can be useful when faced with a limited amount of data: Regularization: Comprises different methods to prevent the network from overfitting, to make it ...\nAccepted\n\n### Which generalization of standard deviation to use for multidimensional input normalization\n\nThis idea is sometimes applied in computer vision, under the name of Whitening Transform, or ZCA sphering transform. The name whitening comes from signal processing, since removing correlation from a ...\n\n### Coherence is classifying time series data\n\nThe following paper from Amazon Alexa Research refers to this topic as keyword spotting (KWS), and more specifically, to wake up words as wake word (WW) spotting. Jose, C., Mishchenko, Y., Senechal, ...\n1 vote\n\n### What is wrong in reasoning here in classification for defect detection?\n\nAlpha represents the significance level, or the probability that you will make a Type I error by rejecting the null hypothesis when it is actually true - in other words, the probability that you're ...\n1 vote\nAccepted\n\n### Markov's Decision Process - calculate value in each iteration\n\nThe value iteration algorithm defines the following update rule (reference is slide 11 in this MIT course): $$V_{i+1}(s) = \\max_{a}\\{R(s,a) + \\gamma E_{s'\\sim T(.|s,a)} V_i(s')\\}$$ for all states $s$, ...\n1 vote\n\n### What can be an example other than batch normalization that uses statistics of batches?\n\nHere's some examples: Group Normalization Layer Normalization Switchable Normalization Attentive Normalization Spectrl Normalization Notice how in general different normalization techniques are ...\n1 vote\n\n### What is the definition of \"confidence interval\" around a (complicated) function?\n\nOff the top of my head, I don't know the very specific definition of confidence interval (or whether it's only defined for the parameters of a model), as I am not a statistician. In any case, ...\n1 vote\nAccepted\n\n### What would be the reason behind using plots (such as box-plots or histograms) for ML development?\n\nAt a basic level, these kinds of low-dimensional plots where you look at one or two variables at a time can help to give you a sense of what types of relationships you might expect to see, such as ...\n1 vote\n\n### Can AI be understood as a generalized statistics tool?\n\nMy understanding is that AI can be understood as a very generalized and abstract statistics software package handling input data in a general way to find the \"best fit\" to some form of ...\n1 vote\nAccepted\n\n### Why is probability that at least one hypothesis out of $k$ being consistent with $m$ training examples $k(1- \\epsilon)^m$?\n\nLet $A$ and $B$ be two events. In general, the probability that either $A$ or $B$ occurs is defined as $$P(A \\text{ or } B) = P(A) + P(B) - P(A \\text{ and } B)$$ If $A$ and $B$ are disjoint, i.e. ...\n\nOnly top scored, non community-wiki answers of a minimum length are eligible" ]

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[ "# Homework 6: Ax=b\n\n1. Solve the following linear system using Gaussian elimination. Show your work.", null, "$\\begin{pmatrix} 4 & 2 & 0 \\\\ 0 & 2 & 1 \\\\ 1 & 0 & 1 \\end{pmatrix} \\begin{pmatrix} x_1 \\\\ x_2 \\\\ x_3 \\end{pmatrix} = \\begin{pmatrix} 1 \\\\ 2 \\\\ 0 \\end{pmatrix}$\n\n2. Solve the same system", null, "$\\mod 3$. Show your work.\n3. Given an efficient subroutine that takes integer", null, "$A,b$ as input and finds a rational", null, "$x$ such that", null, "$Ax=b$, give a simple, efficient algorithm to find a solution to", null, "$Ax=b \\mod p$ for any prime", null, "$p$ that does not divide", null, "$\\det(A)$." ]

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[ "# Answers\n\nSolutions by everydaycalculation.com\n\n## Multiply 9/30 with 30/10\n\n1st number: 9/30, 2nd number: 3 0/10\n\nThis multiplication involving fractions can also be rephrased as \"What is 9/30 of 3 0/10?\"\n\n9/30 × 30/10 is 9/10.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 9/30 × 30/10 = 9 × 30/30 × 10 = 270/300\n3. After reducing the fraction, the answer is 9/10\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:\nAndroid and iPhone/ iPad\n\n#### Multiply Fractions Calculator\n\n×\n\n© everydaycalculation.com" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "Popular numerical techniques for solving the Boltzmann transport equation (BTE) for sub-micron thermal conduction include the discrete ordinates method and the finite volume method. However, the finite wave speed associated with the BTE can cause large errors in the prediction of the equivalent temperature unless fine angular discretizations are used, particularly at low acoustic thicknesses. In this paper, we combine a ray-tracing technique with the finite volume method to substantially improve the predictive accuracy of the finite volume method. The phonon intensity is decomposed into ballistic and in-scattering components. The former is solved using a ray tracing scheme, accounting for finite wave speed; the latter is solved using an unstructured finite volume method. Comparisons between this new technique and traditional finite volume formulations are presented for a range of acoustic thicknesses, and substantial improvement is demonstrated.\n\n1.\nMajumdar\n,\nA.\n,\n1993\n, “\nMicroscale Heat Conduction in Dielectric Thin Films\n,”\nASME J. Heat Transfer\n,\n115\n, pp.\n7\n16\n.\n2.\nJoshi\n,\nA.\n, and\nMajumdar\n,\nA.\n,\n1993\n, “\nTransient Ballistic and Diffusive Phonon Heat Transport in Thin Films\n,”\nJ. Appl. Phys.\n,\n74\n, pp.\n31\n39\n.\n3.\nKumar\n,\nS.\n,\nMajumdar\n,\nA.\n, and\nTien\n,\nC.\n,\n1990\n, “\nThe Differential Discrete-Ordinates Method for Solutions of the Equation of Radiative Transfer\n,”\nASME J. Heat Transfer\n,\n112\n, pp.\n424\n429\n.\n4.\nModest, M. F., 1993, Radiative Heat Transfer, Series in Mechanical Engineering, McGraw Hill, New York, NY.\n5.\nSverdrup, P., Banerjee, K., Dai, K., Shih, W., Dutton, R., and Goodson, K., 2000, “Sub-Contiuum Simulations of Deep Sub-Micron Devices under ESD Conditions,” Proceedings of the International Conference on Simulation of Semiconductor Processes and Devices, IEEE, Piscataway, NJ., pp. 54–57.\n6.\nNarumanchi, S. V. J., Murthy, J. Y., and Amon, C. H., 2003, “Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction,” ASME Journal of Heat Transfer, to appear.\n7.\nChai\n,\nJ.\n,\nLee\n,\nH.\n, and\nPatankar\n,\nS.\n,\n1993\n, “\nRay Effects and False Scattering in the Discrete Ordinates Method\n,”\nNumer. Heat Transfer, Part B\n,\n24\n, pp.\n373\n389\n.\n8.\nCoelho\n,\nP.\n,\n2002\n, “\nThe Role of Ray Effects and False Scattering on the Accuracy of the Standard and Modified Discrete Ordinates Methods\n,”\n,\n73\n, pp.\n231\n238\n.\n9.\nLaney, C., 1998, Computational Gas Dynamics, Cambridge University Press, Cambridge, U.K.\n10.\nMurthy\n,\nJ. Y.\n, and\nMathur\n,\nS. R.\n,\n2002\n, “\nComputation of Sub-Micron Thermal Transport Using an Unstructured Finite Volume Method\n,”\nASME Journal of Heat Transfer\n,\n124\n(\n6\n), pp.\n1176\n1181\n.\n11.\nRamankutty\n,\nM.\n, and\nCrosbie\n,\nA.\n,\n1997\n, “\nModified Discrete Ordinates Solution of Radiative Transfer in Two-Dimensional Rectangular Enclosures\n,”\n,\n57\n(\n1\n), pp.\n107\n140\n.\n12.\nSakami\n,\nM.\n, and\nCharette\n,\nA.\n,\n2000\n, “\nApplication of a Modified Discrete Ordinates Method to Two-Dimensional Enclosures of Irregular Geometry\n,”\n,\n64\n, pp.\n275\n298\n.\n13.\nSakami\n,\nM.\n,\nKasmi\n,\nA. E.\n, and\nCharette\n,\nA.\n,\n2001\n, “\nAnalysis of Radiative Heat Transfer in Complex Two-Dimensional Enclosures with Obstacles Using Modified Discrete Ordinates Method\n,”\nASME J. Heat Transfer\n,\n123\n, pp.\n892\n900\n.\n14.\nOlfe\n,\nD.\n,\n1970\n, “\nRadiative Equilibrium of a Gray Medium Bounded by Non-Isothermal Walls\n,”\nProg. Astronaut. Aeronaut.\n,\n23\n, pp.\n295\n317\n.\n15.\nModest\n,\nM.\n,\n1989\n, “\nThe Modified Differential Approximation for Radiative Transfer in General Three Dimensional Media\n,”\nJ. Thermophys. Heat Transfer\n,\n3\n(\n3\n), pp.\n283\n288\n.\n16.\nChen\n,\nG.\n,\n2001\n, “\nBallistic-Diffusive Heat Conduction Equations\n,”\nPhys. Rev. Lett.\n,\n86\n(\n11\n), pp.\n2297\n2300\n.\n17.\nSverdrup\n,\nP.\n,\nJu\n,\nY.\n, and\nGoodson\n,\nK.\n,\n1998\n, “\nSub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Devices\n,”\nASME J. Heat Transfer\n,\n120\n, pp.\n30\n36\n.\n18.\nMurthy\n,\nJ.\n, and\nMathur\n,\nS.\n,\n1998\n, “\nFinite Volume Method for Radiative Heat Transfer Using Unstructured Meshes\n,”\nJ. Thermophys. Heat Transfer\n,\n12\n(\n3\n), pp.\n313\n321\n.\n19.\nLeonard\n,\nB.\n,\n1979\n, “\nA Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation\n,”\nComput. Methods Appl. Mech. Eng.\n,\n19\n, pp.\n59\n98\n." ]

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[ "", null, "NTE1231A डेटा पत्रक PDF( Datasheet डाउनलोड )\n\nडेटा पत्रक - Integrated Circuit Complete 4 Watt TV Sound Channel - NTE\n\n भाग संख्या NTE1231A समारोह Integrated Circuit Complete 4 Watt TV Sound Channel मैन्युफैक्चरर्स NTE लोगो", null, "पूर्व दर्शन 1 Page", null, "", null, "Electrical Characteristics: (TA = +25°C, fo = 4.5MHz, fm = 400Hz, fd = ±7.5kHz, VCC = 12V, RL = 8Ω, Vin = 1mV unless otherwise specified) Parameter Symbol Test Conditions Min Typ Max Unit Quiesecnt Output Voltage Quiescent Supply Current Input Limiting Threshold AM Rejection Signal–to–Noise Ratio Recovered Audio Output Distortion Output Power Power Supply Rejection Input Resistance Input Capacitance VOUT Vin = 0 5.1 6.0 6.9 V ICC RX = 22kΩ, Vin = 0 – 19 33 mA VTH RX = 0 – 40 100 µV AMR fd = ±25kHz, m = 0.3 40 55 – dB S + N/N POUT = 0.5W, fd = ±25kHz 50 65 – dB Vout RX = 0 – 120 – mV THD POUT = 50mW – 1.0 – % POUT THD = 2%, fd = ±25kHz – 1.4 – W THD = 10%, fd = ±25kHz – 1.5 – W PSR f = 120Hz, RX = 22kΩ, RL = 4Ω – 46 – dB Rin – 30 – kΩ Cin – 5 – pF Electrical Characteristics: (TA = +25°C, fo = 4.5MHz, fm = 400Hz, fd = ±7.5kHz, VCC = 24V, RL = 16Ω, Vin = 1mV unless otherwise specified) Parameter Symbol Test Conditions Min Typ Max Unit Quiesecnt Output Voltage Quiescent Supply Current Input Limiting Threshold AM Rejection Signal–to–Noise Ratio Recovered Audio Output Distortion Output Power Power Supply Rejection Input Resistance Input Capacitance VOUT Vin = 0 11 12 13 V ICC RX = 22kΩ, Vin = 0 11 22 35 mA VTH RX = 0 – 40 100 µV AMR fd = ±25kHz, m = 0.3 40 55 – dB S + N/N POUT = 1W, fd = ±25kHz 50 65 – dB Vout RX = 0 – 120 – mV THD POUT = 50mW – 0.75 – % POUT THD = 2%, fd = ±25kHz – 3.5 – W THD = 10%, fd = ±25kHz – 4.2 – W PSR f = 120Hz, RX = 22kΩ, RL = 4Ω – 46 – dB Rin – 30 – kΩ Cin – 5 – pF विन्यास 3 पेज डाउनलोड [ NTE1231A Datasheet.PDF ]\n\nअनुशंसा डेटापत्रक\n\n भाग संख्या विवरण विनिर्माण NTE1231 Integrated Circuit Complete 4 Watt TV Sound Channel", null, "NTE NTE1231A Integrated Circuit Complete 4 Watt TV Sound Channel", null, "NTE\n\n भाग संख्या विवरण विनिर्माण 30L120CT Schottky Rectifier", null, "PFC Device AT28C010-12DK Space 1-MBit (128K x 8) Paged Parallel EEPROM", null, "ATMEL B20NM50FD N-CHANNEL POWER MOSFET", null, "STMicroelectronics D844 2SD844", null, "SavantIC FAE391-A20 AM/FM Automotive Electronic Tuner", null, "Mitsumi" ]

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[ "1\nNEET 2018\n+4\n-1\nMatch the items given in column I with those in column II and select the correct option given below.\n\nColumn I Column II\nA. Glycosuria (i) Accumulation of uric\nacid in joints\nB. Gout (ii) Mass of crystallised\nsalts within the kidney\nC. Renal calculi (iii) Inflammation in\nglomeruli\nD. Glomerular nephritis (iv) Presence of glucose in urine\nA\nA $$\\to$$ (iv), B $$\\to$$ (i), C $$\\to$$ (ii), D $$\\to$$ (iii)\nB\nA $$\\to$$ (ii), B $$\\to$$ (iii), C $$\\to$$ (i), D $$\\to$$ (iv)\nC\nA $$\\to$$ (iii), B $$\\to$$ (ii), C $$\\to$$ (iv), D $$\\to$$ (i)\nD\nA $$\\to$$ (i), B $$\\to$$ (ii), C $$\\to$$ (iii), D $$\\to$$ (iv)\n2\nNEET 2018\n+4\n-1\nWhich of the following options correctly represents the lung conditions in asthma and emphysema, respectively?\nA\nDecreased respiratory surface; Inflammation of bronchioles\nB\nInflammation of bronchioles; Decreased respiratory surface\nC\nIncreased number of bronchioles; Increased respiratory surface\nD\nIncreased respiratory surface; Inflammation of bronchioles\n3\nNEET 2018\n+4\n-1\nWhich of the following is an occupational respiratory disorder?\nA\nBotulism\nB\nAnthracis\nC\nSilicosis\nD\nEmphysema\n4\nNEET 2018\n+4\n-1\nWhich of these statements is incorrect?\nA\nGlycolysis operates as long as it is supplied with NAD that can pick up hydrogen atoms.\nB\nEnzymes of TCA cycle are present in mitochondrial matrix.\nC\nOxidative phosphorylation takes place in outer mitochondrial membrane.\nD\nGlycolysis occurs in cytosol.\nNEET Papers\n2023\n2022\n2021\n2020\n2019\n2018\n2017\n2016\n2015\n2014\n2013\n2012\n2011\n2010\n2009\n2008\n2007\n2006\n2005\n2004\n2003\n2002\n2001\n2000\nEXAM MAP\nJoint Entrance Examination" ]

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[ "cancel\nShowing results for\nShow  only  | Search instead for\nDid you mean:", null, "", null, "Contributor\n1,265 Views\nRegistered: ‎05-10-2018\n\n## How to print Stream data out ?\n\nI am a new one to using the vivado HLS. I want to figure out the process of data transfer between PL and PS memory. I refer to an example on GitHub(https://github.com/lbielich/PLDataMoveSDSoC), but it only has printing process of memory address. I just want to use the assignment data to verify this process. I added the print function of the data value to this case, but when I print the output data(the value of “sofifo”), the output stream data are all zero. Replace the statement printf(\"sofifo = %llx \\r\\n\", (long long) sofifo) with std::cout << \" sofifo = \" << sofifo << std::endl, the output value is still zero. I want to get the data value which are stored on the sofifo pointer. How can I get the correct value for printout this program? Thank you!!\n\n#include <iostream>\n\n#include <sds_lib.h>\n\n#include <stdio.h>\n\n#include <unistd.h>\n\n#include <queue>\n\n#include <fstream>\n\n#include <unistd.h>\n\n#include <stdint.h>\n\nusing namespace std;\n\n#define BUF_SIZE (1024*8)\n\nvoid stream_dma_pl( ap_uint<64> *din, ap_uint<64> *doutmig, int num_elements)\n\n{\n\nfor(int i = 0; i < num_elements; i++)\n\n{\n\n#pragma HLS pipeline\n\ndoutmig[i] = din[i];\n\n}\n\n}\n\nvoid dma_pl_to_ps(ap_uint<128> *src, ap_uint<128> *dest, unsigned int length)\n\n{\n\nfor(int i = 0; i < length; i++)\n\n{\n\n#pragma HLS pipeline\n\n*dest++ = *src++;\n\n}\n\n}\n\nvoid psddr_2_stream( ap_uint<64> *din, ap_uint<64> *dout, int num_elements)\n\n{\n\nfor(int i = 0; i < num_elements; i++)\n\n{\n\n#pragma HLS pipeline\n\ndout[i] = din[i];\n\n}\n\n}\n\nint main(int argc, char **argv)\n\n{\n\n//PL Buffers\n\nunsigned long long* plddr_buf = (unsigned long long*)sds_mmap((void *)(PL_DDR_ADDR ), BUF_SIZE, NULL);\n\n//Input Stream Sources\n\nap_uint<64> *fifo = (ap_uint<64> *)sds_alloc(BUF_SIZE);\n\n//Output Stream Sink\n\nap_uint<64> *sofifo = (ap_uint<64> *)sds_alloc(BUF_SIZE);\n\n//PS Contiguous Buffers\n\nap_uint<128> * psddr_buf3 = (ap_uint<128> *)sds_alloc(BUF_SIZE);\n\nfor(unsigned i = 0; i < 32; i++) //Initial input Stream Sources\n\n{\n\nfifo[i] = i;\n\n}\n\nstream_dma_pl( fifo, (ap_uint<64> *)plddr_buf, BUF_SIZE/8);\n\nstd::cout << \" fifo = \" << fifo << std::endl;\n\nstd::cout << \" fifo = \" << fifo << std::endl;\n\nstd::cout << \" fifo = \" << fifo << std::endl;\n\nprintf(\"plddr_buf = %llx \\r\\n\", plddr_buf);\n\nprintf(\"plddr_buf = %llx \\r\\n\", plddr_buf);\n\nprintf(\"plddr_buf = %llx \\r\\n\", plddr_buf);\n\ndma_pl_to_ps((ap_uint<128> *)plddr_buf, (ap_uint<128> *)psddr_buf3, BUF_SIZE/16);\n\n//Creates an output stream from received input\n\npsddr_2_stream((ap_uint<64> *)psddr_buf3, sofifo, BUF_SIZE/8);\n\nprintf(\"psddr_buf3 = %llx \\r\\n\", (long long) psddr_buf3);\n\nprintf(\"psddr_buf3 = %llx \\r\\n\", (long long) (psddr_buf3>>64));\n\nprintf(\"sofifo = %llx \\r\\n\", (long long) sofifo);\n\nprintf(\"sofifo = %llx \\r\\n\", (long long) sofifo);\n\n}\n\nThe result is:\n\nfifo = 0\n\nfifo = 1\n\nfifo = 2\n\nplddr_buf = 5ccb2f07a\n\nplddr_buf = 5ccb2f07b\n\nplddr_buf = 5ccb2f07c\n\npsddr_buf3 = 5ccb2f07a\n\npsddr_buf3 = 5ccb2f07b\n\nsofifo = 0\n\nsofifo = 0\n\n2 Replies", null, "", null, "Xilinx Employee\n1,238 Views\nRegistered: ‎09-05-2018\n\nHey @sharpmddr,\n\nCould you try using the ap_uint class's member function to_uint64()? Example:\n\n` std::cout << \" sofifo = \" << sofifo.to_uint64() << std::endl`\n\nPlease let me know if that helps.\n\nNicholas Moellers", null, "", null, "" ]

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[ "# arrayfactor\n\nArray factor of sensor arrays\n\nSince R2022a\n\n## Syntax\n\n``af = arrayfactor(pos,ang)``\n``af = arrayfactor(pos,ang,wts)``\n\n## Description\n\nexample\n\n````af = arrayfactor(pos,ang)` returns the array factor `af` for an array of elements located at positions `pos` and arrival directions `ang`. See Element and Array Radiation and Response Patterns for a discussion of array factors and array responses.```\n\nexample\n\n````af = arrayfactor(pos,ang,wts)` also specifies array steering weights `wts`.```\n\n## Examples\n\ncollapse all\n\nCompute the array factor for an unsteered 8-element ULA operating at 100 MHz. Elements are placed 0.4 wavelengths apart.\n\n```freq = 100e6; c = physconst('LightSpeed'); lam = c/freq; pos = (0:7)*0.4; ang = -90:90; af = arrayfactor(pos,ang); plot(ang,mag2db(abs(af.'))) xlabel('Angle (deg)') ylabel('Array pattern (dB)') ylim([-30 20]) title('Array Factor of Unsteered Uniform Linear Array')```", null, "Display the array beam patterns for an 8-element ULA with half-wavelength spacing. Steer the array to -30, 0, and 30 degrees.\n\nSet the positions of the ULA elements.\n\n`pos = (0:7)*0.5;`\n\nDefine the steering direction weights.\n\n```angsteer = [-30 0 30]; wsteer = steervec(pos,angsteer);```\n\nCompute the array factors for each steering direction for all angles.\n\n```ang = -90:90; af = arrayfactor(pos,ang,wsteer);```\n\nPlot the array factor for each steering direction.\n\n```plot(ang,mag2db(abs(af.'))) xlabel('Angle (deg)') ylabel('Beam pattern (dB)') ylim([-50 20]) legend('Steer to -30 deg','Steer to 0 deg','Steer to 30 deg')```", null, "## Input Arguments\n\ncollapse all\n\nPositions of the elements of a sensor array, specified as a 1-by-N vector, a 2-by-N matrix, or a 3-by-N matrix. In this vector or matrix, N represents the number of elements of the array. Each column of `pos` represents the coordinates of an element. If `pos` is a 1-by-N vector, then it represents the y-coordinate of the sensor elements of a line array. The x and z-coordinates are assumed to be zero. When `pos` is a 2-by-N matrix, it represents the (y,z)-coordinates of the sensor elements of a planar array. This array is assumed to lie in the yz-plane. The x-coordinates are assumed to be zero. When `pos` is a 3-by-N matrix, then the array can have an arbitrary shape. Sensor positions are in terms of signal wavelength.\n\nExample: `[0,0,0; 0.1,0.4,0.3; 1,1,1]`\n\nData Types: `double`\n\nArrival directions of incoming signals specified as a 1-by-M vector or a 2-by-M matrix, where M is the number of incoming signals. If `ang` is a 2-by-M matrix, each column specifies the direction in azimuth and elevation of the incoming signal `[az;el]`. The azimuth angle must lie between –180° and 180° and the elevation angle must lie between –90° and 90°. The azimuth angle is the angle between the x-axis and the projection of the arrival direction vector onto the xy plane. It is positive when measured from the x-axis toward the y-axis. The elevation angle is the angle between the arrival direction vector and xy-plane. It is positive when measured towards the z axis. If `ang` is a 1-by-M vector, then it represents a set of azimuth angles with the elevation angles assumed to be zero. Angle units are specified in degrees.\n\nExample: [45;0]\n\nData Types: `double`\n\nArray weights, specified as a complex-valued N-by-1 vector or complex-valued N-by-L matrix. Each column of `wts` corresponds to a different set of weights for the array. L is the number of weight sets.\n\nData Types: `double`\nComplex Number Support: Yes\n\n## Output Arguments\n\ncollapse all\n\nArray factor of sensor array, returned as a 1-by-M complex-valued vector or L-by-M complex-valued matrix. Each column contains the array factor for a different set of weights `wts`. Each row corresponds to one of the angles specified in `ang`.\n\n Van Trees, Harry L. Detection, Estimation, and Modulation Theory. 4: Optimum Array Processing. Wiley, 2002.\n\n Johnson, Don H. and D. Dudgeon. Array Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1993.\n\n Van Veen, B.D. and K. M. Buckley. “Beamforming: A versatile approach to spatial filtering”" ]

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[ "Let $\\Delta$ be a set of propositional formulas.\nThen $\\Delta$ is contradictory if there exists some propositional formula $P$ such that $P \\in \\Delta$ and $\\neg P \\in \\Delta$." ]

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[ "# How to Calculate Percentiles in SPSS\n\nThis quick tutorial will show you how to calculate percentiles in SPSS using the default HAVERAGE method.\n\n### Quick Steps\n\n1. Click on Analyze -> Descriptive Statistics -> Frequencies\n2. Drag and drop the variable for which you wish to calculate the percentile(s) into the box on the right\n3. Click the Statistics button\n4. Select the Percentile(s) option, type the percentile value into its textbox, and then click the Add button\n5. Repeat for all the percentiles you want to calculate\n6. Click Continue, and then OK\n7. Percentile values will appear in the SPSS output viewer\n\n## The Data\n\nA percentile is the value in a data distribution below which a given percentage of values falls. For example, the 25th percentile (also known as the first quartile) is the value below which 25% of the values fall.", null, "We’re going to calculate the 25th and 83rd percentiles for the Frisbee Throwing Distance in Metres variable (as shown in the SPSS data view above).\n\n## Calculate Percentiles\n\nThere are a number of different ways to calculate percentiles in SPSS, and also a number of different formulae. We’re going to use the Frequencies option, which calculates percentiles using a weighted average formula.\n\nTo begin the calculation, click on Analyze -> Descriptive Statistics -> Frequencies.", null, "This will bring up the Frequencies dialog box. You need to get the variable for which you wish to calculate the percentile(s) into the box on the right. You can drag and drop, or use the arrow button, as shown below.", null, "Once you’ve got your variable into the right column, hit the Statistics button. The Frequencies: Statistics dialog will pop up. As you can see this allows you to choose from a variety of measures.", null, "To add a percentile of your choice, select the Percentile(s) option, type the percentile value into the textbox (where we’ve got 83), and then click the Add button. You can repeat this process if you want SPSS to calculate additional percentiles.\n\nYou’ll see above that we’ve also selected Quartiles (which will generate the 25th, 50th and 75th percentiles), and the Mean and Median. Once you’ve made your selection, click the Continue button, and then click OK in the Frequencies dialog to prompt SPSS to do the calculations.\n\n## The Result\n\nThe result will appear in the SPSS output view. It will look a bit like this.", null, "As you can see, it’s pretty self-explanatory. The percentile values appear in the Statistics table. The value for the 25th percentile is 30.97 and the value of the 83rd percentile is 70.65. You’ll notice that SPSS has also calculated values for the Mean and Median, as we requested.\n\n***************\n\nThat’s really all there is to it. You should now be able to calculate percentiles using the Frequencies option in SPSS." ]

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[ "This library allows to approximate Hermitian (dense and sparse) matrices by positive definite matrices. Furthermore it allows to decompose (factorize) positive definite matrices and solve associated systems of linear equations.\n\n## Project description\n\nThis is matrix-decomposition, a library to approximate Hermitian (dense and sparse) matrices by positive definite matrices. Furthermore it allows to decompose (factorize) positive definite matrices and solve associated systems of linear equations.\n\n## Project details\n\nThis version", null, "1.2", null, "1.1", null, "1.0", null, "0.8", null, "0.7\n\nUploaded `source`\nUploaded `py3`" ]

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[ "Recent zbMATH articles in MSC 14P https://zbmath.org/atom/cc/14P 2023-01-20T17:58:23.823708Z Werkzeug On the Reeb spaces of definable maps https://zbmath.org/1500.03014 2023-01-20T17:58:23.823708Z \"Basu, Saugata\" https://zbmath.org/authors/?q=ai:basu.saugata \"Cox, Nathanael\" https://zbmath.org/authors/?q=ai:cox.nathanael \"Percival, Sarah\" https://zbmath.org/authors/?q=ai:percival.sarah This paper studies the Reeb space of a continuous map $$f:X \\to Y$$ definable in an o-minimal expansion of an ordered real closed field. The Reeb space of $$f$$ denoted by $$\\operatorname{Reeb}(f)$$ is the topological space $$X/\\sim$$ equipped with the quotient topology, where the equivalence relation $$\\sim$$ is defined so that $$x \\sim x'$$ if and only if $$f(x)=f(x')$$ and both $$x$$ and $$x'$$ are contained in the same definably connected component of $$f^{-1}(f(x))$$. The first contribution of this paper is the assertion that the Reeb space of $$f$$ exists as a definably proper quotient of $$X$$ when $$X$$ is closed and bounded in its ambient space. Its proof is constructive, but its known complexity is at least doubly exponential. This paper does not provide a singly exponential algorithm for constructing the Reeb space, but alternatively gives the upper bounds of the sum of its Betti numbers $$b(\\operatorname{Reeb}(f))$$ of the Reeb space. The paper firstly introduces the negative result that $$b(\\operatorname{Reeb}(f_n))$$ is arbitrarily larger than $$b(X_n)$$ for some sequences of maps $$( f _n: X _n \\to Y_n)_{n>0}$$. Its second result is a positive one. It gives a singly exponential upper bound on the sum of the Betti numbers of the Reeb space of a proper semi-algebraic map in terms of the number and degrees of the polynomials defining the map. Reviewer: Fujita Masato (Kure) Principal kinematic formulas for germs of closed definable sets https://zbmath.org/1500.53084 2023-01-20T17:58:23.823708Z \"Dutertre, Nicolas\" https://zbmath.org/authors/?q=ai:dutertre.nicolas The author proves two principal kinematic formulas for germs of closed definable sets in $$\\mathbb{R}^n$$, that generalize the Cauchy-Crofton formula for the density due to Comte and the infinitesimal linear kinematic formula. The paper is very clear, well written, and quite interesting. Reviewer: Euripedes Carvalho da Silva (Maracanaú)" ]

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[ "UP\n\n# SYMBOL PROPERTY SYNTAX\n\n### GENERAL RULES\n\nFor symbols a global property string (to show it press 'q' when nothing is selected). defines at least 3 attributes:\n\n• type defines the the type of symbol. Normally the type attribute describes the symbol and ignored by XSCHEM, but there are some special types:\n• subcircuit: the symbol has an underlining schematic representation, when producing the netlist XSCHEM has to descend into the corresponding schematic. This will be covered in the subcircuits chapter.\n• primitive: the symbol has a schematic representation but the netlister will not use it. This is very useful if you want to netlist a symbol using only the format (or vhdl_format or verilog_format depending on the netlist type) attribute or use the underlying schematic. By setting the attribute back to subcircuit you can quickly change the behavior.\n• label: the symbol is used to label a net. These type of symbols must have one and only one pin, and the template string must define a lab attribute that is passed from component instantiation\n• netlist_commands: the symbol is used to place SPICE commands into a spice netlist. It should also have a value attribute that may contain arbitrary text that is copied verbatim into the netlist. More on this in the netlist slide.\n•", null, "Only symbols of type subcircuit or primitive may be descended into with the 'e' bindkey if they have a schematic view.\n\n• format:The format attribute defines the syntax for the SPICE netlist. the @ character is a 'substitution character', it means that the token that follows is a parameter that will be substituted with the value passed at component instantiation. If no value is given there a value will be picked from the attribute declared in the template string.\nThe @pinlist is a special token that will be substituted with the name of the wires that connect to symbol pins, in the order they are created in the symbol. See the pin ordering section in the xschem properties slide. if the order of pins for a NMOS symbol is for example, d,g,s,b, then @pinlist will be expanded when producing a netlist to the list of nets that connect to the symbol drain, gate, source, body respectively. There is also a special way to define single pins: @@d for example will be replaced by XSCHEM with the net that connects to the d pin of the symbol. so for example @pinlist is equivalent to @@d @@g @@s @@b. However using @pinlist and setting the correct pin ordering in the symbol pins will make netlist generation faster. This is important for very big components with lot of pins, and @pinlist is the default when symbol is generated automatically (Symbol ->Make symbol menu of <Shift>A key).\n• template: Specifies default values for symbol parameters", null, "The order these attributes appear in the property string is not important, they can be on the same line or on different lines:\n\n```type=nmos format=\"@name @pinlist @model w=@w l=@l m=@m\" template=\"name=m1 model=nmos w=5u l=0.18u m=1\"\n```\n\n```format=\"@name @pinlist @model w=@w l=@l m=@m\"\ntemplate=\"name=m1 model=nmos w=5u l=0.18u m=1\"\ntype=nmos\n```\n\nAs you see double quotes are used when attribute values have spaces. For this reason if double quotes are needed in an attribute value they must be escaped with backslash \\\"\n\nsince the symbol global property string is formatted as a space separated list of attribute=value items, if a value has spaces in it it must be enclosed in double quotes, see for example the symbol template attribute: template=\"name=m1 model=nmos w=5u l=0.18u m=1\" or the the format attribute: format=\"@name @pinlist @model w=@w l=@l m=@m\". As a direct consequence a literal double quote in property strings must be escaped (\\\")\n\n### ATTRIBUTE SUBSTITUTION\n\nXSCHEM uses a method for attribute substitution that is very similar to shell variable expansion done with the \\$ character (for example \\$HOME --> /home/user) The only difference is that XSCHEM uses the '@' character. The choice of '@' vs '\\$' is simply because in some simulation netlists shell variables are passed to the simulator for expansion, so to avoid the need to escape the '\\$' in property strings a different and less used character was chosen.\nA literal @ must be escaped to prevent it to be interpreted as the start of a token to be substituted (\\@). Attribute substitution takes place in symbol format attribute and in every text, as shown in below picture.", null, "### OTHER PREDEFINED SYMBOL ATTRIBUTES\n\n• vhdl_ignore\n• spice_ignore\n• verilog_ignore\n• These 3 attributes tell XSCHEM to ignore completely the symbol in the respective netlist formats.\n\n• vhdl_stop\n• spice_stop\n• verilog_stop\n• These 3 attributes will avoid XSCHEM to descend into the schematic representation of the symbol (if there is one) when building the respective netlist format. For example, if an analog block has a schematic (.sch) file describing the circuit that is meaningless when doing a VHDL netlist, we can use a vhdl_stop=true attribute to avoid descending into the schematic. Only the global property of the schematic will be netlisted. This allows to insert some behavioral VHDL code in the global schematic property that describes the block in a way the VHDL simulator can understand.\n\n• place\n• this attribute is only useable in netlist_commands type symbols (netlist.sym, code.sym,...) if set to end it tells XSCHEM that the component instance of that symbol must be netlisted at the end, after all the other elements. This is sometimes needed for SPICE commands that must ge given at the end of the netlist. This will be explained more in detail in the netlisting slide.\n\n• generic_type\n• generic_type defines the type of parameters passed to VHDL components. Consider the following MOS symbol definition; the model attribute is declared as string and it will be quoted in VHDL netlists.", null, "the resulting netlist is shown here, note that without the generic_type attribute the irf5305 string would not be quoted.\n\n```entity test2 is\nend test2 ;\n\narchitecture arch_test2 of test2 is\nsignal d : std_logic ;\nsignal s : std_logic ;\nsignal g : std_logic ;\nbegin\nx3 : pmos3\ngeneric map (\nmodel => \"irf5305\"\n)\nport map (\nd => d ,\ng => g ,\ns => s\n);\n\nend arch_test2 ;\n```\n\n• extra\n• This property specifies that some parameters defined in the format string are to be considered as additional pins. This allows to realize inherited connections, a kind of hidden pins with connections passed as parameters. Example of a symbol definition for the following cmos gate:", null, "the symbol property list defines 2 extra pins , VCCPIN and VSSPIN that can be assigned to at component instantiation. The extra property tells XSCHEM that these 2 parameters are connection pins and not parameters and thus must not be declared as parameters in the .subckt line in a spice netlist:\n\n```type=subcircuit\nvhdl_stop=true\nformat=\"@name @pinlist @VCCPIN @VSSPIN @symname wn=@wn ln=@ln wp=@wp lp=@lp m=@m\"\ntemplate=\"name=x1 m=1\n+ wn=30u ln=2.4u wp=20u lp=2.4u\n+ VCCPIN=VCC VSSPIN=VSS\"\nextra=\"VCCPIN VSSPIN\"\ngeneric_type=\"m=integer wn=real ln=real wp=real lp=real VCCPIN=string VSSPIN=string\"\nverilog_stop=true\n```\n\nwith these definitions the above schematic will be netlisted as:\n\n```**.subckt prova1\nx2 G_y G_a G_b G_c VCC VSS lvnand3 wn=1.8u ln=0.18u wp=1u lp=0.18u m=1\n**.ends\n* expanding symbol: customlogicLib/lvnand3 # of pins=4\n.subckt lvnand3 y a b c VCCPIN VSSPIN\nwn=30u ln=2.4u wp=20u lp=2.4u\n*.opin y\n*.ipin a\n*.ipin b\n*.ipin c\nm1 net2 a VSSPIN VSSPIN nlv w=wn l=ln geomod=0 m=1\nm2 y a VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm2 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm3 y b VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm3 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm6 y c net1 VSSPIN nlv w=wn l=ln geomod=0 m=1\nm4 y c VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm4 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm5 net1 b net2 VSSPIN nlv w=wn l=ln geomod=0 m=1\n.ends\n```\n\nWithout the extra property in the cmos gate symbol the following incorrect netlist will be produced:\n\n```**.subckt prova1\nx2 G_y G_a G_b G_c VCC VSS lvnand3 wn=1.8u ln=0.18u wp=1u lp=0.18u m=1\n**** begin user architecture code\n**** end user architecture code\n**.ends\n\n* expanding symbol: customlogicLib/lvnand3 # of pins=4\n\n.subckt lvnand3 y a b c\nwn=30u ln=2.4u wp=20u lp=2.4u\nVCCPIN=VCC VSSPIN=VSS\n*.opin y\n*.ipin a\n*.ipin b\n*.ipin c\nm1 net2 a VSSPIN VSSPIN nlv w=wn l=ln geomod=0 m=1\nm2 y a VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm2 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm3 y b VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm3 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm6 y c net1 VSSPIN nlv w=wn l=ln geomod=0 m=1\nm4 y c VCCPIN VCCPIN plv w=wp l=lp geomod=0 m=1\ndxm4 0 VCCPIN dnwell area='(wp + 57u)*(lp + 31u)' pj='2*(wp +57u)+2*(lp +31u)'\nm5 net1 b net2 VSSPIN nlv w=wn l=ln geomod=0 m=1\n**** begin user architecture code\n**** end user architecture code\n.ends\n```\n\nas you can see the VSSPIN and VCCPIN are listed as parameters and not as pins in the netlist.\n\n• dir\n• Defines the direction of a symbol pin. Allowed values are in, out, inout.", null, "• global\n• a global=1 property in a label type symbol will declare the corresponding net as 'global'. Global nets in spice netlists are like global variables in a C program, these nets are accessible at any hierarchical level without the need of passing them through pin connections.", null, "• spice_netlist\n• verilog_netlist\n• vhdl_netlist\n• If any of these 3 properties if set to true the symbol will be netlisted in the specified format. This is only valid if the split file netlisting mode is active (Options -> Split netlist). This is very rarely used but is required in mixed mode simulations, where part of the system will be handled by an analog simulator (spice) and another part of the system by a digital Verilog / VHDL simulator.\n\n• verilog_format\n• This is the Verilog equivalent of the format property for Spice primitives. This is a valid definition for a 2 input inverted XOR gate:\n\n```verilog_format=\"xnor #(@risedel , @falldel ) @name ( @@Z , @@A , @@B );\"\n```\n\n• vhdl_format\n• same as above for VHDL primitives.\n\n### PREDEFINED SYMBOL VALUES\n\n• @symname\n• This expands to the name of the symbol\n\n• @pinlist\n• This expands to the list of nets that connect to symbol pins in the order they are set in the symbol\n\n• @@pin\n• This expands to the net that connect to symbol pin named pin. This substitution takes place only when producing a netlist (Spice, Verilog, VHDL, tEDAx) so it is allowed to use this value only in format,vhdl_format, tedax_format or verilog_format attributes (see Netlisting slide)\n\n• @#n\n• This expands to the net that connect to symbol pin at position n in the XSCHEM internal storage. This substitution takes place only when producing a netlist (Spice, Verilog, VHDL, tEDAx) so it is allowed to use this value only in format,vhdl_format, tedax_format or verilog_format attributes (see Netlisting slide)\nThis method of accessing a net that connects to a pin is much faster than previous one since XSCHEM does not need to loop through symbol pin names looking for a match.\nExample: @#2: return net name that connects to the third pin of the symbol (position 2).\n\n• @#n:pin_attribute\n• This expands to the value or property pin_attribute defined in the pin at position n in the XSCHEM internal storage. This method of looking up properties is very fast.\nExample: @#0:pinnumber: This expands to the value of the pinnumber defined in pin object at position 0 in the xschem internal ordering. This format is very useful for slotted devices where the actual displayed pin number depends on the slot information defined in the instance name (example: U1:2, slot number 2 of IC U1). These tokens may be placed as text in the symbol graphic window, not in format strings.\n\n• @sch_last_modified\n• this indicates the last modification time of the .sch file of the symbol.\n\n• @sym_last_modified\n• this indicates the last modification time of the .sym file of the symbol.\n\n• @time_last_modified\n• this indicates the last modification time of the schematic (.sch) containing the symbol instance.\n\n• @schname\n• this expands to the name of the schematic (.sch) containing the symbol instance.\n\n• @prop_ptr\n• this expandes to the entire property string passed to the component.\n\n• @schprop\n• this expandes to the spice global property string of the schematic containing the symbol\n\n• @schvhdlprop\n• this expandes to the VHDL global property string of the schematic containing the symbol\n\n• @schverilogprop\n• this expandes to the Verilog global property string of the schematic containing the symbol" ]

[ null, "http://repo.hu/projects/xschem/xschem_man/netlist_commands.png", null, "http://repo.hu/projects/xschem/xschem_man/general_rules.png", null, "http://repo.hu/projects/xschem/xschem_man/attribute_substitution.png", null, "http://repo.hu/projects/xschem/xschem_man/symbol_properties1.png", null, "http://repo.hu/projects/xschem/xschem_man/symbol_property_syntax1.png", null, "http://repo.hu/projects/xschem/xschem_man/symbol_property_syntax2.png", null, "http://repo.hu/projects/xschem/xschem_man/symbol_property_syntax3.png", null ]

[ "In this post, we will be developing the first project from our list of best beginner python projects– ‘The Anagram Game’. An anagram of a word is another word obtained by shuffling its letters. For example, the words God and dog are anagrams of each other. This is what the anagram game is all about.\n\nThe basic idea of this project is to read a file that contains words and their meaning like a dictionary, pick a random word from this dictionary, shuffle it and ask the user to guess the correct word from its anagram and the original meaning of the word.\n\n### Importing the Libraries\n\nFor this project, we will be using the json and random packages that are built into Python. JSON stands for Java Script Object Notation which is a file format used to store data in key-value pairs. This is similar to the Python ‘dictionary’ data structure. The json package provides methods to handle such data. The random package does exactly what the name suggests and has methods for generating random numbers, making random choices, and shuffling a list, among others.\n\n```import json\nimport random\n```\n\nAs mentioned before, we will need a dataset of words and their associated meanings. You can download a version of Webster’s Unabridged English Dictionary from this repository: click here. As we can see, the file format of this data is a json file and hence we will use the load function of the json package to load this data into a dictionary data structure in Python.\n\n```filename = 'dictionary_data.json'\nfile = open(filename)\n```\n\nThe data is now stored as key-value pairs in the variable named data which is an instance of the dictionary class. A key-value pair in a dictionary is represented as {key : value}. In our data, the keys of the dictionary are 102217 different words and their values are the associated meaning of the respective words.\n\n### Picking a Random Word\n\nLet us write a function that will pick a random word from the 102217 available words. The function will take two arguments – data and length. The data represents the dictionary of words and length is something determined by the programmer to decide the maximum length of words that should be returned from this function. We first have to make a list of all the possible words from the dictionary which can be accessed using the keys method of the dictionary class. We then pick a random word using the choice function and check if the length of the selected word is less than the maximum length specified in the arguments and the greater than two. Since, this can take multiple attempts we put this code in an infinite loop. When a word satisfying the length requirements is picked, the function returns the word. No code inside the function is executed once the function returns a value. The logic is given by the word_prompt function specified below.\n\n```def word_prompt(data, length):\nall_words = list(data.keys())\nwhile True:\nword = random.choice(all_words)\nif len(word) < length and len(word) > 2:\nreturn word\n```\n\n### Shuffling the Word\n\nNext, let us implement a function that will return a shuffled version i.e. an anagram of the word that we have selected. First, the word is converted into a list of characters. Next, we shuffle this list of characters using the shuffle function of the random package. The shuffled list of letters is converted back into a word using the join function that joins a collection of iterables together. Lastly, we run this code in an infinite loop to check that the shuffled word is not equal to the original word itself. If this condition is true the anagram of the word is returned. This logic is given by the shuffle_word function given below.\n\n```def shuffle_word(word):\narray = list(word)\nshuffled = word\nwhile True:\nrandom.shuffle(array)\nshuffled = ''.join(array)\nif shuffled != word:\nreturn shuffled\n```\n\n### Building the Anagram Game\n\nNow let’s move on the last part – building an interactive version of the game for the user to play with. We use our functions defined above to get a word and its anagram form to question the player. We also access the meaning of the word using the data dictionary. We will be giving the user five attempts to guess the correct answer and for that we have used a for loop that starts from 5 goes to 1 decrementing by 1 every loop. Every loop we ask the player to make a guess and check if it is equal to the expected word. If it is, the player is correct and we can break from the loop. Otherwise, the loop continues. Finally, when we reach the last iteration, we give the correct answer to the user. After for loop, we provide an option to allow the player to play the game again. To ensure that the game continues until the player decides to stop, we put the code in an infinite loop and break from it when the player enters ‘n’. The logic described is implemented in the code below.\n\n```print(\"Welcome to the Anagram Game!\")\nwhile(True):\nword = word_prompt(data, 5)\nquestion = shuffle_word(word)\nmeaning = data[word]\n\nquestion = question.lower()\nword = word.lower()\n\nprint(\"\\nSolve:\", question)\nprint(\"Hint:\", meaning)\n\nfor i in range(5, 0, -1):\nprint(\"\\nAttempts Left:\", i)\nguess = input('Make a guess: ').lower()\nif guess == word:\nprint(\"Correct!\")\nbreak\nif i == 1:\n\nchoice = input(\"\\nContinue? [y/n]: \")\nprint('-'*50)\nif choice == 'n':\nprint(\"\\nThank you for playing!\")\nbreak\n```", null, "### Complete Code\n\nFinally, the complete code is given below. The code’s script is placed in a '__main__' scope, which is used when reading from standard input such as the command-line interface. It is good practice to style the code according to conventional standards. You can go forward and build on this project through a scoring system or even a graphical user interface.\n\n```import json\nimport random\n\ndef word_prompt(data, length):\nall_words = list(data.keys())\nwhile True:\nword = random.choice(all_words)\nif len(word) < length and len(word) > 2:\nreturn word\n\ndef shuffle_word(word):\narray = list(word)\nshuffled = word\nwhile True:\nrandom.shuffle(array)\nshuffled = ''.join(array)\nif shuffled != word:\nreturn shuffled\n\nif __name__ == \"__main__\":\nfilename = 'dictionary_data.json'\nfile = open(filename)\n\nprint(\"Welcome to the Anagram Game!\")\nwhile(True):\nword = word_prompt(data, 5)\nquestion = shuffle_word(word)\nmeaning = data[word]\n\nquestion = question.lower()\nword = word.lower()\n\nprint(\"\\nSolve:\", question)\nprint(\"Hint:\", meaning)\n\nfor i in range(5, 0, -1):\nprint(\"\\nAttempts Left:\", i)\nguess = input('Make a guess: ').lower()\nif guess == word:\nprint(\"Correct!\")\nbreak\nif i == 1:\n\nchoice = input(\"\\nContinue? [y/n]: \")\nprint('-'*50)\nif choice == 'n':\nprint(\"\\nThank you for playing!\")\nbreak\n```\n\nHopefully this post has introduced some basic concepts in Python such as conditional statements, looping statements, and file handling. As a beginner, it is expected that you have doubts about such concepts and if you need any clarification, we at FavTutor are always here to provide you help from expert tutors 24/7. Get started by sending a message through the chat on the bottom right. Happy programming!", null, "Siddhartha\n\nAs a technological enthusiast, I am not only passionate about exploring the latest innovations but also firmly believe in promoting its applications. As such, I write about various projects involving Python, Data Science, and Artificial Intelligence" ]

[ null, "https://favtutor.com/resources/images/uploads/anagram_game_output_(1).jpg", null, "https://favtutor.com/resources/images/Author_image.jpg", null ]

[ "LMS teacher’s modules explained by Dr Raima Nazar\n\nLMS teacher’s modules explained:\nDr. Raima Nazar\nLecturer\nDepartment of Economics\n\nContent breakup\n\n00:00:00 – 01:12:00 = Introduction about LMS\n01:13:00 – 02:22:00 = How you can login\n02:22:01 – 03:12:00 = Introduction of dashboard\n03:12:01 – 04:15:00 = Preparation of each course material\n04:15:01 – 09:30:00 = Announcement / Forum\n09:30:01 – 21:55:00 = Make a book\n22:10:10 – 25:16:00 = Insert course outline\n25:17:00 – 27:32:00 = Insert no. of lectures\n27:52:00 – 33:45:00 = Add a lesson\n33:45:00 – 41:20:00 = Add an assignment\n41:20:00 – 44:20:00 = Marking of assignment\n44:30:00 – 49:41:00 = Assign a quiz\n50:08:00 – 01:00:26 = Introduction of big blue button\n01:00:55 – 01:02:00 = Hide lectures from students" ]

[ null ]

[ "# Tutorial on Bethe-Salpeter calculations¶\n\n## Absorption spectra including excitonic effects.¶\n\nThis tutorial discusses how to calculate the macroscopic dielectric function including excitonic effects within the Bethe-Salpeter (BS) approach. Crystalline silicon is used as test case. A brief description of the formalism can be found in the Bether-Salpeter notes.\n\nThe user should be familiarized with the four basic tutorials of ABINIT and the first GW tutorial.\n\nVisualisation tools are NOT covered in this tutorial. Powerful visualisation procedures have been developed in the Abipy context, relying on matplotlib. See the README of Abipy and the Abipy tutorials.\n\nThis tutorial should take about one hour to be completed.\n\nNote\n\nSupposing you made your own install of ABINIT, the input files to run the examples are in the ~abinit/tests/ directory where ~abinit is the absolute path of the abinit top-level directory. If you have NOT made your own install, ask your system administrator where to find the package, especially the executable and test files.\n\nTo execute the tutorials, create a working directory (Work*) and copy there the input files and the files file of the lesson. This will be explicitly mentioned in the first lessons, that will tell you more about the files file (see also section 1.1). The files file ending with _x (e.g. tbase1_x.files) must be edited every time you start to use a new input file.\n\nMost of the tutorials do not rely on parallelism (except specific tutorials on parallelism). However you can run most of the tutorial examples in parallel, see the topic on parallelism.\n\nIn case you work on your own PC or workstation, to make things easier, we suggest you define some handy environment variables by executing the following lines in the terminal:\n\nexport ABI_HOME=Replace_with_the_absolute_path_to_the_abinit_top_level_dir\nexport PATH=$ABI_HOME/src/98_main/:$PATH\nexport ABI_TESTS=$ABI_HOME/tests/ export ABI_PSPDIR=$ABI_TESTS/Psps_for_tests/ # Pseudopotentials used in examples.\n\n\nExamples in this tutorial use these shell variables: copy and paste the code snippets into the terminal (remember to set ABI_HOME first!). The ‘export PATH’ line adds the directory containing the executables to your PATH so that you can invoke the code by simply typing abinit in the terminal instead of providing the absolute path.\n\n## Preparatory steps (WFK and the SCR file)¶\n\nBefore starting, you might consider to work in a different subdirectory as for the other tutorials. Why not Work_bs?\n\nCopy the files file $ABI_TESTS/tutorial/Input/tbs_1.files in the working directory Work_bs. Now run immediately the calculation with the command: abinit < tbs_1.files > tbs_1.log 2> err & so that we can analyze the input file while the code is running. The input file is located in$ABI_TESTS/tutorial/Input/tbs_1.in. The header reports a brief description of the calculation so read it carefully. Don’t worry if some parts are not clear to you as we are going to discuss the calculation in step by step fashion.\n\nThis input file generates the two WFK files and the SCR file needed for the subsequent Bethe-Salpeter computations. The first dataset performs a rather standard ground-state calculation on an $\\Gamma$-centered 4x4x4 grid (64 k points in the full Brillouin Zone, folding to 8 k points in the irreducible wedge). Then the ground-state density is used in dataset 2 and 3 to generate two WFK files with a standard NSCF run and the conjugate-gradient method.\n\nNote that the WFK file computed in dataset 2 contains 100 bands on the 4x4x4 gamma-centered k-mesh whereas the WFK file produced in dataset 3 has only 10 bands on a 4x4x4 k-mesh shifted along the direction\n\nshiftk3 0.11 0.21 0.31 # This shift breaks the symmetry of the k-mesh.\n\n\nThe $\\Gamma$-centered k-mesh contains 8 points in the IBZ while the shifted k-mesh breaks the symmetry of the crystal leading to 64 points in the IBZ (actually the IBZ now coincides with the full Brillouin zone). The second mesh is clearly inefficient, so you might wonder why we are using such a bizarre sampling and, besides, why we need to generate two different WFK files!\n\nIndeed this approach strongly differs from the one we followed in the GW tutorials, but there is a good reason for doing so. It is anticipated that optical spectra converge slowly with the BZ sampling, and that symmetry-breaking k-meshes lead to faster convergence in nkpt than the standard symmetric k-meshes commonly used for ground-state or GW calculations.\n\nThis explains the bizarre shift but still why two WFK files? Why don’t we simply use the WFK file on the shifted k-mesh to compute the screening?\n\nThe reason is that a screening calculation done with many empty bands on the shifted k-mesh would be very memory demanding as the code should allocate a huge portion of memory whose size scales with (nband * nkpt), and no symmetry can be used to reduce the number of k-points.\n\nTo summarize: the WFK with the symmetric k-point sampling and 100 bands will be used to compute the screening, while the WFK file with the shifted k-mesh and 10 bands will be used to construct the transition space employed for solving the Bethe-Salpeter equation. The two k-meshes differ just for the shift thus they produce the same set of q-points (the list of q-points in the screening is defined as all the possible differences between the k-points of the WFK file). This means that, in the Bethe-Salpeter run, we can use the SCR file generated with the symmetric mesh even though the transition space is constructed with the shifted k-mesh.\n\nAfter this lengthy discussion needed to clarify this rather technical point, we can finally proceed to analyze the screening computation performed in the last dataset of tbs_1.in.\n\nThe SCR file is calculated in dataset 4 using nband = 100 and ecuteps = 6.0 Ha. In the first GW tutorial, these values were found to give QP energies converged within 0.01 eV, so we are confident that our SCR file is well converged and it can be safely used for performing convergence tests in the Bethe-Salpeter part.\n\nNote that, for efficiency reasons, only the static limit of W is computed:\n\nnfreqre4 1 # Only the static limit of W is needed for standard BSE calculations.\nnfreqim4 0\n\n\nIndeed, in the standard formulation of the Bethe-Salpeter equation, only the static limit of the screened interaction is needed to construct the Coulomb term of the BS Hamiltonian. Using a single frequency allows us to save some CPU time in the screening part, but keep in mind that this SCR file can only be used either for Bethe-Salpeter computations or for GW calculations employing the plasmon-pole models corresponding to ppmodel = 3, 4.\n\nAt this point the calculation should have completed, but there’s still one thing that we have to do before moving to the next paragraph.\n\nAs we said, we will need the WFK file on the shifted k-mesh and the SCR file for our BS calculations so do not delete them! It is also a good idea to rename these precious files using more meaningful names e.g.:\n\nmv tbs_1o_DS2_WFK 444_gamma_WFK\nmv tbs_1o_DS3_WFK 444_shifted_WFK\nmv tbs_1o_DS4_SCR 444_SCR\n\n\nImportant\n\nThe list of k-points specified in the BS input files must equal the one used to generate the WFK file. Two new WFK files and a new SCR file must be generated from scratch if we want to change the k-point sampling used to construct the transition space.\n\n## Computing the absorption spectrum within the Tamm-Dancoff approximation¶\n\nThis section is intended to show how to perform a standard excitonic calculation within the Tamm-Dancoff approximation (TDA) using the Haydock iterative technique. The input file is $ABI_TESTS/tutorial/tutorial/Input/tbs_2.in. Before running the job, we have to connect this calculation with the output results produced in tbs_1.in. Use the Unix commands: ln -s 444_shifted_WFK tbs_2i_WFK ln -s 444_SCR tbs_2i_SCR to create two symbolic links for the shifted WFK and the SCR file. The reason for doing so will be clear afterwards once we discuss the input file. This job lasts 1-2 minutes on a modern machine so it is worth running it before inspecting the input file. Copy the files file$ABI_TESTS/tutorial/Input/tbs_2.files in the working directory and issue:\n\nabinit < tbs_2.files > tbs_2.log 2> err &\n\n\nto put the job in background so that we can examine tbs_2.in.\n\nNow open $ABI_TESTS/tutorial/Input/tbs_2.in in your preferred editor and go to the next section where we discuss the most important variables governing a typical BS computation. ### The structure of the input file¶ First we need to set optdriver = 99 to call the BSE routines optdriver 99 # BS calculation The variables irdwfk and irdscr are similar to other “ird” variables of ABINIT and are used to read the files produced in the previous paragraph irdwfk 1 # Read the WFK file produced in tbs_1 irdscr 1 # Read the SCR file produced in tbs_1 The code expects to find an input WFK file and an input SCR file whose name is constructed according to prefix specified in the files file tbs_2.files (see this section of the abinit_help file). This is the reason why we had to create the two symbolic links before running the code. Then we have a list of five variables specifying how to construct the excitonic Hamiltonian. bs_calctype 1 # L0 constructed with KS orbitals and energies. mbpt_sciss 0.8 eV # Scissors operator used to correct the KS band structure. bs_exchange_term 1 # Exchange term included. bs_coulomb_term 11 # Coulomb term included using the full matrix W_GG' bs_coupling 0 # Tamm-Dancoff approximation. The value bs_calctype = 1 specifies that the independent-particle polarizability should be constructed with the Kohn-Sham orbitals and energies read from the WFK file. To simulate the self-energy correction, the KS energies are corrected with a scissors operator of energy mbpt_sciss = 0.8 eV. This permits us to avoid a cumbersome GW calculation for each state included in our transition space. The use of the scissors operator is a reasonable approximation for silicon but it might fail in more complicated systems in which the GW corrections cannot be simulated in terms of a simple rigid shift of the initial KS bands structure. The remaining three variables specify how to construct the excitonic Hamiltonian. bs_exchange_term = 1 tells the code to calculate the exchange part of the kernel, hence this calculation includes local-field effects. The variable bs_coulomb_term is used to select among different options that are available for the Coulomb term (please take some time to read the description of the variable and the relevant equations in the Bethe-Salpeter notes. Finally bs_coupling = 0 specifies that the off-diagonal coupling blocks should be neglected (Tamm-Dancoff approximation). This particular combination of parameters thus corresponds to a Bethe-Salpeter calculation within the Tamm-Dancoff approximation with local field effects included. Then we have the specification of the bands used to construct the transition space: bs_loband 2 nband 8 In this case all the bands around the gap whose index is between 2 and 8 are included in the basis set. The frequency mesh for the macroscopic dielectric function is specified by bs_freq_mesh bs_freq_mesh 0 6 0.02 eV # Frequency mesh. This triplet of real values defines a linear mesh that covers the range [0, 6] eV with a step of 0.02 eV. The number of frequency points in the mesh does not have any significant effect on the CPU time, but it is important to stress that the number of bands included in the transition space defines, in conjunction with the number of k-points, the frequency range that can be described. As a consequence bs_loband and nband should be subject to an accurate converge study. Then we have the parameters that define and control the algorithm employed to calculate the macroscopic dielectric function bs_algorithm 2 # Haydock method (this is the default value). bs_haydock_niter 100 # Max number of iterations for the Haydock method. bs_haydock_tol 0.05 # Tolerance for the iterative method. zcut 0.15 eV # Complex shift to avoid divergences in the continued fraction. bs_algorithm specifies the algorithm used to calculate the macroscopic dielectric function. In this case we use the iterative Haydock technique whose maximum number of iterations is given by bs_haydock_niter. The iterative algorithm stops when the difference between two consecutive evaluations of the optical spectra is less than bs_haydock_tol. The input variable zcut gives the complex shift to avoid divergences in the continued fraction. From a physical point of view, this parameters mimics the experimental broadening of the absorption peaks. In this test, due to the coarseness of the k-mesh, we have to use a value slightly larger than the default one (0.1 eV) in order to facilitate the convergence of the Haydock algorithm. Ideally, one should perform a convergence study by decreasing the value of zcut for increasing number of k-points. The k-point sampling is specified by the set of variables. kptopt 1 # Option for the automatic generation of k points, ngkpt 4 4 4 # This mesh is too coarse for optical properties. nshiftk 1 shiftk 0.11 0.21 0.31 # This shift breaks the symmetry of the k-mesh. chksymbreak 0 # Mandatory for using symmetry-breaking k-meshes in the BS code. Important The values of kptopt, ngkpt, nshiftk, and shiftk must equal the ones used to specify the grid for the WFK file. chksymbreak = 0 is used to bypass the check on symmetry breaking that, otherwise, would make the code stop. The last section of the input file ecutwfn 8.0 # Cutoff for the wavefunction. ecuteps 2.0 # Cutoff for W and /bare v used to calculate the BS matrix elements. inclvkb 2 # The Commutator for the optical limit is correctly evaluated. specifies the parameters used to calculate the kernel matrix elements and the matrix elements of the dipole operator. We have already encountered these variables in the first GW tutorial of the GW tutorial so their meaning is (hopefully) familiar to you. A more detailed discussion of the role played by these variables in the BS code can be found in the Bether-Salpeter notes. ### Output files¶ The output file, tbs_2.out, reports the basic parameters of the calculation and eventual WARNINGs that are issued if the iterative method does not converge. Please take some time to understand its structure. Could you answer the following questions? 1. How many transitions are included in the basis set? 2. How many directions are used to evaluate the optical limit? 3. What is the value of the Lorentzian broadening used in the continued fraction? After this digression on the main output file, we can finally proceed to analyse the output data of the computation. The most important results are stored in five different files: • tbs_2o_BSR • tbs_2o_HAYDR_SAVE • tbs_2o_RPA_NLF_MDF • tbs_2o_GW_NLF_MDF • tbs_2o_EXC_MDF In what follows, we provide a brief description of the format and of the content of each output file. tbs_2o_BSR: This binary file stores the upper triangle of the resonant block (the matrix is Hermitian hence only the non-redundant part is computed and saved on file). The BSR file can be used to restart the run from a previous computation using the variables getbsreso or irdbsreso. This restart capability is useful for restarting the Haydock method if convergence was not achieved or to execute Haydock computations with different values of zcut. getbsreso and irdbsreso are also handy if one wants to include the coupling on top of a pre-existing TDA calculation since the code uses two different files to store the resonant and the coupling block (BSC is the prefix used for the files storing the coupling term). tbs_2o_HAYDR_SAVE: It is a binary file containing the results of the Haydock method: the coefficient of the tridiagonal matrix and the three vectors employed in the iterative algorithm. It is usually used to restart the algorithm if convergence has not been achieved (see the related input variables gethaydock and irdhaydock). tbs_2o_RPA_NLF_MDF and tbs_2o_GW_NLF_MDF The RPA spectrum without local field effects obtained with KS energies and the GW energies, respectively (mnemonics: NLF stands for No Local Field, while MDF stands for Macroscopic Dielectric Function). tbs_2o_EXC_MDF Formatted file reporting the macroscopic dielectric function with excitonic effects. The EXC_MDF file contains the most important results of our calculation so it is worth spending some time to discuss its format. First we have a header reporting the basic parameters of the calculation: # Macroscopic dielectric function obtained with the BS equation. # RPA L0 with KS energies and KS wavefunctions LOCAL FIELD EFFECTS INCLUDED # RESONANT-ONLY calculation # Coulomb term constructed with full W(G1,G2) # Scissor operator energy = 0.8000 [eV] # Tolerance = 0.0500 # npweps = 27 # npwwfn = 283 # nbands = 8 # loband = 2 # nkibz = 64 # nkbz = 64 # Lorentzian broadening = 0.1500 [eV] then the list of q-points giving the direction of the incident photon: # List of q-points for the optical limit: # q = 0.938821, 0.000000, 0.000000, [Reduced coords] # q = 0.000000, 0.938821, 0.000000, [Reduced coords] # q = 0.000000, 0.000000, 0.938821, [Reduced coords] # q = 0.000000, 0.813043, 0.813043, [Reduced coords] # q = 0.813043, 0.000000, 0.813043, [Reduced coords] # q = 0.813043, 0.813043, 0.000000, [Reduced coords] By default the code calculates the macroscopic dielectric function considering six different directions in q-space (the three basis vectors of the reciprocal lattice and the three Cartesian axis). It is possible to specify custom directions using the input variables gw_nqlwl and gw_qlwl. Then comes the section with the real and the imaginary part of the macroscopic dielectric as a function of frequency for the different directions: # omega [eV] RE(eps(q=1)) IM(eps(q=1) RE(eps(q=2) ) ... 0.000 1.8026E+01 0.0000E+00 1.7992E+01 0.0000E+00 1.4292E+01 0.0000E+00 1.3993E+01 0.0000E+00 1.7117E+01 0.0000E+00 1.7080E+01 0.0000E+00 .... .... ... You can visualize the data using your preferred software. For instance, with gnuplot p \"tbs_2o_EXC_MDF\" u 1:3 w l will plot the imaginary part of the macroscopic dielectric function (the absorption spectrum) for the first q-point. You should obtain a graphic similar to the one reported below", null, "Note These results are not converged, we postpone the discussion about convergence tests to the next paragraphs of this tutorial. The most important feature of the spectrum is the presence of two peaks located at around 3.4 and 4.3 eV. To understand the nature of these peaks and the role played by the BS kernel, it is useful to compare the excitonic spectra with the RPA results obtained without local field effects. Use the sequence of gnuplot command p \"tbs_2o_EXC_MDF\" u 1:3 w l rep \"tbs_2o_RPA_NLF_MDF\" u 1:3 w l rep \"tbs_2o_GW_NLF_MDF\" u 1:3 w l to plot the absorption spectrum obtained with the three different approaches. The final result is reported in the figure below.", null, "The RPA-KS spectrum underestimates the experimental optical threshold due to the well know band gap problem of DFT. Most importantly, the amplitude of the first peak is underestimated, a problem than is not solved when local-field effects are correctly included in the calculation. The RPA-GW results with QP corrections simulated with mbpt_sciss does not show any significant improvement over RPA-KS: the RPA-GW spectrum is just shifted towards higher frequencies due to opening of the gap, but the shape of the two spectra is very similar, in particular the amplitude of the first peak is still underestimated. On the contrary, the inclusion of the BS kernel leads to important changes both in the optical threshold as well as in the amplitude of the first peak. This simple analysis tells us that the first peak in the absorption spectrum of silicon has a strong excitonic character that is not correctly described within the RPA. Our first BS spectrum is not converged at all and it barely resembles the experimental result, nevertheless this unconverged calculation is already able to capture the most important physics. Tip If AbiPy is installed on your machine, you can use the abiopen script with the --expose option to visualize the dielectric functions stored in the MDF.nc file: abiopen.py tbs_2o_MDF.nc --expose --seaborn", null, "For further information about the MDF file and the post-processing tools provided by AbiPy, please consult the MdfFile notebook . ### Optional Exercises¶ • Change the value of the Lorentzian broadening zcut used to avoid divergences in the continued fraction. Then restart the Haydock algorithm from the _BSR and _HAYDR_SAVE files using the appropriate variables. What is the main effect of the broadening on the final spectrum. Does the number of iterations needed to converge depend on the broadening? • Use the appropriate values for bs_exchange_term and bs_coulomb_term to calculate the BS spectrum without local field effects. Compare the results obtained with and without local field effects. • Modify the input file tbs_2.in so that the code reads in the resonant block produced in the previous run and calculates the spectrum employing the method based on the direct diagonalization (use irdbsreso to restart the run but remember to rename the file with the resonant block). Compare the CPU time needed by the two algorithms as a function of the number of transitions in the transition space. Which one has the best scaling? ### Preliminary discussion about convergence studies¶ Converging the excitonic spectrum requires a careful analysis of many different parameters: Since the memory requirements scale quadratically with the number of k-points in the full Brillouin zone times the number of valence bands times the number of conduction bands included in the transition space, it is very important to find a good compromise between accuracy and computational efficiency. First of all one should select the frequency range of interest since this choice has an important effect on the number of valence and conduction states that have to be included in the transition space. The optical spectrum is expected to converge faster in the number of bands than the GW corrections since only those transitions whose energy is “close” to the frequency range under investigation are expected to contribute. ecutwfn usually plays a secondary role since it only affects the accuracy of the oscillator matrix elements. We suggest avoiding any truncation of the initial basis set by setting ecutwfn to a value slightly larger than the value of ecut used to generate the WFK file. One should truncate the initial planewave basis set only when experiencing memory problems although this kind of problems can be usually solved by just increasing the number of processors or, alternatively, with an appropriate choice of gwmem. The value of ecuteps affects the accuracy of the matrix elements of the Coulomb term, the fundamental term that drives the creation of the excitons. As a consequence ecuteps should be subject to an accurate convergence test. As a rule of thumb, ecuteps can be chosen equal or, sometimes, even smaller than the value needed to converge the GW corrections. As already stated: optical spectra converge slowly with the Brillouin zone sampling. The convergence in the number of k-points thus represents the most important and tedious part of our convergence study. For this reason, this study should be done once converged values for the other parameters have been already found. ## Convergence with respect to the number of bands in the transition space¶ In this section we take advantage of the multi-dataset capabilities of ABINIT to perform calculations with different values for bs_loband and nband Before running the test take some time to read the input file$ABI_TESTS/tutorial/Input/tbs_3.in.\n\nThe convergence in the number of transitions is performed by defining two datasets with different values for nband and bs_loband\n\nndtset 2\nbs_loband1 3 nband1 6\nbs_loband2 2 nband2 7\n\n\nThe parameters defining how to build the excitonic Hamiltonian are similar to the ones used in tbs_2.in. The only difference is in the value used for bs_coulomb_term, i.e.\n\nbs_coulomb_term 10 # Coulomb term evaluated within the diagonal approximation.\n\n\nthat allows us to save some CPU time during the computation of the Coulomb term.\n\nAlso in this case, before running the test, we have to connect tbs_3.in to the WFK and the SCR file produced in the first step. Note that tbs_3.in uses irdwfk and irdscr to read the external files, hence we have to create symbolic links for each dataset:\n\nln -s 444_SCR tbs_3i_DS1_SCR\nln -s 444_SCR tbs_3i_DS2_SCR\nln -s 444_shifted_WFK tbs_3i_DS1_WFK\nln -s 444_shifted_WFK tbs_3i_DS2_WFK\n\n\nNow we can finally run the test with\n\nabinit < tbs_3.files > tbs3.log 2> err &\n\n\nThis job should last 3-4 minutes so be patient!\n\nLet us hope that your calculation has been completed, and that we can examine the output results.\n\nUse the following sequence of gnuplot commands:\n\np \"tbs_3o_DS1_EXC_MDF\" u 1:3 w l\nrep \"tbs_3o_DS2_EXC_MDF\" u 1:3 w l\n\n\nto plot on the same graphic the absorption spectrum obtained with different transition spaces. You should obtain a graphic similar (but not equal) to this one", null, "Note indeed that the above figure has been produced with more datasets in order to highlight the convergence behaviour.\n\nThe results obtained with (bs_loband = 4, nband = 5) are clearly unconverged as the basis set contains too few transitions that are not able to describe the frequency-dependence of the polarizability in the energy range under investigation. For a converged spectrum, we have to include the three higher occupied states and the first four conduction bands (the blue curve corresponding to bs_loband = 2, and nband = 7).\n\nNote that adding the first occupied band, curve (1-8), gives results that are almost on top of (2,8). This is due to the fact that, in silicon, the bottom of the first band is located at around 12 eV from the top of the conduction band therefore its inclusion does not lead to any significant improvement of the transition space in the frequency range [0, 8] eV. For completeness, we also report the results obtained in a separate calculation done with bs_loband = 2 nband = 9 to show that four empty states are enough to converge the spectrum.\n\nWe therefore fix the number of bands for the transition space using bs_loband = 2, nband = 7 and we proceed to analyse the convergence of the spectrum with respect to the number of planewaves in the screening.\n\nTip\n\nIf AbiPy is installed on your machine, you can use the abicomp script with the mdf command and the --expose option to compare multiple dielectric functions:\n\nabicomp.py mdf tbs_3o_DS*_MDF.nc --expose --seaborn", null, "### Tips for expert users¶\n\nThe use of irdwfk and irdscr is not handy when we have several datasets that are reading the same external file as we are forced to use different names for the input of each dataset. To work around this annoyance, one can introduce a fictitious dataset (say dataset 99), and let the code use the output of this nonexistent dataset as the input of the real datasets. An example will help clarify: Instead of using the lengthy list of links as done before, we might use the much simpler sequence of commands\n\nln -s 444_shifted_WFK tbs_3o_DS99_WFK\nln -s 444_SCR tbs_3o_DS99_SCR\n\n\nprovided that, in the input file, we replace irdwfk and irdscr with\n\ngetwfk 99 # Trick to read the same file tbs_o3_DS99_WFK in each dataset\ngetscr 99 # Same trick for the SCR file\n\n\n## Convergence with respect to the number of planewaves in the screening¶\n\nFirst of all, before running the calculation, take some time to understand what is done in $ABI_TESTS/tutorial/Input/tbs_4.in. The structure of the input file is very similar to the one of tbs_3.in, the main difference is in the first section: ndtset 2 ecuteps: 2 ecuteps+ 1 bs_coulomb_term 11 that instructs the code to execute two calculations where the direct term is constructed using different value of ecuteps. We also relax the diagonal-only approximation for the screening by setting bs_coulomb_term = 11 so that the non-locality of $W(\\rr, \\rr')$ is correctly taken into account. It is important to stress that it is not necessary to recalculate the SCR file from scratch just to modify the value of ecuteps used in the BS run. The SCR file calculated in the preparatory step contains G-vectors whose energy extends up to ecuteps = 6.0 Ha. This is the maximum cutoff energy that can be used in our convergence tests. If the value of ecuteps specified in the input file is smaller than the one stored on disk, the code will read a sub- block of the initial matrix. A WARNING message is issued if the value specified in the input file is larger than the one available in the SCR file. Now we can finally run the calculation. As usual, we have to copy$ABI_TESTS/tutorial/Input/tbs_4.files in the working directory Work_bs, then we have to create a bunch of symbolic links for the input WFK and SCR files:\n\nln -s 444_SCR tbs_4i_DS1_SCR\nln -s 444_SCR tbs_4i_DS2_SCR\nln -s 444_shifted_WFK tbs_4i_DS1_WFK\nln -s 444_shifted_WFK tbs_4i_DS2_WFK\n\n\nNow issue\n\nabinit < tbs_4.files > tbs4.log 2> err &\n\n\nto execute the test (it should take around 2 minutes).\n\nOnce the calculation is completed, plot the spectra obtained with different ecuteps using gnuplot :\n\np \"tbs_4o_DS1_EXC_MDF\" u 1:3 w l\nrep \"tbs_4o_DS2_EXC_MDF\" u 1:3 w l\n\n\nHere we show the results of a convergence study done with four different values or ecuteps to highlight the convergence behavior:", null, "The spectrum is found to converge quickly in ecuteps. The curves obtained with ecuteps = 3 and 4 Ha are almost indistinguishable from each other. Our final estimate for ecuteps is therefore 3 Ha.\n\nNote that this value is smaller than the one required to converge the QP corrections within 0.01 eV (in the first GW tutorial of the GW tutorial we obtained 6.0 Ha). This is a general behavior, in the sense that Bethe-Salpeter spectra, unlike GW corrections, are not very sensitive to truncations in the planewave expansion of W. Reasonable BS spectra are obtained even when W is treated within the diagonal approximation or, alternatively, with model dielectric functions.\n\nNote also how the two peaks are affected in a different way by the change of ecuteps, with the first peak affected the most. This behavior is consistent with our affirmation that the first peak of silicon has a strong excitonic character.\n\n## Convergence with respect to the number of k-points¶\n\nThe last parameter that should be checked for convergence is the number of k-points. This convergence study represents the most tedious and difficult part since it requires the generation of new WFK files and of the new SCR file for each k-mesh (the list of k-points for the wavefunctions and the set of q-points in the screening must be consistent with each other).\n\nThe file \\$ABI_TESTS/tutorial/Input/tbs_5.in gathers the different steps of a standard BS calculation (generation of two WFK file, screening calculation, BS run) into a single input. The calculation is done with the converged parameters found in the previous studies, only ngkpt has been intentionally left undefined.\n\nUse tbs_5.in as a template for performing BS calculations with different k-meshes. For example, you might try to compare the three meshes 4x4x4, 5x5x5, and 6x6x6. To facilitate the analysis of the results, we suggest to run the calculations in different directories so that we can keep the output results separated.\n\nBe aware that both the CPU time as well as the memory requirements increase quickly with the number of divisions in the mesh. These are, for example, the CPU times required by different k-meshes on Intel Xeon X5570:\n\n4x4x4: +Overall time at end (sec) : cpu= 112.4 wall= 112.4\n5x5x5: +Overall time at end (sec) : cpu= 362.8 wall= 362.8\n6x6x6: +Overall time at end (sec) : cpu= 914.8 wall= 914.8\n8x8x8: +Overall time at end (sec) : cpu= 5813.3 wall= 5813.3\n10x10x10: +Overall time at end (sec) : cpu= 20907.1 wall= 20907.1\n12x12x12: +Overall time at end (sec) : cpu= 62738.2 wall= 62738.2\n\n\n6x6x6 is likely the most dense sampling you can afford on a single-CPU machine. For you convenience, we have collected the results of the convergence test in the figure below.", null, "As anticipated, the spectrum converges slowly with the number of k-points and our first calculation done with the 4x4x4 grid is severely unconverged. The most accurate results are obtained with the 12x12x12 k-mesh, but even this sampling leads to converged results only for frequencies below 4.5 eV. This is a problem common to all BS computations, in the sense that it is extremely difficult to achieve global converge in the spectra. This analysis shows that we can trust the 12x12x12 results in the [0:4,5] eV range while the correct description of the spectrum at higher energies would require the inclusion of more k-point and, possibly, more bands so that the band dispersion is correctly taken into account (even the RPA spectrum does not converge at high frequencies when 12x12x12 is used).\n\nIt should be stressed that zcut plays a very important role in these converge tests. For example, the results obtained with the 8x8x8 or the 10x10x10 k-mesh can be brought closer to the 12x12x12 by just increasing the Lorentzian broadening. When comparing theory with experiments, it is common to treat zcut as an a posteriori parameter chosen to produce the best agreement with the experiment.\n\n• Use bs_coupling = 1 to perform an excitonic calculation for silicon including the coupling term. Compare the imaginary part of the macroscopic dielectric function obtained with and without coupling. Do you find significant differences? (Caveat: calculations with coupling cannot use the Haydock method and are much more CPU demanding. You might have to decrease some input parameters to have results in reasonable time.)\n\n• Calculate the one-shot GW corrections for silicon following the first GW tutorial. Then use the _GW file produced by the code to calculate the absorption spectrum.\n\n• Learn how to use AbiPy to automate BS calculations as described in this jupyter notebook.\n\n## Notes on the MPI implementation¶\n\nIn this section, we discuss the approach used to parallelize the two steps of the BS run, i.e. the construction of the H matrix and the evaluation of the macroscopic dielectric function.\n\nFirst of all, it is important to stress that, unlike the GW code, the BS routines do not employ any kind of memory distribution for the wavefunctions. The entire set of orbitals used to construct the transition space is stored on each node This choice has been dictated by the fact that the size of H is usually much larger than the array used to store the wavefunction, hence it is much more important to distribute the matrix than the wavefunctions. Besides, having all the states on each node simplifies the calculation of several intermediate quantities needed at run-time.\n\nThe memory allocated for the wavefunctions and the screening thus will not scale with the number of processors. However, for very memory demanding calculations, the real space orbitals can be calculated on the fly with an increase in computational time instead. This option is controlled by the second digit of the input variable gwmem.\n\nWhen discussing the MPI parallelization of the Bethe-Salpeter routines, we have to consider the two steps separately.\n\nIn the first step, the upper triangle of the resonant (coupling) block is distributed among the nodes. Each CPU computes its own portion and stores the results in a temporary array. At the end of the computation, the portions of the upper triangle are communicated to the master node which writes the binary file BSR (BSC).\n\nIn the second step, each node reads the data stored in the external files in order to build the excitonic Hamiltonian. The matrix is distributed using a column-block partitioning, so that the matrix-vector multiplications required in the Haydock iterative scheme can be easily performed in parallel (see the schematic representation reported below). A similar distribution scheme is also employed for the conjugate-gradient minimization. For a balanced distribution of computational work, the number of processors should divide the total number of resonant transitions.", null, "" ]

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[ "HI De Moivre's formula is actually true for all complex numbers x and all real numbers n, but this requires careful extension of several functions to the complex plane. If z = r(cos α + i sin α), and n is a natural number, then . 1 De Moivre’s Theorem - ALL 1. If the imaginary part of the complex number is equal to zero or i = 0, we have: z = r ∙ cosθ and z … Stirling's Formula and de Moivre's Series for the Terms of the Symmetric Binomial, 1730. Approximatio ad summam terminorum binomii ( a + b ) n in seriem expansi is reprinted by R. C. Archibald, “A Rare Pamphlet of De Moivre and Some of His Discoveries,” in Isis , 8 (1926), 671–684. Let $$z$$ be a complex number given in polar form: $$r \\operatorname{cis} \\theta$$. De Moivre's formula (also known as de Moivre's theorem or de Moivre's identity) is a theorem in complex analysis which states $(\\cos(\\theta)+i\\sin(\\theta))^n=\\text{cis}^n(\\theta)=\\cos(n\\theta)+i\\sin(n\\theta)$ This makes computing powers of any complex number very simple. eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA. Therefore, <-- Loisel I'm not so sure this makes any sense$.$ . De Moivre's Formula Examples 1. complex numbers, we know today as De Moivre’s Theorem. Abraham De Moivre: History, Biography, and Accomplishments Abraham de Moivre (1667–1754) was born in Vitry-Vitry-le-François, France. The formula that is also called De Moivre's theorem states . In mathematics, de Moivre's formula or de Moivre's theorem is an equation named after Abraham de Moivre.It states that for any real number x and integer n, (⁡ + ⁡) = ⁡ + ⁡The formulation of De Moivre's formula for any complex numbers (with modulus and angle ) is as follows: = = [(⁡ + ⁡)] = (⁡ + ⁡) Here, is Euler's number, and is often called the polar form of the complex number . Back to top; 1.12: Inverse Euler formula; 1.14: Representing Complex Multiplication as Matrix Multiplication First determine the radius: Since cos α = and sin α = ½, α must be in the first quadrant and α = 30°. Complex Numbers Class 11: De Moivre’s Formula | Theorem | Examples. It is interesting to note that it was Euler and not De Moivre that wrote this result explicitly (Nahin 1998). De Moivre's law first appeared in his 1725 Annuities upon Lives, the earliest known example of an actuarial textbook. “De mensura sortis” is no. Hij hield zich vooral bezig met de waarschijnlijkheidsrekening, de theorie der complexe getallen (met de beroemde stelling van De Moivre) en de theorie der oneindige rijen. de Moivre's formula A complex formula for determining life expectancy; it is not used in practice, given its large number of variables. Daniel Bernoulli's Derivation of the … so . which gives. 62/87,21 is already in polar form. I was courious about the origin of it and i look for the original paper, I found it in the Philosophicis Transactionibus Num. Explanation. De Moivre was een goede vriend van Newton en van de astronoom Edmund Halley. De Moivre's formula. But trying to derive the answer from n = k we get: The polar form of 12 i ± 5 is . I'm starting to study complex numbers, obviously we've work with De Moivre's formula. De Moivre's formula implies that there are uncountably many unit quaternions satisfying xn = 1 for n ≥ 3. Therefore , . We first gain some intuition for de Moivre's theorem by considering what happens when we multiply a complex number by itself. While the formula was named after de Moivre, he never stated it in his works. Assert true for all real powers. Hij leidde de formule voor de normale verdeling af uit de binomiale kansverdeling. (a) Since is a complex number which satisfies 3 –1 = 0, 1. (M1)(A1) Example 2. Example 1: Write in the form s + bi. Example 1. De Moivre discovered the formula for the normal distribution in probability, and first conjectured the central limit theorem. (ii) Sum of all roots of z 1/n is always equal to zero. 1. Table of Contents. Now use De Moivre ¶s Theorem to find the sixth power . De Moivre's Formula states that $z^n = r^n \\operatorname{cis} (n\\theta).$ This formula simplifies computing powers of a complex number provided one has its polar form. Therefore , . Without Euler’s formula there is not such a simple proof. De Moivre's formula can be used to express $\\cos n \\phi$ and $\\sin n \\phi$ in powers of $\\cos \\phi$ and $\\sin \\phi$: DE MOIVRE’S FORMULA. De Moivre's Formula Examples 1 Fold Unfold. (iii) Product of all roots of z 1/n = (−1) n-1 z. Abraham de Moivre (1667 – 1754) was a French mathematician who worked in probability and analytic geometry. Properties of the roots of z 1/n (i) All roots of z 1/n are in geometrical progression with common ratio e 2 πi/n. 309, \"De sectione Anguli\", but only in latin, so some words are difficult to understand, however, on the math part I don't see where's the formula. Synonyms I was asked to use de Moivre's formula to find an expression for $\\sin 3x$ in terms of $\\sin x$ and $\\cos x$. In mathematics, de Moivre's formula or de Moivre's theorem is an equation named after Abraham de Moivre. In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and integer n it holds that. 329; the trigonometric equation called De Moivre’s formula is in 373 and is anticipated in 309. De Moivre's Formula. Application de la formule de Moivre : exercice résolu Énoncé: Calculer S = 23 45 6 7 cos cos cos cos cos cos cos 7 777 77 7 ππ π π π π π ++ ++ + +, puis simplifier l’expression obtenue. See more. where i is the imaginary unit (i 2 = −1). De Moivre's Formula Examples 1. By using De’moivre’s theorem n th roots having n distinct values of such a complex number are given by. Let x and y be real numbers, and be one of the complex solutions of the equation z3 = 1. Deze video geeft uitleg over hoofdstuk 8.4 Stelling van de Moivre voor het vak wiskunde D. Euler's formula and De Moivre's formula for complex numbers are generalized for quaternions. The Edgeworth Expansion, 1905. De Moivre's theorem states that (cosø + isinø) n = cos(nø) + isin(nø).. Laplace's Extension of de Moivre's Theorem, 1812. The formula was found by A. de Moivre (1707), its modern notation was suggested by L. Euler (1748). Let $$n$$ be an integer. Hence, 1 + + 2 = = 0. (12 i ± 5)3 62/87,21 First, write 12 i ± 5 in polar form. Then for every integer 12. qn = ewne = (cos e + w sin e)” = cos ne + w no, (4) De Moivre's Formula, De Moivre's theorem, Abraham de moivre, De Moivre's Theorem for Fractional Power, state and prove de moivre's theorem with examples De Moivre's Theorem is an easy formula which is used for calculating the powers of complex numbers. The reason this simple fact has a name is that historically de Moivre stated it before Euler’s formula was known. He is most remembered for de Moivre’s formula, which links trigonometry and complex numbers. De Moivre's Theorem states that for any complex number as given below: z = r ∙ cosθ + i ∙ r ∙ sinθ the following statement is true: z n = r n (cosθ + i ∙ sin(nθ)), where n is an integer. The French mathematician Abraham de Moivre described this … Let q = ewe cos 0 + w sin 0 E S3, where 8 is real andwES2. He was a passionate mathematician who made significant contributions to analytic geometry, trigonometry, and the theory of probability. From (cosy+isiny)^2=cos2y+isin2y, one obtains cosy+isiny=±SQRT(cos2y+isin2y), or SQRT(cos2y+isin2y)=±(cosy+isiny). Despite the name now given to it, de Moivre himself did not consider his law (he called it a \"hypothesis\") to be a true description of the pattern of human mortality. Letting n = k + 1 we know that (cosø + isinø) k+1 = cos((k + 1)ø) + isin((k + 1)ø). The preceding pattern can be extended, using mathematical induction, to De Moivre's theorem. Evaluate: (a) 1 + + 2; (b) ( x + 2y)( 2x + y). De Moivre's theorem gives a formula for computing powers of complex numbers. De moivre definition, French mathematician in England. Eulers Formula- It is a mathematical formula used for complex analysis that would establish the basic relationship between trigonometric functions and the exponential mathematical functions. Despite De Moivre’s mathematical contributions, he continued to support himself by tutoring. It states that for any real number x and integer n, That is cosT isinT n cosnT isinnT. This theorem can be derived from Euler's equation since it connects trigonometry to complex numbers. In wiskunde, de formule Moivre's (ook bekend als de stelling Moivre's en de identiteit van Moivre's) bepaald dat voor elk reëel getal x en getal n geldt dat (⁡ + ⁡ ()) = ⁡ + ⁡ (), waarbij i de … Abraham de Moivre (French pronunciation: [abʁaam də mwavʁ]; 26 May 1667 – 27 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. Rappel: Pour simplifier les notations, on peut se souvenir qu’on peut écrire cos θ + i sin θ sous la forme eiθ. De Moivre’ s Formula 35 PROPOSITION 2. The identity is derived by substitution of n = nx in Euler's formula, as. De Moivre's Normal Approximation to the Binomial Distribution, 1733. Assuming n = 1 (cosø + isinø) 1 = cos(1ø) + isin(1ø) which is true so correct for n = 1 Assume n = k is true so (cosø + isinø) k = cos(kø) + isin(kø). Now use De Moivre ¶s Theorem to find the third power . Additional information. Use De Moivre ¶s … de Moivre's formula (mathematics) A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, (⁡ + ⁡ ()) = ⁡ + ⁡ (), where i is the imaginary unit.\nAppart' Hôtel Océan, Parc D'attraction Valence Espagne, Friv Piano Tiles 3, Travailler Au Canada Salaire, Champignons Saprophytes Comestibles, Piercing Paris 15, Chase Hudson Wikipedia, Parc D'attraction Valence Espagne, Immobilier Saisie Bancaire France, Facebook Ads Cost-per Country 2020," ]

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[ "# ECMA6中的箭头函数\n\n### ecma6的箭头函数，最初看起来实在让人头大，但其实规则很简单。\n\n```var a=(x,y)=>{return (x+y)};\nconsole.log(a(10,20))```\n\n#### () => { … } // 零个参数用 () 表示； x => { … } // 一个参数可以省略 ()； (x, y) => { … } // 多参数不能省略 ()；\n\n()=>x  //相当于return x\n\nvar a = a=>a;\n\na(22)    //22\n\nvar a = function(a){ return a; };\n\na(22);\n\n### 接下来来个神奇的demo\n\n```var a = (a,b) =>({a,b})\nconsole.log(a(2,3)) //{a:2,b:3}```\n\n### 箭头函数没有自己的this\n\n```let obj = {\ncolor: \"blue\",\ngetColor: () => {\nreturn this.color;//this指向window\n}\n};```" ]

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[ "## How do you write 4 1/5 as a percent?\n\nFirst, convert the mixed fraction to decimal, then multiply by ##100## to get ##420%##\n\nTo write this value as a percentage, we first need to convert the mixed fraction to a decimal. The fraction ##1//5## has a decimal value of ##0.2## so our mixed fraction can be written as\n\n##4 1/5 = 4+ 1/5 = 4+0.2 = 4.2##\n\nConverting a decimal value to a percentage we just multiply by 100:\n\n##4.2 = 4.2 * 100/100 = (4.2 * 100 )/ color(red)100 = 420 color(red)%##\n\nNote the ##%## or “percent” comes from per-cent, meaning per-##100##, which is what replaced the ##1/100## in our final equation!" ]

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[ "# Linear transformations and eigenvectors in 2D\n\nThis worksheet explores the effect of a linear transformation (in ), and its relationship with the eigenvectors, eigenvalues and determinant. Drag the point around the unit circle, and see how its image changes. Can you identify the eigenvectors and eigenvalues?\nThe large blue point is a point on the unit circle. Its image under the transformation T is shown as the smaller point. Drag around the unit circle and see how the image changes. Where are the eigenvectors? What (approximately) are the eigenvalues? Click 'Show eigenvectors' at top-right to check your answer. Click 'Show basis vectors' to see the effect of the transformation on the standard basis vectors , (also called ). You can enter a new linear transformation by entering values in the matrix at top-left. You can also drag the images of the basis vectors to change . Some interesting transformations to try:\n• - enter this as\n• - enter this as\nQuestions to consider:\n• What do the eigenvalues represent, geometrically?\n• What does the determinant represent, geometrically?\n• What is the relationship between the determinant () and the eigenvalues?\n• What does it mean geometrically if the determinant is negative? positive? zero?\n• Look at where (if anywhere) the image of the unit circle intersects with the unit circle. What is the significance of these intersection points? Under what conditions on the eigenvalues do the curves intersect?\n• What is the relationship between the images and the matrix ?\nClock image from Wikipedia by David Ilff - https://en.wikipedia.org/wiki/File:Clock_Tower_-_Palace_of_Westminster,_London_-_May_2007.jpg" ]

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[ "# How to Calculate the Amortization for a Loan on a Seller Carry Back Loan", null, "••• Todd Warnock/Photodisc/Getty Images\nShare It\n\nSeller carry-back financing occurs when the person selling a home holds a second mortgage from the buyer to cover the cost above what is financed by a regular first mortgage. For a simple example, the buyer obtains a mortgage for 80 percent of the home price, and the seller carries a second mortgage for the remaining 20 percent. The monthly payment for the carry-back loan depends on the agreed amount, term and interest rate. With the payment and rate, you can manually calculate an amortization schedule or set up a simple spreadsheet to calculate the entire schedule.\n\nCalculate the monthly loan payment, if you do not have that information, using an online loan payments calculator. Enter the loan amount, the term of the loan, and the annual interest rate into the provided fields for each, and click the \"Calculate\" button, or equivalent. For example, entering a \\$20,000 loan with a 10-year term at 8 percent will return a monthly payment of \\$242.66.\n\nCalculate the monthly interest rate for the loan by dividing the annual rate by 12. In the example, 8 percent per year gives a monthly rate of 0.667 percent.\n\nMultiply the monthly interest rate times the outstanding loan balance to get the interest charge on the next monthly payment. On the example carry-back loan, for the first payment the interest amount will be \\$20,000 time 0.667 percent, equaling \\$133.33.\n\nSubtract the interest amount for the first payment from the monthly payment amount to get the principal portion of the first payment, and subtract that result from the loan balance to get the next loan balance for the amortization table. With the first \\$242.66 payment of the example loan, the principal will be \\$109.33 after subtracting the \\$133.33 of interest. Subtract the payment principal to leave a loan balance after the first payment of \\$19,890.67.\n\nRepeat the interest and principal calculation for each payment based on the loan balance after the previous payment. With each payment the interest amount will drop slightly and the principal reduction will get a little larger. On the example loan, the second payment's interest, principal and balance numbers would be \\$132.60, \\$110.06 and \\$19,780.61. With the last payment the loan balance will be zero.\n\n#### Tips\n\n• There are many free online loan payment calculators, and many allow you to enter the term of the loan in either years or months. If you're familiar with algebraic functions, the loan payment formula can also be done using a financial calculator, or financial functions in a spreadsheet, but many loan payment calculators are freely available online that will calculate it instantly. Any extra principal payment amounts go directly to the loan balance, and the breakdown for all following payments would have to be recalculated. Extra principal does not change the payment but will shorten the time it takes to pay off the loan.\n\n#### Warnings\n\n• The 2010 Dodd-Frank Wall Street Reform and Consumer Protections Act requires that any residential loan including seller carry-back loans be set up to fully amortize over the term of the loan. This means that a carry-back loan cannot be interest-only or have a balloon payment." ]

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[ "# How Do You Find the Length of a Leg of a Right Triangle?\n\n### Note:\n\nFinding the missing length of a side of a right triangle? If you have the other two side lengths, you can use the Pythagorean theorem to solve! Check out this tutorial and see how to use this really helpful theorem to find that missing side measurement!\n\n### Keywords:\n\n• problem\n• triangle\n• right triangle\n• pythagorean theorem\n• solve\n• solve triangle\n• sides\n• side\n• missing side\n• length\n• length of side\n• length of leg\n• leg\n• missing leg\n• root\n• square root" ]

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[ "# Custom Formula Collection\n\nMarket Thrust Oscillator\n\nThe following formulas were taken from the article, \"The Cumulative Market Thrust Line\", by Tushar Chande, in the December 1993 issue of Technical Analysis of Stocks &\nCommodities\n.\n\nTaken from Stocks &\nCommodities\n, V. 11:12 (506-511):The Cumulative Market Thrust Line by Tushar S. Chande, PhD.\n\nSTOCKS &\nCOMMODITIES contributor Tushar Chande originally introduced the concept of market thrust in August 1992 as a method by which to overcome the limitations of the Arms index. Since then, variations have been suggested on the theme and here, Chande offers the variation of a cumulative market thrust line, in which market thrust is cumulated to calculate a volumetric advance-decline line by including the effect of up and down volume.\"\n\nComposite securities are created from 4 separate files. Advances, Declines, Upvolume, Downvolume. The article side bar presupposes the user has these four files.\n\nReuters Trend Data (RTD) supplies this data in two files. The tickers are X.NYSE-A (Advances, number and volume) and X.NYSE-D (Declines, number and volume). To use these two files, you must utilize two different custom formulas and the indicator buffer in MetaStockTM for DOS.\n\nCompuServe supplies this data in 4 files. The tickers are NYSEI (Advances);\nNYSEJ (declines);\nNYUP (Advance volume) and NYDN (decline volume).\n\nDial/Data supplies this data in two files. Advances, number and volume and Declines, number and volume. The tickers are @*NAZ_K and @*NDZ_K.\n\nFor the Windows versions of MetaStock:\n\nFor RTD and Dial Data:\n\n#1:C * V\n#2:100 * ( ( P - ( C * V ) ) / ( ( P + ( C * V ) ) ) )\n\nTo plot it:\n\n• Drag the plotted formula #1 from the advances in to the declines chart.\n\n• Plot the thrust indicator formula (#2) directly on top of the plotted formula #1 in the declines chart.\n\nFor CompuServe data:\n\n#1:C\n#2:100 * ( ( P - C ) / ( ( P + C ) ) )\n\nTo plot it:\n\n• Create a composite of the Advances * Up Volume.\n\n• Create a composite if the Declines * Down Volume.\n\n• Drag the plotted formula #1 from the advances in to the declines chart.\n\n• Plot the thrust indicator formula (#2) directly on top of the plotted formula #1 in the declines chart.\n\n** To create the cumulative thrust oscillator line perform the same steps as above except change formula #2 to:\n\nCum(100*(P-C)/(P+C)) for CompuServe data\nCum(100*(P-(C*V))/(P+(C*V))) for RTD and Dial Data\n\n** To create the cumulative market thrust line, the formula is:\n\nCum(P-C) for CompuServe data\nCum(P-(C*V)) for RTD and Dial Data\n\nYou now have the thrust indicator plotted exactly as the article discusses." ]

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[ "# Wrong order of y values in ggplot barplot\n\nI’ve got 3 groups, each one showing the number of sales for two types of clients (historical and tele-rehab).\nI’m trying to plot the sales in the order I defined them:\n\nIn the BI gain group:\n\nFirst sale is historical, black colour = 30\n\nSecond sale is tele-rehab. white colour = 20\n\nIn the BI efficiency:\n\nFirst sale is historical, black colur = 49\n\nSecond sale is tele-rehab, white colur = 47\n\nIn the BI effectiveness:\n\nFirst sale is historical, black colour =58\n\nSecond sale is tele-rehab, white colur=60\n\nWhen I try to plot it ggplot changes the order of the sales\n\n``````ibrary(ggplot2)\ndf <- data.frame(stadium=c('BI gain', 'BI efficiency', 'BI effectiveness'),\nfood=c('historical','tele-rehab', 'historical','tele-rehab', 'historical','tele-rehab'),\nsales=c(30.0, 20.0, 49.0, 47.0, 58.0, 60.0))\n\ndf\\$sales<-as.numeric(as.character(df\\$sales))\n\ngeom_bar(position='dodge', stat='identity',colour=\"black\")+\nscale_fill_manual ('Where', values = c(\"black\",\"white\"))\n``````\n\nI defined the sales as numeric, but ggplot changes the order.\n\n### >Solution :\n\nThe problem is how you defined your dateframe. You listed the stadiums only once each and thus R does autofill then. Just list all the possible stadiums in your dataframe. See code below:\n\n``````library(ggplot2)\ndf <- data.frame(stadium=c('BI gain', 'BI gain',\n'BI efficiency', 'BI efficiency',\n'BI effectiveness', 'BI effectiveness'),\nfood=c('historical','tele-rehab',\n'historical','tele-rehab',\n'historical','tele-rehab'),\nsales=c(30.0, 20.0,\n49.0, 47.0,\n58.0, 60.0))" ]

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[ "# when moving a Game Object in a circle through it Transform Position, how can I control which arch of the circle to start moving on?\n\n // Unity2D\n// sort of like a rainbow arc motion starting from left to right and vice versa.\nprivate float rotateSpeed = 1.0f;\nprivate Vector2 _centre;\nprivate float _angle;\npublic void Start()\n{\n_centre = transform.position;\n}\nprivate void FixedUpdate()\n{\nTransportPlayer();\n}\npublic void TransportPlayer()\n{\n\nif (true)\n{\n\n_centre = transform.position;\n\n_angle += rotateSpeed * Time.deltaTime;\nvar offset = new Vector2(Mathf.Sin(_angle), Mathf.Cos(_angle)) * radius;\ntransform.position = _centre + offset;\n\n}\nelse\n{\nreturn;\n}\n\n}" ]

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[ "# Product of Indices of Real Number\n\n## Theorem\n\nLet $r \\in \\R_{> 0}$ be a (strictly) positive real number.\n\n### Positive Integers\n\nLet $n, m \\in \\Z_{\\ge 0}$ be positive integers.\n\nLet $r^n$ be defined as $r$ to the power of $n$.\n\nThen:\n\n$\\paren {r^n}^m = r^{n m}$\n\n### Integers\n\nLet $n, m \\in \\Z$ be positive integers.\n\nLet $r^n$ be defined as $r$ to the power of $n$.\n\nThen:\n\n$\\paren {r^n}^m = r^{n m}$\n\n### Rational Numbers\n\nLet $x, y \\in \\Q$ be rational numbers.\n\nLet $r^x$ be defined as $r$ to the power of $x$.\n\nThen:\n\n$\\paren {r^x}^y = r^{x y}$" ]

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[ "login  home  contents  what's new  discussion  bug reports help  links  subscribe  changes  refresh  edit\n\nRef:\n\nhttp://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction\n\n\"The Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras; since they extend the complex numbers, ... \"\n\ncomplex numbers, quaternions, octonions, sedenions, ...\n\nhttp://en.wikipedia.org/wiki/Hypercomplex_number\n\n)abbrev domain CALEY CaleyDickson\nCaleyDickson(C:CommutativeRing,gen:Symbol,gamma:C):ComplexCategory(C) with\nhyper:List % -> %\n++ convert a list of scalars to a hyper-comnplex number\nscalars: % -> List %\n++ convert a hyper-complex number to a list of scalars\nRep := Record(re:C, im:C)\nrep(x:%):Rep == x pretend Rep\nper(x:Rep):% == x pretend %\ncomplex(x:C,y:C):% == per [x,y]\nreal(x:%):C == rep(x).re\nimag(x:%):C == rep(x).im\n--mul(x:C,y:%):% == complex(x * real y, x * imag y)\nmul(x:C,y:%):% == per [x * rep(y).re, x * rep(y).im]\n-- Many funtctions are inherited from ComplexCategory\n--\n-- To Do:\n-- 1) Check which functions are still correct for higher-order algebras!\n0:% == complex(0,0)\n--zero?(x:%):Boolean == zero? real x and zero? imag x\nzero?(x:%):Boolean == x = 0\n1:% == complex(1,0)\n--one?(x:%):Boolean == one? real x and zero? imag x\none?(x:%):Boolean == x = 1\nif C has conjugate:C->C then\n-- In general we need conjugate\n(x:% * y:%):% ==\ncomplex(real x * real y - gamma*conjugate imag y * imag x,\nimag y * real x + imag x * conjugate real y)\nconjugate(x:%):% == complex(conjugate(real x), -imag x)\nelse\n-- If not complex then conjugate is identity\n(x:% * y:%):% ==\ncomplex(real x * real y - gamma*imag y * imag x,\nimag y * real x + imag x * real y)\nconjugate(x:%):% == complex(real x, -imag x)\n-- correct order\nnorm(x:%):C == retract(conjugate(x)*x)\nif C has Field then\ninv(x:%):% == mul(inv norm x, conjugate x)\n(x:% / y:%):% == x * inv(y)\nif C has rank:()->PositiveInteger then\nrank():PositiveInteger == 2*rank()$C else rank():PositiveInteger == 2 if C has basis:()->Vector C then basis():Vector % == concat([complex(i,0) for i in entries basis()$C],\n[complex(0,i) for i in entries basis()$C]) else basis():Vector % == [1,imaginary()] if C has scalars: C -> List C then scalars(x:%):List % == map(coerce,concat(scalars real x, scalars imag x))$ListFunctions2(C,%)\nelse\nscalars(x:%):List % == [ coerce real x, coerce imag x ]\nif C has hyper:List C -> C then\nhyper(x:List %):% ==\nh:Integer := divide(#x,2).quotient\ncomplex(hyper([retract(x.i)@C for i in 1..h]),hyper([retract(x.i)@C for i in h+1..#x]))\nelse\nhyper(x:List %):% == complex(retract x.1,retract x.2)\ncoerce(x:%):OutputForm ==\noutr:=real(x)::OutputForm\nimag x = 0 => return outr\nouti := hconcat(imag(x)::OutputForm, gen::OutputForm)\nif imag x = 1 then\nouti := gen::OutputForm\nif imag x = -1 then\nouti := -(gen::OutputForm)\nif C has imaginary:()->C then\nif imag x = -imaginary()$C then outi := -hconcat(imaginary()$C::OutputForm,gen::OutputForm)\nreal x = 0 => return outi\nreturn outr + outi\n Compiling FriCAS source code from file\nusing old system compiler.\nCALEY abbreviates domain CaleyDickson\n------------------------------------------------------------------------\ninitializing NRLIB CALEY for CaleyDickson\ncompiling into NRLIB CALEY\n****** Domain: C already in scope\ncompiling local rep : $-> Rep CALEY;rep is replaced by x Time: 0.11 SEC. compiling local per : Rep ->$\nCALEY;per is replaced by x\nTime: 0 SEC.\ncompiling exported complex : (C,C) -> $Time: 0 SEC. compiling exported real :$ -> C\nTime: 0 SEC.\ncompiling exported imag : $-> C Time: 0 SEC. compiling local mul : (C,$) -> $Time: 0 SEC. compiling exported Zero : () ->$\nTime: 0.01 SEC.\ncompiling exported zero? : $-> Boolean Time: 0 SEC. compiling exported One : () ->$\nTime: 0 SEC.\ncompiling exported one? : $-> Boolean Time: 0 SEC. augmenting C: (SIGNATURE C conjugate (C C)) compiling exported * : ($,$) ->$\nTime: 0 SEC.\ncompiling exported conjugate : $->$\nTime: 0 SEC.\ncompiling exported * : ($,$) -> $Time: 0.01 SEC. compiling exported conjugate :$ -> $Time: 0 SEC. compiling exported norm :$ -> C\nTime: 0 SEC.\n****** Domain: C already in scope\naugmenting C: (Field)\ncompiling exported inv : $->$\nTime: 0 SEC.\ncompiling exported / : ($,$) -> $Time: 0 SEC. augmenting C: (SIGNATURE C rank ((PositiveInteger))) compiling exported rank : () -> PositiveInteger Time: 0 SEC. compiling exported rank : () -> PositiveInteger CALEY;rank;Pi;19 is replaced by 2 Time: 0 SEC. augmenting C: (SIGNATURE C basis ((Vector C))) compiling exported basis : () -> Vector$\nTime: 0.02 SEC.\ncompiling exported basis : () -> Vector $Time: 0.01 SEC. augmenting C: (SIGNATURE C scalars ((List C) C)) compiling exported scalars :$ -> List $Time: 0 SEC. compiling exported scalars :$ -> List $Time: 0.01 SEC. augmenting C: (SIGNATURE C hyper (C (List C))) compiling exported hyper : List$ -> $Time: 0.02 SEC. compiling exported hyper : List$ -> $Time: 0.01 SEC. compiling exported coerce :$ -> OutputForm\naugmenting C: (SIGNATURE C imaginary (C))\nTime: 0.01 SEC.\n****** Domain: C already in scope\n****** Domain: C already in scope\naugmenting C: (TranscendentalFunctionCategory)\n****** Domain: C already in scope\naugmenting C: (RealNumberSystem)\n****** Domain: C already in scope\naugmenting C: (TranscendentalFunctionCategory)\n****** Domain: C already in scope\naugmenting C: (Comparable)\n****** Domain: C already in scope\naugmenting C: (ConvertibleTo (InputForm))\n****** Domain: C already in scope\naugmenting C: (ConvertibleTo (Pattern (Float)))\n****** Domain: C already in scope\naugmenting C: (ConvertibleTo (Pattern (Integer)))\n****** Domain: C already in scope\naugmenting C: (DifferentialRing)\n****** Domain: C already in scope\naugmenting C: (Eltable C C)\n****** Domain: C already in scope\naugmenting C: (EuclideanDomain)\n****** Domain: C already in scope\naugmenting C: (Evalable C)\n****** Domain: C already in scope\naugmenting C: (Field)\n****** Domain: C already in scope\naugmenting C: (Finite)\n****** Domain: C already in scope\naugmenting C: (FiniteFieldCategory)\n****** Domain: C already in scope\naugmenting C: (InnerEvalable (Symbol) C)\n****** Domain: C already in scope\naugmenting C: (IntegerNumberSystem)\n****** Domain: C already in scope\naugmenting C: (IntegralDomain)\n****** Domain: C already in scope\naugmenting C: (LinearlyExplicitOver (Integer))\n****** Domain: C already in scope\naugmenting C: (PartialDifferentialRing (Symbol))\n****** Domain: C already in scope\naugmenting C: (PatternMatchable (Float))\n****** Domain: C already in scope\naugmenting C: (PatternMatchable (Integer))\n****** Domain: C already in scope\naugmenting C: (RealConstant)\n****** Domain: C already in scope\naugmenting C: (RealNumberSystem)\n****** Domain: C already in scope\naugmenting C: (RetractableTo (Fraction (Integer)))\n****** Domain: C already in scope\naugmenting C: (RetractableTo (Integer))\n****** Domain: C already in scope\naugmenting C: (TranscendentalFunctionCategory)\n(time taken in buildFunctor: 250)\n;;; *** |CaleyDickson| REDEFINED\n;;; *** |CaleyDickson| REDEFINED\nTime: 0.29 SEC.\nWarnings:\n rep: pretendRep -- should replace by @\n per: pretend$-- should replace by @ real: re has no value imag: im has no value mul: re has no value mul: im has no value scalars:$$has no value Cumulative Statistics for Constructor CaleyDickson Time: 0.50 seconds finalizing NRLIB CALEY Processing CaleyDickson for Browser database: --->-->CaleyDickson(constructor): Not documented!!!! --------(hyper (% (List %)))--------- --->-->CaleyDickson((hyper (% (List %)))): Improper first word in comments: convert \"convert a list of scalars to a hyper-comnplex number\" --------(scalars ((List %) %))--------- --->-->CaleyDickson((scalars ((List %) %))): Improper first word in comments: convert \"convert a hyper-complex number to a list of scalars\" --->-->CaleyDickson(): Missing Description ; compiling file \"/var/aw/var/LatexWiki/CALEY.NRLIB/CALEY.lsp\" (written 25 FEB 2018 05:41:10 PM): ; /var/aw/var/LatexWiki/CALEY.NRLIB/CALEY.fasl written ; compilation finished in 0:00:00.120 ------------------------------------------------------------------------ CaleyDickson is now explicitly exposed in frame initial CaleyDickson will be automatically loaded when needed from /var/aw/var/LatexWiki/CALEY.NRLIB/CALEY Test fricas R := FRAC POLY Integer", null, "(1) Type: Type Complex Numbers fricas C := CaleyDickson(R,'i,1)", null, "(2) Type: Type fricas rank()$C", null, "(3)\nType: PositiveInteger?\nfricas\nCe:ILIST(C,0) := construct entries basis()$C", null, "(4) Type: IndexedList?(CaleyDickson(Fraction(Polynomial(Integer)),i,1),0) fricas matrix [[Ce.i * Ce.j for j in 0..#Ce-1] for i in 0..#Ce-1]", null, "(5) Type: Matrix(CaleyDickson(Fraction(Polynomial(Integer)),i,1)) fricas -- -- compare -- Cg:ILIST(Complex R,0) := construct map(x+-> complex(x.1,x.2), 1$SquareMatrix(2,FRAC INT)::List List FRAC INT)", null, "(6)\nType: IndexedList?(Complex(Fraction(Polynomial(Integer))),0)\nfricas\nmatrix [[Cg.i * Cg.j for j in 0..#Cg-1] for i in 0..#Cg-1]", null, "(7)\nType: Matrix(Complex(Fraction(Polynomial(Integer))))\nfricas\n-- normed?\nc1:C := hyper [subscript('c1,[i]) for i in 1..2]", null, "(8)\nType: CaleyDickson(Fraction(Polynomial(Integer)),i,1)\nfricas\nc2:C := hyper [subscript('c2,[i]) for i in 1..2]", null, "(9)\nType: CaleyDickson(Fraction(Polynomial(Integer)),i,1)\nfricas\nc3:C := hyper [subscript('c3,[i]) for i in 1..8]", null, "(10)\nType: CaleyDickson(Fraction(Polynomial(Integer)),i,1)\nfricas\n-- Normed?\ntest(norm(c1*c2)=norm(c1)*norm(c2))", null, "(11)\nType: Boolean\nfricas\n-- Commutative?\ntest( c1 * c2 = c2 * c1 )", null, "(12)\nType: Boolean\nfricas\n-- Associative?\ntest((c1 * c2) * c3 = c1 * (c2 * c3))", null, "(13)\nType: Boolean\nfricas\n-- inverse\nc1inv := inv c1", null, "(14)\nType: CaleyDickson(Fraction(Polynomial(Integer)),i,1)\nfricas\ntest(c1 * c1inv = 1)", null, "(15)\nType: Boolean\n\nQuaternions\n\nfricas\nQ := CaleyDickson(C,'j,1)", null, "(16)\nType: Type\nfricas\nrank()$Q", null, "(17) Type: PositiveInteger? fricas Qe:ILIST(Q,0) := construct entries basis()$Q", null, "(18)\nType: IndexedList?(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),0)\nfricas\nmatrix [[Qe.i * Qe.j for j in 0..#Qe-1] for i in 0..#Qe-1]", null, "(19)\nType: Matrix(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1))\nfricas\n--\n-- compare\n--\nQg:ILIST(Quaternion R,0) := construct map(x+-> quatern(x.1,x.2,x.3,x.4),\n1$SquareMatrix(4,FRAC INT)::List List FRAC INT)", null, "(20) Type: IndexedList?(Quaternion(Fraction(Polynomial(Integer))),0) fricas matrix [[Qg.i * Qg.j for j in 0..#Qg-1] for i in 0..#Qg-1]", null, "(21) Type: Matrix(Quaternion(Fraction(Polynomial(Integer)))) fricas q1:Q := hyper [subscript('q1,[i]) for i in 1..4]", null, "(22) Type: CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1) fricas q2:Q := hyper [subscript('q2,[i]) for i in 1..4]", null, "(23) Type: CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1) fricas q3:Q := hyper [subscript('q3,[i]) for i in 1..8]", null, "(24) Type: CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1) fricas -- Normed? test( norm(q1*q2) = norm(q1)*norm(q2))", null, "(25) Type: Boolean fricas -- Commutative? test( q1 * q2 = q2 * q1 )", null, "(26) Type: Boolean fricas -- Associative? test((q1 * q2) * q3 = q1 * (q2 * q3))", null, "(27) Type: Boolean fricas -- inverse q1inv := inv q1", null, "(28) Type: CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1) fricas test(q1 * q1inv = 1)", null, "(29) Type: Boolean Octonions fricas O:=CaleyDickson(Q,'k,1)", null, "(30) Type: Type fricas rank()$O", null, "(31)\nType: PositiveInteger?\nfricas\nOe:ILIST(O,0) := construct entries basis()$O", null, "(32) Type: IndexedList?(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),0) fricas matrix [[Oe.i * Oe.j for j in 0..#Oe-1] for i in 0..#Oe-1]", null, "(33) Type: Matrix(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1)) fricas -- -- compare -- Og:ILIST(Octonion R,0):=map(x+-> octon(x.1,x.2,x.3,x.4,x.5,x.6,x.7,x.8), 1$SquareMatrix(8,FRAC INT)::List List FRAC INT)", null, "(34)\nType: IndexedList?(Octonion(Fraction(Polynomial(Integer))),0)\nfricas\nmatrix [[Og.i * Og.j for j in 0..#Og-1] for i in 0..#Og-1]", null, "(35)\nType: Matrix(Octonion(Fraction(Polynomial(Integer))))\nfricas\no1:O := hyper [subscript('o1,[i]) for i in 1..8]", null, "(36)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1)\nfricas\no2:O := hyper [subscript('o2,[i]) for i in 1..8]", null, "(37)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1)\nfricas\no3:O := hyper [subscript('o3,[i]) for i in 1..8]", null, "(38)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1)\nfricas\n-- normed?\ntest(norm(o1*o2)=norm(o1)*norm(o2))", null, "(39)\nType: Boolean\nfricas\n-- Commutative?\ntest( o1 * o2 = o2 * o1 )", null, "(40)\nType: Boolean\nfricas\n-- Associative?\ntest((o1 * o2) * o3 = o1 * (o2 * o3))", null, "(41)\nType: Boolean\nfricas\n-- Alternative?\ntest((o1 * o2) * o1 = o1 * (o2 * o1))", null, "(42)\nType: Boolean\n\nSplit-Octonions\n\nNote: Our table below is not identical the one shown in the reference where a different convention is used to define multiplication.\n\nfricas\nsO:=CaleyDickson(Q,'ℓ,-1)", null, "(43)\nType: Type\nfricas\nrank()$sO", null, "(44) Type: PositiveInteger? fricas sOe:ILIST(sO,0) := construct entries basis()$sO", null, "(45)\nType: IndexedList?(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1),0)\nfricas\nmatrix [[sOe.i * sOe.j for j in 0..#sOe-1] for i in 0..#sOe-1]", null, "(46)\nType: Matrix(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1))\nfricas\nso1:sO := hyper [subscript('so1,[i]) for i in 1..8]", null, "(47)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1)\nfricas\nso2:sO := hyper [subscript('so2,[i]) for i in 1..8]", null, "(48)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1)\nfricas\nso3:sO := hyper [subscript('so3,[i]) for i in 1..8]", null, "(49)\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1)\nfricas\n-- Normed?\ntest(norm(so1*so2)=norm(so1)*norm(so2))", null, "(50)\nType: Boolean\nfricas\n-- Commutative?\ntest( so1 * so2 = so2 * so1 )", null, "(51)\nType: Boolean\nfricas\n-- Associative?\ntest((so1 * so2) * so3 = so1 * (so2 * so3))", null, "(52)\nType: Boolean\nfricas\n-- Alternative?\ntest((so1 * so2) * so1 = so1 * (so2 * so1))", null, "(53)\nType: Boolean\nfricas\n-- inverse\nso1inv := inv so1;\nType: CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),ℓ,-1)\nfricas\ntest(so1 * so1inv = 1)", null, "(54)\nType: Boolean\n\nSedenions\n\nfricas\nS:=CaleyDickson(O,'l,1)", null, "(55)\nType: Type\nfricas\nrank()$S", null, "(56) Type: PositiveInteger? fricas Se:ILIST(S,0) := construct entries basis()$S", null, "(57)\nType: IndexedList?(CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1),0)\nfricas\nmatrix [[Se.i * Se.j for j in 0..#Se-1] for i in 0..#Se-1]", null, "(58)\nType: Matrix(CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1))\nfricas\ns1:S := hyper [subscript('s1,[i]) for i in 1..16]", null, "(59)\nType: CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1)\nfricas\ns2:S := hyper [subscript('s2,[i]) for i in 1..16]", null, "(60)\nType: CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1)\nfricas\ns3:S := hyper [subscript('s3,[i]) for i in 1..16]", null, "(61)\nType: CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1)\nfricas\n-- normed?\ntest(norm(s1*s2)=norm(s1)*norm(s2))", null, "(62)\nType: Boolean\nfricas\n-- Commutative\ntest( s1 * s2 = s2 * s1 )", null, "(63)\nType: Boolean\nfricas\n-- Associative?\ntest( (s1 * s2) * s3 = s1 * (s2 * s3) )", null, "(64)\nType: Boolean\nfricas\n-- Alternative?\ntest((s1 * s2) * s1 = - s1 * (s2 * s1))", null, "(65)\nType: Boolean\nfricas\n-- zero divisor\n(Se.3 + Se.10) * (Se.6 - Se.15)", null, "(66)\nType: CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1)\nfricas\n-- inverse\ns1inv := inv s1;\nType: CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Fraction(Polynomial(Integer)),i,1),j,1),k,1),l,1)\nfricas\ntest(s1 * s1inv = 1)", null, "(67)\nType: Boolean\n\nPower Associative?\n\nAlgebra with associative powers\n\nfricas\ntest( s1^2 * s1 = s1 * s1^2 )", null, "(68)\nType: Boolean\nfricas\ntest( (s1^2 * s1) * s1 = s1^2 * s1^2 )", null, "(69)\nType: Boolean\n\nConversions\n\nfricas\ntest(s1=hyper scalars s1)", null, "(70)\nType: Boolean\nfricas\nscalars(s1)::List Symbol", null, "(71)\nType: List(Symbol)\n\n Subject:   Be Bold !! ( 15 subscribers )" ]

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[ "# Principal components analysis\n\nI was working on an exercise that asks me to get a k-dimensional approximation of a data vector using PCA (containing 4096 dimensions - the faces data set). I did this in R, but the last section asks for a \"short mathematical expression for how you construct the approximation where you need to account appropriately for the mean and standard deviation terms\". I am familiar how to derive the PC's of the covariance matrix using eigen decomposition but I don't get the \"accounting for the mean and sd\" part.\n\nCan someone help?\n\n• I think they are asking you to standardize the data before carrying out the PCA. – Vishaal Sudarsan Mar 12 '18 at 1:26\n\nIn PCA, our goal is to find linear combinations of the data such that the variance is maximized subject to certain conditions. If our original data is not all on the same scale, and especially if the scale difference is large, then the result can be somewhat meaningless. We can rectify this by standardizing our data first and then running the procedure - this is equivalent to using our original correlation matrix as the covariance matrix in the PCA. This can be shown as follows: $$Cov\\left(\\frac{X_1-\\mu_1}{\\sigma_1}, \\frac{X_2-\\mu_2}{\\sigma_2}\\right) = \\frac{Cov(X_1,X_2)}{\\sigma_1\\sigma_2} = Corr(X_1, X_2)$$" ]

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[ "Feet To Meters\n\n# 4391 ft to m4391 Foot to Meters\n\nft\n=\nm\n\n## How to convert 4391 foot to meters?\n\n 4391 ft * 0.3048 m = 1338.3768 m 1 ft\nA common question is How many foot in 4391 meter? And the answer is 14406.167979 ft in 4391 m. Likewise the question how many meter in 4391 foot has the answer of 1338.3768 m in 4391 ft.\n\n## How much are 4391 feet in meters?\n\n4391 feet equal 1338.3768 meters (4391ft = 1338.3768m). Converting 4391 ft to m is easy. Simply use our calculator above, or apply the formula to change the length 4391 ft to m.\n\n## Convert 4391 ft to common lengths\n\nUnitLength\nNanometer1.3383768e+12 nm\nMicrometer1338376800.0 µm\nMillimeter1338376.8 mm\nCentimeter133837.68 cm\nInch52692.0 in\nFoot4391.0 ft\nYard1463.66666667 yd\nMeter1338.3768 m\nKilometer1.3383768 km\nMile0.8316287879 mi\nNautical mile0.7226656587 nmi\n\n## What is 4391 feet in m?\n\nTo convert 4391 ft to m multiply the length in feet by 0.3048. The 4391 ft in m formula is [m] = 4391 * 0.3048. Thus, for 4391 feet in meter we get 1338.3768 m.\n\n## 4391 Foot Conversion Table", null, "## Alternative spelling\n\n4391 ft to Meters, 4391 ft to Meter, 4391 Foot to m, 4391 Feet in Meter, 4391 ft in m, 4391 Feet to m, 4391 Foot in Meters, 4391 Foot to Meter, 4391 Foot in Meter, 4391 Feet in Meters," ]

[ null, "https://feet-to-meters.appspot.com/image/4391.png", null ]

[ "# Gosset's Polytopes\n\nI've been learning about the E_6, E_7, and E_8 lattices lately, with a lot of help from David Richter. If one reads about these in Coxeter's \"Regular Polytopes\", one comes across the Gosset polytopes, which Pierre Etevenon has been interested in for some time. It is well-known that the 8-dimensional Gosset polytope, 4_21, has 240 vertices, corresponding to the vertices of two concentric 600-cells. David showed me how to compute the edges of 4_21 by finding all pairs of those 240 vertices that have a dot-product of one. This turned out to be pretty trivial to \"code up\" based on vZome and my existing 600cell.vef dataset, and the result is what you see below.", null, "Here is the vZome save file for this model. Save the model file to disk, then launch vZome via Java Web Start, then use the \"Open\" command in the \"File\" menu. If you use an earlier version of vZome the model file may not open!\n\nIt definitely appears that David's conjecture he stated in Banff may well be correct: that this projection of 4_21 can be constructed by building two concentric 600-cells, scaled by the golden ratio, then connecting any two balls when you can with a red, yellow, or blue strut. The model is quite clearly heavily interconnected, with every strut intersecting several others in the interior. This is the effect of projecting 6720 edges (between 240 vertices) from eight dimensions down to three... there are no edge intersections in the 8-dimensional original.\n\nAlthough it might be difficult to prove, I suspect that the projection of 4_21 into 4-dimensional space has H_4 symmetry. It is certainly true that the E_8 reflection group contains a subgroup isomorphic to the H_4 reflection group, a fact we will explore this weekend in the Chicago Zomeposium hosted by Chris Palmer.\n\nDavid also told me how to compute the vertex figure of 4_21, which turns out to be 3_21, the Gosset polytope in seven dimensions. Where 4_21 has E_8 symmetry, 3_21 has E_7 symmetry. To find a single 3_21 in a 4_21, select any vertex of 4_21, then find the nearest 56 vertices, and all (756) \"short\" edges among them. This turns out to be another trivial exercise in finding vertex pairs with dot product equal to one. The result of this exercise, after centering on the origin, is shown below.", null, "This model is quite a bit less cluttered than the 4_21 projection, but note that there is a high degree of edge intersection near the center. This is made more clear by the beautiful orthogonal projection down a red direction shown below. The model has H_3 symmetry but evidently not H_4, consistent with the fact (?) that E_7 does NOT contain a subgroup isomorphic to H_4. Here is the vZome save file for this model. Constructing this in real Zome would be a real challenge!", null, "Now, I've described two separate algorithms using dot products, one to compute the \"short\" edges given a vertex set, and another to find the vertex figure of a polytope. We can apply these two algorithms to a vertex of 3_21, to produce 2_21, its vertex figure, the Gosset polytope in 6 dimensions. 2_21 has E_6 symmetry. A projection into Zome is shown below. The model has a single axis of fivefold symmetry, and the view below shows the model \"edge-on\".", null, "The view below is looking almost directly down the fivefold symmetry axis. This model is very feasible to construct in real Zome, though probably at one \"tau scale\" larger than shown, to allow for the struts to bypass one another rather than introducing \"false vertices\" at the intersections. Here is the vZome save file for this model.", null, "Do you think these Zome models are complicated? In fact, they are deceptively simple, since such highly symmetric projections of the Gosset polytopes naturally result in a high degree of \"coincidence\", where separate vertices and edges overlay each other when projected to 3-space. To get a clearer sense of the complexity of these polytopes, one really has to move toward less symmetric projections. Fortunately, vZome offers the ability to perform quaternion rotations on the 4D model before projecting to three dimensions. A \"green quaternion\" seems to always put the model into a tetrahedral symmetry system, as we saw a couple of weeks ago. Here is such a projection of the 2_21 we just saw:", null, "Here is the vZome save file for this model. This projection is a model with three-fold symmetry, and the view above shows the model from the side. Note the two corner-wise overlapped blue cubes; these lie along the symmetry axis. Note also the yellow rhombic dodecahedron. The view below shows the model from a viewpoint looking down the symmetry axis. Note how different this projection looks from the \"real Zome\" projection!", null, "Now, one nice thing about \"green quaternion\" projection of these models is that it can be done in many different ways! I've tried at least 5 different green directions, and gotten as many very different projections. There may be as many as 30 different projections, although I expect a smaller number like 5 or 12. One can apply the same projections to 3_21 or 4_21, of course. Here is my current favorite \"green\" projection of 3_21... clearly showing a lot more edges than the icosahedral projection did.", null, "Here is the vZome save file for this model. An orthogonal (parallel) projection of this model is shown below; here you can see some hints of five-fold symmetry, in terms of squashed pentagons all over the place.", null, "Naturally, to really get a sense of these projections, you need to turn them over in real time, using vZome. You can also apply your own quaternion rotations before importing the 4D VEF files. For that purpose, you can download the 4_21, 3_21, and 2_21 VEF datafiles to your disk, then use the \"import 3D...\" vZome command." ]

[ null, "http://vzome.com/gosset/4_21_ryb.jpg", null, "http://vzome.com/gosset/3_21_ryb.png", null, "http://vzome.com/gosset/3_21_ryb_ortho.png", null, "http://vzome.com/gosset/2_21_ryb.jpg", null, "http://vzome.com/gosset/2_21_ryb_5fold.jpg", null, "http://vzome.com/gosset/2_21_tetra_side.png", null, "http://vzome.com/gosset/2_21_tetra_3fold.jpg", null, "http://vzome.com/gosset/3_21_tetra_cubes.png", null, "http://vzome.com/gosset/3_21_tetra_cubes_ortho.png", null ]

[ "## Search\n\nHome > General Relativity Online Course > Tensors and Relativity: Chapter 8 > General discussion of the Schwartzschild solution\nTensors and Relativity: Chapter 8\n\n# General discussion of the Schwartzschild solution\n\nIn order to understand the physical properties of the Schwartzschild solution we first have to clarify the physical significance of the integration constant", null, ". This is best done through a comparison with Newtonian theory. For large values of the coordinate r, the line element deviates only a little from that of flat space, and from our analysis of the Newtonian limit we see that", null, "so", null, "We thus have to interpret the Schwarzschild solution as the gravitational field outside a spherically symmetric mass distribution whose [ Newtonian ] mass is M.\n\nNotice that the line element is singular when", null, ". This is the Schwartzschild radius or the gravitational radius of the source. For example for the Sun", null, "km and for the Earth it is", null, "mm.\n\nFrom the line element, we can immediately deduce some of the effects we derived using the equivalence principle." ]

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[ "Problem F: Math Problem\n\n## Problem F: Math Problem\n\nTime Limit: 1 Sec  Memory Limit: 128 MB\nSubmit: 1066  Solved: 270\n[Submit][Status][Web Board]\n\n## Description\n\nLet $$S(X)$$ be a function with variable $$X$$, it can be represented by the formula as $$S(X)= \\sum_{j=1}^X f(j)$$, where $$f(x)$$ consists of one or more functions in function set $$F=\\{C, C/x, Csinx, Ccosx, C/sinx, C/cosx, C^x, Cx\\}$$ with C is a constant integer ranging from 0 to 109.\n\n## Input\n\nThe 1st line of input contains a single integer $$t \\ (1 \\leq t \\leq 10^4)$$, the number of test cases.\n\nThere is a string $$s (1 \\leq |s| \\leq 100)$$ in each line of the rest t lines.\n\nString s indicates the formula of $$f(x)$$. Fraction is presented as $$a/b$$. Cx is presented as C^x. Note that the constant C will not be omitted when C=1. Two adjacent functions in $$f(x)$$ are connected by +.\n\n## Output\n\nFor each test case, print \"yes\"(without quotes) in a line if $$S(X)$$ is convergent, otherwise print \"no\".\n\n## Sample Input\n\n2\n2sinx+0cosx+4x+1/sinx+0\n0\n\n## Sample Output\n\nno\nyes\n\n## HINT\n\nwe say $$S(X)$$ is convergent if $$\\lim_{X \\rightarrow \\infty} S(X)=A$$\n\n[Submit][Status]" ]

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[ "# Computational Physics\n\n## Lecture details\n\nThe lecture will be given by Professor Mazzarello.\n\nDescription:\n\nComputational physics encompasses a huge variety of topics. Therefore, the lecture can only cover a limited fraction of computational physics problems.\nTopics include:\n\n• What is computational physics and what is it used for? Traditional versus non-traditional computational physics\n• Random numbers and their applications (random number generators, random walk, cellular automata, lattice Boltzman method, event-by-event simulations)\n• Monte Carlo method (integration, statistical error, radioactive decay, percolation, importance sampling, Ising model, Markov chains, Metropolis Monte Carlo method)\n• Molecular dynamics method (Runge Kutta, predictor-corrector, Euler, Euler-Cromer, Verlet, leap-frog, velocity Verlet, Hamiltonian splitting, accuracy and stability ,force calculations: truncation and shift of potentials, linked list method)\n• Diffusion equation (random walk, Brownian motion, Crank-Nicolson, product formula approach, Chebychev algorithm, matrix exponential, stability and accuracy)\n• Computational electrodynamics (Maxwell equation, FDTD: Yee algorithm and product formula approach, ADI, multipole methods, finite element method, dissipative materials, UPML)\n• Time-(in)dependent Schrödinger equation (Leap-frog, Crank-Nicolson, product formula, Lanczos, Davidson, linear algebra: Gauss, LU decomposition)\n• Exact diagonalization\n• Quantum Monte Carlo method\n\nLearning goals:\n\n• Lectures: The students will obtain an overview of various numerical methods to solve by computer a variety of problems in science.\n• Exercises: The students will write their own computer programs for problems drawn from various areas of physics, selected such that they can be worked out in a reasonable time frame, with reasonable computational resources (PC is sufficient).\n\nLiterature:\n\n• T. Pang, An introduction to computational physics, Cambridge Univ. Press.\n• J. M. Thijssen, Computational physics, Cambridge Univ. Press\n• D. P. Landau, K. Binder, A Guide to Monte-Carlo Simulations in Statistical\nPhysics, Cambridge Univ. Press.\n• W. H. Press, S. A. Teukolsky, W. T. Wetterling, and B. P. Flannery,\nNumerical Recipes: the Art of Scientific Computing, Cambridge Univ. Press.\n\nFor more details, you can also refer to the university calender:\n\nTime Room Start/Finish\n\nMon. 10.15am - 11.45am\n\n4282 (28 B 110)\n\n09.04.2018 - 16.07.2018 (14 dates)\n\nWed. 8.15am - 9.45am TBA 11.04.2018 - 18.07.2018 (14 dates)\n\nWed. 1.15pm - 2.45pm\n\n4282 (28 B 110) 11.04.2018 - 18.07.2018 (12 dates)" ]

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[ "Mathematics\nRaiting:\n2\n\nStructure and randomness of primes", null, "Are the primes scattered over the numerical axis like wind-dispersed seeds? Of course not: simplicity is not a matter of chance, but the result of elementary arithmetic. A number is simple if and only if no smaller positive integer except one does not divide it whole.\n\nBut this is not the end of the story. The distribution of prime numbers looks random, with uneven discontinuities and clusters that look rather chaotic. If there is some scheme, it is incomprehensible. In fact, simple numbers look random enough to be played with them in dice. Create a list of successive prime numbers (say, starting with 11, 13, 17, 19, ...) and divide them by modulo 7. In other words, divide each prime number by 7 and save only the remainder. The result is a sequence of integers from the set {1, 2, 3, 4, 5, 6}, which looks almost like the result of several shots of the right bone.", null, "Having worked with a larger sample (the first million prime numbers is greater than", null, "), I calculated the number of primes with each of the six possible residues modulo 7 (also known as the six possible congruence classes modulo 7). I also feigned a million throws of a hexagonal bone. Can you say, looking at these two results, what of them what?\n\n1 2 3 4 5 6\n166 787 166 569 166 714 166 573 166 665 166 692\n120 -98 47 -94 -2 25\n\n1 2 3 4 5 6\n166 768 166 290 166 412 166 638 167 282 166 610\n101 -377 -255 -29 615 -57\n\nIn each table, the first line means the number of results in each of the six classes. The second line shows the difference", null, ", where", null, "- the average value of", null, ". In both cases, it seems that the numbers are distributed fairly evenly, without obvious displacements. The first table shows the remainders of prime numbers from division by modulus 7. Their distribution is slightly flatter in comparison with the simulated bone and with smaller deviations from the mean; the standard deviation of the two samples is 84 and 346, respectively. Judging by these tables, it seems that any of the processes can be used to provide the randomness required in a conventional dice game.\n\nBut the randomness condition is not only the uniform distribution of the results in the admissible interval. In addition, individual events in the sequence must be independent of each other. One roll of the dice should not affect the result of the next throw. To verify independence, one can look at successive events. How many times does one unit, or two, or three, go for the unit, and so on? We will write the number of all 36 possible pairs in the matrix", null, ". If the process is really random, all 36 pairs should have the same frequency, if small statistical fluctuations are not taken into account. You can turn the matrix into a color \"heat map\", in which cells with an amount above the average will be displayed in warm shades of pink and red, and below the average - are filled with colder shades of blue. (The insertion quantities are not the actual number", null, ", but the normalized variable is", null, ", where", null, "is again the average value, in our case", null, ".) Here is the heat map of the simulated right bone:", null, "Figure 1.\n\nThere is nothing interesting. Almost all quantities are so close to the average value that the cells of the matrix appear to be neutral gray, only a few turned out to be pale pink or blue. This is exactly what you expect when successive dice rolls do not correlate with each other, and all possible pairs are equally likely.\n\nNow we pass to the corresponding matrix of successive prime numbers modulo 7:", null, "Figure 2.\n\nWow! It looks like we left the Country of random numbers, here the old gray movie turned into Technicolor. On the thermal map, a blue band appeared along the main diagonal (from the left top to the right bottom), meaning that successive pairs of primes having the same value of the remainder of the division by 7 are very unlikely. In other words, pairs", null, "occur less often than it would in a really random sequence. The off-diagonal (directly above the main diagonal) has a lighter blue color. This means that the pairs", null, ", where", null, ", appear a little less frequently than the average frequency. For example,", null, "and", null, "have slightly negative values ​​of the normalized frequency. On the other hand, the sub-diagonal (under the main diagonal) is completely pink and red; such pairs as", null, "or", null, ", where", null, ", arise with a frequency above the average. Far from the diagonal, in the upper right and lower left corner we see a pastel chess pattern.\n\nIf you prefer dealing with numbers, not with colored squares, here's the matrix of values:\n\npairs of consecutive primes mod 7\n1 2 3 4 5 6\n1 15656 24376 33891 29964 33984 28916\n2 37360 15506 22004 32645 25095 33959\n3 25307 41107 14823 22747 32721 30009\n4 32936 26183 37129 14681 21852 33791\n5 24984 34207 26231 41154 15560 24529\n6 30543 25190 32636 25382 37453 15488\n\nDeviations from uniformity can be called anything, but not \"insignificant.\" In the third row, for example, you can see that if you just met 3 in the sequence of prime numbers mod 7, then the next number is much more likely to be 2, and not yet another 3. If you were playing a game with bones out of prime numbers, then such a shift would have a huge impact on the result. Bones on prime numbers are \"charged\" bones!\n\nThese remarkably strong correlations in pairs were discovered by Robert J. Lemke-Oliver and Kannan Soundararajan of Stanford University. They discussed them in preprint , published on arXiv in March this year. For me, the most surprising thing about this discovery was that no one for many years noticed these structures. They are pretty obvious if you know where to look from.\n\nI think you can not blame Euclid, because he did not find them: in antiquity ideas of chance and probability were not developed. But what about Gauss? He was a connoisseur of prime numbers, and he created his own lists of thousands of primes. In my youth he wrote : \"one of my first projects was to observe the decreasing frequency of prime numbers, for which I calculated several thousand prime numbers ...\" Moreover, Gauss practically invented the idea of ​​congruence classes and modular arithmetic. But obviously, he never suspected that in the congruences of pairs of successive prime numbers something strange could lurk.\n\nIn the 1850s, the Russian mathematician Pafnutii Lvovich Chebyshev pointed to a slight distortion in prime numbers. The division of odd prime numbers modulo 4 divides them into two subsets. All primes in the series 5, 13, 17, 29, 37, ... are congruent to 1 modulo 4; in series 3, 7, 11, 19, 23, 31, ... are congruent to 3 modulo 4. Chebyshev noted that primes in the second category appear to be more numerous. For example, among the first 10 000 odd primes there are 4 943 congruent 1 and 5 057 congruent 3. But this effect is small compared to the irregularities seen in pairs of consecutive primes.\n\nIn our time, several authors have seen a hint of the phenomenon of successive prime numbers. Lemke-Oliver and Soundararajan mention three such testimonies. (See the list of reference materials at the end of the article.) In the 1950s and 60s, Stanislav Knapowski and Pal Turan explored various aspects of the remainder of the prime division by modulo m. In an article posthumously published in 1977, they considered the division of successive prime numbers modulo 4 with residues 1 or 3. They \"assumed\" that successive pairs with the same remainder and pairs with differing remnants \"are not equally probable.\" In 2002, Chun-Min Co. investigated the series of consecutive prime numbers (not just their pairs) and created the elaborated fractal patterns based on their varying frequencies. Then in 2011 Avner Ash and his colleagues published a detailed analysis of \"Frequencies of consecutive pairs of prime numbers\", including several matrices, in which the diagonal decrease is clearly visible.\n\nGiven these precedents, were Lemke-Oliver and Soundararajan actually discoverers of correlations of consecutive primes? In my opinion, the answer should be positive. Although others have seen these patterns before, they did not describe them in such a way that they were fixed in the consciousness of the mathematical community. In fact, when Lemke-Oliver and Soundararajan announced their findings, the reaction was a surprise bordering on mistrust. Erica Clararaich in the article for Quanta quoted the reaction of the Oxford number theorist James Maynard:\nWhen Soundararajan first told Maynard about the opening of the pair, Maynard said: \"I believed him only half.\" As soon as I returned to my office, I conducted a numerical experiment to see for myself. \"<Tgsrbq>\nObviously, this was a general reaction. Evelyn Lamb in an article for Nature quotes Soundararajan: \"Everyone to whom we talked about this, eventually wrote our computer program to see for yourself. \"\n\nI did the same! Over the past few weeks, I've written a bunch of lines of code to analyze the division of prime numbers modulo m. My article is an account of my attempts to understand where these patterns come from. My methods are more computational and visual than mathematical, I can not prove anything. Lemke-Oliver and Soundararajan have applied a more rigorous and analytical approach, at the end of this article I will tell a little more about their results.\n\nIf you want to start your own investigation, you can take as a basis my code. It is written in the Julia programming language, is packaged in Jupyter notebook and is available on GitHub . (It so happened that this program became my first non-trivial experiment with Julia.) In another article, I will tell you more about my work with the language.)\n\nIn all the examples presented above, the division of primes by modulo 7 is given, but in the number 7 there is nothing special. I chose it simply because the six possible residues {1, 2, 3, 4, 5, 6} correspond to the faces of the ordinary cubic bone. Other modules give similar results. Lemke-Oliver and Soundararajan have spent most of the analysis on dividing prime numbers modulo 3, in which there are only two classes of congruences: a prime number greater than 3 must have a remainder of 1 or 2 when dividing by 3. Here is the matrix of pairs for the first million prime numbers", null, ":\n\n1 2\n1 218578 281453\n2 281454 218514", null, "Figure 3.\n\nThe pattern is quite minimalistic, but we still recognize: elements outside the diagonal for sequences", null, "and", null, "more than the elements on the diagonal for", null, "and", null, "Figure 4.\n\nClearly visible is the blue bar on the main diagonal, although in other places of the matrix the pattern is slightly weakened and blurred.\n\nI found that the correlations between consecutive prime numbers appear most clearly when the module itself is a prime number, and yet not too small. Look at the heat cards for consecutive prime numbers mod 13 and mod 17:", null, "Figure 5.", null, "Figure 6.\n\nWhat about module 31?", null, "Figure 7.\n\nFrom these matrices you will get an excellent pattern for the kilt or mosaic floor, right? And in all of them we see interesting patterns. Diagonal bands are allocated not only on the main diagonal, but also in the entire matrix. Such strips also create a chessboard pattern. Along any row or column, cells are usually alternately red and blue. A more inconspicuous feature is the approximate two-sided symmetry along the opposite diagonal (going from the left to the bottom right). If you add a square along this line, then the cells connected together will be approximately the same color. (This fact was noticed by Ash and his co-authors.)\n\nFor further analysis, I decided to focus on consecutive prime numbers mod 19. The module is large enough to result in clearly differentiated strips, but not so large as to make the matrix huge.", null, "Figure 8.\n\nHow to understand the meaning of what we see? We begin by observing that all prime numbers in our sample are odd, and therefore all the intervals between these simple ones are even numbers. For any given simple", null, "the following candidates for the rank of prime number become", null, ". Is this somehow related to the chessboard pattern? If the steps between prime numbers are to be a multiple of 2, this can definitely create correlations between every second cell of any column or row. (Indeed, the correlations with the cell must be clearly seen once, all the even elements must equal zero if the module is an even number.) You can only fill an exact cell with a \"cyclic return\" of the edge of the matrix to an odd boundary.)\n\nThe diagonal bands in the matrix assume a strong correlation between all pairs, separated by a certain numerical interval. For example, the darkest blue diagonal and the brightest red diagonal consist of cells separated by six elements along the j-axis. The first line contains cells 1 and 7, then 2 and 8, 3 and 9, and so on. It seemed to me that this relationship is easier to perceive if the matrix is ​​\"bent\", so that the diagonals become columns. The idea is to apply a circular shift to each line, all values ​​in the line will move to the left, and those that \"fall\" from the left edge will be inserted to the right. The first line is shifted to zero positions, the next line is moved to one position, and so on. (Is there a name for such a transformation? I'll just call it a \"bend\".)\n\nThen I wrote the code for this conversion, but as a result I did not get exactly what I expected:", null, "Figure 9.\n\nWhat are these zigzags along the back diagonal? I assumed that I made a mistake and shifted one extra element. And the root of the problem really turned out to be this, but the \"bug\" is not in the algorithm, but in the data itself. The matrices shown by me in all the previous drawings are only partial, they discard the empty congruence classes. In particular, the matrix for prime numbers modulo 19 ignores all prime numbers congruent to 0 modulo 19 on the logical basis that there are no such primes. In the end, if", null, "and", null, ", then", null, "can not be simple because it is divisible by 19. However, the string and column for", null, "are the real part of the matrix. If you add them, our color-coded display will look like this:", null, "Figure 10.\n\nThe presence of a null row and a column makes the definition of the transformation a bend more accurate: for each line", null, "apply a cyclic shift left at", null, "places. The resulting curved matrix also looks neater:", null, "Figure 11.\n\nWhat do these vertical bands tell us? In the original matrix, the element", null, "was the frequency with which", null, "follows", null, ". Here the cell color", null, "denotes the frequency with which", null, "follows", null, ". In other words, each column combines elements with the same mod 19 interval between two prime numbers. For example, the leftmost column contains all pairs, separated by an interval of the length of <bright> red column (", null, ") in", null, "takes into account all cases where consecutive prime numbers are separated from one another", null, ".\n\nColor coding gives us a qualitative idea of ​​which intervals appear more or less often. For a more accurate quantitative measurement, we can sum along the columns and display the results in a bar graph:", null, "Figure 12.\n\nThree observations:\n\nThe above non-uniformity of even-odd numbers is clearly visible on the graph. With the exception of 0, every even interval is allocated against the background of its odd neighbors.\nThe interval between prime numbers mod 19, equal to 6, is the most popular of all. Numbers that are multiples of 6 (namely 12 and 18) are also frequent, but to a lesser extent.\nThe interval between prime numbers mod 19, equal to 0, is remarkably unpopular. These are the elements along the main diagonal of the original matrix, so it is not surprising that their sum is at the bottom, but the deficit is stronger than I expected.\n\nI wanted to understand the sources of these patterns. What makes the interval 6 so attractive for pairs of successive prime numbers, and why almost all prime numbers eschew the poor interval 0?\n\nI already have a remote guess about popularity 6. In the 1990s Andrew Odlyzhko, Michael Rubinshtein and Marek Wolfe performed a computational study of \"jumping champions\" among prime numbers:\n\n<blockquote> An integer D is called a jumping champion if its most frequently occurring difference between consecutive prime numbers ≤ x for some x.\nAmong the smallest prime numbers (x is less than about 600), the jumping champion is usually 2, but then wins 6 and dominates a fairly large interval of the numerical axis. Approximately near number 6 is inferior to the title of 30, which eventually loses 210. Odlyzhko with colleagues estimated that this last transition occurs approximately at", null, ". The numbers in this sequence of jumping champions - 2, 6, 30, 210, ... - are primaries ; The n-th primitive is the product of the first n prime numbers.\n\nWhy do primaries become the preferred intervals between consecutive prime numbers? If", null, "is a fairly large prime number, then", null, "can not be divided into 2,", null, "can not be divided into 2 and 3,", null, "can not be divided into 2, 3 and 5, and in general", null, ", where", null, "is the n-th primitive, is not divided into any of the first n prime numbers. Of course,", null, "can still be divided into some large prime number, or there may be another simple the number between", null, "and", null, ", such that the interval between prime numbers is not guaranteed to be a primitive. But these intervals have an advantage over other applicants.\n\nWe can see this justification in action, taking the difference between the consecutive elements of our list of one million eight-digit prime numbers and plotting their frequency:", null, "Figure 13.\n\nAgain, the interval 6, which totals 13.7% of the total, clearly stands out, large multiple numbers of 6 also stand out among their immediate neighbors. It is worth noting and the general form of distribution: the cluster on the left (with a peak at 6), followed by a gradual decrease. The trend is similar to the Poisson distribution, and in fact it can be considered a correct description.\n\nThe color scheme cuts a set of data into fractions of 19 values ​​in each. The blue fraction, which includes intervals between prime numbers from 0 to 18, counts 68 percent of all the intervals present in a sample of a million prime numbers; the gold share adds another 23 percent. The remaining 9 percent are distributed widely and evenly. Not all intervals are shown in the graph: the spectrum extends to 210. (One pair of consecutive prime numbers in the sample has a distance of 210, namely 20,831,323 and 20,831,533.)\n\nIt looks like Figure 13 shows most of the pattern of consecutive prime numbers modulo19. I can make the schedule even more informative by making a simple change. We start to shift each part of the 19-elements, until it is aligned with a fraction of 0, going to the columns that are in the same column. Since the second (golden) share moves to the left until column 19 aligns with column 0, and the third (pink) portion connects column 38 to column 0. Physically, this process can be represented as a rotation of the graph around a cylinder with a circumference of 19. It is mathematically a division intervals between prime numbers modulo 19.", null, "Figure 14.\n\nIf you do not pay attention to too bright colors, Figure 14 is similar to Figure 12: the heights of all the columns are the same. This should not surprise us. In Figure 12, we divide primes by modulo 19, and then take the differences between successive separated prime numbers. In Figure 14, we take the differences between the prime numbers themselves, and then divide these differences modulo 19. Two procedures are similar:", null, "Having studied the colors, we can arrange all the fragments of the puzzle into place. Why are the prime numbers mod 19 so often separated by an interval of 6? Well, in fact mod 19 has little to do with this; the very number 6 in this sample is the most frequent interval between prime numbers. The only other significant contribution to the \"third\" share, in particular a few pairs of primes with a distance of 44.\n\nThe superiority of the first fraction also explains the inequality between even and odd intervals. All intervals in the first fraction are necessarily even, odd intervals (mod 19) begin to appear only in the second share (intervals from 19 to 37) and only for this reason they are less frequent. For eight-digit prime numbers in the sample, more than two-thirds of the consecutive pairs are closer than 19 units, and therefore are in the first fraction. (The median distance between prime numbers is 12. The average interval is 16.68, which is close to the theoretical prediction at 16.72.)\n\nFinally, Figure 14 can tell us something about the rarity of the intervals 0 mod 19. No two consecutive prime numbers can fall into one class of congruence mod 19, unless they are separated by a distance of 38 or a multiple of 38. Therefore, such pairs do not go on stage before the third share, and in it there can not be too many. The sample of a million prime numbers contains 8,384 consecutive pairs with a distance of 38 - less than one percent of the total number. And this is the main reason that the bone of primes so often falls out the same face twice in a row. This is the reason for the appearance of the blue diagonal strip in all matrices.\n\nI find it very interesting that we can explain so much about the pattern of successive prime numbers mod m without going into details and not considering the special properties of prime numbers. In fact, we can recreate a significant part of the pattern without using prime numbers at all.\n\nTwo hundred years ago, Gauss and Legendre noticed that in the neighborhood of the number of all integers , which are simple, is about", null, ". In 1936, Swedish mathematician Harald Kramer suggested interpreting this share as a probability. The idea was to go through all the integers in order, taking each", null, "with probability", null, ". Numbers in the accepted set will not be simple except by coincidence, but they will have the same large-scale distribution as the distribution of primes. Here are the first few elements of the list of a million such \"prime Cramer numbers\", where the random selection process begins with", null, ":", null, "Figure 15.\n\nThe prominent diagonal features look similar, but they are much simpler than in the corresponding graphs of prime numbers. For any prime Cramer number p mod 19, the most likely successor is p + 1 mod 19, and the least probable one is p + 19 mod 19. Between these limiting cases, there is a smooth gradient of frequency or probability with only a few small fluctuations, which most likely can be write off for statistical noise.\n\nIn this matrix there is only a chess pattern. We can partially restore its structure, generating a new set of numbers, which I call \"semisimple Cramer numbers.\" They are created by the same probabilistic sifting of integers, but this time we consider only odd numbers as candidates and change the probability to", null, "to keep the same density:", null, "Figure 16.\n\nThat's better! If you exclude from the sequence of even numbers, the minimum interval between semisimple numbers is 2, and this is also the most likely location.\n\nAdding one more change, we will come even closer to imitating to the matrix of true prime numbers. In addition to eliminating all integers multiple of 2, we also get rid of multiples of 3 and change the sampling probability accordingly. We call the resulting numbers \"semi-semisimple numbers of Cramer.\"", null, "Figure 17.\n\nNotice that 6 mod 19 is the most probable interval between half-semisimple Cramer numbers, as well as between true prime numbers, and that the same echoes are present on intervals 12 and 18. Indeed, the only obvious difference between this matrix and Figure 10 (the corresponding graph for true prime numbers) is in the column and row for numbers congruent to 0 modulo 19. There can not be any prime numbers among such numbers. If we eliminate them from the Cramer numbers, then the two matrices become almost indistinguishable. Here they are both:", null, "Figure 18.\n\nIf you look closely, you can find differences - look at the diagonal extension to the southeast of line 1, column 15 - but in general, these modified Cramer numbers surprisingly well simulate prime numbers. In both diagrams, symmetry is also noticeable with respect to the inverse diagonal. And do not forget that these two sets contain in total only 19 percent of their values: Cramer numbers include 189,794 true prime numbers.\n\nI want to add one more twist to this story. All the above examples are based on prime numbers (or their analogs) of eight decimal digits, or in other words, numbers in the neighborhood of", null, ". Are the same results valid for primes with large values? Consider a table created from successive pairs of millions of 40-bit prime numbers, taken modulo19. The pattern turns out to be familiar, but more pale:", null, "Figure 19.\n\nLet's pass to simple numbers of 400 digits, again divided by modulo 19, and get the colors faded almost beyond recognition:", null, "Figure 20.\n\nThe blue band on the main diagonal is hardly distinguishable, and the remaining features turn into simple random spots.\n\nSo, it seems that for pairs of consecutive prime numbers, size matters. To understand the reasons for this, let's look at a group of differences between consecutive prime numbers in a 40-bit sample:", null, "Figure 21.\n\nCompared to the distribution of intervals for eight-digit prime numbers (Figure 13), the spectrum is much wider and flatter. In this form, the graph is truncated at the interval 240; the long \"tail\" actually stretches far to the right, and the largest gap between consecutive prime numbers is in 1 328. Also, as Odlyzhko and his colleagues predicted, the most frequent interval between 40-bit prime numbers is not 6 but 30.\n\nBecause of the wider distribution of intervals, the first share can not dominate the behavior of the system as it does among the eight-digit prime numbers. When we begin to place one of the other mod 19 fractions above (Figure 22 below), the first six or eight shares make a significant contribution. The unevenness of even-odd is still present, but the amplitude of these oscillations is much lower. The leftmost column of the graph, representing intervals congruent to 0 modulo 19, lags behind in growth, but not so much.", null, "Figure 22.\n\nAlignment of the spectrum becomes even more pronounced in the sample of a million 400-bit prime numbers:", null, "Figure 23.\n\nNow the gaps between the prime numbers stretched to 15 080, creating almost 800 shares of mod 19 (however, only 13 are shown). And here in the array there is a very intriguing comb structure. In general, the columns on numbers multiples of 6 stand out almost twice as compared to the height of the nearest neighbors, showing the continuing influence of the smallest prime divisors 2 and 3. Numbers that are multiples of 6, which are also multiple of 30, reach even greater heights. The values ​​in the sequence 42, 84, 126, 168, 210, ... also make a big contribution: these numbers are multiples of", null, ". And notice that 210, which is a multiple of 6 and 30 and 42, is a new interval-champion, again confirming Odlyzhko's prediction.\n\nDespite all this internal structure, when the columns arranged one on another mod 19, the mixture of 800 dol is so accurate that the heights are almost identical. The only thing that remains is a small unevenness of even-odd ones.", null, "Figure 24.\n\nAnd the chronically unpopular class of congruent 0 modulo 19 intervals finally found itself equal. Most of the height of the column is obtained not from a dozen early dots, but from a hundred later, representing intervals between 228 and 15 080 (all of them accumulated in the turquoise region of the graph).\n\nExperiments with large prime numbers allow us to make a plausible assumption: when the size of prime numbers tends to infinity, all traces of correlations gradually fade, and successive pairs of prime numbers will be as random as throws of an ideal bone. But is it? There are several reasons to be skeptical about this hypothesis. First, if we increase the modulus m together with the size of prime numbers, making it comparable in magnitude to the median gap between prime numbers, then correlations will continue to manifest. In my 40-bit sample, the median gap between the prime numbers is 66, so let's look at the matrix of consecutive pairs mod 61. (To limit the statistical noise, I will do calculations with a sample of not one but ten million 40-bit primes.)", null, "Figure 25.\n\nThe bands are back! And in fact, in addition to the familiar bright red bands at intervals of 6, there are more scattered pink and blue frequencies with a period of 30. I would like to look at the matrix for simple 400-bit numbers, which may have even more complex features, with interacting waves in the periods 6, 30 and 210. Unfortunately, I can not show you this picture. The median gap between 400-bit primes is about 640, so we'll have to assign m a value equal to a prime number in this interval, say 641. To fill the matrix,", null, "it takes about one billion consecutive 400-bit numbers, which is more than I'm ready to calculate.\n\nThere are other reasons for doubting that correlations disappear completely as the primes increase. The comb structure, so noticeable in Figures 21 and 23, tells us that the rules of divisibility into small prime numbers strongly affect the distribution of large primes mod m, and this influence still does not disappear when the numbers increase. Moreover, even when m is much smaller than the median interval between prime numbers, the blue band remains weakly visible. Here is the matrix for pairs of consecutive 400-bit primes mod 3:\n\n1 2\n1 248291 251128\n2 251127 249453\nThe difference in the elements on the diagonals and outside the diagonals is much smaller than with the eight-digit prime numbers (compare with Figure 3), but the deviations still do not look like a random variation.\n\nTo get a clearer idea of ​​how correlation varies as a function of the size of prime numbers, I decided to create a sample of primes in the entire range from single-digit to 400-bit numbers. In this project I decided to do better than Gauss: he entered the prime numbers into the tables by chiliads (by groups of 1,000), and I calculated them by myriads (groups of 10,000). To measure correlations among prime numbers mod m, I calculated the mean value of the diagonal elements of the matrix and the average of the elements outside the diagonals, and then took the ratio outside / on the diagonal. If the consecutive prime numbers do not correlate at all, then the ratio should tend to 1.\n\nFigure 26 shows the result for 797 myriads of prime numbers mod 3. The curve is curved upwards, has a sharp initial drop, and then a much flatter segment. Starting from about 100 bits, there are samples with a ratio of less than 1, meaning that the diagonal is more densely populated than the areas outside the diagonal. But even at 400 bits, most of the ratios are still higher than 1. What do we see here? Is the curve slowly approaching the ratio 1, or is there a limiting value, slightly greater than 1? Unfortunately, computational experiments do not allow us to give a definitive answer.", null, "Figure 26.\n\nTo address this problem, Lemke-Oliver and Sounararajan use other tools. Although they use numerical research", null, "Skull 31 october 2017, 10:55", null, "", null, "Vote for this post Bring it to the Main Page", null, "", null, "B\nI\nU\nS\nHelp\nAvaible tags\n• <b>...</b>highlighting important text on the page in bold\n• <i>..</i>highlighting important text on the page in italic\n• <u>...</u>allocated with tag <u> text shownas underlined\n• <s>...</s>allocated with tag <s> text shown as strikethrough\n• ^..., _...text in the tag <sup> appears as a superscript, <sub> - subscript\n• <blockquote>...</blockquote>For  highlight citation, use the tag <blockquote>\n• <code lang=\"lang\">...</code>highlighting the program code (supported by bash, cpp, cs, css, xml, html, java, javascript, lisp, lua, php, perl, python, ruby, sql, scala, text)\n• <a href=\"http://...\">...</a>link, specify the desired Internet address in the href attribute\n• <img src=\"http://...\" alt=\"text\" />specify the full path of image in the src attribute" ]

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[ "# Introduction to", null, "and", null, "using", null, "Python is a powerful and easy to use programming language. It has a large community of developers and given its open source nature, you can find many solutions, scripts, and help all over the web. It is easy to learn and code, and faster than other high-level programming languages...and did I mention it is free because it is open-source\n\nIPython is a very powerful extension to Python that provides: Powerful interactive shells (terminal, Qt-based and Notebooks based on Jupyter).\n\n• A browser-based notebook with support for code, text, mathematical expressions, inline plots and other rich media.\n• Support for interactive data visualization and use of GUI toolkits.\n• Easy to use, high performance tools for parallel computing.\n\nJupyter is an open-source project that provides open-standards, and services for interactive computing across dozens of programming languages, including Python, R, Stata and many others used by economists.\n\n# Getting Python, IPython, R, and Jupyter¶\n\nYou can download and install Python and its packages for free for your computer from Python.org. While this is the official site, which offers the basic installer and you can try do add any packages you require yourself, a much easier approach, which is almost foolproof is to use Continuum Anaconda or Enthought Canopy. Both of these distributions offer academic licenses (Canopy), which allow you to use a larger set of packages. Similarly, you can download R from the r-project website.\n\nI personally have switched to using Continuum Anaconda since it make installing all the packages and software I use much easier. You can follow the instructions below or better yet follow the instructions on the Computation Page of my Economic Growth and Comparative Development Course.\n\n## Installing (I)Python & Jupyter¶\n\nThe easiest and most convenient way to install a working version of IPython with all the required packages and tools is using Continuum's Anaconda Distribution. You can install following the instructions in that website, or if you can just run this script (Mac/Linux). After installing the latest version of Anaconda, add the Anaconda/bin directory to your PATH variable.\n\nTo create an environment useful for these notebooks, in your terminal execute\n\nconda create --name GeoPython3env -c conda-forge -c r -c mro --override-channels python=3.9 georasters geopandas pandas spatialpandas statsmodels xlrd networkx ipykernel ipyparallel ipython ipython_genutils ipywidgets jupyter jupyterlab kiwisolver matplotlib-base matplotlib scikit-image scikit-learn scipy seaborn geoplot geopy geotiff pycountry nb_conda_kernels stata_kernel nltk\n\n\nThis should create an environment with most of the packages we need. We can always install others down the road.\n\nTo start using one of the environment you will need to exectute the following command\n\nsource activate GeoPython3env\n\n\n#### Note¶\n\nI assume you have followed the steps above and have installed Anaconda. Everything that is done should work on any distribution that has the required packages, since the Python scripts should run (in principle) on any of these distributions.\n\nWe will use IPython as our computing environment.\n\n## Let's get started¶\n\nOnce you have your Python distribution installed you'll be ready to start working. You have various options:\n\n• Open the Canopy program and work there\n• Open Anaconda Navigator and open one of the apps from there (python, ipython, jupyter console, jupyter notebook, jupyter lab, R, Stata\n• From the Terminal prompt (command-line in Windows) execute one of the following commands:\n• ipython\n• jupyter console\n• jupyter qtconsole\n• jupyter notebook\n• jupyter lab\n\nWhile theses last are all using IPython, each has its advantages and disadvantages. You should play with them to get a better feeling of which you want to use for which purpose. In my own research I usually use a text editor (TextMate, Atom, Sublime) and the jupyter qtconsole or the jupyter notebook. To see the power of Jupter notebooks (see this excellent and in-depth presentation by its creators). As you will see, this might prove an excellent environment to do research, homework, replicate papers, etc.\n\n#### Note¶\n\nYou can pass some additional commands to ipython in order to change colors and rendering of plots. I usually use jupyter qtconsole --color=linux --pylab=inline. You can create profiles to manage many options within IPython and JuPyter.\n\n# First steps¶\n\nLet's start by running some simple commands at the prompt to do some simple computations.\n\nIn [ ]:\n1+1-2\n\nIn [ ]:\n3*2\n\nIn [ ]:\n3**2\n\nIn [ ]:\n-1**2\n\nIn [ ]:\n3*(3-2)\n\nIn [ ]:\n3*3-2\n\n\nNotice that Python obeys the usual orders for operators, so exponentiation before multiplication/division, etc.\n\nIn [ ]:\n1/2\n\n\nIf you are in Python 2.7 you will notice that this answer is wrong if $1,2\\in\\mathbb{R}$, but Python thinks they are integers, so it forces and integer. In order to have a more natural behavior of division we need\n\nIn [ ]:\nfrom __future__ import division\n1/2\n\n\n#### Note¶\n\nIt is a good idea to include this among the packages to be imported by default\n\n### Getting help¶\n\nSo what else can we do? Where do we start if we are new? You can use ? or help() to get help.\n\nIn [ ]:\n?\n\nIn [ ]:\nhelp()\n\n\nIf you want information about a command, say mycommand you can use help(mycommand), mycommand? or mycommand?? to get information about how it is used or even see its code.\n\nIn [ ]:\nhelp(sum)\n\nIn [ ]:\nsum?\n\nIn [ ]:\nsum??\n\n\n#### Variables, strings, and other objects¶\n\nWe can print information\n\nIn [ ]:\nprint('Hello World!')\n\n\nWe can also create variables, which can be of various types\n\nIn [ ]:\na = 1\nb = 2\na+b\n\n\na and b now hold numerical values we can use for computing\n\nIn [ ]:\nc = [1, 2]\nd = [[1, 2], [3, 4]]\nprint('c=%s' % c)\nprint('d=%s' % d)\n\n\nNotice that we have used %s and % to let Python know we are passing a string to the print function.\n\nWhat kind of variables are c and d? They look like vectors and matrices, but...\n\nIn [ ]:\nprint(' a * c = %s' % (a * c))\nprint(' b * d = %s' % (b * d))\n\nIn [ ]:\nc*d\n\n\nActually, Python does not have vectors or matrices directly available. Instead it has lists, sets, arrays, etc., each with its own set of operations. We defined c and d as list objects\n\nIn [ ]:\ntype(c)\n\nIn [ ]:\ntype(d)\n\nIn [ ]:\ntype(a)\n\n\nLuckily Python has a powerful package for numerical computing called Numpy.\n\n### Extending Python's Functionality with Packages¶\n\nIn order to use a package in Python or IPython, say mypackage, you need to import it, by executing\n\nimport mypackage\n\n\n\nAfter executing this command, you will have access to the functions and objects defined in mypackage. For example, if mypackage has a function squared that takes a real number x and computes its square, we can use this function by calling mypackage.squared(x). Since the name of some packages might be too long, your can give them a nickname by importing them instead as\n\nimport mypackage as myp\n\n\n\nso now we could compute the square of x by calling myp.squared(x).\n\nWe will see various packages that will be useful to do computations, statistics, plots, etc.\n\nIPython has a command that imports Numpy and Matplotlib (Python's main plotting package). Numpy is imported as np and Matplotlib as plt. One could import these by hand by executing\n\nimport numpy as np\nimport matplotlib as plt\n\n\n\nbut the creators of IPython have optimized the interaction between these packages by running the following command:\n\n%pylab\nIn [ ]:\n%pylab?\n\n\nI do recommend using the --no-import-all option in order to ensure you do not contaminate the namespace. Instead it might be best to use\n\n%pylab --no-import-all\n%matplotlib\nIn [ ]:\n%matplotlib?\n\nIn [ ]:\n%pylab --no-import-all\n%matplotlib inline\n\nIn [ ]:\nnp?\n\n\nLet us now recreate c and d, but as Numpy arrays instead.\n\nIn [ ]:\nca = np.array(c)\nda = np.array(d)\nprint('c = %s' % c)\nprint('d = %s' % d)\nprint('ca = %s' % ca)\nprint('da = %s' % da)\n\n\nWe could have created them as matrices intead. Again how you want to cerate them depends on what you will be doing with them. See here for an explanation of the differences between Numpy arrays and matrices.\n\nIn [ ]:\ncm = np.matrix(c)\ndm = np.matrix(d)\nprint('cm = %s' % cm)\nprint('dm = %s' % dm)\n\n\nLet's see some information about these...(this is a good moment to show tab completion...a wonderful feature of IPython, which is not avalable if Python)\n\nIn [ ]:\ncm.shape\n\nIn [ ]:\nca.shape\n\nIn [ ]:\ndm.diagonal()\n\nIn [ ]:\nda.cumsum()\n\n\nLet's try again some operations on our new arrays and matrices\n\nIn [ ]:\ncm*dm\n\nIn [ ]:\nca\n\nIn [ ]:\nda\n\nIn [ ]:\nca*da\n\nIn [ ]:\nca.dot(da)\n\n\nWe can create special matrices using Numpy's functions and classes\n\nIn [ ]:\nprint(np.ones((3,4)))\nprint(np.zeros((2,2)))\nprint(np.eye(2))\nprint(np.ones_like(cm))\n\nIn [ ]:\nnp.random.uniform(-1,1,10)\n\nIn [ ]:\n#np.random.seed(123456)\nx0 = 0\nx = [x0]\n[x.append(x[-1] + np.random.normal() ) for i in range(500)]\nplt.plot(x)\nplt.title('A simple random walk')\nplt.xlabel('Period')\nplt.show()\n\n\n### Extending Capabilities with Functions¶\n\nWe have used some of the functions in Python, Numpy and Matplotlib. But what if we wanted to create our own functions? It is very easy to do so in Python. There are two ways to define functions. Let's use them to define the CRRA utility function $u(c)=\\frac{c^{1-\\sigma}-1}{1-\\sigma}$ and the production function $f(k)=Ak^\\alpha$.\n\nThe first method is as follows:\n\nIn [ ]:\ndef u(c, sigma):\n'''This function returns the value of utility when the CRRA\ncoefficient is sigma. I.e.\nu(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1\nand\nu(c,sigma)=ln(c) if sigma==1\nUsage: u(c,sigma)\n'''\nif sigma!=1:\nu = (c**(1-sigma) - 1) / (1-sigma)\nelse:\nu = np.log(c)\nreturn u\n\n\nThis defined the utility function. Let's plot it for $0< c\\le5$ and $\\sigma\\in\\{0.5,1,1.5\\}$\n\nIn [ ]:\n# Create vector\nc = np.linspace(0.1, 5, 100)\n# Evaluate utilities for different CRRA parameters\nu1 = u(c, .5)\nu2 = u(c, 1)\nu3 = u(c, 1.5)\n# Plot\nplt.plot(c, u1, label=r'$\\sigma=.5$')\nplt.plot(c, u2, label=r'$\\sigma=1$')\nplt.plot(c, u3, label=r'$\\sigma=1.5$')\nplt.xlabel(r'$c_t$')\nplt.ylabel(r'$u(c_t)$')\nplt.title('CRRA Utility function')\nplt.legend(loc=4)\nplt.savefig('./CRRA.jpg', dpi=150)\nplt.savefig('./CRRA.pdf', dpi=150)\nplt.savefig('./CRRA.png', dpi=150)\nplt.show()\n\n\nWhile this is nice, it requires us to always have to put a value for the CRRA coefficient. Furthermore, we need to remember if $c$ is the first or second argument. Since we tend to use log-utilities a lot, let us change the definition of the utility function so that it has a default value for $\\sigma$ equal to 1\n\nIn [ ]:\ndef u(c, sigma=1):\n'''This function returns the value of utility when the CRRA\ncoefficient is sigma. I.e.\nu(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1\nand\nu(c,sigma)=ln(c) if sigma==1\nUsage: u(c,sigma=value), where sigma=1 is the default\n'''\nif sigma!=1:\nu = (c**(1-sigma) - 1) / (1-sigma)\nelse:\nu = np.log(c)\nreturn u\n\nIn [ ]:\nsigma1 = .25\nsigma3 = 1.25\nu1 = u(c, sigma=sigma1)\nu2 = u(c)\nu3 = u(c, sigma=sigma3)\nplt.plot(c, u1, label=r'$\\sigma='+str(sigma1)+'$')\nplt.plot(c, u2, label=r'$\\sigma=1$')\nplt.plot(c, u3, label=r'$\\sigma='+str(sigma3)+'$')\nplt.xlabel(r'$c_t$')\nplt.ylabel(r'$u(c_t)$')\nplt.title('CRRA Utility function')\nplt.legend(loc=4)\nplt.show()\n\n\n### Exercise¶\n\nWrite the function for the Cobb-Douglas production function. Can you generalize it so that we can use it for aggregate, per capita, and per efficiency units without having to write a function for each?\n\nRemember aggregate production is $$Y = F(K, AL) = K^\\alpha (A L)^{1-\\alpha},$$\n\nper capita is\n\n$$\\hat y=\\frac{F(K, AL)}{L} = \\frac{K^\\alpha (A L)^{1-\\alpha}}{L} = Ak^\\alpha,$$\n\nand per effective worker\n\n$$y = \\frac{F(K, AL)}{AL} = \\frac{K^\\alpha (A L)^{1-\\alpha}}{AL} = k^\\alpha,$$\n\nwhere $k=K/AL$.\n\nThe second method is to use the lambda notation, which allows you to define functions in one line or without giving the function a name.\n\nIn [ ]:\nsquared = lambda x: x**2\nsquared(2)\n\n\n# Our first script¶\n\nLet's write a script that prints \"Hello World!\"\n\nIn [ ]:\n%%file?\n\nIn [ ]:\n%%file helloworld.py\n#!/usr/bin/env python\n# coding=utf-8\n'''\nMy First script in Python\n\nAuthor: Me\nE-mail: [email protected]\nWebsite: http://me.com\nGitHub: https://github.com/me\nDate: Today\n\nThis code computes Random Walks and graphs them\n'''\n\n'''\nfrom __future__ import division\nimport numpy as np\nimport matplotlib.pyplot as plt\n'''\nprint('Hello World!')\n\n\nLet's run that script\n\nIn [ ]:\n%run helloworld.py\n\n\n#### Exercise¶\n\nWrite a simple script randomwalk.py that simulates and plots random walks. In particular, create a function randomwalk(x0, T, mu, sigma) that simulates the random walk starting at $x_0=x0$ until $t=T$ where the shock is distributed $\\mathcal{N}(\\mu,\\sigma^2)$\n\nIn [ ]:\nimport randomwalk as rw\n\nIn [ ]:\nrw.randomwalk(0, 500, 0, 1)\n\nIn [ ]:\nfrom randomwalk import randomwalk\n\nIn [ ]:\nrandomwalk??\n\nIn [ ]:\nimport time\ntime.sleep(10)\nprint(\"It's time\")\n\n\nNotebook written by Ömer Özak for his Ph.D. students in Economics at Southern Methodist University. Feel free to use, distribute, or contribute." ]

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[ "blob: e0a62497d0c6eef38d49dbff17fefc525210ca43 [file] [log] [blame]\n Proposal for math Package Robert Burrell Donkin\n\nThe Java programming language and the math extensions in commons-lang provide implementations for only the most basic mathematical algorithms. Routine development tasks such as computing basic statistics or solving a system of linear equations require components not available in java or commons-lang.\n\nMost basic mathematical or statistical algorithms are available in open source implementations, but to assemble a simple set of capabilities one has to use multiple libraries, many of which have more restrictive licensing terms than the ASF. In addition, many of the best open source implementations (e.g. the R statistical package) are either not available in Java or require large support libraries and/or external dependencies to work.\n\nA commons-math community will provide a productive environment for aggregation, testing and support of efficient Java implementations of commonly used mathematical and statistical algorithms.\n\nThe Math project shall create and maintain a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang. The guiding principles for commons-math will be:\n\n1. Real-world application use cases determine priority\n2. Emphasis on small, easily integrated components rather than large libraries with complex dependencies\n3. All algorithms are fully documented and follow generally accepted best practices\n4. In situations where multiple standard algorithms exist, use the Strategy pattern to support multiple implementations\n5. Limited dependencies. No external dependencies beyond Commons components and the JDK\n\nmath relies only on standard JDK 1.2 (or later) APIs for production deployment. It utilizes the JUnit unit testing framework for developing and executing unit tests, but this is of interest only to developers of the component.\n\nNo external configuration files are utilized.\n\nThe initial codebase will consist of implementations of basic statistical algorithms such as the following:\n\n• Simple univariate statistics (mean, standard deviation, n, confidence intervals)\n• Frequency distributions\n• t-test, chi-square test\n• Random numbers from Gaussian, Exponential, Poisson distributions\n• Random sampling/resampling\n• Bivariate regression, corellation\nand mathematical algorithms such as the following:\n• Basic Complex Number representation with algebraic operations\n• Newton's method for finding roots\n• Binomial coefficients\n• Exponential growth and decay (set up for financial applications)\n• Polynomial Interpolation (curve fitting)\n• Basic Matrix representation with algebraic operations\n\nThe proposed package name for the new component is org.apache.commons.math.\n\n• CVS Repository - New directory math in the jakarta-commons CVS repository.\n• Mailing List - Discussions will take place on the general [email protected] mailing list. To help list subscribers identify messages of interest, it is suggested that the message subject of messages about this component be prefixed with [math].\n• Bugzilla - New component \"math\" under the \"Commons\" product category, with appropriate version identifiers as needed.\n• Jyve FAQ - New category \"commons-math\" (when available).\n\nThe initial committers on the math component shall be:" ]

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[ "# Simple Function Example Kotlin Program\n\n## Definition\n\nA function is a block of code written to perform a task. A function may be a parameterized function or a parameter-less function. A function may return a value or it may not return a value. The name of a function starts with a small letter and then follows CamelCase.\n\n## Syntax\n\n``````fun method_name(){\n//Functionality code\n}``````\n\n## Function Example Program\n\n``````fun main(args: Array < String > ) {\nval num1 = 11\nval num2 = 6\n\n//Calling function with no parameters and return type\nprint()\n//Calling function with 2 parameters num1 and num2 and assigning the result to num3\n\n//Printing result\nprintln(\"After addition of num1 and num2, the result is : \" + num3)\n}\n\n//Function with parameters and Int return type\nfun add(i: Int, j: Int): Int {\nreturn i + j\n}\n\n//Function without parameters and no return type\nfun print() {\nprintln(\"I am inside print function.\")\n}``````\n\n## Sample Output\n\n``````I am inside print function.\nAfter addition of num1 and num2, the result is : 17``````" ]

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[ "# Help with IQ balance equations?\n\nI have developed a spectrum scope that plots signal vs. frequency starting from IQ signals. I currently do not have a way to balance the IQ signals, so am looking at various ways to do so. I have come across this article, which is reasonably easy for me to follow since I am fairly new to all DSP. The one question I have is concerning the notation of some of the equations: For example, $a^2 = 2\\langle t(i) * t(i)\\rangle$. What does $\\langle\\cdot \\rangle$ represent? I can find no reference for these in mathematical symbol tables.\n\n• The paper provides a definition: the average of the signal computed over N periods. – pichenettes Nov 1 '14 at 22:29\n• Hi Thanks, yes my math is quite rusty! Can anyone explain how many samples would provide a good value? – Tom Nov 3 '14 at 22:58\n• According to this page, that symbol means \"inner product\". See this answer to this question. – jeremy Oct 5 '16 at 19:20\n\nI wrote code in Java based on that article but it isn't working for me. Alpha (I-data scalar) calculates to be around $100$ and $cos(\\omega)$ often calculates to an imaginary number. Did anyone have any luck with this or could point me to a better IQ Correction algorithm?\n\n(To be clear: calculateMatrix, a, c, and d are all instance variables)\n\npublic void correctIQ(int[] data) {\n\nint length = data.length / 2;\n\n// ( I'(t) & Q'(t) )\nint[] iData = new int[length];\nint[] qData = new int[length];\n\n// Deinterleave IQ data\nfor (int i = 0; i < length; i++) {\niData[i] = data[i * 2];\nqData[i] = data[i * 2 + 1];\n}\n\n// ( I''(t) & Q''(t) )\ndouble[] qDataOffset = new double[length];\ndouble[] iDataOffset = new double[length];\n\n// Calculate DC offset\ndouble qOffset = mean(qData);\ndouble iOffset = mean(iData);\n\n// Apply DC offset\nfor (int i = 0; i < length; i++) {\niDataOffset[i] = iData[i] - iOffset;\nqDataOffset[i] = qData[i] - qOffset;\n}\n\n// Provided equations calculated on frequency change\nif(calculateMatrix) {\ndouble alpha = Math.sqrt(2.0 * multiplyMean(iDataOffset, iDataOffset));\ndouble sinw = (2.0 / alpha) * multiplyMean(iDataOffset, qDataOffset);\ndouble cosw = Math.sqrt(1.0 - (sinw * sinw));\n\na = 1.0f / alpha;\nc = -sinw / (alpha * cosw);\nd = 1.0f / cosw;\n}\n\n// Replace into interleaved array\nfor(int i=0;i<length;i++) {\ndata[i*2]=(int)((iData[i]-iOffset)*a);\ndata[i*2+1]=(int)((iData[i]-iOffset)*c+(qData[i]-qOffset)*d);\n}\n}\n\ndouble mean(int[] values) {\nlong sum = 0L;\nfor(int i=0;i<values.length;i++) {\nsum+=values[i];\n}\nreturn ((double)sum)/values.length;\n}\n\ndouble multiplyMean(double[] values1, double[] values2) {\nlong sum = 0L;\nfor(int i=0;i<values1.length;i++) {\nsum+=values1[i]*values2[i];\n}\nreturn ((double)sum)/values1.length;\n}\n\n\nI didn't get a chance to look through the article in detail, but it looks like taking the inner product between 2 vectors over some index variable (in your case, $i$), as in $<X_i, X_i> = \\frac{1}{N}\\sum_i |X_i|^2$.\n\nThis is the averaging symbol and you see it quite often in DSP and communication systems books and articles. It's right there in article also:", null, "" ]

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[ "MATH 4710\n\nMATH 4710Basic Probability\n\nCourse information provided by the Courses of Study 2018-2019.\n\nIntroduction to probability theory, which prepares the student to take MATH 4720. The course begins with basics: combinatorial probability, mean and variance, independence, conditional probability, and Bayes formula. Density and distribution functions and their properties are introduced. The law of large numbers and the central limit theorem are stated and their implications for statistics are discussed.\n\nWhen Offered Fall, Spring.\n\nPrerequisites/Corequisites Prerequisite: one year of calculus. Recommended prerequisite: some knowledge of multivariate calculus. Students will be expected to be comfortable with proofs.\nForbidden Overlaps Forbidden Overlap: due to an overlap in content, students will receive credit for only one course in the following group:  BTRY 3080/ILRST 3080/STSCI 3080, ECON 3110/ILRST 3110/STSCI 3110, ECON 3130, MATH 4710.\n\nDistribution Category (MQR-AS)\n\nSyllabi: none" ]

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[ "## Analysis and Plots of Solutions to Complex Powers\n\nIn chapter 5 of his mind-blowing “The Road to Reality”, Penrose devotes a section to complex powers, that is, to the solutions to\n\n$$w^z~~~\\text{with}~~~w,z \\in \\mathbb{C}$$\n\nIn this post I develop a bit more what he exposes and explore what the solutions look like with the help of some simple Python scripts. The scripts can be found in this github repo, and all the figures in this post can be replicated by running\n\ngit clone https://github.com/alfonsosanchezbeato/exponential-spiral.git\ncd exponential-spiral; ./spiral_examples.py\n\n\nThe scripts make use of numpy and matplotlib, so make sure those are installed before running them.\n\nNow, let’s develop the math behind this. The values for $$w^z$$ can be found by using the exponential function as\n\n$$w^z=e^{z\\log{w}}=e^{z~\\text{Log}~w}e^{2\\pi nzi}$$\n\nIn this equation, “log” is the complex natural logarithm multi-valued function, while “Log” is one of its branches, concretely the principal value, whose imaginary part lies in the interval $$(−\\pi, \\pi]$$. In the equation we reflect the fact that $$\\log{w}=\\text{Log}~w + 2\\pi ni$$ with $$n \\in \\mathbb{Z}$$. This shows the remarkable fact that, in the general case, we have infinite solutions for the equation. For the rest of the discussion we will separate $$w^z$$ as follows:\n\n$$w^z=e^{z~\\text{Log}~w}e^{2\\pi nzi}=C \\cdot F_n$$\n\nwith constant $$C=e^{z~\\text{Log}~w}$$ and the rest being the sequence $$F_n=e^{2\\pi nzi}$$. Being $$C$$ a complex constant that multiplies $$F_n$$, the only influence it has is to rotate and scale equally all solutions. Noticeably, $$w$$ appears only in this constant, which shows us that the $$z$$ values are what is really determinant for the number and general shape of the solutions. Therefore, we will concentrate in analyzing the behavior of $$F_n$$, by seeing what solutions we can find when we restrict $$z$$ to different domains.\n\nStarting by restricting $$z$$ to integers ($$z \\in \\mathbb{Z}$$), it is easy to see that there is only one resulting solution in this case, as the factor $$F_n=e^{2\\pi nzi}=1$$ in this case (it just rotates the solution $$2\\pi$$ radians an integer number of times, leaving it unmodified). As expected, a complex number to an integer power has only one solution.\n\nIf we let $$z$$ be a rational number ($$z=p/q$$, being $$p$$ and $$q$$ integers chosen so we have the canonical form), we obtain\n\n$$F_n=e^{2\\pi\\frac{pn}{q} i}$$\n\nwhich makes the sequence $$F_n$$ periodic with period $$q$$, that is, there are $$q$$ solutions for the equation. So we have two solutions for $$w^{1/2}$$, three for $$w^{1/3}$$, etc., as expected as that is the number of solutions for square roots, cube roots and so on. The values will be the vertex of a regular polygon in the complex plane. For instance, in figure 1 the solutions for $$2^{1/5}$$ are displayed.", null, "Fig. 1: The five solutions to $$2^{1/5}$$\n\nIf $$z$$ is real, $$e^{2\\pi nzi}$$ is not periodic anymore has infinite solutions in the unit circle, and therefore $$w^z$$ has infinite values that lie on a circle of radius $$|C|$$.\n\nIn the more general case, $$z \\in \\mathbb{C}$$, that is, $$z=a+bi$$ being $$a$$ and $$b$$ real numbers, and we have\n\n$$F_n=e^{-2\\pi bn}e^{2\\pi ani}.$$\n\nThere is now a scaling factor, $$e^{-2\\pi bn}$$ that makes the module of the solutions vary with $$n$$, scattering them across the complex plane, while $$e^{2\\pi ani}$$ rotates them as $$n$$ changes. The result is an infinite number of solutions for $$w^z$$ that lie in an equiangular spiral in the complex plane. The spiral can be seen if we change the domain of $$F$$ to $$\\mathbb{R}$$, this is\n\n$$F(t)=e^{-2\\pi bt}e^{2\\pi ati}~~~\\text{with}~~~t \\in \\mathbb{R}.$$\n\nIn figure 2 we can see one example which shows some solutions to $$2^{0.4-0.1i}$$, plus the spiral that passes over them.", null, "Fig. 2: Roots and spiral for $$2^{0.4-0.1i}$$\n\nIn fact, in Penrose’s book it is stated that these values are found in the intersection of two equiangular spirals, although he leaves finding them as an exercise for the reader (problem 5.9).\n\nLet’s see then if we can find more spirals that cross these points. We are searching for functions that have the same value as $$F(t)$$ when $$t$$ is an integer. We can easily verify that the family of functions\n\n$$F_k'(t)=F(t)e^{2\\pi kti}~~~\\text{with}~~~k \\in \\mathbb{Z}$$\n\nare compatible with this restriction, as $$e^{2\\pi kti}=1$$ in that case (integer $$t$$). Figures 3 and 4 represent again some solutions to $$2^{0.4-0.1i}$$, $$F(t)$$ (which is the same as the spiral for $$k=0$$), plus the spirals for $$k=-1$$ and $$k=1$$ respectively. We can see there that the solutions lie in the intersection of two spirals indeed.", null, "Fig. 3: Roots for $$2^{0.4-0.1i}$$ plus spirals for k=0 and k=-1", null, "Fig. 4: Roots for $$2^{0.4-0.1i}$$ plus spirals for k=0 and k=1\n\nIf we superpose these 3 spirals, the ones for $$k=1$$ and $$k=-1$$ cross also in places different to the complex powers, as can be seen in figure 5. But, if we choose two consecutive numbers for $$k$$, the two spirals will cross only in the solutions to $$w^z$$. See, for instance, figure 6 where the spirals for $$k=\\{-2,-1\\}$$ are plotted. We see that any pair of such spirals fulfills Penrose’s description.", null, "Fig. 5: Roots for $$2^{0.4-0.1i}$$ plus spirals for k=-1,0,1", null, "Fig. 6: Roots for $$2^{0.4-0.1i}$$ plus spirals for k=-1,-2\n\nIn general, the number of places at which two spirals cross depends on the difference between their $$k$$-number. If we have, say, $$F_k’$$ and $$F_l’$$ with $$k>l$$, they will cross when\n\n$$t=…,0,\\frac{1}{k-l},\\frac{2}{k-l},…,\\frac{k-l-1}{k},1,1+\\frac{1}{k-l},…$$\n\nThat is, they will cross when $$t$$ is an integer (at the solutions to $$w^z$$) and also at $$k-l-1$$ points between consecutive solutions.\n\nLet’s see now another interesting special case: when $$z=bi$$, that is, it is pure imaginary. In this case, $$e^{2\\pi ati}$$ is $$1$$, and there is no turn in the complex plane when $$t$$ grows. We end up with the spiral $$F(t)$$ degenerating to a half-line that starts at the origin (which is reached when $$t=\\infty$$ if $$b>0$$). This can be appreciated in figure 7, where the line and the spirals for $$k=-1$$ and $$k=1$$ are plotted for $$20^{0.1i}$$. The two spirals are mirrored around the half-line.", null, "Fig. 7: Roots for $$10^{0.1i}$$, $$F(t)$$, and spirals for k=-1,1\n\nDigging more into this case, it turns out that a pure imaginary number to a pure imaginary power can produce a real result. For instance, for $$i^{0.1i}$$, we see in figure 8 that the roots are in the half-positive real line.", null, "Fig. 8: Roots for $$i^{0.1i}$$, $$F(t)$$, and spirals for k=-1,1\n\nThat something like this can produce real numbers is a curiosity that has intrigued historically mathematicians ($$i^i$$ has real values too!). And with this I finish the post. It is really amusing to start playing with the values of $$w$$ and $$z$$, if you want to do so you can use the python scripts I pointed to in the beginning of the post. I hope you enjoyed the post as much as I did writing it." ]

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[ "Request a call back\n\n# CBSE Class 8 Answered\n\nQuantities x and y vary inversely and when x = 15, y = 6. Which of the following is not a possible pair of corresponding values of x and y.\n\n(i) 10 and 9\n\n(ii) 18 and 6\n\n(iii) 5 and 18\n\nAsked by Topperlearning User | 12 Dec, 2013, 04:02: AM", null, "Expert Answer\n\nSince x and y vary inversely, the product", null, "remains constant.\n\nIt is given that when x = 15, y = 6, therefore,", null, "(i) Let x = 10 and y = 9\n\nSo,", null, "Which is same as in (a), so it a valid pair of values.\n\n(ii) Let x = 18 and y = 6\n\nSo,", null, "Which is not same as in (a), so it not a valid pair of values.\n\n(iii) Let x = 5 and y = 18\n\nSo,", null, "Which is same as in (a), so it a valid pair of values.\n\nAnswered by | 12 Dec, 2013, 06:02: AM\n\n## Application Videos\n\nCBSE 8 - Maths\nAsked by sana.fatema9900 | 23 Feb, 2020, 01:33: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by nitisandhu9 | 10 Dec, 2019, 04:07: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Nimmi | 25 Feb, 2019, 10:38: AM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by ak8757609 | 09 Dec, 2018, 06:39: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 12 Dec, 2013, 01:44: AM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 04 Jun, 2014, 01:23: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 04 Jun, 2014, 01:23: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 12 Dec, 2013, 04:02: AM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 04 Jun, 2014, 01:23: PM", null, "ANSWERED BY EXPERT\nCBSE 8 - Maths\nAsked by Topperlearning User | 04 Jun, 2014, 01:23: PM", null, "ANSWERED BY EXPERT" ]

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[ "# Anomaly Detection of Time Series Data Using Machine Learning & Deep Learning\n\n## Introduction to Time Series Data\n\nTime Series is defined as a set of observations taken at a particular period of time. For example, having a set of login details at regular interval of time of each user can be categorized as a time series. On the other hand, when the data is collected at once or irregularly, it is not taken as a time series data.\n\nTime series data can be classified into two types -\n\nStock Series - It is a measure of attributes at a particular point in time and taken as a stock takes.\n\nFlow Series - It is a measure of activity at a specific interval of time. It contains effects related to the calendar.\n\nTime series is a sequence that is taken successively at the equally pace of time. It appears naturally in many application areas such as economics, science, environment, medicine, etc. There are many practical real life problems where data might be correlated with each other and are observed sequentially at the equal period of time. This is because, if the repeatedly observe the data at a regular interval of time, it is obvious that data would be correlated with each other.\n\nWith the use of time series, it becomes possible to imagine what will happen in the future as future event depends upon the current situation. It is useful to divide the time series into historical and validation period. The model is built to make predictions on the basis of historical data and then this model is applied to the validation set of observations. With this process, the idea is developed how the model will perform in forecasting.\n\nTime Series is also known as the stochastic process as it represents the vector of stochastic variables observed at regular interval of time.\n\n## Components of Time Series Data\n\nIn order to analyze the time series data, there is a need to understand the underlying pattern of data ordered at a particular time. This pattern is composed of different components which collectively yield the set of observations of time series.\n\nThe Components of time series data are given below -\n\n• Trend\n• Cyclical\n• Seasonal\n• Irregular", null, "Trend - It is a long pattern present in the time series. It produces irregular effects and can be positive, negative, linear or nonlinear. It represents the variations of low frequency and the high and medium frequency of data is filtered out from the time series.\n\nIf the time series does not contain any increasing or decreasing pattern, then time series is taken as stationary in the mean.\n\nThere are two types of the trend -\n\nDeterministic - In this case, the effects of the shocks present in the time series are eliminated i.e. revert to the trend in long run.\n\nStochastic - It is the process in which the effects of shocks are never eliminated as they have permanently changed the level of the time series.\n\nThe stochastic process having a stationarity around the deterministic process is known as trend stationary process.\n\nCyclic - The pattern exhibit up and down movements around a specified trend is known as cyclic pattern. It is a kind of oscillations present in the time series. The duration of cyclic pattern depends upon the industries and business problems to be analysed. This is because the oscillations are dependable upon the business cycle.\n\nThey are larger variations that are repeated in a systematic way over time. The period of time is not fixed and usually composed of at least 2 months in duration. The cyclic pattern is represented by a well-shaped curve and shows contraction and expansion of data.\n\nSeasonal - It is a pattern that reflects regular fluctuations. These short-term movements occur due to the seasonal factors and custom factors of people. In this case, the data faces regular and predictable changes that occurred at regular intervals of calendar. It always consist of fixed and known period.\n\nThe main sources of seasonality are given below -\n\n• Climate\n• Institutions\n• Social habits and practices\n• Calendar\n\nHow is the seasonal component estimated?\n\nIf the deterministic analysis is performed, then the seasonality will remain same for similar interval of time. Therefore, it can easily be modelled by dummy variables. On the other hand, this concept is not fulfilled by stochastic analysis. So, dummy variables are not appropriate because the seasonal component changes throughout the time series.\n\nDifferent models to create a seasonal component in time series are given below -\n\nAdditive Model - It is the model in which the seasonal component is added with the trend component.\n\nMultiplicative Model - In this model seasonal component is multiplied with the intercept if trend component is not present in the time series. But, if time series have trend component, sum of intercept and trend is multiplied with the seasonal component.\n\nIrregular - It is an unpredictable component of time series. This component cannot be explained by any other component of time series because these variational fluctuations are known as random component. When the trend cycle and seasonal component is removed, it becomes residual time series. These are short term fluctuations that are not systematic in nature and have unclear patterns.\n\n## Difference between Time Series Data and Cross-Section Data\n\nTime Series Data is composed of collection of data of one specific variable at particular interval of time. On the other hand, Cross-Section Data is consist of collection of data on multiple variables from different sources at a particular interval of time.\n\nCollection of company’s stock market data at regular interval of year is an example of time series data. But when the collection of company’s sales revenue, sales volume is collected for the past 3 months then it is taken as an example of cross-section data.\n\nTime series data is mainly used for obtaining results over an extended period of time but, cross-section data focuses on the information received from surveys at a particular time.\n\n## What is Time Series Analysis?\n\nPerforming analysis of time series data is known as Time Series Analysis. Analysis is performed in order to understand the structure and functions produced by the time series. By understanding the mechanism of time series data a mathematical model could easily be developed so that further predictions, monitoring and control can be performed.\n\nTwo approaches are used for analyzing time series data are -\n\n• In the time domain\n• In the frequency domain\n\nTime series analysis is mainly used for -\n\n• Decomposing the time series\n• Identifying and modeling the time-based dependencies\n• Forecasting\n• Identifying and model the system variation\n\n## Need of Time Series Analysis\n\nIn order to model successfully, the time series is important in machine learning and deep learning. Time series analysis is used to understand the internal structure and functions that are used for producing the observations. Time Series analysis is used for -\n\nDescriptive - In this case, patterns are identified in correlated data. In other words, the variations in trends and seasonality in the time series are identified.\n\nExplanation - In this understanding and modeling of data is performed.\n\nForecasting - Here, the prediction from previous observations is performed for short term trends.\n\nInvention Analysis - In this case, effect performed by any event in time series data is analyzed.\n\nQuality Control - When the specific size deviates it provides an alert.\n\n## Applications of Time Series Analysis", null, "## Time Series Database and its types\n\nTime series database is a software which is used for handling the time series data. Highly complex data such higher transactional data is not feasible for the relational database management system. Many relational systems does not work properly for time series data. Therefore, time series databases are optimised for the time series data. Various time series databases are given below -\n\n• CrateDB\n• Graphite\n• InfluxDB\n• Informix TimeSeries\n• Kx kdb+\n• Riak-TS\n• RRDtool\n• OpenTSDB", null, "## What is Anomaly?\n\nAnomaly is defined as something that deviates from the normal behaviour or what is expected. For more clarity let’s take an example of bank transaction. Suppose you have a saving bank account and you mostly withdraw Rs 10,000 but, one day Rs 6,00,000 amount is withdrawn from your account. This is unusual activity for bank as mostly, Rs 10,000 is deducted from the account. This transaction is an anomaly for bank employees.\n\nThe anomaly is a kind of contradictory observation in the data. It gives the proof that certain model or assumption does not fit into the problem statement.\n\n## Different Types of Anomalies\n\nDifferent types of anomalies are given below -\n\nPoint Anomalies - If the specific value within the dataset is anomalous with respect to the complete data then it is known as Point Anomalies. The above mentioned example of bank transaction is an example of point anomalies.\n\nContextual Anomalies - If the occurrence of data is anomalous for specific circumstances, then it is known as Contextual Anomalies. For example, the anomaly occurs at a specific interval of period.\n\nCollective Anomalies - If the collection of occurrence of data is anomalous with respect to the rest of dataset then it is known as Collective Anomalies. For example, breaking the trend observed in ECG.\n\n## Models of Time Series Data\n\nARIMA Model - ARIMA stands for Autoregressive Integrated Moving Average. Auto Regressive (AR) refers as lags of the differenced series, Moving Average (MA) is lags of errors and I represents the number of difference used to make the time series stationary.\n\nAssumptions followed while implementing ARIMA Model are as under -\n\nTime series data should posses stationary property: this means that the data should be independent of time. Time series consist of cyclic behaviour and white noise is also taken as a stationary.\n\nARIMA model is used for a single variable. The process is meant for regression with the past values.\n\nIn order to remove non-stationarity from the time series data the steps given below are followed -\n\nFind the difference between the consecutive observations.\n\nFor stabilizing the variance log or square root of the time series data is computed.\n\nIf the time series consists of the trend, then the residual from the fitted curve is modulated.\n\nARIMA model is used for predicting the future values by taking the linear combination of past values and past errors. The ARIMA models are used for modeling time series having random walk processes and characteristics such as trend, seasonal and nonseasonal time series.\n\nHolt-Winters - It is a model which is used for forecasting the short term period. It is usually applied to achieve exponential smoothing using additive and multiplicative models along with increasing or decreasing trends and seasonality. Smoothing is measured by beta and gamma parameters in the holt’s method.\n\nWhen the beta parameter is set to FALSE, the function performs exponential smoothing.\n\nThe gamma parameter is used for the seasonal component. If the gamma parameter is set to FALSE, a non-seasonal model is fitted.\n\n## How to find Anomaly in Time Series Data\n\nAnomalyDetection R package -\n\nIt is a robust open source package used to find anomalies in the presence of seasonality and trend. This package is build on Generalised E-Test and uses Seasonal Hybrid ESD (S-H-ESD) algorithm. S-H-ESD is used to find both local and global anomalies. This package is also used to detect anomalies present in a vector of numerical variables. Is also provides better visualization such that the user can specify the direction of anomalies.\n\nPrincipal Component Analysis -\n\nIt is a statistical technique used to reduce higher dimensional data into lower dimensional data without any loss of information. Therefore, this technique can be used for developing the model of anomaly detection. This technique is useful at that time of situation when sufficient samples are difficult to obtain. So, PCA is used in which model is trained using available features to obtain a normal class and then distance metrics is used to determine the anomalies.\n\nChisq Square distribution -\n\nIt is a kind of statistical distribution that constitutes 0 as minimum value and no bound for the maximum value. Chisq square test is implemented for detecting outliers from univariate variables. It detects both lowest and highest values due to the presence of outliers on both side of the data.\n\nWhat are Breakouts in Time Series Data?\n\nBreakout are significant changes observed in the time series data. It consist of two characteristics that are given below -\n\nMean shift - It is defined as a sudden change in time series. For example the usage of CPU is increased from 35% to 70%. This is taken as a mean shift. It is added when the time series move from one steady state to another state.\n\nRamp Up - It is defined as a sudden increase in the value of the metric from one steady state to another. It is a slow process as compared with the mean shift. It is a slow transition process from one stable state to another.\n\nIn Time series often more than one breakouts are observed.\n\nHow to detect Breakouts in Time Series Data?\n\nIn order to detect breakouts in time series Twitter has introduced a package known as BreakoutDetection package. It is an open source package for detecting breakouts at a fast speed. This package uses E-Divisive with Medians (EDM) algorithm to detect the divergence within the mean. It can also be used to detect the change in distribution within the time series.\n\nNeed of Machine Learning and Deep Learning in Time Series Data\n\nMachine learning techniques are more effective as compared with the statistical techniques. This is because machine learning have two important features such as feature engineering and prediction. The feature engineering aspect is used to address the trend and seasonality issues of time series data. The issues of fitting the model to time series data can also be resolved by it.\n\nDeep Learning is used to combine the feature extraction of time series with the non-linear autoregressive model for higher level prediction. It is used to extract the useful information from the features automatically without using any human effort or complex statistical techniques.\n\n## Anomaly Detection using Machine Learning\n\nThere are two most effective techniques of machine learning such as supervised and unsupervised learning.\n\nFirstly, supervised learning is performed for training data points so that they can be classified into anomalous and non-anomalous data points. But, for supervised learning, there should be labeled anomalous data points.\n\nAnother approach for detecting anomaly is unsupervised learning. One can apply unsupervised learning to train CART so that prediction of next data points in the series could be made. To implement this, confidence interval or prediction error is made. Therefore, to detect anomalous data points Generalised ESD-Test is implemented to check which data points are present within or outside the confidence interval\n\nThe most common supervised learning algorithms are supervised neural networks, support vector machine learning, k-nearest neighbors, Bayesian networks and Decision trees.\n\nIn the case of k-nearest neighbors, the approximate distance between the data points is calculated and then the assignment of unlabeled data points is made according to the class of k-nearest neighbor.\n\nOn the other hand, Bayesian networks can encode the probabilistic relationships between the variables. This algorithm is mostly used with the combination of statistical techniques.\n\nThe most common unsupervised algorithms are self-organizing maps (SOM), K-means, C-means, expectation-maximization meta-algorithm (EM), adaptive resonance theory (ART), and one-class support vector machine.", null, "## Anomaly Detection using Deep Learning\n\nRecurrent neural network is one of the deep learning algorithm for detecting anomalous data points within the time series. It consist of input layer, hidden layer and output layer. The nodes within hidden layer are responsible for handling internal state and memory. They both will be updated as the new input is fed into the network. The internal state of RNN is used to process the sequence of inputs. The important feature of memory is that it can automatically learns the time-dependent features.\n\nThe process followed by RNN is described below -" ]

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[ "# R. Sarma\n\nSearch this author in Google Scholar\n\nArticles: 1\n\n### Unbounded translation invariant operators on commutative hypergroups\n\nMethods Funct. Anal. Topology 25 (2019), no. 3, 236-247\n\nLet $K$ be a commutative hypergroup. In this article, we study the unbounded translation invariant operators on $L^p(K),\\, 1\\leq p \\leq \\infty.$ For $p \\in \\{1,2\\},$ we characterize translation invariant operators on $L^p(K)$ in terms of the Fourier transform. We prove an interpolation theorem for translation invariant operators on $L^p(K)$ and we also discuss the uniqueness of the closed extension of such an operator on $L^p(K)$. Finally, for $p \\in \\{1,2\\},$ we prove that the space of all closed translation invariant operators on $L^p(K)$ forms a commutative algebra over the field of complex numbers. We also prove Wendel's theorem for densely defined closed linear operators on $L^1(K).$" ]

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[ "## Precalculus (6th Edition)\n\n(a) center-radius: $\\color{blue}{(x-3)^2+(y+3)^2=9}$ (b) general form:$\\color{red}{x^2+y^2-6x+6y+9=0}$\nRECALL: (1) The center-radius form of a circle's equation is $(x-h)^2+(y-k)^2=r^2$ with center at $(h, k)$ and a radius of $r$ units. (2) The general form of a circle's equation is $x^2+y^2+Dx+Ey+F=0$ The center of the circle can be found by finding the the midpoint of $(3, 0)$ and $(3, -6)$. Note that the midpoint of these two points is $(3, -3)$. Thus, the circle has its center at $(3, -3)$. The radius of the circle can be found by finding the distance from the center $(3, -3)$ to $(3, 0)$, which is $3$ units. Thus, the radius of the circle is $3$. (a) The circle has its center at $(3, -3)$ and has a radius of $3$ units. Therefore, the equation of the circle in center-radius form is: $(x-3)^2+(y-(-3))^2=3^2 \\\\\\color{blue}{(x-3)^2+(y+3)^2=9}$ (b) To find the equation of the circle in general form, expand the equation in (a) above then put all terms on the left side to obtain: $(x-3)^2+(y+3)^2=9 \\\\x^2-6x+9+y^2+6y+9=9 \\\\x^2+y^2-6x+6y+18=9 \\\\x^2+y^2-6x+6y+18-9=0 \\\\\\color{red}{x^2+y^2-6x+6y+9=0}$" ]

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[ "# Fractional indexing and interpolation to reconstruct an image\n\nI have a c++ project written as a Matlab Mex program that is constructing an image composed of IxJ pixels. Each pixel value is calculated by finding the contributions to that pixel from all the channels (columns) in a KxL RF data matrix. The exact value of the row index 'k' of a given column 'l' that contributes to the pixel (i,j) can be a fractional value, so I need to interpolate between values in the RF data matrix. For each pixel (i,j), I calculate the row indices across all columns L that contribute to that pixel, interpolate and extract the corresponding values from the RF data matrix, sum them and store them at (i,j). Here are the code chunks that accomplish this:\n\nMain Loop:\n\nfor(int i = 0; i < p.na; i++) {\nbfm(p,i,reconFrame,\nSIG(Eigen::seq(p.startSample(i)-1,p.endSample(i)-1),p.ConnMap.array()-1));\nRecon += hilbert(p,reconFrame,p1,p2);\n}\n\n\nbfm method:\n\nvoid bfm(const Parameters& p, int& idx, Eigen::Ref<Eigen::MatrixXd> bfFrame,\nconst Eigen::Ref<const Eigen::Matrix<short int, -1, -1>>& SIG) {\n\n#pragma omp parallel for\nfor (int i = 0; i < p.nPoints; i++) {\nEigen::VectorXd idxt(p.numEl);\nint col = i / p.szZ;\nint row = i % p.szZ;\ncalcIDXT(p,p.xCoord(col),p.zCoord(row),idx,idxt);// Calculate delay indices\ncalcPoint(idxt,SIG,bfFrame(row,col));\n}\n}\n\n\nCalcIDXT method:\n\nvoid calcIDXT(const Parameters& p, const double& XPSF, const double& ZPSF,\nconst int& idx, Eigen::Ref<Eigen::VectorXd> idxt) {\n\ndouble dTX = ( (sgn(-p.TXangle(idx))*p.L/2 - XPSF)*sin(-p.TXangle(idx)) + ZPSF*cos(p.TXangle(idx)))*p.fs/p.c + p.t0*p.fs;\n\nidxt = ( (XPSF - p.ElemPos.array()).square() + ZPSF*ZPSF ).sqrt()*p.fs/p.c + dTX - 1;\nidxt = ((abs(XPSF-p.ElemPos.array()) <= ZPSF*0.5/p.fnumber) && (idxt.array() <= (p.szRFframe - 2)) ).select(idxt,0.0);\n}\n\n\nCalcPoint method:\n\nvoid calcPoint(const Eigen::Ref<const Eigen::VectorXd>& idxt,\nconst Eigen::Ref<const Eigen::Matrix<short int, -1, -1>>& SIG,\ndouble& bfVal) {\n\nfor (int j = 0; j < idxt.size(); j++) {\nbfVal += computePoint(idxt.data()+j,SIG.col(j).data());\n}\n}\n\n\nComputePoint Method:\n\n// pIndex: pointer to the current idxt value.\n// pSignsColumn: pointer to the first element in the column of SIG\ninline double computePoint( const double* pIndex, const int16_t* pSignsColumn)//, const double* validIDX )\n{\n// Load the index value into both lanes of the vector\n__m128d idx = _mm_loaddup_pd( pIndex );\n\n// Convert into int32 with truncation; this assumes the number there ain't negative.\nconst int iFloor = _mm_cvttsd_si32( idx );\n\n// Compute fractional part\nidx = _mm_sub_pd( idx, _mm_floor_pd( idx ) );\n// Compute interpolation coefficients, they are [ 1.0 - idx, idx ]\n// _mm_set_sd copies 1.0 to lower half and zero to upper half\n// _mm_addsub_pd(a,b) subtracts lower half of b from a and adds upper half of b to a\nidx = _mm_addsub_pd( _mm_set_sd( 1.0 ), idx );\n\nconst __m128i signsInt = _mm_loadu_si32( pSignsColumn + iFloor );\n// Upcast them to int32, then to fp64\nconst __m128d signs = _mm_cvtepi32_pd( _mm_cvtepi16_epi32( signsInt ) );\n\n// Load validation index into vector\n// __m128d vIdx = _mm_loaddup_pd( validIDX );\n\n// Compute the result\n// __m128d res = _mm_mul_pd( idx, signs );\n// res = _mm_add_sd( res, _mm_unpackhi_pd( res, res ) );\n// The above 2 lines (3 instructions) can be replaced with the following one:\nconst __m128d res = _mm_dp_pd( idx, signs, 0b110001 );\n// It may or may not be better, the dppd instruction is not particularly fast.\n\nreturn _mm_cvtsd_f64( res );\n}\n\n\nThe main loop calculates multiple images that correspond to different chunks of the RF (SIG) matrix. CalcIDXT calculates the row indices for each channel or column of the RF matrix that correspond to a given point while calcPoint serves as a wrapper for the SIMD intrinsic instructions and iterates through each channel of data. The SIMD method actually performs the interpolation (linear interpolation in this case). There is a hilbert transform of all the data that uses the fftw library.\n\nI'm looking for feedback on best practices and performance here. To give you some idea of the current performance I'm seeing, I used the c++ chrono library to measure the execution time of various chunks of my code. Here are the results:\n\nParameter initialization: 0.3419\nRF Data initialization: 22.7536\nbfm total runtime over all loop iterations: 349.5448\nHilbert total runtime over all loop iterations: 45.8686\nSum of above numbers: 418.5088\nTotal runtime of mex function according to tic/toc in matlab: 423.7401\n\n\nThese are averaged over 100 runs and units are in milliseconds. In this test case, the main loop has 15 iterations so each call to hilbert and bfm are the above values divided by 15. I believe I should be able to do better than this, particularly in the calls to bfm. I suspect I should be able to improve by a factor of 2 at least since a commercial software that performs a similar function is about a factor of 2 faster.\n\n• What do the \"signs\" look like? If it's ones and negative ones, that could be useful for perf tricks. Mar 26, 2022 at 3:46\n• Those are poorly named. They aren't signs, they correspond to values from the SIG (RF data) array loaded into a vector register. The RF data array is of int16 data format and needs to be upcast. Mar 26, 2022 at 5:12\n\n## dppd\n\nthe dppd instruction is not particularly fast.\n\nYes, there is a general principle: try to delay horizontal operations until after the loop. That's not always possible, but that principle can be applied here by having computePoint return the product of idx and signs as an __m128d without horizontally summing it, then calcPoint can add up those vectors and only do one horizontal sum, after the loop.\n\n## Passing doubles by reference or address\n\nGenerally, when primitive types can be passed by value (even if that requires returning a new value), they should be. It's not always bad to pass them by reference, but it's rarely good. In the case of computePoint, it makes sense to pass in pIndex by address, because it's going to get movddup'ed and it's better to do that directly from memory, but in the case of calcPoint I expect that passing bfVal by reference is not good, resulting in a load/store (vaddsd xmm0, xmm0, QWORD PTR [r12] \\ vmovsd QWORD PTR [r12], xmm0) to update the variable \"at a distance\" rather than summing into a register and storing it once in the end. This is also automatically fixed if dppd is removed in the way that I described above.\n\n## SIG.col(j).data()\n\nI seriously underestimated how bad such an innocent-looking expression could be, anything I just mentioned looks really small compared to this. After compiling the code though (with optimization level -O3), it seems that all or most of this is associated with just that column-data access:\n\n imul rdx, rbx\nmov r8, QWORD PTR [rbp+8]\nmov rax, QWORD PTR [rbp+0]\nmov rdi, rsp\nmov ecx, 1\nlea rsi, [rax+rdx*2]\nmov rdx, r8\ncall Eigen::MapBase<Eigen::Block<Eigen::Ref<Eigen::Matrix<short, -1, -1, 0, -1, -1> const, 0, Eigen::OuterStride<-1> > const, -1, 1, true>, 0>::MapBase(short const*, long, long) [base object constructor]\nmov rdx, QWORD PTR [rbp+24]\nmov QWORD PTR [rsp+24], rbp\nmov QWORD PTR [rsp+32], 0\nmov QWORD PTR [rsp+40], rbx\nmov QWORD PTR [rsp+48], rdx\ncmp QWORD PTR [rbp+16], rbx\njle .L20\nmov rax, QWORD PTR [r13+0]\nvmovq xmm2, QWORD PTR .LC9[rip]\nmov rcx, QWORD PTR [rsp]\nvmovsd xmm1, QWORD PTR [rax+rbx*8]\n\n\nHorrible. I'm not sure what to do about it, maybe SIG.data() + j * SIG.rows() works, assuming that the matrix is column-major? You probably know more about Eigen than I do though.\n\n## CalcIDXT\n\nI don't really know what's going on there, but it may be possible to increase performance by doing all or most of that with vector intrinsics so that the resulting indexes can be fed directly into the interpolation math, rather than going through memory first.\n\n## AVX2\n\nIt seems to me that a AVX2 version of computePoint is worth investigating, it could do twice the amount of work in (I think) less than twice the amount of time. It wouldn't reach 2x throughput overall because there would be some annoying shuffles and inserts and two independent signs would be loaded, but it could still be a win.\n\n• I would be careful with SIG.data() + j * SIG.rows(); Eigen allows matrices to have a different stride than the number of rows. Mar 26, 2022 at 10:20\n• @G.Sliepen what do you recommend as a replacement? Mar 26, 2022 at 10:28\n• I'm not sure a better replacement is possible, then again I'm not a big user of Eigen myself. Mar 26, 2022 at 10:37\n• Eigen has a new interface for indexing that looks more like the way matlab does indexing. There's a description in the documentation somewhere that I'm too lazy to find right now for anyone reading this who's curious about it. However, I fortunately have the sizes of SIG stored in my 'p' data structure. I'll just try using that. Mar 26, 2022 at 15:59\n• Thanks for all this feedback. I'll try it later and lyk how it works. Mar 26, 2022 at 16:00" ]

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[ "# Two cars moving evenly and in a straight line along two intersecting roads at right angles simultaneously\n\nTwo cars moving evenly and in a straight line along two intersecting roads at right angles simultaneously cross the intersection. After a time interval Δt = 20s after passing the intersection, the distance between the cars became (el) l = 500m. Determine the module of speed of the second car, if the speed of movement of the first v (1) = 15m / s\n\nFrom the condition, the modulus of the speed of the first car and the distance between the cars in time Δt are known. The path traveled by cars is the legs of a right-angled triangle, and the distance l is its hypotenuse. Let’s find the length of the path covered by the first car:\n1) l1 = v1 * Δt = 15 * 20 = 300 meters;\nBy the Pythagorean theorem, knowing the length of the hypotenuse and one and the legs, we find the length of the second leg:\n2) l2 ^ 2 = 500 ^ 2-300 ^ 2 = 1600; l2 = 400;\nLet’s find the speed with which the second car was moving:\n3) v2 = l2 / Δt = 400/20 = 20 m / s", null, "" ]

[ null, "https://www.univerkov.com/01.jpg", null ]

[ "# Answers\n\nSolutions by everydaycalculation.com\n\n## Add 1/7 and 4/40\n\n1/7 + 4/40 is 17/70.\n\n#### Steps for adding fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 7 and 40 is 280\n\nNext, find the equivalent fraction of both fractional numbers with denominator 280\n2. For the 1st fraction, since 7 × 40 = 280,\n1/7 = 1 × 40/7 × 40 = 40/280\n3. Likewise, for the 2nd fraction, since 40 × 7 = 280,\n4/40 = 4 × 7/40 × 7 = 28/280\n4. Add the two like fractions:\n40/280 + 28/280 = 40 + 28/280 = 68/280\n5. 68/280 simplified gives 17/70\n6. So, 1/7 + 4/40 = 17/70\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:\nAndroid and iPhone/ iPad\n\n#### Add Fractions Calculator\n\n+\n\n© everydaycalculation.com" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "Color Comparison\n\n Author: Bill O'Connell (woc at attbi.com) History: 2002/03/08: First version 2002/07/31: Added Regression option 2002/09/23: New features 2004/03/09: Updated to work with byte masks used in ImageJ 1.32c and later Requires: ImageJ 1.32c or later Source: ColorComparison_.java Installation: Download ColorComparison_.java to the plugins folder and compile it using Plugins/Compile and Run. There will be a new \"ColorComparison\" command in the Plugins menu the next time you restart ImageJ. Description: ```Color comparison of two 8-bit identically dimensioned gray scale images. Each pixel has an intensity in image A and in image B. Plot each point on a plain with image A intensity as abcissa and B intensity as ordinate. ColorComparison allows the user to compare Image1 with Image2 intensities using one of the methods below - 1) Polar Comparison: In polar coordinates, a pixel's location is given by magnitude and angle. The color image shows pixel magnitude (or image A or image B intensity) as intensity. Polar angle is shown as hue. With positive valued images, pixel angle is between 0 and 90 degrees. Pixel angles are mapped to any continuous swatch of a color wheel where R=0, G=120, B=240 degrees. 2) Percentage: p = 100 * (B intensity) / (A intensity + B intensity) may be used to specify hue. With methods 1) and 2) the mapping is isomorphic - all information in the two gray scale images is retained in the color image. ColorComparison also generates a histogram of pixel pair angles(0 to 90 degrees) or percentages(0 to 100%) sorted into a user specified number of bins. 3) Regression: A linear regression and standard error of regression are calculated predicting Image2 from Image1 pixel intensities. The hue of each pixel in the color image expresses the residual, the difference between the predicted and actual Image2 intensity divided by the standard error of regression. The range of differences mapped by the color image is set by the number of histogram bins specified. For instance, sepecifying 10 bins sets a range of -5 to +5 standard errors. The hue of pixels outside this range are clamped to the max or min standard error. After the color image is generated, the user is allowed to draw ROIs on Image1. The mean residual within the ROI and its probability are displayed in a table. If the histogram uses weighted intensities the mean is calculated using weighted intensities. if HighlightPixels is checked, the program highlights all color image pixels with values outside regression confidence limits at the specified probability level alpha. Percentages of pixels above and below the confidences limits are displayed in the Results window. Pixels below the specified Theshold Intensity are excluded, and percentages are weighted by Image1 intensities if the weight histogram box is checked. ```\n\n|Plugins | Home |" ]

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[ "# How to Round Up in Excel\n\n## Jun 28, 2020 · 6 minute read\n\nIf we have numbers in our table and we have to limit the decimals, we can use these commands.\n\n## How to Round Number in Excel.\n\nIn this command, if your integrated or decimal part is less than 5, you will be rounded to a smaller value, and if it is equal to or greater than 5, it will be rounded to a larger amount.\n\nHere we want to explain this command with an example.\n\nIn this table, we have a salary of the employees in one company in this year and we want to calculate the amount of their salary in the next year if their salaries increase 7.3 per cent in the next year.\n\nIn column C, we have the salaries of employees in this company in the current year, in column “D” we have the salary of the employees in the new year, we want to round the new salaries in a penny in Column “E”, in column “G” we want to round the salaries into the dollar and, we want to around them into one hundred dollars in column “I”.\n\n• At first, we should calculate the amount of salary in the new year.", null, "Now we want to round them in Penny, Dollar and one hundred dollars.\n\n### How to Round Number to Penny.\n\nFor rounding numbers to Penny, we should have 2 decimal places in our content.\n\nFor that we should use this command;\n\n=ROUND(D4,2)\n\nIn this formula, “D4” is the address of the cell which we want to round its content and number 2 means that we want to round our numbers to the nearest two decimal places to the right of the decimals.\n\nIn this example, you can see in column “D”, If the numbers which are placed in the 3 decimal places are lower than 5 they will be rouned toward lower digit ( the rows number 4&5&7) but If the numbers are equal or higher than 5 they will be rounded toward higher digit.", null, "### How to Round Number to Dollar.\n\nFor rounding numbers to the dollar, we should exclude decimal places in our content.\n\nFor that we should use this command;\n\n=ROUND(D4,0)\n\nIn this formula, “D4” is the address of the cell which we want to round its content and number 0 means that we want to remove all decimals from our contents.\n\nAlso, you can see in the column “D” when the first decimal was equal or higher than five, our numbers were rounded to the higher digit in this example you can see rows number five and six and seven, when it was lower than five, it was rounded to lower digit like the column four.", null, "### How to Round Number to Hundred Dollars.\n\nFor rounding salaries to the nearest hundred dollars. we should round our numbers to the nearest two digit places to the left side of the decimal point. for that, we should place minus 2 instead of zero in the previous formula.\n\n=ROUND(D4,-2)", null, "## How to Round Up in Excel;\n\nIf you want to round your digits up, you can use from other commands.\n\nHere I am going to introduce two commands for rounding up the digits in excel.\n\n### How to Round Up in Excel with CEILING.MATH Command;\n\nThis command used for roundup to the nearest integer or to the nearest multiple of significance and it has 3 different part which two of them are optional.\n\n• The first part is “Number” and that is the value which you want to round.\n\n• The second part is “Significance” and it is optional and is the multiple to which you want to round numbers.\n\n• The third part is “Mode” and It does not work for positive numbers and shows that number should round away or toward from zero.\n\nIn the below picture we use this command with “Mode” and without “Mode”.\n\nAs we said you can use this part only for negative numbers.\n\nIn the first and second rows, we wrote number 1 in the third part of the formula and you can see these numbers rounded away from zero,\n\nand in the other rows, we didn’t write anything in the third part of the formula and you can see the numbers rounded toward zero.", null, "Here we are going to explain them with some example.\n\n#### How to Round Up Numbers to 0.5\n\nAs you see in the first-row number remained the same because it is the multiple of 0.5 and rows number two and three rounded up to 315.5 and the last row rounded up to 316.", null, "#### How to Round Up Numbers to 1;\n\nin this table you can see the value in the first table did not change but in other rows, the value rounded up to the next digit.", null, "#### How to Round Up Numbers to 10;\n\nIn this table, you can see the numbers rounded up to the next multiple 10 digits.", null, "#### How to Round Up Numbers to 100;\n\nIn this table, you can see the numbers rounded up to the next multiple 100 digits.", null, "### How to Round Up in Excel with Round Up Command;\n\nThis command has two-part,\n\n• The first part is the number which you want to round it.\n\n• The second part is the number of digits to which you want to round number.\n\nIf you enter a negative number in this part the numbers will be rounded to the left side of the decimal point and the number zero will be rounded up the numbers to the nearest integer and positive number will be rounded up numbers to the specified number of the decimal.\n\nNow we will explain this command with some example;\n\nIn this picture, you can see negative numbers in the first column and you can see these numbers round away zero.", null, "In this formula, we entered number -2 in the second part and you can see the numbers in the table were rounded from the two left-side digits of the decimal point.\n\nIn this table, the first row did not round up because it was equal to multiple hundred.", null, "In this formula, we entered number -1 in the second part and you can see the numbers in the table were rounded from the one left side digit of the decimal point.\n\nIn the first and third rows because they were integer the program did not round them up.", null, "In this formula, we entered number zero in the second part and you can see the numbers in the table were rounded up to the nearest integer.\n\nBut in the first row because the number was integer the program did not round it up.", null, "In this formula, we entered number +1 in the second part so the numbers will be rounded up to the first decimal number.", null, "## How to Round Up digits to 0.99\n\nSometimes you want to round up the digits to 0.99 for instance round 6.3 to 6.99\n\nFor that you can use this formula;\n\n=ROUNDUP(E5,0)-0.01", null, "" ]

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[ "This site uses cookies. By continuing to browse the ConceptDraw site you are agreeing to our Use of Site Cookies.\n\n# 2 Circle Venn Diagram. Venn Diagram Example\n\nUsing the ready-to-use predesigned objects, samples and templates from the Venn Diagrams Solution for ConceptDraw PRO you can create your own professional looking Venn Diagrams quick and easy.\n\n##", null, "Venn Diagrams\n\nVenn Diagrams are actively used to illustrate simple set relationships in set theory and probability theory, logic and statistics, mathematics and computer science, linguistics, sociology, and marketing. Venn Diagrams are also often used to visually summarize the status and future viability of a project.\n\n## Venn Diagram Examples for Problem Solving. Venn Diagram as a Truth Table\n\nVenn diagrams are illustrations used in the branch of mathematics known as set theory. They show the mathematical or logical relationship between different groups of things (sets). A Venn diagram shows all the possible logical relations between the sets.\n\n## Circles Venn Diagram\n\nThis example shows the 4 Circle Venn Diagram. The Venn Diagram visualizes all possible logical relations between several sets. The sets are represented as circles on the Venn Diagram. On this example you can see the intersections of 4 sets. Venn Diagrams are widely used in mathematics, logic, statistics, marketing, sociology, etc.\n\n## 3 Circle Venn Diagram. Venn Diagram Example\n\nThis template shows the Venn Diagram. It was created in ConceptDraw PRO diagramming and vector drawing software using the ready-to-use objects from the Venn Diagrams Solution from the \"What is a Diagram\" area of ConceptDraw Solution Park.\nVenn Diagrams visualize all possible logical intersections between several sets and are widely used in mathematics, logic, statistics, marketing, sociology, etc.\n\n## What Is a Circle Spoke Diagram\n\nWhat Is a Circle Spoke Diagram? It is a diagram which have a central item surrounded by other items in a circle. The Circle Spoke Diagrams are often used to show the features or components of the central item in marketing and management documents and presentations. ConceptDraw PRO extended with Circle-Spoke Diagrams Solution from the \"What is a Diagram\" Area is the best software for creating Circle-Spoke Diagrams.\n\n## Circle Spoke Diagram Template\n\nConceptDraw PRO diagramming and vector drawing software offers the Circle Spoke Diagram Template included in the Circle-Spoke Diagrams Solution from the \"What is a Diagram\" Area. Use of ready template is the easiest way of drawing professional looking Circle-Spoke Diagrams.\n\n## Venn Diagram\n\nVenn diagrams are illustrations used in the branch of mathematics known as set theory. They show the mathematical or logical relationship between different groups of things (sets). A Venn diagram shows all the possible logical relations between the sets.\n\n## Circle Diagrams\n\nThe Circle Diagrams are the diagrams which represent the central element surrounded by other items in a circle. This type of diagram is very popular and widely used in marketing and management, for process modeling, market, resource, time and cost analysis, for visualization causes and effects. If you dream to design the Circle Diagrams quick and easy – the ConceptDraw PRO software extended with Circle-Spoke Diagrams Solution from the \"What is a Diagram\" Area is exactly what you need.\n\n## Multi Layer Venn Diagram. Venn Diagram Example\n\nTo visualize the relationships between subsets of the universal set you can use Venn diagrams. To construct one, you should divide the plane into a number of cells using n figures. Each figure in the chart represents a single set of, and n is the number of represented sets. Splitting is done in a way that there is one and only one cell for any set of these figures, the points of which belong to all the figures from the set and do not belong to others. The plane on which the figures are represented, is the universal set U. Thus, the point which does not belong to any of the figures, belongs only to U.\n\n##", null, "Circle-Spoke Diagrams\n\nExamples of subject areas that are well suited to this approach are marketing, business, products promotion, process modeling, market, resource, time, and cost analysis. Circle-Spoke Diagrams are successfully used in presentations, conferences, management documents, magazines, reportages, reviews, reports, TV, and social media.\n\n## Basic Circles Venn Diagram. Venn Diagram Example\n\nVenn Diagrams visualize all possible logical relations between several sets and are widely used in mathematics, logic, statistics, marketing, sociology, etc.\nThis Venn Diagram shows the relative complement of the set A with respect to the set B. It is the set of the elements in B, but not in A. In other words it is the set-theoretic difference B-A.\nHelpDesk\n\n## How to Create a Venn Diagram in ConceptDraw PRO\n\nVenn diagrams were invented by John Venn as a method of depicting relationships between different components. A Venn diagram consists of two or more circles. Each circle represents a specific group or set. The entities which are depicted by circles generally have some common characteristics. A Venn Diagram shows all the possible logical relations between these entities. Any properties that belong to more than one set should be indicated in the sections where the circles overlap. A Venn Diagram can be useful to visually summarize the status and future viability of a project. ConceptDraw PRO allows you to make a Venn diagrams using the Venn Diagrams solution.\n\n## 3 Circle Venn. Venn Diagram Example\n\nThis example shows the 3 Circle Venn Diagram. The Venn Diagrams visualize all possible logical intersections between several sets. On this example you can see the intersections of 3 sets. Venn Diagrams are widely used in mathematics, logic, statistics, marketing, sociology, etc.\n\n## Venn Diagram Template for Word\n\nThis template shows the Venn Diagram. It was created in ConceptDraw PRO diagramming and vector drawing software using the ready-to-use objects from the Venn Diagrams Solution from the \"What is a Diagram\" area of ConceptDraw Solution Park." ]

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[ "As a forex trader, you are always looking for ways to increase your chances of success. One technique that has gained popularity in recent years is the use of Fibonacci retracement levels. These levels are based on the Fibonacci sequence and can be used to identify potential levels of support and resistance.\n\nIn this article, I will explain what Fibonacci retracement levels are, how they are calculated, and how you can use them in your forex trading.\n\n## What are Fibonacci Retracement Levels\n\nFibonacci retracement levels are a technical analysis tool used to identify potential levels of support and resistance in a market. They are based on the idea that markets tend to retrace a predictable portion of a move before resuming their trend. The levels are derived from the Fibonacci sequence, which is a mathematical sequence that occurs throughout nature.\n\n## How Fibonacci Retracement Levels are used in Forex Trading\n\nFibonacci retracement levels are used in forex trading to identify potential levels of support and resistance.\n\nThese levels can be used to enter and exit trades, as well as to set stop-loss orders. The most commonly used levels are the 38.2%, 50%, and 61.8% retracement levels. Traders will often look for confluence between these levels and other technical analysis tools, such as trend lines and moving averages, to increase the probability of a successful trade.\n\n## The Fibonacci Sequence\n\nTo understand how Fibonacci retracement levels are calculated, it is important to first understand the Fibonacci sequence. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.\n\n## Explanation of the Fibonacci Sequence\n\nThe Fibonacci sequence is an example of a recursive sequence, where each term is calculated from the previous two terms. The sequence occurs throughout nature, from the branching patterns of trees to the arrangement of leaves on a stem. In forex trading, the Fibonacci sequence is used to identify potential levels of support and resistance.\n\n## Examples of the Fibonacci Sequence\n\nIn forex trading, the Fibonacci sequence is used to calculate retracement levels. The most commonly used levels are the 23.6%, 38.2%, 50%, 61.8%, and 100% retracement levels. These levels are calculated by multiplying the distance of the move by the Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%.\n\n## Why the Fibonacci Sequence is used in Forex Trading\n\nThe Fibonacci sequence is used in forex trading because it has been shown to be a reliable tool for identifying potential levels of support and resistance. Markets tend to retrace a predictable portion of a move before resuming their trend, and the Fibonacci retracement levels can be used to identify these levels.\n\n## How Fibonacci Retracement Levels are calculated\n\nFibonacci retracement levels are calculated by multiplying the distance of the move by the Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%. For example, if a currency pair moves from 1.0000 to 1.0100, the distance of the move is 100 pips. The 38.2% retracement level would be calculated by multiplying 100 by 0.382, which equals 38.2 pips.\n\n## Formula for calculating Fibonacci Retracement Levels\n\nThe formula for calculating Fibonacci retracement levels is:\n\n``Retracement Level = Move Distance x Fibonacci Ratio``\n\n## Explanation of each level (23.6%, 38.2%, 50%, 61.8%, and 100%)\n\nThe 23.6% retracement level is considered the shallowest level and is often used as a potential entry point for a trade. The 38.2% level is the most commonly used level and is often used as a level of support or resistance.\n\nThe 50% level is also a commonly used level and is often used as a confirmation level. The 61.8% level is considered a deep retracement level and is often used as a potential reversal point. The 100% level is not a Fibonacci retracement level, but it represents the starting point of the move and can be used as a reference point.\n\n## Using Fibonacci Retracement Levels in Forex Trading\n\nTo use Fibonacci retracement levels in forex trading, you first need to identify a move in the market. This can be a move up or down, depending on the direction you want to trade. Once you have identified the move, you can use the Fibonacci retracement tool to draw the retracement levels on your chart.\n\nYou can then look for potential trading opportunities at these levels. For example, if the market is in an uptrend and retraces to the 38.2% level, you can look for a potential entry point to go long. You can also use Fibonacci retracement levels to set stop-loss orders or to take profit levels.\n\n## Examples of using Fibonacci Retracement Levels in Forex Trading\n\nLet’s say you have identified an uptrend in the EUR/USD currency pair. The pair has moved from 1.2000 to 1.2200, and you want to use Fibonacci retracement levels to identify potential levels of support. You can draw the retracement levels on your chart and see that the 38.2% level is at 1.2124, the 50% level is at 1.2100, and the 61.8% level is at 1.2076.\n\nIf the price retraces to the 38.2% level, you can look for a potential entry point to go long. You can also use the 50% and 61.8% levels as potential levels of support.\n\n## How to identify potential trading opportunities using Fibonacci Retracement Levels\n\nTo identify potential trading opportunities using Fibonacci retracement levels, you can look for confluence between the levels and other technical analysis tools.\n\nFor example, if the 38.2% retracement level is also a key level of support or resistance, this increases the probability of a successful trade. You can also look for candlestick patterns or other indicators that confirm the potential trading opportunity.\n\n## Limitations of Fibonacci Retracement Levels\n\nIt is important to note that Fibonacci retracement levels are not always accurate and should be used in conjunction with other technical analysis tools. They can also be subjective, as different traders may draw the levels differently. Additionally, markets can be unpredictable and may not always follow the Fibonacci ratios.\n\n## Other tools and indicators to use alongside Fibonacci Retracement Levels\n\nTo increase the probability of a successful trade, it is recommended to use Fibonacci retracement levels in conjunction with other technical analysis tools.\n\nThese can include trend lines, moving averages, and other indicators such as the Relative Strength Index (RSI) or the Moving Average Convergence Divergence (MACD).\n\n## Trading Strategies using Fibonacci Retracement Levels\n\nThere are many different trading strategies that use Fibonacci retracement levels. One common strategy is to enter a trade at the 38.2% level and set a stop-loss order below the 50% level. Another strategy is to enter\n\na trade at the 50% level and set a stop-loss order below the 61.8% level. Traders may also use Fibonacci retracement levels in conjunction with other technical analysis tools to identify potential trading opportunities.\n\n## Examples of trading strategies using Fibonacci Retracement Levels\n\nLet’s say you have identified a downtrend in the USD/JPY currency pair. The pair has moved from 110.00 to 108.00, and you want to use Fibonacci retracement levels to identify potential levels of resistance. You can draw the retracement levels on your chart and see that the 38.2% level is at 108.88, the 50% level is at 109.00, and the 61.8% level is at 109.12.\n\nIf the price retraces to the 38.2% level, you can look for a potential entry point to go short. You can also use the 50% and 61.8% levels as potential levels of resistance. You can set a stop-loss order above the 50% level and take profit at the 61.8% level.\n\n## Common Mistakes to avoid when using Fibonacci Retracement Levels\n\nOne common mistake when using Fibonacci retracement levels is to rely solely on them without using other technical analysis tools. It is also important to use the levels in conjunction with price action and market context. Another mistake is to draw the levels incorrectly, as this can lead to incorrect trading decisions. It is important to use a consistent methodology when drawing the levels.\n\n## Historical Analysis of Fibonacci Retracement Levels\n\nFibonacci retracement levels have been used in financial markets for many years and have been shown to be a reliable tool for identifying potential levels of support and resistance. By analyzing historical price action, traders can see how the levels have performed in the past and use this information to make trading decisions in the future.\n\n## Examples of historical analysis of Fibonacci Retracement Levels\n\nHistorical analysis of Fibonacci retracement levels can be used to identify potential levels of support and resistance in the market. Traders can look at past price action and see how the levels have performed in the past. This information can be used to make trading decisions in the future.\n\n### What is the Fibonacci sequence?\n\nThe Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers. The sequence occurs throughout nature and is used in forex trading to identify potential levels of support and resistance.\n\n### How are Fibonacci retracement levels calculated?\n\nFibonacci retracement levels are calculated by multiplying the distance of the move by the Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%.\n\n### What are the most commonly used Fibonacci retracement levels?\n\nThe most commonly used Fibonacci retracement levels are the 38.2%, 50%, and 61.8% levels.\n\n## Conclusion\n\nFibonacci retracement levels are a powerful tool for forex traders looking to identify potential levels of support and resistance.\n\nBy understanding the Fibonacci sequence and how the levels are calculated, traders can use this tool to enter and exit trades, set stop-loss orders, and take profit levels. While there are limitations to using Fibonacci retracement levels, they can be used in conjunction with other technical analysis tools to increase the probability of a successful trade." ]

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[ "## [LATEST]\\$type=sticky\\$show=home\\$rm=0\\$va=0\\$count=4\\$va=0\n\nMathematics is an important subject in SSC,DSSB & Other Exams. .\n\nQ1. A circle which passes through origin and cuts intercepts on axes a and b, the equation of circle is :\n•  x^2+y^2-ax-by=0\n•  x^2+y^2+ax+by=0\n•  x^2+y^2-ax+by=0\n•  x^2+y^2+ax-by=0\nSolution\nx^2+y^2-ax-by=0\n\nQ2.Let L1 be a straight line passing through the origin and L2 be the straight line x+y=1. If the intercepts made by the circle x^2+y^2-x+3y=0 on L1 and L2 are equal, then which of the following equations can represent L1:\n•  x+y=0:\n•  x-y=0\n•  x+7y=0\n•  x-7y=0\nSolution\nx-y=0\n\nQ3.  The two lines through (2, 3) from which the circle x^2+y^2=25 intercepts chords of length 8 units have equations :\n•  2x+3y=13,x+5y=17\n•  y=3,12x+5y=39\n•  x=2,9x-11y=51\n•  None of these\nSolution\ny=3,12x+5y=39\n\nQ4. Circles are drawn through the point (2, 0) to cut intercepts of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is\n•  x^2+y^2-9x+2ky+14=0\n•  3x^2+3y^2+27x-2ky+42=0\n•  x^2+y^2-9x-2ky+14=0\n•  x^2+y^2-2kx-9y+14=0\nSolution\nx^2+y^2-9x-2ky+14=0\n\nQ5.A circle touches the y-axis at (0, 2) and has an intercept of 4 units on the positive side of the x-axis. Then the equation of the circle is\n•  x^2+y^2-4(√2 x+y)+4=0\n•  x^2+y^2-4(x+√2 y)+4=0\n•  x^2+y^2-2(√2 x+y)+4=0\n•  None of these\nSolution\nx^2+y^2-4(√2 x+y)+4=0\n\nQ6. Circles are drawn through the point (3, 0) to cut an intercept of length 6 units on the negative direction of the x-axis. The equation of the locus of their centres is\n•  The x-axis\n•  x-y=0\n• The y-axis\n•  x+y=0\nSolution\nThe y-axis\n\nQ7.Circles x^2+y^2=1 and x^2+y^2-8x+11=0 cut off equal intercepts on a line through the point (-2,1/2). The slope of the line is\n•  (-1+√29)/14\n•  (1+√7)/4\n•  (-1-√29)/14\n•  None of these\nSolution\n(-1+√29)/14\n\nQ8.If 2l be the length of the intercept made by the circle x^2+y^2=a^2 on the line y=mx+c, then c^2 is equal to\n•  (1+m^2)(a^2+l^2)\n•  T(1+m^2)(a^2-l^2)\n•  (1-m^2)(a^2+l^2)\n•  (1-m^2)(a^2-l^2)\nSolution\n(1+m^2)(a^2-l^2)\n\nQ9.For the circle x^2+y^2+4x-7y+12=0 the following statement is true\n•  The length of tangent from (1, 2) is 7\n•  Intercept on y-axis is 2\n•  Intercept on x-axis is 2-√2\n•  None of these\nSolution\nNone of these\n\nQ10. The length of the chord joining the points in which the straight line x/3+y/4=1 cuts the circle x^2+y^2=169/25 is\n•  1\n•  2\n•  4\n• 8\nSolution\n2", null, "## Want to know more\n\nWant to Know More\nPlease fill in the details below:\n\n## Latest NEET Articles\\$type=three\\$c=3\\$author=hide\\$comment=hide\\$rm=hide\\$date=hide\\$snippet=hide\n\nName\n\nltr\nitem\nBEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET, IIT JEE COACHING INSTITUTE: Intersection of a Line and a Circle - Advance Quiz\nIntersection of a Line and a Circle - Advance Quiz\nhttps://1.bp.blogspot.com/31Aq5tTN68kHYqNcKf4nPft5KAUkuMQoNevVugpyMEui3ZP-hiPHvF3ZOPFJMflE9kVnSQ1ULq_cKOg=w400-h209\nhttps://1.bp.blogspot.com/31Aq5tTN68kHYqNcKf4nPft5KAUkuMQoNevVugpyMEui3ZP-hiPHvF3ZOPFJMflE9kVnSQ1ULq_cKOg=s72-w400-c-h209\nBEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET, IIT JEE COACHING INSTITUTE" ]

[ null, "https://1.bp.blogspot.com/31Aq5tTN68kHYqNcKf4nPft5KAUkuMQoNevVugpyMEui3ZP-hiPHvF3ZOPFJMflE9kVnSQ1ULq_cKOg=w400-h209", null ]

[ "# The relationship between downsampling and frequency resolution\n\nI am having trouble understanding a concept that I have seen in many published papers. For example, in this paper (http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0082748) they wrote in their methods that to \"obtain adequate frequency resolution we downsampled from 44.1 kHz to 8 kHz\".\n\nMy understanding is that the sample rate is how many times (per second) the actual sound wave was \"sampled\", and that the maximum frequency that can be detected is 1/2 the sampling rate (or the Nyquist frequency). So by downsampling, you will lose the ability to detect higher frequencies, and in a sense downsampling acts as a sort of filter, as it gets rid of the higher frequency sounds from the recording.\n\nThis makes sense to do if your signal of interest is at lower frequencies, but I still don't understand how this gives \"adequate frequency resolution\". Does downsampling have any influence on the ability to detect lower frequencies? What do they mean by \"frequency resolution\"? Thank you so much in advance!\n\n• My interpretation: When analyzing a DFT, it makes sense to limit the sampling rate to something close to Nyquist. Otherwise, one ends up with a lot of bins that do not have any information. When plotting (either on screen or on paper), it makes sense to use as many pixels or inches of paper as possible to display the frequencies of interest. – MBaz Apr 26 '16 at 14:57\n\nYour understanding is correct. I don't have the full text of the paper, but it sounds like they aren't being very precise with their description. As you pointed out, downsampling doesn't improve frequency resolution in and of itself, it merely reduces the amount of bandwidth that can be represented unambiguously.\n\nHowever, I can take a guess at what they were referring to. Assuming they are using a DFT for spectral analysis (the common choice), note that the fact that for a given DFT size $N$, the output bin spacing is a function of the sample rate:\n\n$$f_{res} = \\frac{f_s}{N}$$\n\nSo, if a smaller frequency resolution in your spectral calculation is desired, decreasing the sample rate of the data can help you do that. Of course, you could also increase the DFT size $N$ as well; there are some applications where that's not an option, though (e.g. if you're using hardware that is limited to certain FFT sizes). Also, this method can have advantages when the signal of interest is in a small band of frequencies relative to the original sample rate; in this case, downsampling followed by a smaller DFT can be more computationally advantageous than doing one large DFT (this is known as the zoom FFT technique).\n\nNote that there isn't a free lunch here: to actually realize an increase in resolution, you need $N$ samples at the lower sample rate, which requires a longer observation time. This is the same total observation time that is required by just collecting more data at the higher sample rate and then doing a larger DFT.\n\nIt took me a while to visualize this stuff.\n\nIn the $z$-domain, the frequencies from 0 to Nyquist are always represented as 0 to $\\pi$. This means that if you increase the sampling rate, there are more frequencies that must be represented in your 0 to $\\pi$ region (represented by $\\omega$). This means as the sample rate increases, a 50Hz signal, say, is represented by a smaller $\\omega$.\n\nSome types of digital filter (FIR) and also FFT have a poor resolution at the lower frequencies, so you downsample to effectively increase their frequency resolution at lower frequencies. Downsampling increases the $\\omega$ value you need to represent say, 50Hz.\n\nAn interesting problem will arise though if you want to increase your FFT resolution. Downsampling will not help, you must increase your sample set and ultimately the number of FFT bins you have.\n\nI've mainly hit this problem designing IIRs where trying to design certain types of IIR of, say, 5Hz at a sampling rate of 192KHz can be more prone to problems than at 48KHz." ]

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[ "# Why is the adjugate matrix the null matrix? [duplicate]\n\nThis question already has an answer here:\n\nI struggle to understand why if $$A\\in M_n(\\mathbb{C})$$, $$\\det A=0$$ and $$rank A \\le n-2$$, then $$A^*=O_n$$. Could you please tell me why this claim holds? My textbook offers no proof for this.\n\n## marked as duplicate by Namaste, Dietrich Burde, Nosrati, Lord Shark the Unknown, Key FlexOct 21 '18 at 19:21\n\nThis question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.\n\n• Have you seen the result that $A$ has rank at most $n-2$ if and only if all $n-1$ minors are non-zero? That is, have you seen anything about \"determinantal rank\"? – Omnomnomnom Oct 21 '18 at 18:20\n• The result is explained/proved nicely in this post – Omnomnomnom Oct 21 '18 at 18:22\n• @Omnomnomnom You also explained it nicely here yourself. – Dietrich Burde Oct 21 '18 at 18:42\n\n## 1 Answer\n\nIf $$A$$ has rank$${} then all $$(n-1)\\times(n-1)$$ minors are equal to zero, and so $${\\mathrm adj}(A)$$ has rank$$~0$$.\n\n• Could you give me some further explainations? How come $adj(A)$ has rank 0? – user69503 Oct 21 '18 at 18:39\n• See the answers here. – Dietrich Burde Oct 21 '18 at 18:42" ]

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[ "# Watt-Hours to Megajoules Converter\n\nEnter the energy in watt-hours below to get the value converted to megajoules.\n\nResults in Megajoules:", null, "1 Wh = 0.0036 MJ\n\nDo you want to convert megajoules to watt-hours?\n\n## How to Convert Watt-Hours to Megajoules\n\nTo convert a measurement in watt-hours to a measurement in megajoules, multiply the energy by the following conversion ratio: 0.0036 megajoules/watt-hour.\n\nSince one watt-hour is equal to 0.0036 megajoules, you can use this simple formula to convert:\n\nmegajoules = watt-hours × 0.0036\n\nThe energy in megajoules is equal to the energy in watt-hours multiplied by 0.0036.\n\nFor example, here's how to convert 500 watt-hours to megajoules using the formula above.\nmegajoules = (500 Wh × 0.0036) = 1.8 MJ\n\n## What Is a Watt-Hour?\n\nThe watt-hour is a measure of electrical energy equal to one watt of power over a one hour period.\n\nWatt-hours are usually abbreviated as Wh, although the formally adopted expression is W·h. The abbreviation W h is also sometimes used. For example, 1 watt-hour can be written as 1 Wh, 1 W·h, or 1 W h.\n\nIn formal expressions, the centered dot (·) or space is used to separate units used to indicate multiplication in an expression and to avoid conflicting prefixes being misinterpreted as a unit symbol.\n\n## What Is a Megajoule?\n\nOne megajoule is equal to 1,000,000 joules, which is the energy equal to the force on an object of one newton at a distance of one meter.\n\nThe megajoule is a multiple of the joule, which is the SI derived unit for energy. In the metric system, \"mega\" is the prefix for millions, or 106. Megajoules can be abbreviated as MJ; for example, 1 megajoule can be written as 1 MJ.\n\n## Watt-Hour to Megajoule Conversion Table\n\nTable showing various watt-hour measurements converted to megajoules.\nWatt-hours Megajoules\n1 Wh 0.0036 MJ\n2 Wh 0.0072 MJ\n3 Wh 0.0108 MJ\n4 Wh 0.0144 MJ\n5 Wh 0.018 MJ\n6 Wh 0.0216 MJ\n7 Wh 0.0252 MJ\n8 Wh 0.0288 MJ\n9 Wh 0.0324 MJ\n10 Wh 0.036 MJ\n20 Wh 0.072 MJ\n30 Wh 0.108 MJ\n40 Wh 0.144 MJ\n50 Wh 0.18 MJ\n60 Wh 0.216 MJ\n70 Wh 0.252 MJ\n80 Wh 0.288 MJ\n90 Wh 0.324 MJ\n100 Wh 0.36 MJ\n200 Wh 0.72 MJ\n300 Wh 1.08 MJ\n400 Wh 1.44 MJ\n500 Wh 1.8 MJ\n600 Wh 2.16 MJ\n700 Wh 2.52 MJ\n800 Wh 2.88 MJ\n900 Wh 3.24 MJ\n1,000 Wh 3.6 MJ\n\n## References\n\n1. Bureau International des Poids et Mesures, The International System of Units (SI), 9th edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf" ]

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