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https://www.bosssealing.com/rubber-tensile-strength-at-break/	[ "# Rubber tensile strength at break\n\nIn a tensile test, the maximum tensile stress of the sample until it breaks is the tensile strength, which is called tensile strength in academia, and the result is expressed in MPa.\n\nCalculation formula:\nDuring the tensile process of the sample, the material passes through the yield stage and enters the strengthening stage. After the transverse section size is significantly reduced, the maximum force (Fb) that it bears when it breaks is divided by the original cross-sectional area (So) of the sample. Stress (σ) is called tensile strength or strength limit (σb), and the unit is N/(MPa). It represents the maximum ability of a metal material to resist damage under tensile force. The calculation formula is:\nσ=Fb/So\nIn the formula: Fb–the maximum force that the sample bears when it is broken, N (Newton); So–the original cross-sectional area of the sample, mm².\n\n(1) When using the instrument to test the tensile strength of the sample, the tensile breaking stress, tensile yield stress, elongation at break and other data can be obtained together.\n(2) In the stress-strain curve, the point where the elongation will rise even if the load does not increase is usually called the yield point, the stress at this time is called the yield strength, and the deformation rate at this time is called the yield elongation; In the same way, the stress and deformation rate at the breaking point are called tensile strength at break and elongation at break, respectively.\n\nThe main factors affecting resistance are:\n1. Uncertainty of material performance\nMainly refers to the variability of material properties (such as strength, elastic modulus) in the structure or component caused by material factors, process, loading, environment, size and other factors;\n\n2. Uncertainty of component geometric parameters\nMainly refers to the variability of the geometrical dimensions of components caused by dimensional deviation and installation errors;\n\n3. Uncertainty of calculation model\n\nMainly refers to the variability caused by the basic assumptions and calculation formulas used in the calculation of resistance." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8916352,"math_prob":0.9738595,"size":2227,"snap":"2023-40-2023-50","text_gpt3_token_len":459,"char_repetition_ratio":0.1565452,"word_repetition_ratio":0.031976745,"special_character_ratio":0.1894926,"punctuation_ratio":0.1075,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9957361,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T06:17:56Z\",\"WARC-Record-ID\":\"<urn:uuid:457e7a1e-f1de-4113-9ebd-9af896005a75>\",\"Content-Length\":\"112377\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3774fa48-c394-40bd-aae3-9f2d2f96c03a>\",\"WARC-Concurrent-To\":\"<urn:uuid:6310a0a9-66dd-413d-8036-8322ae042d82>\",\"WARC-IP-Address\":\"172.67.171.195\",\"WARC-Target-URI\":\"https://www.bosssealing.com/rubber-tensile-strength-at-break/\",\"WARC-Payload-Digest\":\"sha1:PYRWTRYBM5EGGZKMLIUSTTKP6YFFHJRG\",\"WARC-Block-Digest\":\"sha1:7WYVSPAIDAZWYBCFKHUIYTVLKOTE6VCW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510149.21_warc_CC-MAIN-20230926043538-20230926073538-00665.warc.gz\"}"}
https://nanohub.org/resources/comphe/about	[ "## Computational Helium\n\n1. Purdue University\n\nThis notebook solves the ground state for the helium atom computationally within the mean field approximation using four Gaussian functions as the basis set.\n\nYou must login before you can run this tool.\n\nVersion 1.0 - published on 07 Jul 2017\n\ndoi:10.4231/D32R3NZ97 cite this\n\n#### Abstract\n\nSummary. This notebook solves the ground state for the helium atom computationally within the mean field approximation using four Gaussian functions as the basis set. Assuming the two-electron wavefunction to be the product of two like orbitals, the two-particle Schrodinger equation reduces to single particle one but the effective Hamiltonian depends on the orbital one is trying to find (to describe electron-electron repulsion within mean field). This equation can be solved iteratively using self-consistent field (SCF) approach.\nThe initial part of the notebook go over the initial step in the SCF calculation starting from a guess wave function. All steps are described in detail. The second part performs the iterative SCF calculation until convergence is achieved.\n\n#### Cite this work\n\nResearchers should cite this work as follows:\n\n• Alejandro Strachan (2017), \"Computational Helium,\" https://nanohub.org/resources/comphe. (DOI: 10.4231/D32R3NZ97).\n\n#### Submitter\n\nMartin Hunt\n\nPurdue University" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87245595,"math_prob":0.46467304,"size":1220,"snap":"2020-34-2020-40","text_gpt3_token_len":251,"char_repetition_ratio":0.09950658,"word_repetition_ratio":0.22222222,"special_character_ratio":0.18688525,"punctuation_ratio":0.07317073,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9738759,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-13T03:16:35Z\",\"WARC-Record-ID\":\"<urn:uuid:76f419aa-28df-430a-b652-ae8d75cda3d5>\",\"Content-Length\":\"32739\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:959c6008-845d-421c-9dee-acc6ebeb02c6>\",\"WARC-Concurrent-To\":\"<urn:uuid:482b6188-0acc-4466-93f8-69ee5d2e9ba7>\",\"WARC-IP-Address\":\"132.249.202.76\",\"WARC-Target-URI\":\"https://nanohub.org/resources/comphe/about\",\"WARC-Payload-Digest\":\"sha1:XBFYP4PW2J4HL2LPXGOTAF3Y5DHCZUOM\",\"WARC-Block-Digest\":\"sha1:DTRVQQHVTOSFOHLR4VQMFGZYN57ZCANK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738950.61_warc_CC-MAIN-20200813014639-20200813044639-00236.warc.gz\"}"}
https://community.articulate.com/discussions/articulate-storyline/how-do-i-assign-points-to-options-for-questions-how-do-i-add-up-all-the-points	[ "# How do I assign points to options (for questions)? How do I add up all the points?\n\nHi Everyone! I'd like to build an assessment/survey with 10 questions. Each question would have 5 options (never, almost never, sometimes, fairly often, often). And, each option would be assigned a point (a.=1, b.=2, c. = 3, ...) At the end of the test, I want to add up all the points. Depending on the total points, users would get different feedback (e.g., 0-5 points show a green slide, 6-15 points show a red slide, 16-25 points show a yellow slide...) How do I start? Can I use regular test questions or am I building custom questions? I haven't used number variables but this might be the time? Let me know! Thanks.\n\n###### 5 Replies", null, "1. You need to use variables. If you don't know how, let us know and we can point you to some training webinars we've done.\n2. Assign a value to a variable when a decision is made. For example, you could have one total points variable and just keep adding to it.\n3. At the end have triggers that say, go to X if the value is between these values, got to y if the value is between these values, etc" ]	[ null, "https://api.articulate.com/id/v1/avatars/auth0\|55ff0860-b37f-0131-2ee8-22000b2f96a1", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.901333,"math_prob":0.8540888,"size":739,"snap":"2021-43-2021-49","text_gpt3_token_len":185,"char_repetition_ratio":0.12653062,"word_repetition_ratio":0.0,"special_character_ratio":0.26792964,"punctuation_ratio":0.20114942,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96795285,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-02T05:00:20Z\",\"WARC-Record-ID\":\"<urn:uuid:dc533f88-4f03-4b12-8b03-19ee561759fb>\",\"Content-Length\":\"51292\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eb98a177-bcc1-480e-91be-2427244e877e>\",\"WARC-Concurrent-To\":\"<urn:uuid:f5821039-cbe5-41a8-af86-55c727984e95>\",\"WARC-IP-Address\":\"18.67.65.73\",\"WARC-Target-URI\":\"https://community.articulate.com/discussions/articulate-storyline/how-do-i-assign-points-to-options-for-questions-how-do-i-add-up-all-the-points\",\"WARC-Payload-Digest\":\"sha1:IB4XET2FU6GXADDZAFUJD6VO74ZBNT6F\",\"WARC-Block-Digest\":\"sha1:SLEP4EKF6EJW22JCZL3HX3KUI3ZI4X5D\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964361064.69_warc_CC-MAIN-20211202024322-20211202054322-00320.warc.gz\"}"}
https://www.judicialwatch.org/document-archive/naomi-r-buchwald-2012/	[ "DONATE\n\nJudicial Watch • Naomi R. Buchwald – 2012\n\n# Naomi R. Buchwald – 2012", null, "Category:Federal Judges\n\nNumber of Pages:28\n\nDate Created:January 3, 2014\n\nDate Uploaded to the Library:May 22, 2014", null, "Donate now to keep these documents public!\n\nSee Generated Text ∨\n\nAutogenerated text from PDF\n\n```Rev. 112013\nFOR CALENDAR YEAR 2012 U.S.C. app. 101-111) Person Reporting (last name, first, middle initial) Buchwald, Naomi Court Organization SOUTHERN DISTRICT NEW YORK Date Report 0510412013 Title (Article Ill judges indicate active senior status; magistrate judges indicate full-or part-time) U.S. District Judge (Senior) Sa. Report Type (check appropriate type) Nomination Date Initial Annual Sb. Amended Report Final Reporting Period 01/01/2012 12/31/2012 Chambers Office Address\nDaniel Patrick Moynihan Courthouse 500 Pearl Street --ROOM 2270 New York, 10007\n/MPO ANT NOTES: The instructions accompanying this form must followed. Complete all parts, checking the NONE box for each part where you have reportable information. POSITIONS. (Reporting individual only; see pp. 9-13 filing instructions.) NONE (No reportable positions.)\n\nNAME ORGANIZATION/ENTITY POA: Accounts 1-7\n\nII. AGREEMENTS. (Reporting individual only; see pp. 14-16 filing instructions.)\n[{] NONE (No reportable agreements.)\n\nPARTIES AND TERMS\n\nBuchwald, Naomi\n05/04/2013\nIll. 0N-INVESTMENT ME. (Reporting individual and spouse; see pp. 17-24 filing instructions.) Filer's Non-Investment Income [{] NONE (No reportable non-investment income.)\nSOURCE AND TYPE INCOME (yours, not spouse's) Spouse's Non-Investment Income -If you were married during any portion the reporting year, complete this section.\n(Dollar amount not required except for honoraria.) NONE (No reportable non-investment income.)\nSOURCE AND TYPE\n\nPartner law firm Kelley, Drye Warren LLP\n\nIV REIMBURSEMENTS -transportation, lodging, food, entertainmenL (Includes those spouse and dependent children; see pp. 25-27 filing instructions.)\n[{] NONE (No reportable reimbursements.) SOURCE DATES LOCATION PURPOSE ITEMS PAID PROVIDED\n\nBuchwald, Naomi\n05/04/2013 GIFTS. (Includes those spouse and dependent children; see pp. 28-31 filing instructions.)\nSOURCE DESCRIPTION VALUE\n\nVI. LIABILITIES. (Includes those spouse and dependent children; see pp. 32-33 filing instructions.)\n[{] NONE (No reportable liabilities.)\nCREDITOR DESCRIPTION VALUE CODE\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and -income, value, transactions (Includes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (2) (2) (3) (4) (5)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value\nGain Identity\nexempt from prior disclosure Code (A-H) div., rent, int.) Code (J-P) Method Code (Q-W) buy, sell, redemption) mm/dd/yy Code (J-P) Code (A-H) buyer/seller (if private transaction) Citibank Accounts Interest Vanguard Voyager (IRA) Dividend Income Gain Codes: =\\$1 .000 less =\\$1.00 \\$2.500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000 =\\$15.001 -\\$50.000\n(Sec Columns and 04) =\\$50.001 -\\$!00.000 =\\$I 00.00 -\\$1.000.000 fl] =\\$1 .000.00 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$1 5.000 less =\\$15.001 -\\$50.000 =\\$50.001 -\\$I 00.000 I00.00 -\\$250.000\n(See Columns and 03) =\\$250.001 -\\$500.000 =\\$500.00 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.00 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(See Column C2) =Book Value V=Othcr =Estimated\n\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period ofreporting period\n\n(I) (I) (2) (I) (4) Income Gain Codes: 41.000 less =\\$1.001 -\\$2.500 c=\\$2.501 -\\$5.000 0=\\$5.001 -\\$15.000 E=\\$15.00 -\\$50.000\n(Sec Columns and 04) F=\\$50.001 -\\$100.000 =\\$!00.001 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 112 =More than \\$5.000.000 Value Codes J=\\$15.000 less K=\\$15.001 -\\$50.000 =\\$50.00I -\\$I 00.000 =\\$100.001 -\\$250,000\n{Sec Columns and D3) =\\$250.001 -\\$500.000 0=\\$500.00I -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 P4=More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment T=Cash Market\n(Sec Column C2) U=Book Value =Other =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 instructions.; NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period ofreporting period\nPlace \"(X)\" after each asset exempt from prior disclosure (I) Amount Code (2) Type (e.g., div., rent, (I) Value Code (2) Value Method (I) Type (e.g., buy, sell, (2) Date mm/dd/yy (3) Value Code (4) Gain Code (5) Identity buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n(Q-W) transaction)\nSold 12/6/12\n36.\n--International Rectifier (Common)\n\nNone Sold 917112\n37.\n\n--Amazon (Common) None Buy 01/3/12 Income Gain Codes: .000 less =\\$1.001 -\\$2.500 =\\$2.501 -\\$5.000 D=\\$5,00I -\\$15.000 =\\$15.001 -\\$50.000\n(Sec Columns and D4) =\\$50.00 -\\$I 00.000 =\\$I 00.00 -\\$1 .000.000 =\\$1 .000 .001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$1 5.000 Jess =\\$15.001 -\\$50.000 =\\$50.00 J00.000 =\\$I 00.00 -\\$250.000\n(Sec Columns and D3) =\\$250.00 -\\$500.000 =\\$500.00 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50,000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nctudes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period reporting period\n(2) (2) (3) (4) (5) Place \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code (A-H) div., rent, int.) Code (J-P) Method Code (Q-W) buy, sell, redemption) mm/dd/yy Code (J-P) Code (A-H) buyer/seller (if private transaction)\n52. Sold 11/15/12\n\n--Valero (Common) Dividend\nSold 2/8/12\n55.\nBuy 3/3/12 Income Gain Codes: =\\$1.000 less =\\$1,001 -\\$2.500 =\\$2.501 -\\$5,000 0=\\$5.001 -\\$1 5.000 =\\$15.001 -\\$50.000\n(Sec Columns and 04) =\\$50.00 -\\$I 00.000 100.00 -\\$1.000.000 =\\$1 .000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$1 5.000 less K=\\$15.00I \\$50.000 =\\$50.001 -\\$100.000 100.00 -\\$250.000\n(See Columns and 03) =\\$250.001 -\\$500.000 =\\$500,00I -\\$1.000.000 Pl =\\$1,000.001 -\\$5,000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(See Column C2) =Book Value V=Other =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end\n(including trust assets) reporting period ofreporting period\n\nTransactions during reporting period\n(I) (I)\n(2) (I) (2) (3) (4) (5)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n\nSold 08/6/12\n71.\nBuy 0817/12 Income Gain Codes: =\\$1 .000 less 41.001 -\\$2.500 =\\$2.501 -\\$5.000 0=\\$5.001 -\\$15.000 E=\\$1 5.001 -\\$50.000\n(Sec Columns and 04) F=\\$50.00l -\\$100.000 =\\$I 00.00 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 112 =More than \\$5.000.000 Value Codes =\\$15.000 less =\\$15,001 -\\$50.000 =\\$50.001 -\\$100.000 =\\$!00.001 -\\$250.000\n(Sec Columns and 03) =\\$250.001 -\\$500.000 =\\$500,00 -\\$1.000.000 =\\$1.000.001 -\\$5,000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Other =Estimated\n\nVII. INVESTMENTS and TRUSTS -income, value, transactions (lnc/11des those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (I) (I) (3) (4) (5)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n87. Sold 2/29/12\n\n90.\n91.\n92.\n93. Sold 1111 5/12\n\n--M icrosoft (Common) Dividend Buy 3/20/12\nSold 8/17/12 (part)\nSold 8/26/12 (part)\n99.\nSold 8/27/12\n\n100.\n--Research Motion (Common) None Buy 09115112\n\nIOI. Sold 12/16/12\n102. JPMorgan Chase Accounts Interest Income Gain Codes: =\\$1.000 less =\\$1.001 -\\$2.500\n(See Colmnns and 04) =\\$50.00 -\\$100.000 =\\$100.00 I.000.000 Value Codes =\\$1 5.000 less =\\$15.001 -\\$50.000\n(See Columns and 03) =\\$250.00 -\\$500.000 =\\$500.00 I.000.000 =\\$25.000.00! -\\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only)\n(Sec Column C2) =Book Value V=Othcr =\\$2.501 -\\$5.000 Ill =\\$!.000.001 -\\$5.000.000 =\\$50.00 -\\$100.000 =\\$1.000.001 -\\$5.000.000 =More than \\$50.000.000 =Assessment =Estimated 0=\\$5.001-\\$1 5.000 =More than \\$5.000.000 =\\$100.00 -\\$250.000 =\\$5.000.001 -\\$25.000.000 =Cash Market =\\$15.001 -\\$50.000\n\nBuchwald, Naomi\n0510412013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 14-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period reporting period\n(2) (2) (I) (2) (4)\n\nPlace \"{X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code2 (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n!03. Schwab Account --NY Muni Money Mkt Int./Div.\n104. 105. Merrill Lynch Cash Ace-formerly America cash reserve Treasury Direct Dividend Interest 06. Time Warner Common Stock Dividend Buy 7/13/12\n107. 108. Sold (part) Buy 7/17/I2 9126112\n109. IO. Applied Materials mmon Stock (IRA) Dividend Sold (part) Buy I/20/I2 1112 Sold 8/16/12 I2. Blount Common Stock None\n113. Intel mmon Stock (IRA) Dividend Buy 01/17/12 Buy 01/18/12 Sold 01/18/12\n118. Sold 3/2/12 Buy 3/5/12 Income Gain Codes: =\\$1.000 less =\\$1 .001 -\\$2.500 =\\$2.501 -\\$5.000 0=\\$5.001 -\\$15.000 =\\$15.001 -\\$50.000\n(Sec Columns and 04) F=\\$50,00l -\\$100.000 =\\$I 00.00 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes J=\\$15.000 lcss =\\$15,001 -\\$50.000 =\\$50.00 -\\$I 00.000 100.00 -\\$250.000\n(Sec Columns and 03) =\\$250.00 -\\$500.000 =\\$500.00 -\\$I .000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instmctions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period ofreporting period\n\n(2) (l) (2) (3) (4) (5) Place \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity exempt from prior disclosure\n(A-H) int.) (J-P) \tCode redemption) (J-P) (A-H) (if private (Q-W) transaction)\n120.\n121.\nSold 3/9/12 (part) Income Gain Codes: =\\$1.000 less =\\$1 .00 -\\$2.500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000 =\\$15.00 -\\$50,000\n(Sec Colunms and 04) =\\$50.00I -\\$I 00.000 =\\$100,001 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 112 =More than \\$5.000.000 Value Codes J=\\$15.000 less K=\\$15.00l -\\$50.000 =\\$50.00I -\\$I 00.000 I00.00 -\\$250.000\n(Sec Columns and D3) =\\$250,00 -\\$500.000 =\\$500,00 -\\$1.000.000 =\\$1 .000.001 -\\$5.000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.00 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(See Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\n\nVII. INVESTMENTS and -income, value, transactions (Includes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (2) (I) (I) (3) (4) (5)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n137. Buy 5/2/12 Income Gain Codes: 41,000 less =\\$1 ,001 -\\$2.500 =\\$2.501 -\\$5.000 0=\\$5,001 -\\$15.000 =\\$15.00I -\\$50.000\n(Sec Columns and 04) =\\$50.001 -\\$100.000 =\\$100.001 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$15.000 less =\\$15.001 -\\$50.000 =\\$50.001 -\\$1 00.000 =\\$100.001 -\\$250.000\n(Sec Columns and 03) =\\$250.001 -\\$500.000 =\\$500.001 -\\$1 .000.000 =\\$1 .000.001 -\\$5,000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/20\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see pp. 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period reporting period\n\n(2) (I) (2) (I) (2) (3) (4) (5)\nPlace \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code div., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n\ntransaction)\n154.\nSold 3/26/12\n\n155.\n\n156.\nSold 04/18/12 (part)\n\n157.\nSold 4/19/12 (part) Income Gain Codes: 41.000 less ,001 -\\$2,500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000 =\\$15.00 -\\$50.000\n(Sec Columns and D4) F=\\$50.00l -\\$100.000 =\\$100.00 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$15.000 less K=\\$15,00l -\\$50.000 =\\$50.001 100.000 =\\$100.001 -\\$250.000\n(Sec Columns and 03) =\\$250.00 -\\$500.000 =\\$500.00 -\\$1 .000.000 =\\$1.000.001 -\\$5,000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Coctcs =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\n\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 offiling instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(2) (I) (2) (3) (4)\nPlace \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code div., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n\ntransaction)\n171.\n172.\nSold 3/8/12\n173.\n\n174.\nSold 3/14/12\n\n175.\n\n176.\n\n178. 179. Sold (part) Buy 3/26/12 3/29/12\n180. Sold (part) 4/3/12\n181. Sold (part) 4/12/12\n182. 183. 184. Sold (part) Sold (part) Sold (part) 4/18/12 4/24/12 4/25/\n185. Sold 4/30/12\n187. Buy 5/2/12 Income Gain Codes: =\\$1 .000 less =\\$1.00 -\\$2.500 =\\$2.501 -\\$5.000 D45.00t 15.000 =\\$15.001 -\\$50.000\n(See Columns and D4) =\\$50.00 -\\$I 00.000 =\\$100.001 -\\$1 .000.000 =\\$1 .000.001 -\\$5.000.000 112 =More than \\$5.000.000 Value Codes =\\$15.000 less =\\$15.001 -\\$50.000 =\\$50.00 -\\$1 00.000 =\\$100.00 -\\$250.000\n(See Columns and DJ) =\\$250.00 -\\$500.000 =\\$500.00 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\n\nVII. INVESTMENTS and TRUSTS --income, vatue, transactions r1nc1udes those spouse and dependent children; see PP 34-60 offiting instructions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(1) (2)\n(2) (3) (4) (5)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n188. Buy 515112 Income Gain Codes: =\\$1.000 less 41.001 -\\$2.500 c=\\$2.501 -\\$5.000 045,001 -\\$15.000 =\\$15,001 -\\$50,000\n(See Columns and 04) =\\$50.001 -\\$1 00.000 =\\$100.00 -\\$1 .000.000 Ill =\\$1.000.001 -\\$5.000.000 112 =More than \\$5.000.000 Value Codes J=\\$1 5.000 less =\\$1 5.001 -\\$50.000 L=\\$50.00 -\\$100.000 I00.00 -\\$250.000\n(See Columns and DJ) N=\\$250.001 -\\$500.000 0=\\$500.00 -\\$1.000.000 =\\$1 .000.001 -\\$5.000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment T=Cash Market\n(Sec Column C2) U=Book Value V=Othcr W=Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period ofreporting period\n(I) (2) (I) (2) (I) (2) (3) (4) (5) Place \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity exempt from prior disclosure\nCode\n(A-H) int.) (J-P) \tCode redemption) (J-P) (A-H) (if private (Q-W) transaction)\n205.\nSold 7112112 (part)\n206.\n207.\nSold Jncomc Gain Codes: =\\$1.000 less 641.001 -\\$2.500 =\\$2.501 \\$5.000 D=\\$5.001 \\$15.000 =\\$15.001 -\\$50.000\n(See Columns and 04) F=\\$50.001 -\\$1 00.000 =\\$I 00.00 -\\$1 .000.000 =\\$1 .000.001 \\$5.000.000 fl2 =More than \\$5.000.000 Value Codes J=\\$15.000 less =\\$15.001 -\\$50.000 L=\\$50.00 \\$100.000 =\\$100.00 -\\$250.000\n(Sec Columns and D3) =\\$250.001 -\\$500.000 =\\$500.00 .000.000 =\\$1.000.00 -\\$5.000.000 =\\$5.000.001 \\$25.000.000 =\\$25.000.001 \\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr W=Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 offilinc instructions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (2) (l) (l) (3) (4)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n222. Sold (part) 12112\n\n223.\nBuy 1117/12 Income Gain Codes: I.000 less =\\$1,001 -\\$2.500 c=\\$2.501 -\\$5.000 D=\\$5.001 -\\$15.000 =\\$15.001 -\\$50.000 (Sec Columns and 04) =\\$50.00 -\\$I 00.000 =\\$100.001 -\\$1.000.000 =\\$1.000.001-\\$5.000.000 fl2 =More than \\$5.000.000\nValue Codes J=\\$15.000 less K=\\$15.00l -\\$50.000 L=\\$50.00 -\\$I 00.000 =\\$100.00 -\\$250.000\n\n(Sec Columns and 03) \tN=\\$250.001 -\\$500.000 0=\\$500.00 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 P2=\\$5.000.00 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000\nValue Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market (Sec Colunm C2) =Book Value =Other W=Estimated\n\nBuchwald, Naomi\n0510412013\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nc1udes those spouse and dependent children; see pp. 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period ofreporting period\n(2) (I) (2) (2) (3) (4)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nCode\nexempt from prior disclosure\n(A-H) int.) Code redemption) (J-P) (A-H) (if private (Q-W) transaction) Jncomc Gain Codes: =\\$1.000 less =\\$1 .00 -\\$2.500 =\\$2.501 -\\$5.000 D=\\$5.001 -\\$15.000 =\\$15.00 -\\$50.000\n(See Columns and 04) =\\$50.00 -\\$I 00.000 =\\$I 00.00 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =More than \\$5,000.000 Value Codes J=\\$1 5,000 less =\\$15,001 -\\$50.000 =\\$50.00I -\\$I 00.000 =\\$100.001 -\\$250,000\n(See Columns and 03) =\\$250.001 -\\$500.000 0=\\$500.001 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) U=Book Value V=Othcr W=Estimated\n\nBuchwald, Naomi\n05/04/20\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.; NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (I) (2) (2) (3) (4) (5)\nPlace \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code div., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n\ntransaction)\n256.\n257.\n\nSold 10/15/12\n258.\nBuy 1117/12 Income Gain Codes: A=\\$1,000or lcss =\\$1 ,00 -\\$2,500 =\\$2.501 -\\$5,000 =\\$5.001 -\\$1 5,000 =\\$15.001 -\\$50.000\n(Sec Columns and 04) =\\$50,001 -\\$100.000 I00,00 -\\$1 ,000.000 =\\$1.000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$15.000 less =\\$15.001 -\\$50.000 =\\$50.00 -\\$I 00.000 I00.00 -\\$250.000\n(See Columns and 03) =\\$250.001 -\\$500.000 0=\\$500,00 -\\$1.000.000 =\\$1.000.001 -\\$5,000.000 =\\$5.000.00 -\\$25,000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period ofreporting period\n\n(1) (2) (1) (2)\n(2) (4) (5)\nPlace \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code div., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n\ntransaction)\n273. Sold 2/28/12 Income Gain Codes: =\\$1.000 less =\\$1 ,00 -\\$2,500 =\\$2.501 -\\$5.000 0=\\$5.001 -\\$1 5.000 =\\$1 5.00 -\\$50.000\n(See Columns and 04) F=\\$50,001 -\\$100.000 =\\$I 00.00 -\\$1 .000.000 =\\$1 .000.001 -\\$5.000.000 ll2 =More than \\$5.000.000 Value Codes =\\$15,000 less =\\$15,001 -\\$50.000 =\\$50.00 100.000 100.00 -\\$250.000\n(Sec Columns and D3) =\\$250.001 -\\$500.000 0=\\$500.001 1,000.000 =\\$1,000.001 -\\$5.000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) \"\"Assessment ==Cash Market\n(See Column C2) =Book Value =Other =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.; NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end\n(including trust assets) reporting period reporting period\n\nTransactions during reporting period\n(I) (2) (2) (I) (2) (4) (5)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nCode\nexempt from prior disclosure\n(A-H) int.)\nCode redemption) (J-P) (A-H) (if private\ntransaction) Income Gain Codes: =\\$1.000 lcss =\\$1,001 -\\$2.500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15,000 =\\$15.001 -\\$50.000\n(See Columns and D4) 450.001 -\\$100.000 =\\$1 00.001 -\\$1 .000.000 Ill =\\$1 .000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$15.000 less K=\\$1 5,00I -\\$50.000 =\\$50.00 -\\$I 00.000 =\\$100.00 -\\$250.000\n(See Columns and D3) =\\$250.00 -\\$500.000 =\\$500.00 -\\$1 .000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(See Column C2) =Book Value V=Othcr =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent children; see PP 34-60 filing instructions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period (including trust assets) reporting period ofreporting period\n(2) (2) (4) (5)\nPlace \"(X)\" after each asset exempt from prior disclosure Amount Code (A-H) Type (e.g., div., rent, int.) Value Code (J-P) Value Method Code (Q-W) Type (e.g., buy, sell, redemption) Date mm/dd/yy Value Code (J-P) Gain Code (A-H) Identity buyer/seller (if private transaction)\n308. Buy 4/8/12 Income Gain Codes: =\\$1 .000 less =\\$1.001 -\\$2.500 =\\$2.501 -\\$5,000 =\\$5.001 -\\$15.000 =\\$15.001 -\\$50.000\n(Sec Columns and 04) =\\$50.001 -\\$100.000 =\\$100.00 -\\$1.000.000 =\\$1 .000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$1 5.000 less =\\$15.001 -\\$50,000 =\\$50.001 -\\$100.000 I00.00 -\\$250.000\n(Sec Columns and 03) =\\$250.001 -\\$500.000 =\\$500.00 -\\$1 .000.000 =\\$1.000.001 -\\$5,000.000 =\\$5.000.001 -\\$25.000.000\n1'3 =\\$25.000.00 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Othcr =Estimated\n\nVII. INVESTMENTS and TRUSTS -income, vatue, transactions r1nc1udes those ofspo11se and dependent children; see pp. 34-60 filing instr11c1ions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n{including trust assets) reporting period reporting period\n\n(I) (2) (I) (2) (I) (2) (4) (5)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nCode\nexempt from prior disclosure\ndiv., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller Jncomc Gain Codes: =\\$1.000 Jess =\\$1,00 -\\$2.500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000 =\\$15,001 -\\$50.000\n(Sec Columns and 04) F=\\$50.001 -\\$100.000 =\\$I 00.00 -\\$1 .000.000 Ill =\\$1.000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes =\\$15.000 less =\\$15.001 -\\$50.000 =\\$50.001 -\\$1 00.000 I00.00 -\\$250.000\n(See Columns and 03) =\\$250.00 -\\$500.000 0=\\$500,001 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=Other =Estimated\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions (Includes those spouse and dependent children; see PP 34-60 filing instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end\n(including trust assets) reporting period reporting period\n\nTransactions during reporting period\n(I) (2)\n(I)\n(2) (3) (5)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nCode\nexempt from prior disclosure\n(A-H) int.) Code redemption) (J-P) (A-H) (if private (Q-W) transaction)\n341.\n\nSold 8/24/12\n342.\nTime Warner Cable Common Dividend Buy 7/13/12 Income Gain Codes: =\\$1 ,000 Jess =\\$1,001 -\\$2.500 =\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000 =\\$15.001 -\\$50.000\n(See Columns and 04) F=\\$50.00I -\\$1 00.000 =\\$100.001 -\\$1.000.000 =\\$1 .000.001 -\\$5.000.000 =More lhan \\$5.000.000 Value Codes =\\$15.000 less =\\$15.001 -\\$50.000 =\\$50.001 -\\$100.000 =\\$100.001 -\\$250,000\n(Sec Columns and 03) =\\$250.00 -\\$500.000 =\\$500.00 -\\$1.000.000 =\\$1.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More 1han \\$50.000.000 Value Method Codes =Appraisal =Cos1 (Real Es1a1c Only) =Assessment =Cash Market\n(Sec Column C2) =Book Value V=01hcr =Estimated\n\n.VII. INVESTMENTS and TRUSTS -income, value, transactions r1nc1udes those spouse and dependent chitdren; see PP 34-60 offiting instructions.) NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end Transactions during reporting period\n(including trust assets) reporting period reporting period\n\n(I) (I) (2) (3) (4) (5)\nPlace \"(X)\" after each asset Amount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nexempt from prior disclosure Code div., rent, Code Method buy, sell, mm/dd/yy Code Code buyer/seller\n(A-H) int.) (J-P) Code redemption) (J-P) (A-H) (if private\n\ntransaction) Income Gain Codes: A=\\$1.000or less =\\$1,001 -\\$2,500 c=\\$2.501 -\\$5.000 =\\$5.001 -\\$15.000\n(Sec Columns and 04) F=\\$50.00l -\\$100.000 =\\$100.001 -\\$1 .000.000 =\\$1 .000.001 -\\$5.000.000 =More than \\$5.000.000 Value Codes J=\\$1 5.000 lcss K=SIS,001 -\\$50.000 L=\\$50.00 -\\$I 00.000 =\\$100.00 -\\$250.000\n(Sec Columns and 03) N=\\$250.00 -\\$500.000 0=\\$500.00 \\$1.000.000 =Sl.000.001 -\\$5.000.000 =\\$5.000.001 -\\$25,000.000 =\\$25.000.001 \\$50.000.000 =More than \\$50.000.000 Value Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(Sec Column C2) U=Book Value V=Othcr W=Estimated =\\$15.001 -\\$50.000\n\nBuchwald, Naomi\n05/04/2013\nVII. INVESTMENTS and TRUSTS -income, value, transactions r1nc111des those spouse and dependent children; see PP 34-60 filing instructions.J NONE (No reportable income, assets, transactions.)\nDescription Assets Income during Gross value end\nTransactions during reporting period\n(including trust assets) reporting period reporting period\n(I) (2) (I) (2) (I) (2) (4) (5)\nPlace \"(X)\" after each asset\nAmount Type (e.g., Value Value Type (e.g., Date Value Gain Identity\nCode\nexempt from prior disclosure\n(A-H) int.)\nCode redemption) (J-P) (A-H) (if private (Q-W) transaction)\n375.\n\n376.\n-JP Morgan Mid Cap Value Fund\n\n377.\n-Growth Fund America\n\n378.\n-Invesco Van Kampen Senior. Loan Fund\n\n-Touchtone Mid Cap Growth Fund\n380.\n-Escrow Leiner Health Products exchanged for Lehman\n\n381.\n-Express Scripts Holding Co. Common Stock (X) Income Gain Codes: =\\$1.000 less =\\$1.001 -\\$2.500 =\\$2.501 -\\$5.000 0=\\$5.001 \\$15.000 E=\\$15.00I -\\$50,000 (Se Columns and 04) =\\$50.001 -\\$100.000 =\\$100.00I -\\$1.000.000 =\\$1 .000.001 \\$5.000.000 112 =More than \\$5.000.000\nValue Codes =\\$15.000 less =\\$15.001 \\$50.000 =\\$50.00 I00.000 =\\$100.001 -\\$250.000\n\n(Sec Columns and D3) =\\$250.00 -\\$500.000 =\\$500,00 -\\$1,000.000 =\\$1,000.001 \\$5.000.000 =\\$5.000.001 -\\$25.000.000 =\\$25.000.001 -\\$50.000.000 =More than \\$50.000.000\nValue Method Codes =Appraisal =Cost (Real Estate Only) =Assessment =Cash Market\n(See Column C2) =Book Value V=Othcr =Estimated\n\nName Person Reporting\nDate Report\nBuchwald, Naomi\n05/04/2013\n\nVIII. ADDITIONAL INFORMATION EXPLANATIONS. (lndicate part ofreport.)\n\n05104120\nBuchwald, Naomi\nIX. CERTIFICATION. certify that all information given above (including information pertaining spouse and minor dependent children, any) accurate, true, and complete the best knowledge and belief, and that any information not reported was withheld because met applicable statutory provisions permitting non-disclosure. further certify that earned income from outside employment and honoraria and the acceptance gifts which have been reported are compliance with the provisions U.S.C. app. 501 et. seq., U.S.C. 7353, and Judicial Conference regulations.\nSignature: Naomi Buchwald\n\nNOTE: ANY INDIVIDUAL WHO KNOWINGLY AND WILLFULLY FALSIFIES FAILS FILE THIS REPORT MAY SUBJECT CIVIL AND CRIMINAL SANCTIONS U.S.C. app. 104)\n\nCommittee Financial Disclosure Administrative Office the United States Courts Suite 2-301 One Columbus Circle, N.E. Washington, D.C. 20544```\n\nWWW.JUDICIALWATCH.ORG\n\nJudicial Watch is a 501(c)(3) nonprofit organization. Contributions are received from individuals, foundations, and corporations and are tax-deductible to the extent allowed by law.\n\n425 Third Street SW, Suite 800\nWashington, DC 20024\n888-593-8442" ]	[ null, "https://www.judicialwatch.org/wp-content/uploads/2014/05/Naomi_R_Buchwald-2012.jpg", null, "https://www.judicialwatch.org/t/images/da/security-checked.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7314879,"math_prob":0.9818949,"size":33734,"snap":"2019-26-2019-30","text_gpt3_token_len":10983,"char_repetition_ratio":0.238067,"word_repetition_ratio":0.5932497,"special_character_ratio":0.45322227,"punctuation_ratio":0.22078907,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95650715,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-16T07:29:44Z\",\"WARC-Record-ID\":\"<urn:uuid:b854ecc7-de81-46e5-9d7e-26d8da3be9ef>\",\"Content-Length\":\"67919\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dd0b9ef0-9ffc-4b64-ae69-5495a2946549>\",\"WARC-Concurrent-To\":\"<urn:uuid:7aadcd0e-3d00-4cd7-af37-d95b1804301a>\",\"WARC-IP-Address\":\"151.101.250.133\",\"WARC-Target-URI\":\"https://www.judicialwatch.org/document-archive/naomi-r-buchwald-2012/\",\"WARC-Payload-Digest\":\"sha1:2XTKMY7M6VK3PVWYHBGAFSZ7CISIX4T3\",\"WARC-Block-Digest\":\"sha1:EZHCXWBUV6AML46VS25GLDRQSMKSD724\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195524503.7_warc_CC-MAIN-20190716055158-20190716081158-00282.warc.gz\"}"}
https://www.colorhexa.com/00e02e	[ "# #00e02e Color Information\n\nIn a RGB color space, hex #00e02e is composed of 0% red, 87.8% green and 18% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 79.5% yellow and 12.2% black. It has a hue angle of 132.3 degrees, a saturation of 100% and a lightness of 43.9%. #00e02e color hex could be obtained by blending #00ff5c with #00c100. Closest websafe color is: #00cc33.\n\n• R 0\n• G 88\n• B 18\nRGB color chart\n• C 100\n• M 0\n• Y 79\n• K 12\nCMYK color chart\n\n#00e02e color description : Pure (or mostly pure) lime green.\n\n# #00e02e Color Conversion\n\nThe hexadecimal color #00e02e has RGB values of R:0, G:224, B:46 and CMYK values of C:1, M:0, Y:0.79, K:0.12. Its decimal value is 57390.\n\nHex triplet RGB Decimal 00e02e `#00e02e` 0, 224, 46 `rgb(0,224,46)` 0, 87.8, 18 `rgb(0%,87.8%,18%)` 100, 0, 79, 12 132.3°, 100, 43.9 `hsl(132.3,100%,43.9%)` 132.3°, 100, 87.8 00cc33 `#00cc33`\nCIE-LAB 78.172, -76.636, 67.879 27.147, 53.505, 11.481 0.295, 0.581, 53.505 78.172, 102.375, 138.468 78.172, -73.356, 90.344 73.147, -61.761, 41.897 00000000, 11100000, 00101110\n\n# Color Schemes with #00e02e\n\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #e000b2\n``#e000b2` `rgb(224,0,178)``\nComplementary Color\n• #42e000\n``#42e000` `rgb(66,224,0)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #00e09e\n``#00e09e` `rgb(0,224,158)``\nAnalogous Color\n• #e00042\n``#e00042` `rgb(224,0,66)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #9e00e0\n``#9e00e0` `rgb(158,0,224)``\nSplit Complementary Color\n• #e02e00\n``#e02e00` `rgb(224,46,0)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #2e00e0\n``#2e00e0` `rgb(46,0,224)``\n• #b2e000\n``#b2e000` `rgb(178,224,0)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #2e00e0\n``#2e00e0` `rgb(46,0,224)``\n• #e000b2\n``#e000b2` `rgb(224,0,178)``\n• #00941e\n``#00941e` `rgb(0,148,30)``\n``#00ad24` `rgb(0,173,36)``\n• #00c729\n``#00c729` `rgb(0,199,41)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #00fa33\n``#00fa33` `rgb(0,250,51)``\n• #14ff44\n``#14ff44` `rgb(20,255,68)``\n• #2eff59\n``#2eff59` `rgb(46,255,89)``\nMonochromatic Color\n\n# Alternatives to #00e02e\n\nBelow, you can see some colors close to #00e02e. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #0ae000\n``#0ae000` `rgb(10,224,0)``\n• #00e009\n``#00e009` `rgb(0,224,9)``\n• #00e01b\n``#00e01b` `rgb(0,224,27)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #00e041\n``#00e041` `rgb(0,224,65)``\n• #00e053\n``#00e053` `rgb(0,224,83)``\n• #00e066\n``#00e066` `rgb(0,224,102)``\nSimilar Colors\n\n# #00e02e Preview\n\nText with hexadecimal color #00e02e\n\nThis text has a font color of #00e02e.\n\n``<span style=\"color:#00e02e;\">Text here</span>``\n#00e02e background color\n\nThis paragraph has a background color of #00e02e.\n\n``<p style=\"background-color:#00e02e;\">Content here</p>``\n#00e02e border color\n\nThis element has a border color of #00e02e.\n\n``<div style=\"border:1px solid #00e02e;\">Content here</div>``\nCSS codes\n``.text {color:#00e02e;}``\n``.background {background-color:#00e02e;}``\n``.border {border:1px solid #00e02e;}``\n\n# Shades and Tints of #00e02e\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, #000802 is the darkest color, while #f4fff6 is the lightest one.\n\n• #000802\n``#000802` `rgb(0,8,2)``\n• #001c06\n``#001c06` `rgb(0,28,6)``\n• #002f0a\n``#002f0a` `rgb(0,47,10)``\n• #00430e\n``#00430e` `rgb(0,67,14)``\n• #005712\n``#005712` `rgb(0,87,18)``\n• #006a16\n``#006a16` `rgb(0,106,22)``\n• #007e1a\n``#007e1a` `rgb(0,126,26)``\n• #00921e\n``#00921e` `rgb(0,146,30)``\n• #00a522\n``#00a522` `rgb(0,165,34)``\n• #00b926\n``#00b926` `rgb(0,185,38)``\n• #00cc2a\n``#00cc2a` `rgb(0,204,42)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\n• #00f432\n``#00f432` `rgb(0,244,50)``\n• #08ff3b\n``#08ff3b` `rgb(8,255,59)``\n• #1cff4a\n``#1cff4a` `rgb(28,255,74)``\n• #2fff5a\n``#2fff5a` `rgb(47,255,90)``\n• #43ff6a\n``#43ff6a` `rgb(67,255,106)``\n• #57ff79\n``#57ff79` `rgb(87,255,121)``\n• #6aff89\n``#6aff89` `rgb(106,255,137)``\n• #7eff98\n``#7eff98` `rgb(126,255,152)``\n• #92ffa8\n``#92ffa8` `rgb(146,255,168)``\n• #a5ffb8\n``#a5ffb8` `rgb(165,255,184)``\n• #b9ffc7\n``#b9ffc7` `rgb(185,255,199)``\n• #ccffd7\n``#ccffd7` `rgb(204,255,215)``\n• #e0ffe6\n``#e0ffe6` `rgb(224,255,230)``\n• #f4fff6\n``#f4fff6` `rgb(244,255,246)``\nTint Color Variation\n\n# Tones of #00e02e\n\nA tone is produced by adding gray to any pure hue. In this case, #67796b is the less saturated color, while #00e02e is the most saturated one.\n\n• #67796b\n``#67796b` `rgb(103,121,107)``\n• #5f8166\n``#5f8166` `rgb(95,129,102)``\n• #568a61\n``#568a61` `rgb(86,138,97)``\n• #4e925c\n``#4e925c` `rgb(78,146,92)``\n• #459b57\n``#459b57` `rgb(69,155,87)``\n• #3ca452\n``#3ca452` `rgb(60,164,82)``\n• #34ac4c\n``#34ac4c` `rgb(52,172,76)``\n• #2bb547\n``#2bb547` `rgb(43,181,71)``\n• #22be42\n``#22be42` `rgb(34,190,66)``\n• #1ac63d\n``#1ac63d` `rgb(26,198,61)``\n• #11cf38\n``#11cf38` `rgb(17,207,56)``\n• #09d733\n``#09d733` `rgb(9,215,51)``\n• #00e02e\n``#00e02e` `rgb(0,224,46)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00e02e is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5156286,"math_prob":0.8154209,"size":3673,"snap":"2022-40-2023-06","text_gpt3_token_len":1658,"char_repetition_ratio":0.13818479,"word_repetition_ratio":0.007352941,"special_character_ratio":0.55077595,"punctuation_ratio":0.22989808,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99168307,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T07:52:55Z\",\"WARC-Record-ID\":\"<urn:uuid:8d7f1d11-0801-451d-a20b-42f4dc0003a0>\",\"Content-Length\":\"36113\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7024d64a-4c7d-4dba-a3d2-1d3f93ec18f0>\",\"WARC-Concurrent-To\":\"<urn:uuid:a374de9a-8343-4b07-884e-05f9a4ab213b>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/00e02e\",\"WARC-Payload-Digest\":\"sha1:EHOOIWGMTBC2VGE7CG5UOJZFS2L5TDK3\",\"WARC-Block-Digest\":\"sha1:7USAL4TIIULUSVHVNXDHDWFMFMNFZ4YA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335573.50_warc_CC-MAIN-20221001070422-20221001100422-00760.warc.gz\"}"}
http://www.mock4exam.org/quiz-mixture-and-alligation-set-3/	[ "# Quiz: Mixture and Alligation Set 3\n\n1. The average weekly salary per head of the entire staff of a factory consisting ofsupervisors and the labourers is Rs. 55. The average salary per head of the supervisors is Rs. 300 and that of the labourers is Rs. 40. Given that the number of supervisors is 10, find the number of labourers in the factory.\nA.160\nB.120\nC.155\nD.143\nE.None of these\n\nSolution:\n40…………………………………..300\n………………….55…………………….\n245…………………………………15\n(Number of labourers)/(Number of supervisors) = 245/15 = 16.33/1 = 16/1\n16:1 = 160:10\n2. A man travelled a distance of 40 km. in 5 hours partly on foot at the rate of 7 km per hour and partly on bicycle at 12 km. per hour. Find the distance travelled on foot ?\nA.36km\nB.24km\nC.32km\nD.28km\nE.None of these\n\nSolution:\n7……………………………………….12\n…………………..40/5=8………………..\n4………………………………………..1\nTime taken on foot /Time taken on bicycle = 4:1\nDistance travelled on foot = 47 = 28km\n3. Milk contains 15% water. What quantity of pure milk should be added to 50 litres of milk to reduce the quantity of water to 12% ?\nA.16litres\nB.14litres\nC.12.5litres\nD.17litres\nE.None of these\n\nSolution:\nAns: 5015/100 = (50+x)12/100\n7.5 100 = 600+12x\n12x = 150\nX = 150/12 = 12.5litre\n4. Dhal worth Rs. 110 per kg and Rs. 95 per kg are mixed with a third variety in the ratio 1:1:2. If the mixture is worth Rs. 115 per kg, the price of the third variety per kg will be\nA.Rs.127.5\nB.Rs.115.75\nC.Rs.125\nD.Rs.117.5\nE.None of these\n\nSolution:\n1st two type of Dhal = 110+95/2 = 102.5\n102.5…………………………………..X\n……………..115……………………….\nx-115……………………………………12.5\nx-115 = 12.5\nx = 127.5\n5. A zookeeper counted the heads of the animals in a zoo and found it to be 100. When he counted the legs of the animals he found it to be 340. If the zoo had either pigeons or elephants, how many pigeons were there in the zoo?\nA.45\nB.30\nC.70\nD.50\nE.None of these\n\nSolution:\ntotal number of legs = 4x + 2(100-x) = 340\n4x + 200 – 2x = 340\n2x = 140\nx = 70\nP = 100-70 =30\n6. In a 70 litres mixture of milk and water, % of water is 30%. The milkman gave 20 litres of this mixture to a customer and then added 20 litres of water to the remaining mixture. What is the % of milk in the final mixture ?\nA.48%\nB.50%\nC.40%\nD.53%\nE.None of these\n\nSolution:\n20litre given remaining = 70-20 = 50litre\nQuantity of milk = 5070/100 = 35litre\nQuantity of water = 50-35 = 15litre\n20litres of water added = 50+20 = 70\n% of milk = 35100/70 =50%\n7. A company is creating a new signature drink. They are using two alcoholic ingredients in the drink vodka and gin. They are using two non-alcoholic ingredients in the drink: orange juice and cranberry juice. The alcoholic ingredients contain 50% alcohol. The non-alcoholic ingredients contain no alcohol. How many litres of non-alcoholic ingredients must be added to 5 litres of alcoholic ingredients to produce a mixture that is 20% alcohol?\nA.8\nB.6.5\nC.7.5\nD.9\nE.None of these\n\nSolution:\n(5+x) (20%) = 5(50%) + x(0%)\n(5+x) 0.2 = 5(0.5) + 0\n1+0.2x = 2.5\nX = 2.5-1/0.2 = 1.5/0.2 = 7.5\n8. A can contains 30liter of juice, from this container 5litres of juice was taken out and replaced by water. This process was repeated further two times. How much juice is now contained by the container?\nA.21\nB.13\nC.15\nD.17\nE.None of these\n\nSolution:\nQuantity of milk in the final mixture = 30[1-(5/30)]3\n= 30(5/6) 3\n= 30125/216 = 17.36 liter = 17\n9. Rani mixes 70kg of sugar worth Rs.28.50 per kg with 100kg of sugar worth Rs.30.50 per kg. At what rate shall he sell the mixture to gain 10% ?\nA.Rs.32.64\nB.Rs.31.50\nC.Rs.30.46\nD.Rs.29.75\nE.None of these\n\nSolution:\n70/100 = 100x – 30.50(110)/28.50(110)-100x\n0.7 = 100x-3355/3135-100x\n2194.5 – 70x = 100x-3355\n170x = 5549.5\nX = 32.64\n10. 90 litres of a mixture of milk and water contains 20% water. How much water should be added so that the mixture has 28% water ?\nA.18litres\nB.12litres\nC.10litres\nD.8litres\nE.None of these" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9086154,"math_prob":0.9898276,"size":2892,"snap":"2021-04-2021-17","text_gpt3_token_len":872,"char_repetition_ratio":0.15443213,"word_repetition_ratio":0.01119403,"special_character_ratio":0.3008299,"punctuation_ratio":0.1673699,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9885225,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-19T02:10:40Z\",\"WARC-Record-ID\":\"<urn:uuid:e1f8a983-91c0-4683-8c0a-79e923ade958>\",\"Content-Length\":\"55589\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3dd4c9d2-0096-4bb3-9252-b857e545dd8e>\",\"WARC-Concurrent-To\":\"<urn:uuid:fbe944d9-366a-4c08-a40d-eaa75f6fa0a2>\",\"WARC-IP-Address\":\"166.62.28.114\",\"WARC-Target-URI\":\"http://www.mock4exam.org/quiz-mixture-and-alligation-set-3/\",\"WARC-Payload-Digest\":\"sha1:DPC7PU5EF7IJPHWNDR6YKA365LN5JADP\",\"WARC-Block-Digest\":\"sha1:EY7CMWASEA4OI4G5JG2ZHP6GHDT5TSMB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703517559.41_warc_CC-MAIN-20210119011203-20210119041203-00363.warc.gz\"}"}
https://planspace.org/20150417-negative_r_squared/	[ "# R Squared Can Be Negative\n\nFriday April 17, 2015\n\nLet's do a little linear regression in Python with scikit-learn:\n\n``````import numpy as np\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.cross_validation import train_test_split\n\nX, y = np.random.randn(100, 20), np.random.randn(100)\nX_train, X_test, y_train, y_test = train_test_split(X, y)\n\nmodel = LinearRegression()\nmodel.fit(X_train, y_train)``````\n\nIt is a property of ordinary least squares regression that for the training data we fit on, the coefficient of determination R2 and the square of the correlation coefficient r2 of the model's predictions with the actual data are equal.\n\n``````# coefficient of determination R^2\nprint model.score(X_train, y_train)\n## 0.203942898079\n\n# squared correlation coefficient r^2\nprint np.corrcoef(model.predict(X_train), y_train)[0, 1]2\n## 0.203942898079``````\n\nThis does not hold for new data, and if our model is sufficiently bad the coefficient of determination can be negative. The squared correlation coefficient is never negative but can be quite low.\n\n``````# coefficient of determination R^2\nprint model.score(X_test, y_test)\n## -0.277742673311\n\n# squared correlation coefficient r^2\nprint np.corrcoef(model.predict(X_test), y_test)[0, 1]2\n## 0.0266856746214``````\n\nThese declines in performance worsen with overfitting." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7298183,"math_prob":0.9672059,"size":1297,"snap":"2022-40-2023-06","text_gpt3_token_len":323,"char_repetition_ratio":0.15003867,"word_repetition_ratio":0.047904193,"special_character_ratio":0.27833462,"punctuation_ratio":0.16595745,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99978596,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T13:39:17Z\",\"WARC-Record-ID\":\"<urn:uuid:dac8a973-9cf0-4b49-a23c-954be6534e13>\",\"Content-Length\":\"5180\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e0caee5a-3c4d-45da-9a76-73b458dbd173>\",\"WARC-Concurrent-To\":\"<urn:uuid:11c0dcee-df1b-4bcc-bf9b-30849093a6cd>\",\"WARC-IP-Address\":\"104.21.24.198\",\"WARC-Target-URI\":\"https://planspace.org/20150417-negative_r_squared/\",\"WARC-Payload-Digest\":\"sha1:AN4TVMKAYDQ45EWS2GHAZFZWVKRE5JEC\",\"WARC-Block-Digest\":\"sha1:KVRGKL4WJZ6VA7BX5MZ2NMCKBCKAZVRA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337504.21_warc_CC-MAIN-20221004121345-20221004151345-00586.warc.gz\"}"}
https://books.google.gr/books?id=BMc2AAAAMAAJ&pg=PA198&vq=%22How+many+bricks+8+inches+long,+4+inches+wide,+and+2+inches+thick,%22&dq=editions:HARVARD32044096994090&lr=&hl=el&output=html_text	[ "Ĺéęüíĺň óĺëßäáň PDF Çëĺęôń. Ýęäďóç\n .flow { margin: 0; font-size: 1em; } .flow .pagebreak { page-break-before: always; } .flow p { text-align: left; text-indent: 0; margin-top: 0; margin-bottom: 0.5em; } .flow .gstxt_sup { font-size: 75%; position: relative; bottom: 0.5em; } .flow .gstxt_sub { font-size: 75%; position: relative; top: 0.3em; } .flow .gstxt_hlt { background-color: yellow; } .flow div.gtxt_inset_box { padding: 0.5em 0.5em 0.5em 0.5em; margin: 1em 1em 1em 1em; border: 1px black solid; } .flow div.gtxt_footnote { padding: 0 0.5em 0 0.5em; border: 1px black dotted; } .flow .gstxt_underline { text-decoration: underline; } .flow .gtxt_heading { text-align: center; margin-bottom: 1em; font-size: 150%; font-weight: bold; font-variant: small-caps; } .flow .gtxt_h1_heading { text-align: center; font-size: 120%; font-weight: bold; } .flow .gtxt_h2_heading { font-size: 110%; font-weight: bold; } .flow .gtxt_h3_heading { font-weight: bold; } .flow .gtxt_lineated { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; } .flow .gtxt_lineated_code { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; font-family: monospace; } .flow .gtxt_quote { margin-left: 2em; margin-right: 2em; margin-top: 1em; margin-bottom: 1em; } .flow .gtxt_list_entry { margin-left: 2ex; text-indent: -2ex; } .flow .gimg_graphic { margin-top: 1em; margin-bottom: 1em; } .flow .gimg_table { margin-top: 1em; margin-bottom: 1em; } .flow { font-family: serif; } .flow span,p { font-family: inherit; } .flow-top-div {font-size:83%;} 29. At \\$2.67\\$ per yard, what will 400 yards of cloth cost? 30. At \\$54 per barrel, what will 1560 barrels of flour cost? DIVISION OF FEDERAL MONEY. Ex. 1. A man bought 6 hats for \\$25.68: how much did they cost apiece ? Operation. If 6 hats cost \\$25.68, 1 hat will cost 6)25.68 one sixth of \\$25.68. Divide as in sim\\$4.28 Ans, ple numbers, and point off two decimal figures in the quotient. (Art. 194.) Proof. \\$4.28 If i hat costs \\$4.28, 6 hats will cost 6 times 6 as much ; and \\$4.28 x6=\\$25.68, which is the cost. Hence, \\$25.68 217. When the number of articles, pounds, yards, &c., and the cost of the whole are given, to find the price of one article, pound, &c. Divide the whole cost by the whole number of articles, fc., and point off the quotient as in division of decimal fractions. (Art. 194.) 2. How many yards of cloth, at \\$3.13 per yard, can be bought for \\$20.345 ? Operation. Since \\$3.13 will buy 1 yard, 3.13)20.345(6.5 Ans. \\$20.345 will buy as many yards 18 78 as \\$3.13 is contained times in \\$20.345. Divide as in simple 1 565 1 565 numbers, and point off one decimal figure in the quotient. (Art. 194.) Proof.—\\$3.13 X 6.5=20.345. Hence, , QUEST.-217. When the number of articles, pounds, &c., and the cost of the whole, are given, how is the cost of one article found ? 218. When the price of one article, pound, yard, &c., and the cost of the whole are given, to find the number of articles, &c. Divide the whole cost by the price of one, and point of the quotient as in Art. 217. 3. Divide \\$149.625 by \\$2.375. Ans. 63 cents. 4. If \\$75 are divided equally among 18 men, how much will each receive ? Operation. 18)75(\\$4.16 6 Ans. 72 3000 18 120 108 120 108 After dividing the \\$75 by 18, there is a remainder of 3 dollars, which must be reduced to cents and mills, (Art. 208,) and then be divided as before. The ciphers thus annexed must be regarded as decimals; consequently there will be three decimal figures in the quotient. 12 rem. 219. From the preceding illustrations we derive the following GENERAL RULE. Divide as in simple numbers, and point of the quotient as in division of decimal fractions. (Art. 194.) Obs. After all the figures of the dividend are divided, if there is a remainder, ciphers may be annexed to it, and the operation may be continued as in division of decimals. (Art. 194. Obs. 3.) The ciphers thus annexed must be regarded as decimal places of the dividend. 5. How many pounds of cheese, 'at 7 cts. a pound, can you buy for \\$1.47? QUEST.-218. When the price of 1 article, 1 pound, &c., and the cost of the whole, are given, how is the number of articles found? 219. What is the rule for Division of Federal Money? Obs. When there is a remainder after all the figures of the dividend are divided, how proceed? 6. A man paid \\$0.75 for the use of a horse and buggy to go 8 miles : how much was that per mile? 7. How many quarts of cherries, at 7 cents a quart, can you buy for \\$1.12? 8. How many pounds of figs, at 14 cents a pound, can you buy for \\$3.57 ? 9. How many watermelons, at 12 cts. apiece, can be bought for \\$3 ? 10. How many pen-knives, at 20 cts. apiece, can be bought for \\$7.20 ? 11. At 174 cts. a quart, how many quarts of molasses can be bought for \\$4.40 ? 12. A man bought 50 pair of thick boots for \\$175 : how much did he give a pair ? 13. A man paid \\$485.50 for 260 sheep: how much did he give per head ? 14. At \\$2.50 a cord, how many cords of wood can I buy for \\$165 ? 15. At \\$4.75 per barrel, how many barrels of flour can I buy for \\$8.50 ? 16. If a man's income is \\$1.68 per day, how much is it per hour ? 17. If a man pays \\$3.62} per week for board, how long can he board for \\$188.50 ? 18. Suppose a man's income is \\$500 a year, how much is that per day? 19. Suppose a man's interest money is \\$28.80 per day, how much is it per minute ? 20. A mason received \\$94.375 for doing a job, which took him 75} days : how much did he receive per day? 21. At \\$1.123 per bushel, how many bushels of wheat can be bought for \\$523.75 ? 22. If \\$1285.20 were divided equally among 125 men, what would each receive ? 23. If \\$1637.10 were divided equally among 150 men, what would each receive ? 24. The salary of the President of the United States is \\$25000 a year: how much does he receive per day? APPLICATIONS OF FEDERAL MONEY. BILLS, ACCOUNTS, &C. 220. A Bill, in mercantile operations, is a written paper, containing a statement of particulars, or amount of goods sold. Ex. 1. What is the cost of the several articles, and what the amount, of the following bill ? at · Boston, May 25th, 1845. James Brown, Esq. Bought of Fairfield f Lincoln, 5 yds. of Broadcloth, \\$3.25 3 yds. of Cambric, .12) 3 doz. Buttons, .15 6 skeins Sewing Silk, .06 4 yds. Wadding, .08 Amount, \\$17.77. Received Pay't, Fairfield f Lincoln. ( 2.)", null, "NEW HAVEN, Sept.20, 1845. Hon. R. S. Baldwin, Bought of Durrie of Peck, 4 Lovell's Young Speaker, at \\$ .621 5 Olmsted's Rudiments, .58 6 Morse's Geography, .50 8 Webster's Spelling Book, .10 3 Day's Algebra, 1.25 What was the cost of the several articles, and what the amount of his bill ? (3.) NEW YORK, Aug. 18th, 1845. John Jacob Astor, Esq. Bought of G. W. Lewis of Co. 25 lbs. Sugar, at \\$.09 50 lbs. Coffee, .11 12 lbs. Tea, .75 14 lbs. Raisins, .14 9 doz. Eggs, .10 15 lbs. Butter, .125 What was the cost of the several articles, and what the amount of his bill ? ( 4.) PHILADELPHIA, June 30, 1845. W. A. Sandford, Esq. To James Conrad, Dr. For 28 yds. Silk, at \\$1.25 “ 22 yds. Muslin, .56 “ 16 pair Cotton Hose, .37) Silk 1.10 66 25 \" Shoes, 1.25 What was the cost of the several articles, and how much is due on his account? 66 35 ( 5.) CINCINNATI, July 4th, 1845. Messrs. Holmes f Homer, To H. W. Morgan f Co. Dr. For 100 bls. Flour, at \\$4.50 50 8.25 25 Beef, 9.75 “ 112 kegs of Lard, 3.25 25 bush. of Corn, .34 What was the cost of the several articles, and how much is due on his account? “ Pork,", null, "66", null, "« ĐńďçăďýěĺíçÓőíÝ÷ĺéá »" ]	[ null, "https://books.google.gr/books/content", null, "https://books.google.gr/books/content", null, "https://books.google.gr/books/content", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9536078,"math_prob":0.9137359,"size":5780,"snap":"2021-31-2021-39","text_gpt3_token_len":1835,"char_repetition_ratio":0.12742382,"word_repetition_ratio":0.14197531,"special_character_ratio":0.3647059,"punctuation_ratio":0.2422078,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9622906,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-29T19:36:33Z\",\"WARC-Record-ID\":\"<urn:uuid:f5b87517-a3da-4695-a8b8-0ca18a91fdd8>\",\"Content-Length\":\"40662\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f19dc509-481a-4b59-8066-fe965bab7b5f>\",\"WARC-Concurrent-To\":\"<urn:uuid:39876019-9e88-4733-9fc2-879a3adc8d46>\",\"WARC-IP-Address\":\"142.250.188.206\",\"WARC-Target-URI\":\"https://books.google.gr/books?id=BMc2AAAAMAAJ&pg=PA198&vq=%22How+many+bricks+8+inches+long,+4+inches+wide,+and+2+inches+thick,%22&dq=editions:HARVARD32044096994090&lr=&hl=el&output=html_text\",\"WARC-Payload-Digest\":\"sha1:P6MG47HDOULROWV3TKPWTB2KM3X6UC4D\",\"WARC-Block-Digest\":\"sha1:HO6DRVE4ZTWKCLNLRXZMFLEOAPKCZN3R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153892.74_warc_CC-MAIN-20210729172022-20210729202022-00464.warc.gz\"}"}
https://cran.microsoft.com/snapshot/2017-02-25/web/packages/RcppShark/vignettes/RcppShark.html	[ "# Tutorial\n\nRcppShark is basically a bridge to allow creating packages based on Shark. It also allows for rapid prototyping using Shark as the underlying machine learning library. Therefore, the most important part is to understand how to use RcppShark in your own packages. For this reason, RcppShark contains (the usual) package skeleton creator. To develop your own package using RcppShark, you simply call after installing RcppShark\n\nlibrary (RcppShark)\n\nRcppShark.package.skeleton (“myOwnPackage”)\n\n(make sure your own name is valid). This will create a empty package structure where you can freely use Shark in the C++ part. Let us wrap the KMeans algorithm, following the tutorial from the Shark homepage (http://image.diku.dk/shark/sphinx_pages/build/html/rest_sources/tutorials/algorithms/kmeans.html).\n\nFor this we want basically two functions: One that will ‘learn’ the clustering and cluster the given training data, and one that will ‘predict’ the clustering to new data. Let us start with the first part. We start with the C++ code, and will only add R code, if it is necessary. Rcpp will export our C++ function to R in a very nice fashion, so it is not always necessary to add R code, at least not for our little tutorial.\n\nNow we can write the corresponding C++ function. For this we follow the Shark tutorial by creating a new file in the src folder of our new package, called KMeans.cpp, and importing all the headers we need:\n\n#include <shark/Algorithms/KMeans.h> //k-means algorithm\n#include <shark/Models/Clustering/Centroids.h>//model performing hard clustering of points\n#include <shark/Models/Clustering/HardClusteringModel.h>//model performing hard clustering of points\n\n#include <Rcpp.h>\n#include \"utils.h\" // some conversion helpers\n\nusing namespace shark;\nusing namespace std;\n\nusing namespace Rcpp;\n\nNote that we have skipped the CSV and normalizer header, as we have full control over both in R, and added Rcpp as well as our small utils.h header which contains some code to convert from the Shark to the Rcpp data format (and back). Lets continue with the main routine. This will take a matrix, the number of clusters $$k$$ to find and will return a list with the following two information: The final clustering in form of a model consisting of the centroids and a vector with the cluster assignments. So we start with the header:\n\n//' Simple KMeans Train\n//'\n//' @export\n//'\n// [[Rcpp::depends(BH)]]\n// [[Rcpp::export]]\nList SharkKMeansTrain (NumericMatrix X, ssize_t k) {\n\nThe first thing to do is to convert the given data in form of a matrix into an object, Shark can work with. For this, we call the corresponding function from the utils.h class:\n\n // convert data\nUnlabeledData<RealVector> data = NumericMatrixToUnlabeledData(X);\nstd::size_t elements = data.numberOfElements();\n\nNow comes the Shark code. For more details on this, please consult the Shark tutorial. We drop here everything that we do not need, e.g. printing information.\n\n // compute centroids using k-means clustering\nCentroids centroids;\nkMeans (data, k, centroids);\n\n// convert cluster centers/centroids\nData<RealVector> const& c = centroids.centroids();\nNumericMatrix cM = DataRealVectorToNumericMatrix (c);\n\n// cluster training data we are given and convert to Rcpp object\nHardClusteringModel<RealVector> model(&centroids);\nData<unsigned> clusters = model(data);\nNumericVector labels = LabelsToNumericVector (clusters);\n\nFinally we just need to put all the bits into a list and return it to R:\n\n // return solution found\nRcpp::List rl = R_NilValue;\nrl = Rcpp::List::create(\nRcpp::Named(\"labels\") = labels,\nRcpp::Named(\"centroids\") = cM );\nreturn (rl);\n\nPlease note that for sake of brevity we dropped all kind of checks. For production code such checks obviously should be done.\n\nBefore we test this code, let us quickly write the corresponding predict function (which is more or less already part of the training function, so we could drop that there):\n\n//' Simple KMeans Predict\n//'\n//' @export\n//'\n// [[Rcpp::depends(BH)]]\n// [[Rcpp::export]]\nList SharkKMeansPredict (NumericMatrix X, NumericMatrix centroids) {\n\n// convert data\nUnlabeledData<RealVector> data = NumericMatrixToUnlabeledData (X);\nstd::size_t elements = data.numberOfElements();\n\n// convert centroids\nCentroids c (NumericMatrixToDataRealVector (centroids));\n\n// cluster data we are given and convert to Rcpp object\nHardClusteringModel<RealVector> model (&c);\nData<unsigned> clusters = model (data);\nNumericVector labels = LabelsToNumericVector (clusters);\n\n// return solution found\nrl = Rcpp::List::create(Rcpp::Named(\"labels\") = labels);\nreturn (rl);\n}\n\nRunning this code is now easy, as by Rcpp::export tag, Rcpp will automatically create a wrapper to be called from R. This is good enough for us, though usually you really want to wrap the C++ function in a nice R routine. So we can now write a small function that will use our KMeans routine by creating first some example data and then calling our KMeans:\n\nlibrary (devtools)\n\n# convert iris to matrix\ndata = as.matrix(iris[,1:4])\n\nmodel = SharkKMeansTrain (data, 3)\nlabels = SharkKMeansPredict (data, model$centroids) Note that we need the devtools package, as we develop a new package. The output should be look similar to this: > model$labels\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2\n 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2\n 2 1\n\n$centroids [,1] [,2] [,3] [,4] [1,] 5.006000 3.428000 1.462000 0.246000 [2,] 5.901613 2.748387 4.393548 1.433871 [3,] 6.850000 3.073684 5.742105 2.071053 > labels$labels\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2\n 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 1 2\n 2 1\n\nFor convenience every new created skeleton contains the above KMeans example." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.70448655,"math_prob":0.94023794,"size":6147,"snap":"2022-27-2022-33","text_gpt3_token_len":1987,"char_repetition_ratio":0.18167019,"word_repetition_ratio":0.3013453,"special_character_ratio":0.32519928,"punctuation_ratio":0.12075472,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9524905,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-27T03:02:36Z\",\"WARC-Record-ID\":\"<urn:uuid:62b47d85-c0df-403e-a81e-2a776fc2a1f8>\",\"Content-Length\":\"25521\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4833740c-13af-4dcc-8903-0b9a585e9fe9>\",\"WARC-Concurrent-To\":\"<urn:uuid:e7d6689a-b14a-4b4d-b929-abd05636188e>\",\"WARC-IP-Address\":\"13.66.202.75\",\"WARC-Target-URI\":\"https://cran.microsoft.com/snapshot/2017-02-25/web/packages/RcppShark/vignettes/RcppShark.html\",\"WARC-Payload-Digest\":\"sha1:ZH7H3JYGW73NS5A2TSJVAJEKFQXUXTII\",\"WARC-Block-Digest\":\"sha1:DXM425OFEG535UGF7NAEDJHJROMFJ5JD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103324665.17_warc_CC-MAIN-20220627012807-20220627042807-00462.warc.gz\"}"}
https://www.ams.org/journals/tran/1974-193-00/S0002-9947-1974-0352427-3/	[ "", null, "", null, "", null, "ISSN 1088-6850(online) ISSN 0002-9947(print)\n\nInequalities for polynomials with a prescribed zero\n\nAuthors: A. Giroux and Q. I. Rahman\nJournal: Trans. Amer. Math. Soc. 193 (1974), 67-98\nMSC: Primary 30A06\nDOI: https://doi.org/10.1090/S0002-9947-1974-0352427-3\nMathSciNet review: 0352427\nFull-text PDF Free Access\n\nAbstract: Inequalities for the derivative and for the maximum modulus on a larger circle of a polynomial with a given zero on the unit circle are obtained in terms of its degree and maximum modulus on the unit circle; examples are given to show that these are sharp with respect to the degree (best constants are not known). Inequalities for \\${L^p}\\$ norms, in particular \\${L^2}\\$ norms, are also derived. Also certain functions of exponential type are considered and similar inequalities are obtained for them. Finally, the problem of estimating \\${P_n}(r)\\$ (with \\$0 < r < 1\\$) given \\${P_n}(1) = 0\\$ is taken up.\n\n[Enhancements On Off] (What's this?)\n\nRetrieve articles in Transactions of the American Mathematical Society with MSC: 30A06\n\nRetrieve articles in all journals with MSC: 30A06\n\nAdditional Information\n\nKeywords: Derivative of a polynomial, Bernstein’s inequality, growth of maximum modulus, problem of Halász, <IMG WIDTH=\"29\" HEIGHT=\"20\" ALIGN=\"BOTTOM\" BORDER=\"0\" SRC=\"images/img1.gif\" ALT=\"\\${L^p}\\$\"> norm of a polynomial, trigonometric polynomial, entire function of exponential type, interpolation formula\nArticle copyright: © Copyright 1974 American Mathematical Society" ]	[ null, "https://www.ams.org/images/remote-access-icon.png", null, "https://www.ams.org/publications/journals/images/journal.cover.tran.gif", null, "https://www.ams.org/publications/journals/images/open-access-green-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5388817,"math_prob":0.90033984,"size":4462,"snap":"2021-21-2021-25","text_gpt3_token_len":1446,"char_repetition_ratio":0.12673844,"word_repetition_ratio":0.025,"special_character_ratio":0.37180635,"punctuation_ratio":0.26559356,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97856116,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-20T00:17:16Z\",\"WARC-Record-ID\":\"<urn:uuid:f40a045c-172a-40c8-b718-6fb3c6e780f2>\",\"Content-Length\":\"54536\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ae08cb18-30da-468e-9fa7-d71fd4fe11d9>\",\"WARC-Concurrent-To\":\"<urn:uuid:b120f428-95d1-4ad2-8314-e94b2f4cf641>\",\"WARC-IP-Address\":\"130.44.204.100\",\"WARC-Target-URI\":\"https://www.ams.org/journals/tran/1974-193-00/S0002-9947-1974-0352427-3/\",\"WARC-Payload-Digest\":\"sha1:3E5OLS6CB6466PXCUFW377JMQ5PE5EXD\",\"WARC-Block-Digest\":\"sha1:NXWXQWZJJRUTSQP4RELQOJFNZYO7KVHL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487653461.74_warc_CC-MAIN-20210619233720-20210620023720-00597.warc.gz\"}"}
https://jneuroinflammation.biomedcentral.com/articles/10.1186/s12974-020-01808-2/tables/2	[ "# Table 2 The number and distribution of the animals included for the present study\n\nGroups (n) Mortality (n)\nTime course study WB (6, 12, 24, and 72 h post-ROSC) Sham (n = 4) 0\nACA (6 h, 12 h, 24 h, 72 h) (n = 16) 3 (1 died at 12 h, 1 died at 15 h, and 1 died at 22 h post-ROSC)\nCellular localization (24 h post-ROSC) Sham (n = 1), ACA (n = 1) 0\nToluidine blue staining (24 h post-ROSC) Sham (n = 1) 0\nACA (n = 1) 0\nShort-term outcome study (up to 7-day post ROSC) Fluoro-Jade C staining Sham (n = 6) 0\nACA + vehicle (n = 6) 2 (1 at 24 h post-ROSC, 1 died at 48 h post-ROSC)\nACA + APC366 (50 μg) (n = 6) 2 (1 died at 48 h post-ROSC, 1 died at 70 h post-ROSC)\nACA + APC366 (150) (n = 6) 1 (died at 6 h post-ROSC)\nACA + AC55541 (30 μg) (n = 6) 2 (1 died on 5th day post-ROSC, 1 died on 6th post-ROSC)\nLong-term outcome study (30-day post-ROSC) Fluoro-Jade C staining Sham (n = 6) 0\nACA + vehicle (n = 6) 0\nACA + APC366 (50 μg) (n = 6) 0\nMechanism study (24 h post-ROSC) Western blot Sham (n = 6) 0\nACA + vehicle (n = 6) 0\nACA + APC366 (50 μg) (n = 6) 0\nACA + AC55541 (30 μg) (n = 6) 0\nACA + APC366 (50 μg) + AC55541 (30 μg) (n = 6) 1 (died at 8 h post-ROSC)\nACA + AC55541 (30 μg) + SB203580 (300 μg) (n = 6) 0\nMass spectrometry APC366 (n = 1) 0\nTotal 120 109 11\n1. ACA asphyxial cardiac arrest, h hours, ROSC return of spontaneous circulation", null, "" ]	[ null, "https://jneuroinflammation.biomedcentral.com/track/article/10.1186/s12974-020-01808-2", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8949904,"math_prob":0.9860531,"size":1370,"snap":"2022-27-2022-33","text_gpt3_token_len":637,"char_repetition_ratio":0.24670571,"word_repetition_ratio":0.33217993,"special_character_ratio":0.49635038,"punctuation_ratio":0.044067796,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95011437,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-28T12:30:44Z\",\"WARC-Record-ID\":\"<urn:uuid:6949f969-69e2-4074-aeb5-c6220c6758ea>\",\"Content-Length\":\"196744\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e767c2b1-21df-4165-bd26-5f4c71c64e9d>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4b50cb6-2b07-4669-98bd-5ede9cb4e7a1>\",\"WARC-IP-Address\":\"146.75.32.95\",\"WARC-Target-URI\":\"https://jneuroinflammation.biomedcentral.com/articles/10.1186/s12974-020-01808-2/tables/2\",\"WARC-Payload-Digest\":\"sha1:HX5WYA3CWQID7NKXJRTBYYS5Y2XAVPS3\",\"WARC-Block-Digest\":\"sha1:RGNCY4O3SLP5Q2BDRGRT5PZ2VB2R5Y3H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103516990.28_warc_CC-MAIN-20220628111602-20220628141602-00674.warc.gz\"}"}
https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/	[ "", null, "# Euler's Generating Function for the Partition Numbers\n\nInitializing live version", null, "Requires a Wolfram Notebook System\n\nInteract on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.\n\nThis Demonstration shows the partition numbers", null, "up to", null, "as the coefficients of", null, "in the polynomial on the right.\n\n[more]\n\nThe partition numbers", null, "are 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, …. They count the number of ways of splitting an integer", null, "into a sum of positive integers, without regard to order. For instance,", null, ", the number of ways to partition 4, is 5 because there are 5 possible sums that add to 4: 4, 1+3, 2+2, 1+1+2, 1+1+1+1. By convention,", null, ".\n\nThe left-hand side of the identity shows the product of geometric series", null, "with common ratios", null, ",", null, ",", null, ",…,", null, ", each truncated to", null, "terms. The right-hand side multiplies them out and collects terms.\n\nAs an example, let", null, "; the term", null, "on the right is the sum of the five products", null, ",", null, ",", null, ",", null, ",", null, ", where the factors in each product are in the order of the series they come from. These products correspond to the partitions 4, 1+3, 2+2, 1+1+2, 1+1+1+1.\n\nIn general, an uncollected term in the expansion of the left side is of the form", null, ". The factor", null, "comes from the", null, "term of the", null, "truncated series", null, "and contributes", null, "(", null, "times) in the corresponding partition. Collecting terms amounts to counting the number of ways", null, "can be partitioned.\n\nThe generating function for", null, "is thus", null, ".\n\n[less]\n\nContributed by: George Beck (March 2011)\nOpen content licensed under CC BY-NC-SA\n\n## Snapshots", null, "", null, "", null, "## Permanent Citation\n\nGeorge Beck\n\n Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send" ]	[ null, "https://demonstrations.wolfram.com/app-files/assets/img/header-spikey2x.png", null, "https://demonstrations.wolfram.com/img/demonstrations-branding.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc4482206331905177358.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc82616708308991493.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc2929249350788845788.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc4482206331905177358.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc82616708308991493.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc4246801932808068846.png", null, 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"https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc7265650061190378567.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc4898160201763885787.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc1664046408703118620.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc5103742537509943587.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc8443332026663453010.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc8127801085306454081.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc130336331222482860.png", null, "https://demonstrations.wolfram.com/EulersGeneratingFunctionForThePartitionNumbers/img/desc6194894642775152751.png", null, 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https://www.colorhexa.com/00d55b	[ "# #00d55b Color Information\n\nIn a RGB color space, hex #00d55b is composed of 0% red, 83.5% green and 35.7% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 57.3% yellow and 16.5% black. It has a hue angle of 145.6 degrees, a saturation of 100% and a lightness of 41.8%. #00d55b color hex could be obtained by blending #00ffb6 with #00ab00. Closest websafe color is: #00cc66.\n\n• R 0\n• G 84\n• B 36\nRGB color chart\n• C 100\n• M 0\n• Y 57\n• K 16\nCMYK color chart\n\n#00d55b color description : Strong cyan - lime green.\n\n# #00d55b Color Conversion\n\nThe hexadecimal color #00d55b has RGB values of R:0, G:213, B:91 and CMYK values of C:1, M:0, Y:0.57, K:0.16. Its decimal value is 54619.\n\nHex triplet RGB Decimal 00d55b `#00d55b` 0, 213, 91 `rgb(0,213,91)` 0, 83.5, 35.7 `rgb(0%,83.5%,35.7%)` 100, 0, 57, 16 145.6°, 100, 41.8 `hsl(145.6,100%,41.8%)` 145.6°, 100, 83.5 00cc66 `#00cc66`\nCIE-LAB 75.039, -69.17, 47.455 25.681, 48.341, 17.874 0.279, 0.526, 48.341 75.039, 83.884, 145.547 75.039, -68.423, 70.737 69.528, -55.742, 33.427 00000000, 11010101, 01011011\n\n# Color Schemes with #00d55b\n\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #d5007a\n``#d5007a` `rgb(213,0,122)``\nComplementary Color\n• #0fd500\n``#0fd500` `rgb(15,213,0)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #00d5c6\n``#00d5c6` `rgb(0,213,198)``\nAnalogous Color\n• #d5000f\n``#d5000f` `rgb(213,0,15)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #c600d5\n``#c600d5` `rgb(198,0,213)``\nSplit Complementary Color\n• #d55b00\n``#d55b00` `rgb(213,91,0)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #5b00d5\n``#5b00d5` `rgb(91,0,213)``\n``#7ad500` `rgb(122,213,0)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #5b00d5\n``#5b00d5` `rgb(91,0,213)``\n• #d5007a\n``#d5007a` `rgb(213,0,122)``\n• #00893a\n``#00893a` `rgb(0,137,58)``\n• #00a245\n``#00a245` `rgb(0,162,69)``\n• #00bc50\n``#00bc50` `rgb(0,188,80)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #00ef66\n``#00ef66` `rgb(0,239,102)``\n• #09ff72\n``#09ff72` `rgb(9,255,114)``\n• #23ff81\n``#23ff81` `rgb(35,255,129)``\nMonochromatic Color\n\n# Alternatives to #00d55b\n\nBelow, you can see some colors close to #00d55b. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #00d526\n``#00d526` `rgb(0,213,38)``\n• #00d538\n``#00d538` `rgb(0,213,56)``\n• #00d549\n``#00d549` `rgb(0,213,73)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #00d56d\n``#00d56d` `rgb(0,213,109)``\n• #00d57f\n``#00d57f` `rgb(0,213,127)``\n• #00d590\n``#00d590` `rgb(0,213,144)``\nSimilar Colors\n\n# #00d55b Preview\n\nThis text has a font color of #00d55b.\n\n``<span style=\"color:#00d55b;\">Text here</span>``\n#00d55b background color\n\nThis paragraph has a background color of #00d55b.\n\n``<p style=\"background-color:#00d55b;\">Content here</p>``\n#00d55b border color\n\nThis element has a border color of #00d55b.\n\n``<div style=\"border:1px solid #00d55b;\">Content here</div>``\nCSS codes\n``.text {color:#00d55b;}``\n``.background {background-color:#00d55b;}``\n``.border {border:1px solid #00d55b;}``\n\n# Shades and Tints of #00d55b\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, #001107 is the darkest color, while #fcfffd is the lightest one.\n\n• #001107\n``#001107` `rgb(0,17,7)``\n• #002410\n``#002410` `rgb(0,36,16)``\n• #003818\n``#003818` `rgb(0,56,24)``\n• #004c20\n``#004c20` `rgb(0,76,32)``\n• #005f29\n``#005f29` `rgb(0,95,41)``\n• #007331\n``#007331` `rgb(0,115,49)``\n• #008739\n``#008739` `rgb(0,135,57)``\n• #009a42\n``#009a42` `rgb(0,154,66)``\n• #00ae4a\n``#00ae4a` `rgb(0,174,74)``\n• #00c153\n``#00c153` `rgb(0,193,83)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\n• #00e963\n``#00e963` `rgb(0,233,99)``\n• #00fc6c\n``#00fc6c` `rgb(0,252,108)``\n• #11ff77\n``#11ff77` `rgb(17,255,119)``\n• #24ff82\n``#24ff82` `rgb(36,255,130)``\n• #38ff8d\n``#38ff8d` `rgb(56,255,141)``\n• #4cff98\n``#4cff98` `rgb(76,255,152)``\n• #5fffa4\n``#5fffa4` `rgb(95,255,164)``\n• #73ffaf\n``#73ffaf` `rgb(115,255,175)``\n• #87ffba\n``#87ffba` `rgb(135,255,186)``\n• #9affc5\n``#9affc5` `rgb(154,255,197)``\n• #aeffd0\n``#aeffd0` `rgb(174,255,208)``\n• #c1ffdc\n``#c1ffdc` `rgb(193,255,220)``\n• #d5ffe7\n``#d5ffe7` `rgb(213,255,231)``\n• #e9fff2\n``#e9fff2` `rgb(233,255,242)``\n• #fcfffd\n``#fcfffd` `rgb(252,255,253)``\nTint Color Variation\n\n# Tones of #00d55b\n\nA tone is produced by adding gray to any pure hue. In this case, #627369 is the less saturated color, while #00d55b is the most saturated one.\n\n• #627369\n``#627369` `rgb(98,115,105)``\n• #5a7b68\n``#5a7b68` `rgb(90,123,104)``\n• #528367\n``#528367` `rgb(82,131,103)``\n• #4a8b66\n``#4a8b66` `rgb(74,139,102)``\n• #429365\n``#429365` `rgb(66,147,101)``\n• #399c63\n``#399c63` `rgb(57,156,99)``\n• #31a462\n``#31a462` `rgb(49,164,98)``\n• #29ac61\n``#29ac61` `rgb(41,172,97)``\n• #21b460\n``#21b460` `rgb(33,180,96)``\n• #19bc5f\n``#19bc5f` `rgb(25,188,95)``\n• #10c55d\n``#10c55d` `rgb(16,197,93)``\n• #08cd5c\n``#08cd5c` `rgb(8,205,92)``\n• #00d55b\n``#00d55b` `rgb(0,213,91)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00d55b is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5080168,"math_prob":0.86883485,"size":3678,"snap":"2023-40-2023-50","text_gpt3_token_len":1644,"char_repetition_ratio":0.133914,"word_repetition_ratio":0.0073664826,"special_character_ratio":0.5541055,"punctuation_ratio":0.23224352,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9887068,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-07T14:15:42Z\",\"WARC-Record-ID\":\"<urn:uuid:5cb6f384-e2f5-4aa6-9172-ae88e85808d8>\",\"Content-Length\":\"36181\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5e86c6c1-14fc-40e8-b781-2abb2051afb0>\",\"WARC-Concurrent-To\":\"<urn:uuid:e732371f-5ff7-4754-b881-499e9ce3461b>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/00d55b\",\"WARC-Payload-Digest\":\"sha1:LKTA7M55RKWGMU7VQWTO5AE6UIYVSAB4\",\"WARC-Block-Digest\":\"sha1:WKYSJ6PBBA7IVHAX2DPEDIXWTJKSZUZQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100674.56_warc_CC-MAIN-20231207121942-20231207151942-00364.warc.gz\"}"}
https://markupuk.org/webhelp/ar08s02s02.html	[ "### Showing linked changes to JSON Structure in diff3x\n\nFor JSON, the issue of handling curly braces (for objects) and square brackets (for arrays) is similar to XML start and end tags. Again, some representation of connected change is needed to maintain syntactic correctness.\n\nObject members and array members are comma separated and this is tricky to get right in some situations. The syntax is shown below.\n\n```object = begin-object [ member ( value-separator member ) ]\nend-object\narray = begin-array [ value ( value-separator value ) ] end-array\n\nThese are the six structural characters:\nbegin-array = ws %x5B ws ; [ left square bracket\nbegin-object = ws %x7B ws ; { left curly bracket\nend-array = ws %x5D ws ; ] right square bracket\nend-object = ws %x7D ws ; } right curly bracket\nname-separator = ws %x3A ws ; : colon\nvalue-separator = ws %x2C ws ; , comma\n\nInsignificant whitespace is allowed before or after any of the six\nstructural characters.\nws = *(\n%x20 / ; Space\n%x09 / ; Horizontal tab\n%x0A / ; Line feed or New line\n%x0D ) ; Carriage return```\n\nHere is an example of a change to an array of strings.\n\nTable 3. JSON structural change\n\nA.txtO.txtB.txt\n`[[12,13,14],20,21,22]`\n`[12,13,14,20,21,22]`\n`[[12,13,14,20,21,22]]`\n\nThis could be represented in the diff3 format as shown below, but note that this is not how diff3 would process the above files which each have a single line. However the result below could be generated by careful use of line breaks in the input files.\n\n```[\n<<<<<<<< A.txt\n[\n\|\|\|\|\|\|\| O.txt\n\n=======\n\n>>>>>>> B.txt\n\n<<<<<<<< A.txt\n\n\|\|\|\|\|\|\| O.txt\n\n=======\n[\n>>>>>>> B.txt\n12,13,14\n<<<<<<<< A.txt\n]\n\|\|\|\|\|\|\| O.txt\n\n=======\n\n>>>>>>> B.txt\n,20,21,22\n<<<<<<<< A.txt\n\n\|\|\|\|\|\|\| O.txt\n\n=======\n]\n>>>>>>> B.txt\n]```\n\nThe above will only produce syntactically correct results if the correct choices are made, which is not easy. It is also not easy to see what is going on in the diff3 file because of the extra whitespace lines that have to be inserted to make this work.\n\nWe introduce here a way to connect the relevant consistent choices so that if the '[' is selected then the appropriate choice of the end ']' is also made automatically.\n\nA choice consists of one or more options. An option may have an id. An option may also have a select attribute which provides a boolean value made up of one or a combination of other ids and if these are 'true', i.e. have been chosen to be included, then this option is selected automatically.\n\nThis could be represented in diff3x as shown below. We show here the id attribute on an option to identify it uniquely within the file. We then use that id to reference that option where another option needs to be linked to it. In this case, the '[' in the A.txt has `id=\"a42\"` and this is then referenced in the select attribute of the corresponding ']' option later in the file. Similarly the pair of square brackets in B.txt are linked with the id \"b44\".\n\n```<diff3x a=\"A.txt\" b=\"B.txt\" o=\"O.txt\">\n[\n<choice2>\n<a id=\"a42\">[</a>\n<ob/></choice2>\n<choice2>\n<b id=\"b44\">[</b>\n<ao/></choice2>\n12,13,14\n<choice2>\n<a select=\"a42\">]</a>\n<ob/></choice2>\n,20,21,22\n<choice2>\n<b select=\"b44\">]</b>\n<ao/></choice2>\n]</diff3x>```\n\nNote that the '[' in A could be selected either instead of or as well as the '[' in B even though they are at the same position in the array. Whichever choice is made, the other choices with a select attribute identifying the same id are chosen and the result is syntactically correct. This is a powerful way to represent connected choices." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8647367,"math_prob":0.8602997,"size":3432,"snap":"2021-43-2021-49","text_gpt3_token_len":890,"char_repetition_ratio":0.11201867,"word_repetition_ratio":0.010169491,"special_character_ratio":0.3161422,"punctuation_ratio":0.13018598,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95514524,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-08T22:36:38Z\",\"WARC-Record-ID\":\"<urn:uuid:119435a1-9cf7-4f29-a50c-d527e0f42ffd>\",\"Content-Length\":\"12629\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f726a41b-84d9-4ced-887f-aeaae1ab1c81>\",\"WARC-Concurrent-To\":\"<urn:uuid:cbd7117d-79e5-4c1a-9bf9-78231f73c368>\",\"WARC-IP-Address\":\"185.199.108.153\",\"WARC-Target-URI\":\"https://markupuk.org/webhelp/ar08s02s02.html\",\"WARC-Payload-Digest\":\"sha1:XBC7RHQSMJHTP5S3RQSHR6FWJMDOAGS7\",\"WARC-Block-Digest\":\"sha1:VKQGEUHOKLXNU26CICJQPUWWZBDST57T\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363598.57_warc_CC-MAIN-20211208205849-20211208235849-00219.warc.gz\"}"}
https://www.numbers.education/2683.html	[ "Is 2683 a prime number? What are the divisors of 2683?\n\n## Is 2683 a prime number?\n\nYes, 2683 is a prime number.\n\nIndeed, the definition of a prime numbers is to have only two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 2683, the only two divisors are 1 and 2683. Therefore 2683 is a prime number.\n\nAs a consequence, 2683 is only a multiple of 1 and 2683.\n\nSince 2683 is a prime number, 2683 is also a deficient number, that is to say 2683 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 2683 without 2683 itself (that is 1, by definition!).\n\n## Parity of 2683\n\n2683 is an odd number, because it is not evenly divisible by 2.\n\n## Is 2683 a perfect square number?\n\nA number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 2683 is about 51.798.\n\nThus, the square root of 2683 is not an integer, and therefore 2683 is not a square number.\n\nAnyway, 2683 is a prime number, and a prime number cannot be a perfect square.\n\n## What is the square number of 2683?\n\nThe square of a number (here 2683) is the result of the product of this number (2683) by itself (i.e., 2683 × 2683); the square of 2683 is sometimes called \"raising 2683 to the power 2\", or \"2683 squared\".\n\nThe square of 2683 is 7 198 489 because 2683 × 2683 = 26832 = 7 198 489.\n\nAs a consequence, 2683 is the square root of 7 198 489.\n\n## Number of digits of 2683\n\n2683 is a number with 4 digits.\n\n## What are the multiples of 2683?\n\nThe multiples of 2683 are all integers evenly divisible by 2683, that is all numbers such that the remainder of the division by 2683 is zero. There are infinitely many multiples of 2683. The smallest multiples of 2683 are:\n\n• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 2683 too, since 0 × 2683 = 0\n• 2683: indeed, 2683 is a multiple of itself, since 2683 is evenly divisible by 2683 (we have 2683 / 2683 = 1, so the remainder of this division is indeed zero)\n• 5 366: indeed, 5 366 = 2683 × 2\n• 8 049: indeed, 8 049 = 2683 × 3\n• 10 732: indeed, 10 732 = 2683 × 4\n• 13 415: indeed, 13 415 = 2683 × 5\n• etc.\n\n## Nearest numbers from 2683\n\nFind out whether some integer is a prime number" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9221668,"math_prob":0.9992335,"size":2252,"snap":"2019-35-2019-39","text_gpt3_token_len":685,"char_repetition_ratio":0.20996441,"word_repetition_ratio":0.022222223,"special_character_ratio":0.37699822,"punctuation_ratio":0.13690476,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994609,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-09-17T11:14:51Z\",\"WARC-Record-ID\":\"<urn:uuid:0c12f134-e8f8-4df3-a707-07443b6d6217>\",\"Content-Length\":\"12119\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:52e96bd7-c7c6-47c1-933d-2c5d3b0dea2c>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ed49d31-0fcc-416f-8a37-d49e93234aa7>\",\"WARC-IP-Address\":\"213.186.33.19\",\"WARC-Target-URI\":\"https://www.numbers.education/2683.html\",\"WARC-Payload-Digest\":\"sha1:BGYY3MGVW4KA3TUIXY7XL4JOYGHLTEOB\",\"WARC-Block-Digest\":\"sha1:W2OY56DLFZM4THEQQH3A6IYGR7BC6OLT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-39/CC-MAIN-2019-39_segments_1568514573070.36_warc_CC-MAIN-20190917101137-20190917123137-00504.warc.gz\"}"}
http://ltcconline.net/greenl/courses/106/explogtrig/arcsechPrime.htm	[ "Derivative of sech-1(x) We use the fact from the definition of the inverse that sech(sech-1(x)) = x and the fact that sech'(x) = -tanh(x)sech(x) Now take the derivative of both sides (using the chain rule on the left hand side) to get -tanh(sech-1x)sech(sech-1(x))(sech-1(x))' = 1 or -x tanh(sech-1x)(sech-1(x))' = 1 We know that cosh2(x) - sinh2(x) = 1 Dividing by the cosh2(x) gives 1 - tanh2(x) = sech2(x) or", null, "so that", null, "Finally substituting into gives", null, "Back to the Page on Hyperbolic Trig Back to Math 105 Home Page Back to the Math Department Home e-mail Questions and Suggestions" ]	[ null, "http://ltcconline.net/greenl/courses/106/explogtrig/arcsec1.gif", null, "http://ltcconline.net/greenl/courses/106/explogtrig/arcsec2.gif", null, "http://ltcconline.net/greenl/courses/106/explogtrig/arcsec3.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.78464526,"math_prob":0.99340194,"size":561,"snap":"2019-51-2020-05","text_gpt3_token_len":203,"char_repetition_ratio":0.15978456,"word_repetition_ratio":0.0,"special_character_ratio":0.315508,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99549246,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-24T07:18:31Z\",\"WARC-Record-ID\":\"<urn:uuid:ab41367e-4034-4321-b1f5-fe46b26d139c>\",\"Content-Length\":\"6113\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:10fd930f-f514-499e-888a-b1db57a9bbe5>\",\"WARC-Concurrent-To\":\"<urn:uuid:a188f97d-fdeb-4b68-bb82-ee739322f3f0>\",\"WARC-IP-Address\":\"198.189.128.39\",\"WARC-Target-URI\":\"http://ltcconline.net/greenl/courses/106/explogtrig/arcsechPrime.htm\",\"WARC-Payload-Digest\":\"sha1:QKH4GDRWFOAFBM7JU6QRGQDB3OJMTKUR\",\"WARC-Block-Digest\":\"sha1:A3ABVQOVUZR4CRH6MF7PES6A6HIWDSFM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250616186.38_warc_CC-MAIN-20200124070934-20200124095934-00260.warc.gz\"}"}
https://simple-accounting.org/how-to-calculate-straight-line-depreciation/	[ "# How To Calculate Straight Line Depreciation Formula\n\nThese accounts have credit balance (when an asset has a credit balance, it’s like it has a ‘negative’ balance) meaning that they decrease the value of your assets as they increase. Straight-line depreciation is a simple method for calculating how much a particular fixed asset depreciates over time. Understanding asset depreciation is an important part of running any business. When you’re able to accurately determine the condition of your assets as well as its current depreciation rate, you’ll improve your overall efficiency.\n\nMost tax systems provide different rules for real property (buildings, etc.) and personal property (equipment, etc.). The carrying value would be \\$200 on the balance sheet at the end of three years. The depreciation expense would be completed under the straight line depreciation method, and management would retire the asset. Any gain or loss above or below the estimated salvage value would be recorded, and there would no longer be any carrying value under the fixed asset line of the balance sheet.\n\n• However, when using the double-declining balance method of depreciation, an entity is not required to only accelerate depreciation by two.\n• To evaluate the lease classification, we used the capital vs. operating lease criteria test.\n• Office furniture, for example, is an appropriate asset for straight line depreciation.\n• Although, all the amount is paid for the machine at the time of purchase, however, the expense is charged over a period of time.\n• With the double-declining balance method, higher depreciation is posted at the beginning of the useful life of the asset, with lower depreciation expenses coming later.\n• It is calculated for intangible assets as the actual cost less amortization expense/impairments.\n\nHowever, in most countries the life is based on business experience, and the method may be chosen from one of several acceptable methods. The straight line depreciation calculation should make it clear how much leeway management has in managing reported earnings in any given period. It might seem that management has a lot of discretion in determining how high or low reported earnings are in any given period, and that’s correct.\n\nOr you can also come up with an estimation of how many units the asset can produce during its useful life. Straight-line depreciation has advantages and disadvantages, and is only one of many other methods used to calculate depreciation.\n\nA company may also choose to go with this method if it offers them tax or cash flow advantages. Four standard types of calculationsare used to determine depreciation expenses. The most common methods are straight-line depreciation, double declining balance depreciation, units of production depreciation, and sum of years digits depreciation. With the double-declining balance method, higher depreciation is posted at the beginning of the useful life of the asset, with lower depreciation expenses coming later. This method is an accelerated depreciation method because more expenses are posted in an asset’s early years, with fewer expenses being posted in later years. This approach works by calculating depreciation as a percentage and then depreciating the asset at twice the percentage rate. Accumulated depreciation is the associated balance sheet line item for depreciation expense.\n\n## Other Methods Of Calculating Depreciation\n\nTo calculate composite depreciation rate, divide depreciation per year by total historical cost. To calculate depreciation expense, multiply straight line depreciation the result by the same total historical cost. The result, not surprisingly, will equal the total depreciation per year again.\n\nHowever, the straight line method does not accurately reflect the difference in usage of an asset and may not be the most appropriate value calculation method for some depreciable assets. This method is regarded as the most accurate representation of devaluation, as it more closely reflects the actual wear and tear that assets go through. When using the units of production method, more resources are needed to collect enough data over long periods of time. Because of additional efforts required for this method, it is typically used for higher-value equipment. Besides capital expenditures, businesses also incur operating expenditures.\n\n## Retiring Assets\n\nWe discuss these briefly in the last section of our Beginners Guide to Depreciation. After an asset has been fully depreciated, it can remain in use as long as it is needed and is in good working order. To learn how to handle the retiring of assets, please see last section of our tutorial Beginner’s Guide to Depreciation. They have estimated the useful life of the machine to be 8 years with a salvage value of \\$ 2,000. Here, we are simply taking an average of the useful value of the asset over its useful life.\n\nFurther, the full value of the asset resides in the accumulated depreciation account as a credit. Combining the total asset and accumulated depreciation amounts equals a net book value of \\$0. Using the facts and circumstances presented, we can use LeaseQuery’s present value calculator to calculate the present value of the lease payments.\n\n## Accountingtools\n\nThe straight-line method of depreciation assumes a constant rate of depreciation. It calculates how much a specific asset depreciates in one year, and then depreciates the asset by that amount every year after that. As buildings, tools and equipment wear out over time, they depreciate in value. Being able to calculate depreciation is crucial for writing off the cost of expensive purchases, and for doing your taxes properly.\n\nEach of those \\$1,600 charges would be balanced against a contra account under property, plant, and equipment on the balance sheet. This is known as accumulated depreciation, which effectively reduces the carrying value of the asset. For example, the balance sheet would show a \\$5,000 computer offset by a \\$1,600 accumulated depreciation contra account after the first year, so the net carrying value would be \\$3,400. Straight-line depreciation is a method used to calculate the decline in value of fixed assets, such as vehicles or office equipment. If your company uses a piece of equipment, you should see more depreciation when you use the machinery to produce more units of a commodity. If production declines, this method lowers the depreciation expenses from one year to the next. The straight-line method of depreciation isn’t the only way businesses can calculate the value of their depreciable assets.\n\nWe’ll do one month of your bookkeeping and prepare a set of financial statements for you to keep. You can’t get a good grasp of the total value of your assets unless you figure out how much they’ve depreciated. This is especially important for businesses that own a lot of expensive, long-term assets that have long useful lives. Compared to the other three methods, straight line depreciation is by far the simplest. Learn accounting fundamentals and how to read financial statements with CFI’s free online accounting classes. Note how the book value of the machine at the end of year 5 is the same as the salvage value.\n\nOne method is called partial year depreciation, where depreciation is calculated exactly at when assets start service. Simply select “Yes” as an input in order to use partial year depreciation when using the calculator. You will find the depreciation expense used for each period until the value of the asset declines to its salvage value. Even if you’re still struggling with understanding some accounting terms, fortunately, straight line depreciation is pretty straightforward.\n\nThe total cost of the furniture and fixtures, including tax and delivery, was \\$9,000. Sally estimates the furniture will be worth around \\$1,500 at the end of its useful life, which, according to the chart above, is seven years. The final cost of the tractor, including tax and delivery, is \\$25,000, and the expected salvage value is \\$6,000. According to the table above, Jim can depreciate the tractor over a three-year period. In the last line of the chart, notice that 25% of \\$3,797 is \\$949, not the \\$797 that’s listed. However, the total depreciation allowed is equal to the initial cost minus the salvage value, which is \\$9,000.\n\n## The Best Method Of Calculating Depreciation For Tax Reporting Purposes\n\nContra AccountContra Account is an opposite entry passed to offset its related original account balances in the ledger. It helps a business retrieve the actual capital amount & amount of decrease in the value, hence representing the account’s net balances. As can be seen from the above table – At the end of 8 years, i.e., after its useful life is over, the machine has depreciated to its salvage value. Cost Of SalesThe costs directly attributable to the production of the goods that are sold in the firm or organization are referred to as the cost of sales.\n\nBut keep in mind this opens up the risk of overestimating the asset’s value. Reed, Inc. also evaluates the incremental borrowing rate for the lease to be 4%. For this example we will assume no other lease incentives, accruals, or initial direct costs are applicable for this lease. A depreciation schedule that treats all property acquired during the year as being acquired exactly in the middle of the year. But the IRS uses the accelerated/MACRS or Section 179 for certain assets, including intangible assets like copyrights, patents and trademarks.\n\nAs such, the income statement is expensed evenly, so is the value of the asset on the balance sheet. The carrying amount of the asset on the balance sheet reduces by the same amount. There are many methods of distributing depreciation amount over its useful life. The total amount of depreciation for any asset will be identical in the end no matter which method of depreciation is chosen; only the timing of depreciation will be altered. There are a lot of reasons businesses choose to use the straight line depreciation method. The straight-line depreciation method is one of the most popular depreciation methods used to charge depreciation expenses from fixed assets equally period assets’ useful life.\n\n### How do you record adjusting entries for depreciation?\n\nHow to Record Depreciation Expense. Depreciation is recorded by debiting Depreciation Expense and crediting Accumulated Depreciation. This is recorded at the end of the period (usually, at the end of every month, quarter, or year). Depreciation Expense: An expense account; hence, it is presented in the income statement …\n\nThe declining balance method calculates more depreciation expense initially, and uses a percentage of the asset’s current book value, as opposed to its initial cost. So, the amount of depreciation declines over time, and continues until the salvage value is reached. The most common types of depreciation methods include straight-line, double declining balance, units of production, and sum of years digits. Straight-line depreciation is the most common method of allocating the cost of a plant asset to expense in the accounting periods during which the asset is used. With the straight-line method of depreciation, each full accounting year will report the same amount of depreciation. The total amount of depreciation over the years of the asset’s useful life will be the asset’s cost minus any expected or assumed salvage value. Four types of depreciation systems are commonly available within accounting.\n\n## Step 4: Divide 1 By The Number Of Years Of Useful Life To Determine Annual Depreciation Rate\n\nThe annual depreciation expense is a measure of the loss of value of the item. In the article, we have seen how the straight line depreciation method can be used to depreciate the value of the asset over the useful life of the asset. It is the easiest and simplest method of depreciation where the cost of the asset is depreciated uniformly over its useful life. The depreciation rate is the rate an asset is depreciated each period.\n\nIn our example, the title transfers, which means at the end of the lease term the lessee will own the asset and continue depreciating it. However, the useful life of the equipment in this example equals the lease term so at the end of the lease, the asset will be depreciated to \\$0. Now, let’s consider a full example of a finance lease to illustrate straight-line depreciation expense. Below we will describe each method and provide the formula used to calculate the periodic depreciation expense. Depreciation is an accounting method of allocating the cost of a tangible asset over its useful life and is used to account for declines in value over time. To calculate depreciation using a straight line basis, simply divide net price by the number of useful years of life the asset has. Straight line basis is calculated by dividing the difference between an asset’s cost and its expected salvage value by the number of years it is expected to be used.\n\nDouble declining balance is the most widely used declining balance depreciation method, which has a depreciation rate that is twice the value of straight line depreciation for the first year. Use a depreciation factor of two when doing calculations for double declining balance depreciation. Regarding this method, salvage values are not included in the calculation for annual depreciation. For accounting, in particular, depreciation concerns allocating the cost of an asset over a period of time, usually its useful life. When a company purchases an asset, such as a piece of equipment, such large purchases can skewer the income statement confusingly. Instead of appearing as a sharp jump in the accounting books, this can be smoothed by expensing the asset over its useful life.\n\nWhile operating expenditures are tax-deductible during the year they are incurred, capital expenditures are not. Businesses may be able to use these two accounting categories to their advantage if they have particular challenges.\n\nAny smaller expenses that are incurred and used in a single accounting period cannot be depreciated. Instead these expenses are considered operating expenditures and can be taxed deducted in the same fiscal year when they were incurred. Typical expenses that cannot be depreciated include things like office supplies, rent and utilities, taxes, and labor expenses. Just about any major piece of tangible property as well as some intangible propertycan be depreciated over time. Examples of tangible property may include buildings, production machinery, computer and technology systems, transportation vehicles, and furniture. According to the Internal Revenue Service, businesses may also depreciate particular intangible assets like copyrights, computer software, and patents. And to calculate the annual depreciation rate, we need to divide one by the number of useful life." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9314696,"math_prob":0.93497896,"size":15844,"snap":"2022-27-2022-33","text_gpt3_token_len":3017,"char_repetition_ratio":0.19968434,"word_repetition_ratio":0.031126872,"special_character_ratio":0.18783136,"punctuation_ratio":0.096448466,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98975986,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T13:35:57Z\",\"WARC-Record-ID\":\"<urn:uuid:27a5dbc2-0ba4-47ba-bb53-6ad9a78b1ceb>\",\"Content-Length\":\"136227\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:acc3c894-f271-4e15-ae77-d5c75cab594d>\",\"WARC-Concurrent-To\":\"<urn:uuid:a565627c-ef72-4854-8e4c-44f8404b30bd>\",\"WARC-IP-Address\":\"104.21.25.133\",\"WARC-Target-URI\":\"https://simple-accounting.org/how-to-calculate-straight-line-depreciation/\",\"WARC-Payload-Digest\":\"sha1:IAHXFDRLLRGXHHU36LCSJWFOQQT4EC2O\",\"WARC-Block-Digest\":\"sha1:U7CAUM2BFOYGG3KI2FGUFPYMVOUVW3VH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103821173.44_warc_CC-MAIN-20220630122857-20220630152857-00185.warc.gz\"}"}
https://statsidea.com/a-easy-rationalization-of-numpy-axes-with-examples/	[ "# A Easy Rationalization of NumPy Axes (With Examples)\n\nMany purposes in NumPy require that you simply specify an axis alongside which to use a definite calculation.\n\nUsually refer to rule of thumb applies:\n\n• axis=0: Follow the calculation “column-wise”\n• axis=1: Follow the calculation “row-wise”\n\nPlease see symbol presentations a ocular illustration of the axes on a NumPy matrix with 2 rows and four columns:", null, "Please see examples display methods to importance the axis argument in numerous eventualities with refer to NumPy matrix:\n\n```import numpy as np\n\n#assemble NumPy matrix\nmy_matrix = np.matrix([[1, 4, 7, 8], [5, 10, 12, 14]])\n\n#view NumPy matrix\nmy_matrix\n\nmatrix([[ 1, 4, 7, 8],\n[ 5, 10, 12, 14]])\n```\n\n## Instance 1: In finding Cruel Alongside Other Axes\n\nWe will importance axis=0 to seek out the ruthless of every column within the NumPy matrix:\n\n```#to find ruthless of every column in matrix\nnp.ruthless(my_matrix, axis=0)\n\nmatrix([[ 3. , 7. , 9.5, 11. ]])\n```\n\nThe output presentations the ruthless worth of every column within the matrix.\n\nFor instance:\n\n• The ruthless worth of the primary column is (1 + 5) / 2 = 3.\n• The ruthless worth of the second one column is (4 + 10) / 2 = 7.\n\nAnd so forth.\n\nWe will additionally importance axis=1 to seek out the ruthless of every row within the matrix:\n\n```#to find ruthless of every row in matrix\nnp.ruthless(my_matrix, axis=1)\n\nmatrix([[ 5. ],\n[10.25]])```\n\nThe output presentations the ruthless worth of every row within the matrix.\n\nFor instance:\n\n• The ruthless worth within the first row is (1+4+7+8) / 4 = 5.\n• The ruthless worth in the second one row is (5+10+12+14) / 4 = 10.25.\n\n## Instance 2: In finding Sum Alongside Other Axes\n\nWe will importance axis=0 to seek out the sum of every column within the matrix:\n\n```#to find sum of every column in matrix\nnp.sum(my_matrix, axis=0)\n\nmatrix([[ 6, 14, 19, 22]])\n```\n\nThe output presentations the sum of every column within the matrix.\n\nFor instance:\n\n• The sum of the primary column is 1 + 5 = 6.\n• The sum of the second one column is 4 + 10 = 14.\n\nAnd so forth.\n\nWe will additionally importance axis=1 to seek out the sum of every row within the matrix:\n\n```#to find sum of every row in matrix\nnp.sum(my_matrix, axis=1)\n\nmatrix([,\n])```\n\nThe output presentations the sum of every row within the matrix.\n\nFor instance:\n\n• The sum of the primary row is 1+4+7+8 = 20.\n• The sum of the second one row is 5+10+12+14 = 41.\n\n## Extra Sources\n\nPlease see tutorials give an explanation for methods to carry out alternative regular operations in NumPy:\n\nThe best way to Build a NumPy Matrix with Random Numbers\nThe best way to Normalize a NumPy Matrix\nThe best way to Upload Row to Matrix in NumPy" ]	[ null, "https://www.statology.org/wp-content/uploads/2022/06/numpyaxis1.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7828539,"math_prob":0.9871077,"size":2581,"snap":"2023-40-2023-50","text_gpt3_token_len":705,"char_repetition_ratio":0.16841288,"word_repetition_ratio":0.31154683,"special_character_ratio":0.29639673,"punctuation_ratio":0.12825279,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99986804,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-01T10:08:23Z\",\"WARC-Record-ID\":\"<urn:uuid:098f5a46-148b-444e-989c-d5e86b0dddc9>\",\"Content-Length\":\"56589\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7bfe965a-da63-45de-8531-a4ca76079c5b>\",\"WARC-Concurrent-To\":\"<urn:uuid:ae50dcdf-8d46-4f5f-a893-0c50667b5257>\",\"WARC-IP-Address\":\"103.157.97.104\",\"WARC-Target-URI\":\"https://statsidea.com/a-easy-rationalization-of-numpy-axes-with-examples/\",\"WARC-Payload-Digest\":\"sha1:BKMZ3Y4IROAD2J7PN6O54HEQ2QQJLOIX\",\"WARC-Block-Digest\":\"sha1:XFINK3E63E5PIPMARECZFNCC2J7YGLJ2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100286.10_warc_CC-MAIN-20231201084429-20231201114429-00563.warc.gz\"}"}
https://easystats.github.io/insight/reference/is_gam_model.html	[ "Small helper that checks if a model is a generalized additive model.\n\n## Usage\n\nis_gam_model(x)\n\nx\n\nA model object.\n\n## Value\n\nA logical, TRUE if x is a generalized additive model and has smooth-terms\n\n## Note\n\nThis function only returns TRUE when the model inherits from a typical GAM model class and when smooth terms are present in the model formula. If model has no smooth terms or is not from a typical gam class, FALSE is returned.\n\n## Examples\n\nif (require(\"mgcv\")) {\ndata(iris)\nmodel1 <- lm(Petal.Length ~ Petal.Width + Sepal.Length, data = iris)\nmodel2 <- gam(Petal.Length ~ Petal.Width + s(Sepal.Length), data = iris)\nis_gam_model(model1)\nis_gam_model(model2)\n}\n#> TRUE" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8585175,"math_prob":0.99219364,"size":390,"snap":"2022-27-2022-33","text_gpt3_token_len":89,"char_repetition_ratio":0.1373057,"word_repetition_ratio":0.09677419,"special_character_ratio":0.1974359,"punctuation_ratio":0.09210526,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9941738,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-13T09:15:54Z\",\"WARC-Record-ID\":\"<urn:uuid:1ecf75cb-ec42-448a-83c9-6b273cdb2c8b>\",\"Content-Length\":\"13747\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7122db3a-f760-49a5-864c-b1c00c1b16dd>\",\"WARC-Concurrent-To\":\"<urn:uuid:c02ba756-c610-49cf-af00-43e93a6f3afb>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"https://easystats.github.io/insight/reference/is_gam_model.html\",\"WARC-Payload-Digest\":\"sha1:XRGPCUQX5DVNMCMQ7T3PJBDPMFCSPEGA\",\"WARC-Block-Digest\":\"sha1:GD4ORPR53Z4EFYLRNMTAQWKIYV222FFN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571911.5_warc_CC-MAIN-20220813081639-20220813111639-00503.warc.gz\"}"}
https://www.electronics-tutorial.net/lab-test-and-measurement/Circuit-simulation-and-Tools/exp-3/	[ "EXPERIMENT NO.3\n\nTITLE: COMPUTE AUTO CORRELATION AND CROSS CORRELATION OF TWO SEQUENCES\n\nTHEORY:-\n\nAuto-correlation:-\n\nCorrelation is a mathematical tool used frequently in signal processing for analyzing function or series of values such as time domain signals correlation is mutual relationship between two or more random variables. Auto-correlation is correlation of signal with itself. This is unlike of two different signals.\n\nAuto-correlation is useful for finding repeating patterns in a signal such as determining presence of periodic signal which has been buried under noise or identifying fundamental frequency of signal which doesnâ€™t actually contains that frequency components but implies it with many harmonic frequency.\n\nDifferent definitions of auto-correlation are in us depending on field of study which is being considered and not all of them are equivalent. In some fields the term is used interchangeability with auto covariance.\n\nIn signal processing given signal f(t), the continues auto-correlation Rf(t) is the continues cross-correlation of f(t) with itself.\n\nThe auto-correlation of a periodic function is itself periodic with the very same period.\n\nThe auto-correlation of sum of two completely uncorrelated functions is the sum of auto-correlation each function separately.\n\nSince auto-correlation is specific type of cross-correlation, it maintains all properties of cross-correlation.\n\nThe auto-correlation of a white noise signal will have strong peak at t=0 & will be close for all other T. This shows that a sampled instance of white noise signal is not statically correlated to sampled instance of same white noise signal at another time.\n\nThe Wiener-khinchin theorem relates the auto-correlation function to power spectral density via Fourier transform.\n\nCross-correlation:-\n\nIn signal processing cross-correlation is a measure of similarities of two waveforms as function of time lag applied to one of them. This is also known as a sliding dot product or inner product. It is commonly used for searching a long duration signal for a shorter known feature. It also has applications in pattern recognition, single practical analysis & neurophysiology.\n\nThe cross-correlation is similar in nature to convolution of two functions. Whereas convolution involves reversing signal & then shifting it & multiplying by another signal, correlation only involves shifting it & multiplying (no reversing).\n\nIn an auto-correlation, which is the cross-correlation of signal with itself, there will always be a peak at lag of zero.\n\nIf x & y are two independent random variables with probability distribution f & q respectively, then probability distribution of difference y - x is given by cross-correlation f * q . In contrast the convolution f q gives probability distribution of the sum x + y.\n\nIn probability theorems & statistics the term cross-correlation us also sometimes used to referred to the convenience conv(x,y) between two random variables x & y in order to distinguish that concept from â€œCovarianceâ€ of a random variable x, which is understood to be matrix of covariance between the scalar components of x.\n\nProperties:-\n\nThe cross-correlation of function f(t) & g(t) is equivalent to the convolution of f(-t) & g(t)\n\ni.e.fg=(t ->f(-t))g\n\nIf either for g is hermitical then:\n\nF g= f * g\n\n(f * g) * (f * g) = (f * f) * (g * g)\n\nAnalysis to convolution theorem\n\nThe cross-correlation satisfies,\n\nF{ f * g} = ( F {f} )* F{g} ,\n\nWhere F denotes Fourier transform & an asterisk again indicates complex conjugates coupled with fast Fourier transform algorithms, this property is often explained for the efficiency numerical computation of cross-correlation.\n\nThe cross-correlation is related to the spectral density.\n\nThe cross-correlation of a convolution of f & h with function g is convolution of the correlation of f & g with kernel h:\n\n(f * h) * g = h -> * (f * g)\n\nMATLAB CODE\n\nAuto and Cross Correlation\n\ndisp('autocorrelation and crosscorelation of sequences');\n\ndisp('4 autocorrelation 5 crosscorelation');\n\nchoice=input('enter the choice of corelation=');\n\nswitch(choice)\n\ncase{4}\n\nx=input('enter the input seqence for auto,x=');\n\ny=fliplr(x);\n\nr=conv(x,y);\n\nsubplot(3,1,1);\n\nstem(x);\n\nsubplot(3,1,2);\n\nstem(y);\n\nsubplot(3,1,3);\n\nstem(r);\n\nxlabel('input bit sequence');\n\nylabel('amplitude');\n\ntitle('autocorrelation');\n\ncase{5}\n\nd=input('enter input sequence for cross,d=');\n\ny=input('enter input sequence for cross,y=');\n\nz=conv(d,y);\n\nsubplot(4,1,1);\n\nstem(d);\n\nsubplot(4,1,2);\n\nstem(y);\n\nsubplot(4,1,3);\n\nstem(z);\n\nxlabel('input bit sequence');\n\nylabel('amplitude');\n\ntitle('crosscorelation');\n\nend;\n\nOUTPUT:-\n\nautocorrelation and crosscorelation of sequences\n\n4 autocorrelation 5 crosscorelation\n\nenter the choice of corelation=5\n\nenter input sequence for cross,d=[7 8 9]\n\nenter input sequence for cross,y=[4 5 6]", null, "CONCLUSION" ]	[ null, "https://www.electronics-tutorial.net/lab-test-and-measurement/Circuit-simulation-and-Tools/exp-3/clip_image002.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84213936,"math_prob":0.9839918,"size":4811,"snap":"2021-04-2021-17","text_gpt3_token_len":1080,"char_repetition_ratio":0.18826711,"word_repetition_ratio":0.0,"special_character_ratio":0.22115985,"punctuation_ratio":0.10844749,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983651,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-26T05:18:20Z\",\"WARC-Record-ID\":\"<urn:uuid:78caefa8-2cd3-494e-bd06-b842dd9c97aa>\",\"Content-Length\":\"121976\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2dd89e83-c898-4ddc-87e9-e38c52414820>\",\"WARC-Concurrent-To\":\"<urn:uuid:12ba5a23-90be-49ec-a02e-b8e3454ed012>\",\"WARC-IP-Address\":\"104.21.96.155\",\"WARC-Target-URI\":\"https://www.electronics-tutorial.net/lab-test-and-measurement/Circuit-simulation-and-Tools/exp-3/\",\"WARC-Payload-Digest\":\"sha1:KMBWGPZGL32CTNZBJLMYDRSZGH5AASCC\",\"WARC-Block-Digest\":\"sha1:43DGMAHMXHJ7JTEZXUIP67BEJSGO65GW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610704798089.76_warc_CC-MAIN-20210126042704-20210126072704-00505.warc.gz\"}"}
https://questions.llc/questions/1112138/if-x-represents-the-present-age-of-father-and-y-represents-the-present-age-of-son-then	[ "# if x represents the present age of father and y represents the present age of son,then what will be the equation of the statement \"present age of father is 5 times more than 6 times the age of son\"\n\n1. 👍\n2. 👎\n3. 👁\n4. ℹ️\n5. 🚩\n1. present age of father = x\n6 times the age of son = 6y\nso, we have\n\nx = 6y+5y\n\nI suspect you meant\n\nfive more than\n\nIf so, x=6y+5\n\nIf you meant\n\nfive times as much as, then x=5*6y\n\n1. 👍\n2. 👎\n3. ℹ️\n4. 🚩\n2. Blah\n\n1. 👍\n2. 👎\n3. ℹ️\n4. 🚩" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84706485,"math_prob":0.9980777,"size":379,"snap":"2022-27-2022-33","text_gpt3_token_len":130,"char_repetition_ratio":0.168,"word_repetition_ratio":0.15662651,"special_character_ratio":0.28759894,"punctuation_ratio":0.045454547,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.989816,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-13T00:38:55Z\",\"WARC-Record-ID\":\"<urn:uuid:e216c507-2c2f-4316-a853-e73117ad39b5>\",\"Content-Length\":\"16191\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1682238e-d0b9-4726-a05c-7b29afa4b8f0>\",\"WARC-Concurrent-To\":\"<urn:uuid:5cdebf2f-0e7b-4422-b90a-6fdb65528a10>\",\"WARC-IP-Address\":\"66.228.55.50\",\"WARC-Target-URI\":\"https://questions.llc/questions/1112138/if-x-represents-the-present-age-of-father-and-y-represents-the-present-age-of-son-then\",\"WARC-Payload-Digest\":\"sha1:OB6URO6HZ7WGVW7U47EMDN4AUKH6543E\",\"WARC-Block-Digest\":\"sha1:DLO27BU25OQIJD3TVTJGGMXIZ4NVCWTY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571847.45_warc_CC-MAIN-20220812230927-20220813020927-00295.warc.gz\"}"}
https://number.academy/36368	[ "# Number 36368\n\nNumber 36,368 spell 🔊, write in words: thirty-six thousand, three hundred and sixty-eight . Ordinal number 36368th is said 🔊 and write: thirty-six thousand, three hundred and sixty-eighth. The meaning of number 36368 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 36368. What is 36368 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 36368.\n\n## What is 36,368 in other units\n\nThe decimal (Arabic) number 36368 converted to a Roman number is (X)(X)(X)(V)MCCCLXVIII. Roman and decimal number conversions.\n\n#### Weight conversion\n\n36368 kilograms (kg) = 80176.9 pounds (lbs)\n36368 pounds (lbs) = 16496.4 kilograms (kg)\n\n#### Length conversion\n\n36368 kilometers (km) equals to 22599 miles (mi).\n36368 miles (mi) equals to 58529 kilometers (km).\n36368 meters (m) equals to 119317 feet (ft).\n36368 feet (ft) equals 11086 meters (m).\n36368 centimeters (cm) equals to 14318.1 inches (in).\n36368 inches (in) equals to 92374.7 centimeters (cm).\n\n#### Temperature conversion\n\n36368° Fahrenheit (°F) equals to 20186.7° Celsius (°C)\n36368° Celsius (°C) equals to 65494.4° Fahrenheit (°F)\n\n#### Time conversion\n\n(hours, minutes, seconds, days, weeks)\n36368 seconds equals to 10 hours, 6 minutes, 8 seconds\n36368 minutes equals to 3 weeks, 4 days, 6 hours, 8 minutes\n\n### Codes and images of the number 36368\n\nNumber 36368 morse code: ...-- -.... ...-- -.... ---..\nSign language for number 36368:", null, "", null, "", null, "", null, "", null, "Number 36368 in braille:", null, "Images of the number\nImage (1) of the numberImage (2) of the number", null, "", null, "More images, other sizes, codes and colors ...\n\n#### Number 36368 infographic", null, "## Share in social networks", null, "## Mathematics of no. 36368\n\n### Multiplications\n\n#### Multiplication table of 36368\n\n36368 multiplied by two equals 72736 (36368 x 2 = 72736).\n36368 multiplied by three equals 109104 (36368 x 3 = 109104).\n36368 multiplied by four equals 145472 (36368 x 4 = 145472).\n36368 multiplied by five equals 181840 (36368 x 5 = 181840).\n36368 multiplied by six equals 218208 (36368 x 6 = 218208).\n36368 multiplied by seven equals 254576 (36368 x 7 = 254576).\n36368 multiplied by eight equals 290944 (36368 x 8 = 290944).\n36368 multiplied by nine equals 327312 (36368 x 9 = 327312).\nshow multiplications by 6, 7, 8, 9 ...\n\n### Fractions: decimal fraction and common fraction\n\n#### Fraction table of 36368\n\nHalf of 36368 is 18184 (36368 / 2 = 18184).\nOne third of 36368 is 12122,6667 (36368 / 3 = 12122,6667 = 12122 2/3).\nOne quarter of 36368 is 9092 (36368 / 4 = 9092).\nOne fifth of 36368 is 7273,6 (36368 / 5 = 7273,6 = 7273 3/5).\nOne sixth of 36368 is 6061,3333 (36368 / 6 = 6061,3333 = 6061 1/3).\nOne seventh of 36368 is 5195,4286 (36368 / 7 = 5195,4286 = 5195 3/7).\nOne eighth of 36368 is 4546 (36368 / 8 = 4546).\nOne ninth of 36368 is 4040,8889 (36368 / 9 = 4040,8889 = 4040 8/9).\nshow fractions by 6, 7, 8, 9 ...\n\n### Calculator\n\n 36368\n\n#### Is Prime?\n\nThe number 36368 is not a prime number. The closest prime numbers are 36353, 36373.\n\n#### Factorization and factors (dividers)\n\nThe prime factors of 36368 are 2 * 2 * 2 * 2 * 2273\nThe factors of 36368 are 1 , 2 , 4 , 8 , 16 , 2273 , 4546 , 9092 , 18184 , 36368\nTotal factors 10.\nSum of factors 70494 (34126).\n\n#### Powers\n\nThe second power of 363682 is 1.322.631.424.\nThe third power of 363683 is 48.101.459.628.032.\n\n#### Roots\n\nThe square root √36368 is 190,703959.\nThe cube root of 336368 is 33,131401.\n\n#### Logarithms\n\nThe natural logarithm of No. ln 36368 = loge 36368 = 10,501445.\nThe logarithm to base 10 of No. log10 36368 = 4,560719.\nThe Napierian logarithm of No. log1/e 36368 = -10,501445.\n\n### Trigonometric functions\n\nThe cosine of 36368 is 0,603078.\nThe sine of 36368 is 0,797682.\nThe tangent of 36368 is 1,322685.\n\n### Properties of the number 36368\n\nIs a Friedman number: No\nIs a Fibonacci number: No\nIs a Bell number: No\nIs a palindromic number: No\nIs a pentagonal number: No\nIs a perfect number: No\n\n## Number 36368 in Computer Science\n\nCode typeCode value\n36368 Number of bytes35.5KB\nUnix timeUnix time 36368 is equal to Thursday Jan. 1, 1970, 10:06:08 a.m. GMT\nIPv4, IPv6Number 36368 internet address in dotted format v4 0.0.142.16, v6 ::8e10\n36368 Decimal = 1000111000010000 Binary\n36368 Decimal = 1211212222 Ternary\n36368 Decimal = 107020 Octal\n36368 Decimal = 8E10 Hexadecimal (0x8e10 hex)\n36368 BASE64MzYzNjg=\n36368 MD5e60af3c102de8282382170efa4972471\n36368 SHA1b18fae2c5b80cbb9166979e9291170a91810486a\n36368 SHA224f91354585218076a29cb628e08af020f732097d8b4e674dcfc85b1c7\n36368 SHA2567f67a5f99444c06499cfd205c1d251d1a92fb701c16f16c86d8c530d79939644\n36368 SHA384a1468a17b66ca76abc99b02cb87abd2f0f4bd49a978b3b75a16370a5cc70a5b20351f9f404d90af323c9d8075a8249bd\nMore SHA codes related to the number 36368 ...\n\nIf you know something interesting about the 36368 number that you did not find on this page, do not hesitate to write us here.\n\n## Numerology 36368\n\n### Character frequency in number 36368\n\nCharacter (importance) frequency for numerology.\n Character: Frequency: 3 2 6 2 8 1\n\n### Classical numerology\n\nAccording to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 36368, the numbers 3+6+3+6+8 = 2+6 = 8 are added and the meaning of the number 8 is sought.\n\n## Interesting facts about the number 36368\n\n### Asteroids\n\n• (36368) 2000 OG12 is asteroid number 36368. It was discovered by LINEAR, Lincoln Near-Earth Asteroid Research from Lincoln Laboratory, Socorro on 7/23/2000.\n\n## Number 36,368 in other languages\n\nHow to say or write the number thirty-six thousand, three hundred and sixty-eight in Spanish, German, French and other languages. The character used as the thousands separator.\n Spanish: 🔊 (número 36.368) treinta y seis mil trescientos sesenta y ocho German: 🔊 (Anzahl 36.368) sechsunddreißigtausenddreihundertachtundsechzig French: 🔊 (nombre 36 368) trente-six mille trois cent soixante-huit Portuguese: 🔊 (número 36 368) trinta e seis mil, trezentos e sessenta e oito Chinese: 🔊 (数 36 368) 三万六千三百六十八 Arabian: 🔊 (عدد 36,368) ستة و ثلاثون ألفاً و ثلاثمائةثمانية و ستون Czech: 🔊 (číslo 36 368) třicet šest tisíc třista šedesát osm Korean: 🔊 (번호 36,368) 삼만 육천삼백육십팔 Danish: 🔊 (nummer 36 368) seksogtredivetusinde og trehundrede og otteogtreds Dutch: 🔊 (nummer 36 368) zesendertigduizenddriehonderdachtenzestig Japanese: 🔊 (数 36,368) 三万六千三百六十八 Indonesian: 🔊 (jumlah 36.368) tiga puluh enam ribu tiga ratus enam puluh delapan Italian: 🔊 (numero 36 368) trentaseimilatrecentosessantotto Norwegian: 🔊 (nummer 36 368) tretti-seks tusen, tre hundre og seksti-åtte Polish: 🔊 (liczba 36 368) trzydzieści sześć tysięcy trzysta sześćdziesiąt osiem Russian: 🔊 (номер 36 368) тридцать шесть тысяч триста шестьдесят восемь Turkish: 🔊 (numara 36,368) otuzaltıbinüçyüzaltmışsekiz Thai: 🔊 (จำนวน 36 368) สามหมื่นหกพันสามร้อยหกสิบแปด Ukrainian: 🔊 (номер 36 368) тридцять шiсть тисяч триста шiстдесят вiсiм Vietnamese: 🔊 (con số 36.368) ba mươi sáu nghìn ba trăm sáu mươi tám Other languages ...\n\n## News to email\n\nPrivacy Policy.\n\n## Comment\n\nIf you know something interesting about the number 36368 or any natural number (positive integer) please write us here or on facebook." ]	[ null, "https://numero.wiki/s/senas/lenguaje-de-senas-numero-3.png", null, "https://numero.wiki/s/senas/lenguaje-de-senas-numero-6.png", null, "https://numero.wiki/s/senas/lenguaje-de-senas-numero-3.png", null, "https://numero.wiki/s/senas/lenguaje-de-senas-numero-6.png", null, "https://numero.wiki/s/senas/lenguaje-de-senas-numero-8.png", null, "https://number.academy/img/braille-36368.svg", null, "https://numero.wiki/img/a-36368.jpg", null, "https://numero.wiki/img/b-36368.jpg", null, "https://number.academy/i/infographics/8/number-36368-infographic.png", null, "https://numero.wiki/s/share-desktop.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.54982567,"math_prob":0.9752393,"size":6927,"snap":"2022-05-2022-21","text_gpt3_token_len":2568,"char_repetition_ratio":0.15051278,"word_repetition_ratio":0.009225092,"special_character_ratio":0.41504258,"punctuation_ratio":0.16367888,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99132586,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,1,null,1,null,1,null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-26T10:16:20Z\",\"WARC-Record-ID\":\"<urn:uuid:fbbadadf-66f8-412a-9cc1-57592858cd9a>\",\"Content-Length\":\"40507\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e51e3692-48e5-4154-92c6-13a42fdc7ccd>\",\"WARC-Concurrent-To\":\"<urn:uuid:c95ff862-110e-4208-8b51-65354e96e138>\",\"WARC-IP-Address\":\"162.0.227.212\",\"WARC-Target-URI\":\"https://number.academy/36368\",\"WARC-Payload-Digest\":\"sha1:ENGUBFXP6GTOROVTWJ7UQVU2YTKZT67Z\",\"WARC-Block-Digest\":\"sha1:HE5OQHG3ZETZDDTPQHRUQNOGIN3Q44JT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662604794.68_warc_CC-MAIN-20220526100301-20220526130301-00730.warc.gz\"}"}
https://www.colorhexa.com/0354e7	[ "# #0354e7 Color Information\n\nIn a RGB color space, hex #0354e7 is composed of 1.2% red, 32.9% green and 90.6% blue. Whereas in a CMYK color space, it is composed of 98.7% cyan, 63.6% magenta, 0% yellow and 9.4% black. It has a hue angle of 218.7 degrees, a saturation of 97.4% and a lightness of 45.9%. #0354e7 color hex could be obtained by blending #06a8ff with #0000cf. Closest websafe color is: #0066ff.\n\n• R 1\n• G 33\n• B 91\nRGB color chart\n• C 99\n• M 64\n• Y 0\n• K 9\nCMYK color chart\n\n#0354e7 color description : Vivid blue.\n\n# #0354e7 Color Conversion\n\nThe hexadecimal color #0354e7 has RGB values of R:3, G:84, B:231 and CMYK values of C:0.99, M:0.64, Y:0, K:0.09. Its decimal value is 218343.\n\nHex triplet RGB Decimal 0354e7 `#0354e7` 3, 84, 231 `rgb(3,84,231)` 1.2, 32.9, 90.6 `rgb(1.2%,32.9%,90.6%)` 99, 64, 0, 9 218.7°, 97.4, 45.9 `hsl(218.7,97.4%,45.9%)` 218.7°, 98.7, 90.6 0066ff `#0066ff`\nCIE-LAB 41.419, 37.648, -79.195 17.629, 12.128, 77.009 0.165, 0.114, 12.128 41.419, 87.688, 295.426 41.419, -18.346, -115.676 34.825, 29.413, -106.729 00000011, 01010100, 11100111\n\n# Color Schemes with #0354e7\n\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #e79603\n``#e79603` `rgb(231,150,3)``\nComplementary Color\n• #03c6e7\n``#03c6e7` `rgb(3,198,231)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #2403e7\n``#2403e7` `rgb(36,3,231)``\nAnalogous Color\n• #c6e703\n``#c6e703` `rgb(198,231,3)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #e72403\n``#e72403` `rgb(231,36,3)``\nSplit Complementary Color\n• #54e703\n``#54e703` `rgb(84,231,3)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #e70354\n``#e70354` `rgb(231,3,84)``\n• #03e796\n``#03e796` `rgb(3,231,150)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #e70354\n``#e70354` `rgb(231,3,84)``\n• #e79603\n``#e79603` `rgb(231,150,3)``\n• #02399b\n``#02399b` `rgb(2,57,155)``\n• #0242b5\n``#0242b5` `rgb(2,66,181)``\n• #034bce\n``#034bce` `rgb(3,75,206)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #085efc\n``#085efc` `rgb(8,94,252)``\n• #216ffc\n``#216ffc` `rgb(33,111,252)``\n• #3a7ffc\n``#3a7ffc` `rgb(58,127,252)``\nMonochromatic Color\n\n# Alternatives to #0354e7\n\nBelow, you can see some colors close to #0354e7. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #038de7\n``#038de7` `rgb(3,141,231)``\n• #037ae7\n``#037ae7` `rgb(3,122,231)``\n• #0367e7\n``#0367e7` `rgb(3,103,231)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #0341e7\n``#0341e7` `rgb(3,65,231)``\n• #032ee7\n``#032ee7` `rgb(3,46,231)``\n• #031be7\n``#031be7` `rgb(3,27,231)``\nSimilar Colors\n\n# #0354e7 Preview\n\nText with hexadecimal color #0354e7\n\nThis text has a font color of #0354e7.\n\n``<span style=\"color:#0354e7;\">Text here</span>``\n#0354e7 background color\n\nThis paragraph has a background color of #0354e7.\n\n``<p style=\"background-color:#0354e7;\">Content here</p>``\n#0354e7 border color\n\nThis element has a border color of #0354e7.\n\n``<div style=\"border:1px solid #0354e7;\">Content here</div>``\nCSS codes\n``.text {color:#0354e7;}``\n``.background {background-color:#0354e7;}``\n``.border {border:1px solid #0354e7;}``\n\n# Shades and Tints of #0354e7\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, #000712 is the darkest color, while #fefeff is the lightest one.\n\n• #000712\n``#000712` `rgb(0,7,18)``\n• #000e25\n``#000e25` `rgb(0,14,37)``\n• #011539\n``#011539` `rgb(1,21,57)``\n• #011c4c\n``#011c4c` `rgb(1,28,76)``\n• #01235f\n``#01235f` `rgb(1,35,95)``\n• #012a73\n``#012a73` `rgb(1,42,115)``\n• #023186\n``#023186` `rgb(2,49,134)``\n• #02389a\n``#02389a` `rgb(2,56,154)``\n``#023fad` `rgb(2,63,173)``\n• #0246c0\n``#0246c0` `rgb(2,70,192)``\n• #034dd4\n``#034dd4` `rgb(3,77,212)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\n• #035bfa\n``#035bfa` `rgb(3,91,250)``\n• #1567fc\n``#1567fc` `rgb(21,103,252)``\n• #2974fc\n``#2974fc` `rgb(41,116,252)``\n• #3c80fc\n``#3c80fc` `rgb(60,128,252)``\n• #4f8dfd\n``#4f8dfd` `rgb(79,141,253)``\n• #639afd\n``#639afd` `rgb(99,154,253)``\n• #76a6fd\n``#76a6fd` `rgb(118,166,253)``\n• #89b3fd\n``#89b3fd` `rgb(137,179,253)``\n• #9dbffe\n``#9dbffe` `rgb(157,191,254)``\n• #b0ccfe\n``#b0ccfe` `rgb(176,204,254)``\n• #c4d8fe\n``#c4d8fe` `rgb(196,216,254)``\n• #d7e5fe\n``#d7e5fe` `rgb(215,229,254)``\n• #eaf2ff\n``#eaf2ff` `rgb(234,242,255)``\n• #fefeff\n``#fefeff` `rgb(254,254,255)``\nTint Color Variation\n\n# Tones of #0354e7\n\nA tone is produced by adding gray to any pure hue. In this case, #6f737b is the less saturated color, while #0354e7 is the most saturated one.\n\n• #6f737b\n``#6f737b` `rgb(111,115,123)``\n• #667184\n``#667184` `rgb(102,113,132)``\n• #5d6e8d\n``#5d6e8d` `rgb(93,110,141)``\n• #546b96\n``#546b96` `rgb(84,107,150)``\n• #4b699f\n``#4b699f` `rgb(75,105,159)``\n• #4266a8\n``#4266a8` `rgb(66,102,168)``\n• #3964b1\n``#3964b1` `rgb(57,100,177)``\n• #3061ba\n``#3061ba` `rgb(48,97,186)``\n• #275ec3\n``#275ec3` `rgb(39,94,195)``\n• #1e5ccc\n``#1e5ccc` `rgb(30,92,204)``\n• #1559d5\n``#1559d5` `rgb(21,89,213)``\n• #0c57de\n``#0c57de` `rgb(12,87,222)``\n• #0354e7\n``#0354e7` `rgb(3,84,231)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #0354e7 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.51808107,"math_prob":0.70368654,"size":3682,"snap":"2019-13-2019-22","text_gpt3_token_len":1653,"char_repetition_ratio":0.12833062,"word_repetition_ratio":0.011111111,"special_character_ratio":0.5602933,"punctuation_ratio":0.23809524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9931504,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T13:29:45Z\",\"WARC-Record-ID\":\"<urn:uuid:cc605ce5-84af-4185-808f-5b27809125c6>\",\"Content-Length\":\"36375\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:08303f1f-5a22-4496-b951-2eb1adad0eea>\",\"WARC-Concurrent-To\":\"<urn:uuid:327a6b5c-6052-43ed-92c6-505918b57c55>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/0354e7\",\"WARC-Payload-Digest\":\"sha1:W7UTMKGZRGXW4QLSKRS75TT3QPHPIW6K\",\"WARC-Block-Digest\":\"sha1:4DHO2BQZV7652E6PKT3J6SAB4DIPPSB7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202525.25_warc_CC-MAIN-20190321132523-20190321154523-00014.warc.gz\"}"}
https://stats.stackexchange.com/questions/30002/mad-equivalent-for-standard-error	[ "# MAD equivalent for standard error\n\nAs far as I know, one can calculate the relative standard error from the standard deviation of a data sample. I am looking for the Median Absolute Deviation equivalent for standard error.\n\nDoes one exist? Also which methods exist to calculate the relative standard error, that do not require the standard deviation?\n\n• What properties do you want of a \"standard error\" (of the mean, presumably) that is a \"MAD equivalent\"? – whuber Jun 7 '12 at 16:53\n• What do you mean by equivalent? Are you looking for a formula that applies generally for distributions that relates MAD to se? – Michael R. Chernick Jun 7 '12 at 16:54\n• The goal is to find the statistical significance of a certain metric. Lots of data is involved, so best to come up with an efficient method. I started looking into MAD, because of possible outliers due to data problems ... – Navi Jun 7 '12 at 20:25\n\nWhen you say standard error, you should be talking about the standard error of something, such as the standard error of the sample mean.\n\nSimilarly you could for example talk about the median absolute deviation of the sample median. It is possible to calculate this, at least as an approximation for large samples.\n\nIt is well known that for a continuous random variable with population median $m$, continuous probability density of the median $f(m)$ and a large odd sample size $n$, the sample median is approximately normally distributed with median $m$ and variance $\\frac{1}{4 n f(m)^2}$, i.e. with median absolute deviation approximately $\\dfrac{\\Phi^{-1}\\left(\\frac34 \\right)}{2 \\sqrt{n} f(m)}$ where $\\frac{\\Phi^{-1}\\left(\\frac34 \\right)}{2} \\approx 0.337$.\n\nIf you want to have this as a relative median absolute deviation of the sample median, then presumably you divide by $m$.\n\n• Did you notice that \"MAD\" is a median absolute deviation? It is used as a robust statistic. Its utility in the role of a putative SE is something to be doubted because it does not enjoy the asymptotic properties of a standard error, nor does it have a comparable interpretation. – whuber Jun 7 '12 at 20:04\n• @whuber: I had typed mean absolute deviation when I meant median absolute deviation. The median absolute deviation of the sample median has the asymptotic property of being roughly proportional to $\\frac{1}{\\sqrt{n}}$, similar to the standard error of the sample mean. – Henry Jun 8 '12 at 6:22\n• @whuber: For large samples the absolute difference between the population median and the sample median has a roughly 95% chance of being less than 2.906 times the expression I gave, similar to the 1.96 property of the standard error. – Henry Jun 8 '12 at 6:30\n• @whuber: though I accept the point that the median absolute deviation of the sample median depends on the underlying population distribution near the median, and this may not be so immediately easy to estimate from the sample. – Henry Jun 8 '12 at 8:17\n• Thanks for the extended analysis--clear and to the point. (+1) – whuber Jun 8 '12 at 12:29\n\nAn alternative approach is to look at the quantiles of the the sample: order the observations so $x_1 \\le x_2 \\le x_3 \\le \\cdots \\le x_n$ and (for reasonably large samples from a continuous distribution) there is a 95% probability that the interval $$\\left[x_{\\frac{n}{2} - 0.98 \\sqrt{n}}, x_{\\frac{n}{2} + 0.98 \\sqrt{n}}\\right]$$ contains the population median.\n\nClearly ${\\frac{n}{2} \\pm 0.98 \\sqrt{n}}$ may not be an integer: you can round outwards to be conservative or use one of the many possibilities for interpolating quantiles: you are now looking for $Q_p$ where $p = {\\frac{1}{2} \\pm 0.98 /\\sqrt{n}}$.\n\nAgain for relative, you can divide by the median." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9200064,"math_prob":0.9888264,"size":884,"snap":"2020-34-2020-40","text_gpt3_token_len":205,"char_repetition_ratio":0.1534091,"word_repetition_ratio":0.031007752,"special_character_ratio":0.25339368,"punctuation_ratio":0.08982036,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99846065,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-15T17:37:54Z\",\"WARC-Record-ID\":\"<urn:uuid:f963b4db-e00a-4084-aa53-4a81c6f5ad79>\",\"Content-Length\":\"161863\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a4c121d9-b430-487d-91c2-0a3107bfaf49>\",\"WARC-Concurrent-To\":\"<urn:uuid:84c69a3c-f10a-4490-9461-55b7746b00d3>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://stats.stackexchange.com/questions/30002/mad-equivalent-for-standard-error\",\"WARC-Payload-Digest\":\"sha1:WP6LU4PRDFLOEADOGI7VKAFQPAWNKZHO\",\"WARC-Block-Digest\":\"sha1:MYLVDMNRBTW3FTNVUHUOXZNRT5LNMIPK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439740929.65_warc_CC-MAIN-20200815154632-20200815184632-00046.warc.gz\"}"}
https://web2.0calc.com/questions/algebra_25180	[ "+0\n\n# Algebra\n\n0\n232\n1\n\n(a) Let f : R -> R be defined by f(x) = x^2. Show that f(x) has no inverse function.\n\n(b) Let g : (0,inf) -> R be defined by g(x) = x^2. Show that g(x) has an inverse function.\n\nJun 18, 2021\n\n#1\n+2\n\nA function does not have an inverse function when 2 different x values can produce the same y value.\n\nf(-3) = 9\n\nf(3) = 9\n\nSo if we were to inverse it, f(9) could be 3 or -3, making it not a function.\n\nThink about why g(x) has an inverese.\n\nCan 2 different x in the domain produce the same y?\n\n=^._.^=\n\nJun 18, 2021" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.878146,"math_prob":0.9991652,"size":471,"snap":"2022-40-2023-06","text_gpt3_token_len":155,"char_repetition_ratio":0.15203427,"word_repetition_ratio":0.020408163,"special_character_ratio":0.35456476,"punctuation_ratio":0.125,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9969737,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T18:11:57Z\",\"WARC-Record-ID\":\"<urn:uuid:2e9092cc-e8b2-439f-ba3c-dfa0cbf01e32>\",\"Content-Length\":\"20354\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1ffb70a4-555b-401a-8992-b829e1544ade>\",\"WARC-Concurrent-To\":\"<urn:uuid:8b6ef7f5-195a-4c52-a6db-4bbadc758630>\",\"WARC-IP-Address\":\"49.12.23.161\",\"WARC-Target-URI\":\"https://web2.0calc.com/questions/algebra_25180\",\"WARC-Payload-Digest\":\"sha1:A7FKUCHTC4UXSHDVZGFBINKPFVMESGHH\",\"WARC-Block-Digest\":\"sha1:WQFBHILZCKTLGSKYLLPZKFRCMYOLT5EA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337853.66_warc_CC-MAIN-20221006155805-20221006185805-00246.warc.gz\"}"}
https://www.tutorialsteacher.com/python/getattr-method	[ "# Python getattr() Method\n\nThe `getattr()` method returns the value of the attribute of an object. If the named attribute does not exist, default is returned if provided, otherwise `AttributeError` is raised.\n\n### Syntax:\n\n``getattr(object, name, default)``\n\n#### Parameters:\n\n1. object: An object of the class whose attribute value needs to be returned.\n2. name: The string name of the attribute.\n3. default. (Optional) A value to be returned if the attribute is not found.\n\n#### Return Value:\n\n• Returns value of the attribute of the given object.\n• If the default value not specified, then throws `AttributeError`.\n\nThe following example demonstrates the `getattr()` method.\n\nExample: getattr()\n``````class student:\nname = 'John'\nage = 18\n\nstd = student() # creating object\n\nprint('student name is ', getattr(std, 'name'))\n\nstd.name = 'Bill' # updating value\nprint('student name changed to ', getattr(std, 'name'))\n``````\nOutput\n``````student name is John\nstudent name changed to Bill\n``````\n\nAbove, `getattr(std, 'name')` returns the value of the `name` property of the `std` object, which is `John`. It always returns the latest value even after updating a property value.\n\nIf the attribute specified in the argument is not found, an `AttributeError` exception is thrown.\n\nExample: getattr()\n``````class student:\nname = 'John'\nage = '18'\n\nstd = student()\nattr = getattr(std, 'subject')\n``````\nOutput\n``````Traceback (most recent call last):\nattr = getattr(std, 'subject')\nAttributeError: type object 'student' has no attribute 'subject'\n``````\n\nThe default parameter can be passed to avoid the above error, which returns the default value if the attribute is not found.\n\nExample: getattr()\n``````class student:\nname = 'John'\nage = '18'\n\nstd = student()\nsubject = getattr(std, 'subject', 'Not supported')\nprint(\"student's subject: \", subject)\n``````\nOutput\n``````student's subject: Not supported\n``````\n\nInstead of `getattr()` method, the `.` operator can also be used to access the attribute value if you are sure that an object has that attribute.\n\nExample: getattr()\n``````class student:\nname = 'John'\nage = '18'\n\nstd = student()\nprint('student name is ', std.name)\n``````\nOutput\n``````student name is John\n``````\n\nThe following get's the method of the built-in list object.\n\nExample: getattr()\n``````nums= [1, 2, 3, 4, 5]\nrev = getattr(nums, 'reverse')\nrev()\nprint(nums)\n``````\nOutput\n``````[5, 4, 3, 2, 1]\n``````\nWant to check how much you know Python?" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.60015506,"math_prob":0.4889397,"size":2156,"snap":"2021-31-2021-39","text_gpt3_token_len":508,"char_repetition_ratio":0.18773234,"word_repetition_ratio":0.09221902,"special_character_ratio":0.25788498,"punctuation_ratio":0.155,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98874015,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T13:18:32Z\",\"WARC-Record-ID\":\"<urn:uuid:9aa07110-4570-4245-b32b-a9636d4095c0>\",\"Content-Length\":\"39037\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:19ac484a-dcab-4533-8fce-a177df588fda>\",\"WARC-Concurrent-To\":\"<urn:uuid:d11943e0-811a-4fe6-a336-643dd94b0da3>\",\"WARC-IP-Address\":\"172.66.40.122\",\"WARC-Target-URI\":\"https://www.tutorialsteacher.com/python/getattr-method\",\"WARC-Payload-Digest\":\"sha1:LMRWXU7C74ZMM347RHXVCQFZNHE5JO7F\",\"WARC-Block-Digest\":\"sha1:NKS7R54DMGSS5PWQZOYSW3K7BAWT56JT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056890.28_warc_CC-MAIN-20210919125659-20210919155659-00626.warc.gz\"}"}
https://convertoctopus.com/601-cubic-centimeters-to-tablespoons	[ "## Conversion formula\n\nThe conversion factor from cubic centimeters to tablespoons is 0.06762804511761, which means that 1 cubic centimeter is equal to 0.06762804511761 tablespoons:\n\n1 cm3 = 0.06762804511761 tbsp\n\nTo convert 601 cubic centimeters into tablespoons we have to multiply 601 by the conversion factor in order to get the volume amount from cubic centimeters to tablespoons. We can also form a simple proportion to calculate the result:\n\n1 cm3 → 0.06762804511761 tbsp\n\n601 cm3 → V(tbsp)\n\nSolve the above proportion to obtain the volume V in tablespoons:\n\nV(tbsp) = 601 cm3 × 0.06762804511761 tbsp\n\nV(tbsp) = 40.644455115684 tbsp\n\nThe final result is:\n\n601 cm3 → 40.644455115684 tbsp\n\nWe conclude that 601 cubic centimeters is equivalent to 40.644455115684 tablespoons:\n\n601 cubic centimeters = 40.644455115684 tablespoons\n\n## Alternative conversion\n\nWe can also convert by utilizing the inverse value of the conversion factor. In this case 1 tablespoon is equal to 0.024603602069551 × 601 cubic centimeters.\n\nAnother way is saying that 601 cubic centimeters is equal to 1 ÷ 0.024603602069551 tablespoons.\n\n## Approximate result\n\nFor practical purposes we can round our final result to an approximate numerical value. We can say that six hundred one cubic centimeters is approximately forty point six four four tablespoons:\n\n601 cm3 ≅ 40.644 tbsp\n\nAn alternative is also that one tablespoon is approximately zero point zero two five times six hundred one cubic centimeters.\n\n## Conversion table\n\n### cubic centimeters to tablespoons chart\n\nFor quick reference purposes, below is the conversion table you can use to convert from cubic centimeters to tablespoons\n\ncubic centimeters (cm3) tablespoons (tbsp)\n602 cubic centimeters 40.712 tablespoons\n603 cubic centimeters 40.78 tablespoons\n604 cubic centimeters 40.847 tablespoons\n605 cubic centimeters 40.915 tablespoons\n606 cubic centimeters 40.983 tablespoons\n607 cubic centimeters 41.05 tablespoons\n608 cubic centimeters 41.118 tablespoons\n609 cubic centimeters 41.185 tablespoons\n610 cubic centimeters 41.253 tablespoons\n611 cubic centimeters 41.321 tablespoons" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.68902546,"math_prob":0.9938461,"size":2120,"snap":"2021-43-2021-49","text_gpt3_token_len":515,"char_repetition_ratio":0.28355387,"word_repetition_ratio":0.013157895,"special_character_ratio":0.31745282,"punctuation_ratio":0.10055866,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9935954,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-05T22:55:04Z\",\"WARC-Record-ID\":\"<urn:uuid:0f1b2429-e8e0-4dc0-9d7f-580964bc210a>\",\"Content-Length\":\"31759\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2a599bff-ca57-4ea6-ab0b-453c5a266aeb>\",\"WARC-Concurrent-To\":\"<urn:uuid:6e57886f-f8a6-4e93-a80c-b41169bcb7de>\",\"WARC-IP-Address\":\"104.21.56.212\",\"WARC-Target-URI\":\"https://convertoctopus.com/601-cubic-centimeters-to-tablespoons\",\"WARC-Payload-Digest\":\"sha1:ANB3XY7D7YZF3CYSNYVSLXDLO4GNR7HW\",\"WARC-Block-Digest\":\"sha1:H2UCZZKROLXRTYAG3WSQSKLK5EDEJZD3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363226.68_warc_CC-MAIN-20211205221915-20211206011915-00025.warc.gz\"}"}
https://hal.archives-ouvertes.fr/hal-01735374	[ "# Surface derivatives computation using Fourier Transform\n\n1 GeoMod - Modélisation Géométrique, Géométrie Algorithmique, Fractales\nLIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information\nAbstract : We present a method for computing high order derivatives on a smooth surface S at a point p by analyzing the vibrations of the surface along circles in the tangent plane, centered at p. By computing the Discrete Fourier Transform of the deviation of S from the tangent plane restricted to those circles, a linear relation between the Fourier coefficients and the derivatives can be expressed. Thus, given a smooth scalar field defined on the surface, all its derivatives at p can be computed simultaneously. The originality of this method is that no direct derivation process is applied to the data. Instead, integration is performed through the Discrete Fourier Transform, and the result is expressed as a one dimensional polynomial. We derive two applications of our framework namely normal correction and curvature estimation which we demonstrate on synthetic and real data.\nDocument type :\nConference papers\nDomain :\n\nCited literature [10 references]\n\nhttps://hal.archives-ouvertes.fr/hal-01735374\nContributor : Julie Digne <>\nSubmitted on : Friday, March 16, 2018 - 1:57:18 PM\nLast modification on : Saturday, February 29, 2020 - 1:34:43 AM\nDocument(s) archivé(s) le : Monday, September 10, 2018 - 9:31:23 PM\n\n### File\n\nafig_2016.pdf\nFiles produced by the author(s)\n\n### Identifiers\n\n• HAL Id : hal-01735374, version 1\n\n### Citation\n\nYohann Béarzi, Julie Digne. Surface derivatives computation using Fourier Transform. JFIG 2016, Nov 2016, Grenoble, France. ⟨hal-01735374⟩\n\nRecord views" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92571616,"math_prob":0.5190812,"size":888,"snap":"2020-24-2020-29","text_gpt3_token_len":158,"char_repetition_ratio":0.115384616,"word_repetition_ratio":0.0,"special_character_ratio":0.17454955,"punctuation_ratio":0.08387097,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9532476,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-03T16:58:06Z\",\"WARC-Record-ID\":\"<urn:uuid:2d61bd7d-82ec-4e65-8a8f-05d8d10610c6>\",\"Content-Length\":\"46533\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:db8f0fa2-5862-46c8-90e6-20557366298d>\",\"WARC-Concurrent-To\":\"<urn:uuid:0255713c-e3c6-40e3-9b79-317b53f9f117>\",\"WARC-IP-Address\":\"193.48.96.10\",\"WARC-Target-URI\":\"https://hal.archives-ouvertes.fr/hal-01735374\",\"WARC-Payload-Digest\":\"sha1:QHNIQ32K5D63DHQDQSZZKRTTHHSHV37T\",\"WARC-Block-Digest\":\"sha1:YOAF2YALXBXSD67OLFN2MPOCJH2XTRHC\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655882634.5_warc_CC-MAIN-20200703153451-20200703183451-00397.warc.gz\"}"}
http://wikip.com/sotaychame.com/duoi-3-tuoi/	[ "## (605) 682-3465\n\nFasttrees provides a Fast-and-Frugal Tree classifier for Python.\n\nFast-and-frugal trees are classification trees that are especially useful for making decisions under uncertainty.\nDue their simplicity and transparency they are very robust against noise and errors in data.\nThey are one of the heuristics proposed by Gerd Gigerenzer in 4807866776. This particular implementation is based on on the R package 8333675197, developed by Phillips, Neth, Woike and Grassmaier.\n\nFirst, let’s install it. This can be done from the command line using pip:\n\n``````pip install fasttrees\n``````\n\nOnce it’s installed, let’s import the Fast-and-Frugal Tree classifier.\n\n``````from fasttrees.fasttrees import FastFrugalTreeClassifier\n``````\n\nNow let’s get some data to fit our classifier to. Fast-and-Frugal Trees tend to do well on real-world data prone to (human) error, as they disregard information that doesn’t seem very predictive of the outcome. A typical use case is in an operational setting where humans quickly have to take decisions. You could then fit a fast-and-frugal tree to the data in advance, and use the simple resulting tree to quickly make decisions.\n\nAs an example of this, let’s have a look at credit decisions. UCI provides a credit approval dataset. Download the `crx.data` file from the data folder.\n\nLet’s load the data as CSV to a Pandas dataframe:\n\n``````import pandas as pd\n``````\n\nAs there is no header, the columns are simply numbered 1, 2, 3 etc. Let’s make clear they’re attributes by naming them A1, A2, A3 etc.\n\n``````data.columns = ['A{}'.format(nr) for nr in data.columns]\n``````\n\nThe fasttrees implementation of fast-and-frugal trees can only work with categorical and numerical columns, so let’s assign the appropriate dtype to each column:\n\n``````import numpy as np\n\ncat_columns = ['A0', 'A3', 'A4', 'A5', 'A6', 'A8', 'A9', 'A11', 'A12']\nnr_columns = ['A1', 'A2', 'A7', 'A10', 'A13', 'A14']\n\nfor col in cat_columns:\ndata[col] = data[col].astype('category')\n\nfor col in nr_columns:\n# only recast columns that have not been correctly inferred\nif data[col].dtype != 'float' and data[col].dtype != 'int':\n# change the '?' placeholder to a nan\ndata.loc[data[col] == '?', col] = np.nan\ndata[col] = data[col].astype('float')\n``````\n\nThe last column is the variable we want to predict, the credit decision. It’s denoted by `+` or `-`. For our FastFrugalTreeClassifier to work we need to convert this to boolean:\n\n``````data['A15'] = data['A15'].apply(lambda x: True if x=='+' else False).astype(bool)\n``````\n\nYour data should now look something like this:\n\nA0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15\n0 b 30.83 0 u g w v 1.25 t t 1 f g 202 0 True\n1 a 58.67 4.46 u g q h 3.04 t t 6 f g 43 560 True\n2 a 24.5 0.5 u g q h 1.5 t f 0 f g 280 824 True\n3 b 27.83 1.54 u g w v 3.75 t t 5 t g 100 3 True\n4 b 20.17 5.625 u g w v 1.71 t f 0 f s 120 0 True\n\nNow let’s do a train test split (we use two thirds of the data to train on):\n\n``````from sklearn.model_selection import train_test_split\n\nX_train, X_test, y_train, y_test = train_test_split(data.drop(columns='A15'), data['A15'], test_size=0.33, random_state=0)\n``````\n\nWe can now finally instantiate our fast-and-frugal tree classifier. Let’s use the default parameters:\n\n``````fc = FastFrugalTreeClassifier()\n``````\n\nLet’s fit the classifier to our training data (this can take a few seconds):\n\n``````fc.fit(X_train, y_train)\n``````\n\nWe can take a look at the resulting tree, which can be used for decision making:\n\n``````fc.get_tree()\n``````\nIF NO feature direction threshold IF YES\n0 decide NO A8 in (‘t’,) â\n1 â A10 > 1 decide YES\n2 â A9 in (‘t’,) decide YES\n3 decide NO A7 > 1.25 decide YES\n\nNow somebody making a decision can simply look at the 3 central columns, which read, for example `A8 in ('t',)` and have a look whether this is the case. If it isn’t, they take the action in `IF NO`, which would be to decide NO (in this case that would mean not to grant this specific person a credit). If it is, they take the action in `IF YES`, which is to look at the next feature, for which they then repeat the process.\n\nHow well does this simple tree classifier perform? Let’s score it against the test data. By default the balanced accuracy score is used:\n\n``````fc.score(X_test, y_test)\n``````\n\nThis returns a balanced accuracy of 0.86, pretty good!\n\nWe can also have a look at how much information it actually used to make its decisions:\n\n``````fc.get_tree(decision_view=False)\n``````\nfeature direction threshold type balanced_accuracy_score fraction_used exit\n0 A8 in (‘t’,) categorical 0.852438 1 0\n1 A10 > 1 numerical 0.852438 0.528139 1\n2 A9 in (‘t’,) categorical 0.852438 0.238095 1\n3 A7 > 1.25 numerical 0.852438 0.192641 0.5\n\nWhile the first cue is used for all decisions, the second is only used for 52% of all decisions. This means that 48% of decisions could be made by just looking at one single feature.\n\nHence, fast and frugal trees provide a very easy way to generate simple decision criteria from a large dataset, which often perform better than more advanced machine learning algorithms, and are much more transparent." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7994299,"math_prob":0.9121814,"size":5124,"snap":"2019-13-2019-22","text_gpt3_token_len":1484,"char_repetition_ratio":0.10429688,"word_repetition_ratio":0.00472255,"special_character_ratio":0.32142857,"punctuation_ratio":0.13799448,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9783418,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-22T19:08:58Z\",\"WARC-Record-ID\":\"<urn:uuid:e4d7eb03-18ca-4872-b03e-dab215b517c2>\",\"Content-Length\":\"28382\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ed60eddb-b6e9-46b2-bd0a-8097a43599fd>\",\"WARC-Concurrent-To\":\"<urn:uuid:a5deb126-5bc7-4ef9-aa29-1af2cbbe9fa8>\",\"WARC-IP-Address\":\"216.194.105.200\",\"WARC-Target-URI\":\"http://wikip.com/sotaychame.com/duoi-3-tuoi/\",\"WARC-Payload-Digest\":\"sha1:HLQ64IURPGHEPXL4RU3576KNU6NFU722\",\"WARC-Block-Digest\":\"sha1:GUSZG4MSPYHYH45SL5O4OJCAED7D6B7A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202688.89_warc_CC-MAIN-20190322180106-20190322202106-00227.warc.gz\"}"}
https://socratic.org/questions/5862800eb72cff63940728e3	[ "# Question #728e3\n\nJan 2, 2017\n\nAlkali earth metals have a valance configuration of ${s}^{2}$\nHalogens have a valance configuration of ${s}^{2} {p}^{5}$\nBoth families of elements are chemically active.\n\n#### Explanation:\n\nAlkali Earth metals with a valance configuration of ${s}^{2}$ can most easily become stable by sharing these valance electrons with an element that is electrophilic. This leaves the Alkali Earth metals with the outside valance electron structure of a noble gas of the next lower electron shell.\n\nHalogens with a valance configuration of ${s}^{2} {p}^{5}$ can most easily become stable by acquiring an electron from another element. This leaves the Halogens with the outside valance electron structure of a noble gas in the same period.\n\nBoth of these families of elements are very active chemically.\n\nJan 25, 2017\n\nHere's what I get.\n\n#### Explanation:\n\n$\\boldsymbol{\\text{Alkaline Earth\"color(white)(ml)\"Halogen}}$\n${\\text{Be\"color(white)(m)[\"He\"] \"2s\"^2color(white)(mmmm)\"F\"color(white)(m)[\"He\"] \"2s\"^2 \"2p}}^{5}$\n${\\text{Mg\"color(white)(ll)[\"Ne\"] \"3s\"^2color(white)(m)color(white)(mmm)\"Cl\"color(white)(ll)[\"Ne\"] \"3s\"^2 \"3p}}^{5}$\n\n${\\text{Ca\"color(white)(m)[\"Ar\"] \"4s\"^2color(white)(m)color(white)(mmm)\"Br\"color(white)(ll)[\"Ar\"]\"4s\"^2 \"3d\"^10 \"4p}}^{5}$\n${\\text{Sr\"color(white)(ml)[\"Kr\"] \"5s\"^2color(white)(m)color(white)(mmm)\"I\"color(white)(ml)[\"Kr\"] \"5s\"^2 \"4d\"^10 \"5p}}^{5}$\n\n${\\text{Ba\"color(white)(m)[\"Xe\"] \"6s\"^2color(white)(m)color(white)(mmm)\"At\"color(white)(ll)[\"Xe\"]\"6s\"^2 \"4f\"^14 \"5d\"^10 \"6p}}^{5}$\n${\\text{Ra\"color(white)(m)[\"Rn\"] \"7s\"^2color(white)(m)color(white)(mmll)\"Ts\"color(white)(m)[\"Rn\"] \"7s\"^2 \"5f\"^14 \"6d\"^10 \"7p}}^{5}$\n\nThe alkaline earth metals have a electron configuration ending in $n {\\text{s}}^{2}$.\n\nThey can get a noble gas configuration by losing their two $\\text{s}$ electrons.\n\nThe halogens have an electron configuration ending in $n {\\text{s\"^2 n\"p}}^{5}$.\n\nThey can get a noble gas configuration by gaining one electron to complete their octet.\n\nThus, an alkali metal $\\text{M}$ will react by donating an electron to each of two halogen $\\text{X}$ atoms.\n\nThe metal will become a metal cation $\\text{M\"^\"2+}$ and the halogen will become an anion $\\text{X\"^\"-}$.\n\n$\\text{M + 2X\" → \"M\"^\"2+\", \"2X\"^\"-}$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.787264,"math_prob":0.994972,"size":775,"snap":"2023-40-2023-50","text_gpt3_token_len":180,"char_repetition_ratio":0.1763943,"word_repetition_ratio":0.20168068,"special_character_ratio":0.20387097,"punctuation_ratio":0.06153846,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9884824,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-06T07:47:52Z\",\"WARC-Record-ID\":\"<urn:uuid:957e4600-a421-4c5a-a888-2bfb118194bf>\",\"Content-Length\":\"37599\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b4659e22-9585-41ae-9f39-0f167d030db8>\",\"WARC-Concurrent-To\":\"<urn:uuid:fd9e18bc-3ad1-459b-a53d-01a378bd70b5>\",\"WARC-IP-Address\":\"216.239.34.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/5862800eb72cff63940728e3\",\"WARC-Payload-Digest\":\"sha1:K4ORI4WMZM45LWFQC5G2DYI3UPIESE2Z\",\"WARC-Block-Digest\":\"sha1:JSE5WBLBKNGOQF6NSQBA437SAD3C5734\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100583.31_warc_CC-MAIN-20231206063543-20231206093543-00292.warc.gz\"}"}
https://www.nature.com/articles/s41598-018-34443-2?error=cookies_not_supported	[ "## Introduction\n\nDevelopment of method for determining crystal and magnetic structure is an important issue1,2,3. The magnetic structure of a compound is directly related to the microscopic origins of various intriguing magnetic phenomena observed in physics, chemistry, biology and geology4,5,6,7,8,9,10,11. Accurate information on the experimentally determined magnetic structures can be potentially used to effectively design functional materials and opens multiple opportunities for utilizing advanced first-principle calculations and informatics approaches. Furthermore, the responses of the analysed magnetic structure to external factors such as temperature, pressure, electromagnetic field, light and environment are usually related to the corresponding changes in the macroscopic properties of minerals and biomolecules.\n\nSince the pioneering work of Shull et al. published in 19511, many studies on the determination of the magnetic structures of various materials by neutron diffraction have been performed. Thus, Izymov, Kovalev and Bertaut developed the irreducible representation (IR) theory, which successfully classified magnetic structures by their magnetic point symmetries obtained through the analysis of neutron diffraction data12,13,14. Moreover, the modern neutron diffractometers exhibit relatively high statistical accuracy and resolution15,16. However, analysing neutron diffraction data to determine the correct magnetic structure represents a challenging task. The major issue here is the existence of so-called local solutions to the optimization problem (Fig. 1A). The analysis procedure is mathematically categorized as the nonlinear optimization, in which the obtained diffraction data points are fitted with the function of neutron scattering cross-section characterized by high-dimensional nonlinear parameters such as magnetic moment vectors17. After performing nonlinear optimization, it is very difficult to prove that the best solution obtained via various numerical models is the global one. Furthermore, multiple or many solutions are hidden in some cases, and no solutions exist in other cases. To mitigate these issues, global optimization techniques including a simulated annealing method, the Monte Carlo method and genetic algorithms can be used18,19,20,21,22,23. However, none of these approaches can determine the global solution(s) with 100% probability.\n\nIn this study, a new analytical method for the determination of magnetic structure is proposed, which allows (i) judging whether the obtained solution is a truly global one; (ii) evaluating the uniqueness of the solution obtained for a given set of experimental data; and (iii) completing the global optimization procedure in a very short time (typically, less than several seconds). Furthermore, the applicability of the proposed method is demonstrated using polarized-neutron powder diffraction data.\n\n## Mathematical Formulation for Applications of Semidefinite Relaxation Method\n\nRelaxation techniques have been previously developed in the field of mathematical programming. In particular, semidefinite relaxation (SDR) combined with semidefinite programming (SDP) has found many applications in applied mathematics and engineering (for example, see Chapter 2.2 in ref.24). SDR is an efficient technique for solving nonlinear optimization problems, such as quadratic programs (QPs), namely the minimization of multivariate quadratic polynomials under constraints. It should be noted that SDR could provide both fast convergence and a numerical proof of the global optimality of the obtained solutions using the global convergence property and duality theorem of the convex programming methods, as schematically shown in Fig. 1(B,C).\n\nIn the field of optical imaging, Candès et al. published a pioneering work (called the PhaseLift method), in which a sparse modelling approach was adopted for general phase retrieval25. Furthermore, one of the authors (ROT) developed an SDR-based mathematical approach to investigate whether a crystal structure could be uniquely identified using only diffraction data and independent atomic model26.\n\nIn this study, this method was applied to magnetic structure analysis by replacing the optimized parameters with magnetic moments. The problem of magnetic structure determination can be mathematically described by the following set of N quadratic equations:\n\n$${I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})\\approx {I}_{{\\rm{mag}},{\\rm{cal}}}({Q}_{k})={{\\boldsymbol{x}}}^{{\\rm{T}}}{S}_{k}{\\boldsymbol{x}}=\\sum _{1\\le i,j\\le n}{S}_{k}(i,j){x}_{i}{x}_{j}\\,(1\\,\\le \\,k\\,\\le N),$$\n(1)\n\nwhere $${I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k})\\,$$and $${I}_{\\mathrm{mag},\\mathrm{cal}}({Q}_{k})$$ denote the observed and calculated integrated magnetic diffraction intensities at the magnetic reflection $${Q}_{k}={h}_{{\\rm{mag}}}\\,{k}_{{\\rm{mag}}}\\,{l}_{{\\rm{mag}}}$$, respectively; x = (x1, …, xn)T and $${S}_{k}$$ represents the coefficient matrix numerically obtained using the scattering cross-section formula for each $${Q}_{k}$$, which consists of the absolute intensity scale factor, magnetic form factor, Lorentz factor, multiplicity and structural weight factor (the details of this formula are summarized in Supplementary Information).\n\nThe symbol $$\\approx$$ indicates that each $${I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})$$ value includes an experimental error. In order to incorporate all errors, the following optimization problem is solved:\n\n$$\\{\\begin{array}{c}{\\rm{Minimize}}\\sum _{k=1}^{N}\\frac{\|{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})-{{\\boldsymbol{x}}}^{{\\rm{T}}}S{\\boldsymbol{x}}\|}{{\\rm{Err}}[{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})]},\\\\ {\\rm{subject}}\\,{\\rm{to}}:\|{x}_{i}\|\\le {R}_{i}(1\\le i\\le n).\\end{array}$$\n(2)\n\nThe inequality $$\|{x}_{i}\|\\le {R}_{i}$$ can be also removed if the permitted range of $$\|{x}_{i}\|$$ ($${R}_{i}$$, for example, the upper limit of magnetic moment) is uncertain while maintaining the validity of the subsequent discussion of the SDR and SDP techniques.\n\nEquation (2) is classified as a so-called l1-norm minimization problem, which is equivalent to the following form of the quadratic programming problem:\n\n$$\\{\\begin{array}{c}{\\rm{Minimize}}\\,\\sum _{k=1}^{N}\\,\\frac{{\\eta }_{k}^{+}+{\\eta }_{k}^{-}}{2}\\\\ {\\rm{subject}}\\,{\\rm{to}}:\\frac{{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})-{{\\boldsymbol{x}}}^{{\\rm{T}}}{S}_{k}{\\boldsymbol{x}}}{{\\rm{Err}}[{I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k})]}=\\frac{{\\eta }_{k}^{+}-{\\eta }_{k}^{-}}{2}(1\\le k\\le N),\\\\ {{x}_{i}}^{2}+{y}_{i}={{R}_{i}}^{2},\\,{y}_{k}\\ge 0\\,(1\\le i\\le n),\\\\ {\\eta }_{k}^{+}\\ge 0,{\\eta }_{k}^{-}\\ge 0\\,(1\\le k\\le N).\\end{array}$$\n(3)\n\nThe problems described by equations (2) and (3) are equivalent since they have the same set of solutions x and the minimized values of the objective functions (more details are provided in Supplementary Information). The basic strategy utilized in this work is to apply SDR to equation (3) in order to solve equation (2) and then provide a computational proof on the global convergence property of the solution. The least-squares minimization of the $$\\,\\sum _{k=1}^{N}{\|({I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k})-{{\\boldsymbol{x}}}^{T}S{\\boldsymbol{x}})/{\\rm{Err}}[{I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k})]\|}^{2}$$ function is avoided because a small increase in the polynomial degree considerably magnifies the size of the SDR problem (it increases proportionally to the power of N). Thus, it is possible to locate the global optimum by performing l1-norm minimization, which can be subsequently used as the initial parameter of the normal least-squares method to calculate the refined parameters and then compare them with literature data.\n\n## Application to Experimental Data Analysis\n\n### Experimental results\n\nThe developed SDR method was verified by applying it to the experimental data obtained for pyrochlore Nd2Ir2O7, which served as a proximate material for a three-dimensional Weyl semimetal and a component of spintronic devices on the basis of its geometrically frustrated magnetism and 5d-electron configuration27,28,29,30,31,32. This state theoretically corresponds to the all-in all-out type of magnetic structure described by the magnetic propagation vector kmag = (0, 0, 0), in which all the magnetic moments are oriented either towards the centre of the participating tetrahedron or in the opposite direction30,32. This prediction was experimentally confirmed in previous unpolarized neutron diffraction studies33,34. However, the superposition of the nuclear and magnetic reflections observed for the magnetic structures with kmag = (0, 0, 0) produces ambiguous results during their separation. Furthermore, it is not possible to mathematically prove with 100% certainty the absence of other acceptable solutions to the problem of magnetic structure determination. Thus, in this work, polarized neutron diffraction studies were performed for this material, and the obtained magnetic structure was verified mathematically.\n\nFigure 2 shows the representative neutron diffraction data obtained for Nd2Ir2O7 at the minimum temperature T = 1.4 K. The non-spin-flip and spin-flip parameters IOFF and ION roughly correspond to the nuclear and magnetic reflection components Inuc and Imag, respectively. The magnitude of IOFF is systematically larger than ION at all temperatures, thus confirming the necessity of conducting polarized neutron diffraction experiments. For ION, the intensity of the 113 reflection increases with decreasing temperature, indicating the existence of strong temperature dependence for this reflection, which is not observed for the 222 reflection. Moreover, as the flipping ratio of the neutron beam in the actual experiments is finite, the magnitudes of ION and IOFF can be expressed by the following formulas:\n\n$$\\{\\begin{array}{c}{I}_{{\\rm{OFF}}}=(1-{r}_{{\\rm{mix}}}){I}_{{\\rm{nuc}}}+\\,{r}_{{\\rm{mix}}}{I}_{{\\rm{mag}}},\\,\\\\ {I}_{{\\rm{ON}}}={r}_{{\\rm{mix}}}{I}_{{\\rm{nuc}}}+\\,(1-{r}_{{\\rm{mix}}}){I}_{{\\rm{mag}}},\\,\\end{array}$$\n\nwhere rmix = N/(N+ + N) is the mixing rate, and N+ (N) denotes the number of majority-spin (minority-spin) neutrons. The value of rmix is selected to satisfy the condition Imag = 0; hence, ION = rmix·Inuc at the paramagnetic T = 40 K. As a result, the pure magnetic intensity Imag can be determined by combining IOFF and ION. A more detailed explanation and data obtained for other reflections are presented in Supplementary Information, while the calculated Imag,obs values are listed in Table 1.\n\n### Magnetic structure analysis results\n\nThe arbitrary magnetic structure with kmag = (0, 0, 0) in the space group $$Fd\\bar{3}m$$ is described as the function of xarb = (m(Nd)1, , m(Nd)12, m(Ir)1, , m(Ir)12) containing narb = 24 variables generated by the eight magnetic atoms of the unit cell and three Cartesian coordinates. Here, the magnetic symmetry was classified by performing IR analysis (this procedure is generally not required for the proposed method; however, it may be potentially useful because of the reduction of the number of variables if the number of observed reflection points is limited). The possible magnetic structures are described by the representations ΓNd = Γ3 + 2Γ5 + 3Γ7 + 6Γ9 and ΓIr = Γ3 + 2Γ5 + 3Γ7 + 6Γ9, where Γ3 corresponds to the all-in all-out type of the magnetic structure, and the coefficients denote the numbers of basis vectors summarized in Table 218,35. Hence, the total numbers of variables are reduced to nΓ3 = 2, nΓ5 = 4, nΓ7 = 6 and nΓ9 = 12. Furthermore, representation Γ9 includes six ferromagnetic basis vectors. However, the Nd2Ir2O7 structure exhibits only extremely weak spontaneous magnetization (around 10−4μB/formula unit)29, which is significantly below the detection limit of the neutron diffraction technique. Therefore, the ferromagnetic basis vectors are precluded and the value of nΓ9 is further reduced from 12 to 6 during the analysis of the neutron diffraction data.\n\nThus, the variables used for the magnetic structure analysis in this work are defined as follows: xΓ3 = (m(Γ3,Nd)1, m(Γ3,Ir)1), xΓ5 = (m(Γ5,Nd)1, m(Γ5,Nd)2, m(Γ5,Ir)1, m(Γ5,Ir)2), xΓ7 = (m(Γ7,Nd)1, m(Γ7,Nd)2, m(Γ7,Nd)3, m(Γ7,Ir)1, m(Γ7,Ir)2, m(Γ7,Ir)3) and xΓ9 = (m(Γ9,Nd)1, m(Γ9,Nd)2, m(Γ9,Nd)3, m(Γ9,Ir)1, m(Γ9,Ir)2, m(Γ9,Ir)3). The goal is to determine the globally optimal solutions x for representations Γ3, Γ5, Γ7 and Γ9 using the Imag,obs magnitudes listed in Table 1. After that, the solution characterized by the best fit can be selected.\n\nThe output values produced by the SDP solver are as follows.\n\n1. (1)\n\nThe convergence procedure results in the following coefficients:\n\n$$\\begin{array}{c}{{X}_{{\\rm{\\Gamma }}3}}^{({\\rm{opt}})}\\approx {{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}3}}^{({\\rm{opt}}1)}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}3}}^{({\\rm{opt}}1)T};\\\\ {{X}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}})}\\approx ({{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}1)}{{x}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}1)T}+{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}2)}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}2)T})/2;\\\\ {{X}_{{\\rm{\\Gamma }}7}}^{({\\rm{opt}})}\\approx 0;\\\\ {{X}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}})}\\approx ({{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}1)}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}1)T}+{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}2)}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}2)T}+{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}3)}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}3)T})/3;\\end{array}$$\n\nand\n\n$$\\begin{array}{c}{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}3}}^{({\\rm{opt}})}=(-\\,1.20,\\,0.19);\\\\ {{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}1)}=(0.55,\\,0.,\\,0.48,\\,0.),\\,{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}}^{({\\rm{opt}}2)}=(0.,\\,0.55,\\,0.,\\,0.48);\\\\ {{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}7}}^{(opt)}=(0.,\\,0.,\\,0.,\\,0.,\\,0.,\\,0.);\\\\ {{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}1)}=(0.55,\\,0.,\\,0.,\\,-\\,0.52,\\,0.,\\,0.),\\,{{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}2)}=(0.,\\,0.55,\\,0.,\\,0.,\\,-\\,0.52,\\,0.),\\\\ {{{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}}^{({\\rm{opt}}3)}=(0.,\\,0.,\\,0.55,\\,0.,\\,0.,\\,-\\,0.52);\\end{array}$$\n\nwhere the values of x are expressed the μB units, and the negative sign indicates the nearest ferromagnetic Nd–Ir correlation. While a single optimum solution is determined for representation Γ3, multiple solutions are obtained for Γ5 and Γ9, respectively, in accordance with the rank values of XΓ5(opt) and XΓ9(opt), which indicate the existence of an infinite number of solutions with the same objective functions $${{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}^{({\\rm{opt}})}=\\,\\cos \\,\\theta {{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}^{({\\rm{opt}}1)}+\\,\\sin \\,\\theta {{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}5}^{({\\rm{opt}}2)}$$ and $${{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}^{({\\rm{opt}})}=\\,\\cos \\,\\theta {{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}^{({\\rm{opt}}1)}+\\,\\sin \\,\\theta \\,\\cos \\,\\varphi {{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}^{({\\rm{opt}}2)}+\\,\\sin \\,\\theta \\,\\sin \\,\\varphi {{\\boldsymbol{x}}}_{{\\rm{\\Gamma }}9}^{({\\rm{opt}}3)}$$, where $$\\theta$$ and $$\\varphi$$ are arbitrary. Without SDR, it is difficult to find the optimum solutions for this type of problems and prove that better solutions do not exist. Furthermore, the zero magnitude of xΓ7(opt) is obtained for representation Γ7. Indeed, when xΓ7 values are finite (non-zero), the $${I}_{{\\rm{mag}},{\\rm{cal}}}$$ values for $${I}_{{\\rm{mag}},{\\rm{obs}}}=0$$ indices increase more rapidly than those for $${I}_{{\\rm{mag}},{\\rm{obs}}}\\ne 0$$ indices. Thus, the SDR method automatically overcomes these issues.\n\n2. (2)\n\nThe obtained indicator values for representations Γ3, Γ5, Γ7 and Γ9 are as follows.\n\n1. a)\n\nThe corresponding duality gaps determined by the SDP solver are equal to $${\\rm{\\Delta }}f=2.1\\times {10}^{-7}$$, $$1.4\\times {10}^{-6}$$, $$3.1\\times {10}^{-6}$$ and $$8.0\\times {10}^{-7}$$, respectively. Their magnitudes are close to zero, indicating that the convergence to the global optimums is achieved.\n\n2. b)\n\nThe minimized objective function $${f}^{({\\rm{gl}})}\\underline{\\underline{{\\rm{def}}}}\\,\\sum _{k=1}^{N}\\,\|{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})-{I}_{{\\rm{mag}},{\\rm{cal}}}({Q}_{k})\|/{\\rm{Err}}[{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})]$$ = 4.5, 19, 32 and 27, and the more familiar R-factor, $${R}_{{\\rm{Bragg}}}\\underline{\\underline{{\\rm{def}}}}\\,(\\sum _{k=1}^{N}\|{I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k})-{I}_{\\mathrm{mag},\\mathrm{cal}}({Q}_{k})\|)/(\\sum _{k=1}^{N}\\,{I}_{\\mathrm{mag},\\mathrm{obs}}({Q}_{k}))$$ = 0.13, 0.63, 1.0 and 0.81, respectively. These results show that the smallest values are obtained for representation Γ3.\n\n3. c)\n\nThe goodness of the fit $${\\chi }^{2}\\underline{\\underline{{\\rm{def}}}}\\,(\\sum _{k=1}^{N}{\|{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})-{I}_{{\\rm{mag}},{\\rm{cal}}}({Q}_{k})\|}^{2}\\,/\\,\\,{\\rm{Err}}{[{I}_{{\\rm{mag}},{\\rm{obs}}}({Q}_{k})]}^{2})/(N-{n}_{{\\rm{\\Gamma }}})$$ = 2.6, 14, 25 and 20, and the related statistical parameter $${f}^{({\\rm{gl}})}/(N-{n}_{{\\rm{\\Gamma }}})=0.75$$, 4.8, 16 and 14, respectively. The value closest to the expected value (1 for $${\\chi }^{2}$$; $$\\sqrt{2/\\pi }\\approx 0.798$$ for the latter parameter) is obtained for Γ3.\n\nAll these facts suggest that Γ3 represents the best solution, whereas representations Γ5, Γ7 and Γ9 are excluded for the first time. For clarity, the values of Imag,cal are listed in Table 2 and also shown in Fig. 3. The magnitude of Imag,cal-Γ3 matches Imag,obs very well, whereas the globally optimal Imag,cal-Γ5, Imag,cal-Γ7 and Imag,cal-Γ9 parameters substantially differ from the corresponding Imag,obs values.\n\nAfter proving mathematically the uniqueness of representation Γ3, the refined values mNd = −1.22(5)μB and mIr = 0.14(5)μB are obtained using the xΓ3(opt) values as the initial parameters in the normal least-squares method. These results are comparable with the reported values of mNd = −1.27(1)μB and mIr = 0.34(1)μB34.\n\n## Discussion\n\nRepresentation Γ9 (the only IR containing ferromagnetic basis vectors35) is rejected as the optimal solution despite the existence of weak ferromagnetism29. The observed inconsistency suggests that this ferromagnetism is symmetrically decoupled from the bulk magnetic structure (for example, as a surface or interface-protected property). In fact, by performing careful measurements of the macroscopic magnetization and electrical resistivity of isomorphic Cd2Os2O7, it was found that the surface ferromagnetism coupled with novel spin-polarized conductivity emerged on the walls between the all-in all-out and all-out all-in antiferromagnetic domains36. The macroscopic observation is consistent with the findings of this study verified both microscopically and mathematically, indicating their potential applicability in domain wall spin electronics.\n\nWe discuss the expected application scope of the SDR method. After determining the list of (hmag, kmag, lmag, Imag,obs) values, the described SDR method can be used to find the corresponding magnetic structures as the global solutions. First, the configurations with kmag = (0, 0, 0) are considered, indicating their high potential applicability in various fields (including magnet materials). Second, this method is not restricted to polarized neutron diffraction experiments, but can be also used in studies involving unpolarized neutrons when the magnetic structure is characterized by kmag ≠ (0, 0, 0) or kmag = (0, 0, 0) with detectable magnetic moment. Both the magnetic and crystallographic structures can be simultaneously refined by the normal least-squares method, in which the obtained SDR solutions are utilized as the initial values of the magnetic structural parameters. Third, the SDR technique is able to easily process thousands of independent variables. Therefore, magnetic structures of arbitrary types can be theoretically determined using the advanced diffractometers that provide a relatively large number of reflection points (even for the target materials with complex compositions).\n\nThe diffraction intensities are not represented by quadratic functions of the atomic positions rj; hence, the SDR technique seems to be inapplicable for determining the values of rj (crystal structure). However, the neutron and X-ray diffraction intensities are represented by those of the nuclear and electron densities (generalized crystal structure), respectively. Likewise, a magnetic structure is also generalized to the magnetic moment density. Thus, the SDR technique is expected to enable analysing the global solutions of the generalized structures together with the aforementioned high-volume processing ability, such as protonic/ionic distributions in the conductors and electronic spin-orbital distributions.\n\n## Materials and Methods\n\n### Calculations\n\nThe system of quadratic equations was solved using the SDP solver SDPA37. To find the global optima of SDP problems, interior point methods were efficiently used38.\n\n### Experiments\n\nThe polarized neutron elastic scattering experiments were performed using the HB1 thermal neutron three-axis spectrometer located at the High Flux Isotope Reactor (HFIR) of the Oak Ridge National Laboratory (ORNL). Heusler alloy 111 reflection crystals were utilized as the monochromator and analyser. The flipping ratio R = 10 was obtained using the nuclear 222 reflection at a paramagnetic temperature of 40 K corresponding to the beam polarization P = 0.82. The polarization vector was set parallel to the scattering vector (P//Q). The incident energy of neutrons was Ei = 13.5 meV. The horizontal collimator sequence was 48′(open)–80′–80′–240′. A pyrolytic graphite Bragg-reflection filter was used to efficiently eliminate the contamination caused by higher-order wavelengths.\n\nA powder Nd2Ir2O7 sample was synthesized by a solid-state reaction method inside a quartz tube. About 4.8 g of the sample was wrapped in thin aluminium foil and shaped to a hollow cylinder with a thickness of 0.8 mm and diameter of 20 mm to mitigate the effect of the strong neutron absorption of Ir nuclei. The cylinder was stored in an aluminium container filled with He gas and placed under the cold heads of a He-closed-cycle (Displex) or liquid-He-type (Orange) cryostat." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8130939,"math_prob":0.99808526,"size":30224,"snap":"2023-14-2023-23","text_gpt3_token_len":8040,"char_repetition_ratio":0.14592984,"word_repetition_ratio":0.014962593,"special_character_ratio":0.27071202,"punctuation_ratio":0.1732049,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99883324,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-10T04:19:39Z\",\"WARC-Record-ID\":\"<urn:uuid:0438c777-726d-40ea-a9df-3b41dcd7b892>\",\"Content-Length\":\"350757\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3f97bd67-485b-42ce-a4e0-29a450d7e0f3>\",\"WARC-Concurrent-To\":\"<urn:uuid:7406e81e-13f4-44e9-b354-819f2d112fe6>\",\"WARC-IP-Address\":\"146.75.32.95\",\"WARC-Target-URI\":\"https://www.nature.com/articles/s41598-018-34443-2?error=cookies_not_supported\",\"WARC-Payload-Digest\":\"sha1:Z63MUMDQQYSHWI32FG44HE2FX7OKHPYU\",\"WARC-Block-Digest\":\"sha1:PTXF7JBZZIKQPR5OOWJMOW5HPIECTU63\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224656963.83_warc_CC-MAIN-20230610030340-20230610060340-00154.warc.gz\"}"}
http://mymathforum.com/calculus/343053-lnx-e-x.html	[ "Calculus Calculus Math Forum\n\n December 11th, 2017, 09:18 AM #1 Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 lnx and e^x $\\displaystyle \\ln x$ and e$\\displaystyle ^{x}$ are inverse functions: $\\displaystyle e^{\\ln x}=x$ and $\\displaystyle \\ln e^{x}=x$ But what are $\\displaystyle \\ln x$ and $\\displaystyle e^{x}$? Options: 1) Define $\\displaystyle e^{x}$ and $\\displaystyle \\ln x$ independently: $\\displaystyle e^{x} = 1+{}\\sum_{n=1}^{\\infty}\\frac{x^{n}}{n!}$ $\\displaystyle \\ln x=\\int_{1}^{x}\\frac{dx}{x}$ Then show they are inverses and derive the usual properties. 2) Choose either series or integral definition as fundamental, and define the other as inverse. If you choose integral definition, the series for $\\displaystyle e^{x}$ is easily derived: By definition $\\displaystyle e^{x}$ is the inverse function of $\\displaystyle \\ln x$. If $\\displaystyle y=\\ln^{-1}x. x=\\ln y$ and $\\displaystyle dx=\\frac{1}{y}dy$ so that $\\displaystyle \\frac{dy}{dx}= y =\\ln^{-1}(x)$, and $\\displaystyle \\frac{d^{2}y}{dx^{2}}=\\ln^{-1}(x)$,..... In general $\\displaystyle \\frac{d^{n}y}{dx^{n}}=\\ln^{-1}(x)$ and $\\displaystyle \\frac{d^{n}y}{dx^{n}}\|_{x=0}=1$ from which Taylor series for $\\displaystyle e^x = \\ln^{-1}(x)$ follows. But I do have a question (surprise): Show, $\\displaystyle \\ln ab = \\ln a + \\ln b$ from the lntegral definition, i.e., Show $\\displaystyle \\int_{1}^{ab}\\frac{dx}{x}= \\int_{1}^{a}\\frac{dx}{x}+\\int_{1}^{b}\\frac{dx}{x}$ ------------------------------------------------------------------------------- skipjack has a way of editing typography so that text and equations are uniform. How? Last edited by skipjack; December 11th, 2017 at 02:44 PM.", null, "December 11th, 2017, 09:30 AM #2 Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra \\begin{align} \\int_1^{ab}\\frac1t\\,\\mathrm dt &= \\int_1^{a}\\frac1t\\,\\mathrm dt + \\int_a^{ab}\\frac1t\\,\\mathrm dt \\\\ &= \\int_1^{a}\\frac1t\\,\\mathrm dt + \\int_1^{b}\\frac1u\\,\\mathrm du & \\text{(where $u=at$)} \\end{align} Thanks from Maschke and zylo", null, "December 11th, 2017, 10:11 AM #3 Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Actually, u=t/a, but it's the thought that counts. 10/10, no deduction for typo. Many thanks.", null, "December 11th, 2017, 01:30 PM #4 Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra Oh, well perhaps some admin can correct it.", null, "December 11th, 2017, 02:14 PM #5 Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Exponents from scratch based on above. (till now, e$\\displaystyle ^{x}$ is not an exponential, it is just symbol for inverse of $\\ln x$ which is defined by integral.) $\\displaystyle a^{x} = e^{a\\ln x}$, which is a definition in terms of known, calculable, quantities. Otherwise, what is .8375^{4.2319}? Usual laws of exponents should follow. $\\displaystyle \\ln_{a}a^{x}=x$ is definition of inverse function ln$\\displaystyle _{a}$. (Since $\\displaystyle \\ln e^{x}-x, \\ln \\equiv \\ln_{e}$). $\\displaystyle a^{\\ln_{a}x}=x$, and take ln of both sides. $\\displaystyle \\ln_{a}x(\\ln a)=\\ln x$, and $\\displaystyle \\ln_{10}x=\\ln x/\\ln10$. Last edited by skipjack; December 11th, 2017 at 02:26 PM.", null, "December 11th, 2017, 02:49 PM #6 Global Moderator Joined: Dec 2006 Posts: 21,128 Thanks: 2337 Obviously, $\\displaystyle a^{x} = e^{a\\ln x}$ is wrong. I assume you meant $\\displaystyle a^{x} = e^{x\\ln a}\\!$. Thanks from zylo", null, "December 11th, 2017, 04:03 PM #7\nBanned Camp\n\nJoined: Mar 2015\nFrom: New Jersey\n\nPosts: 1,720\nThanks: 126\n\nQuote:\n Originally Posted by skipjack", null, "Obviously, $\\displaystyle a^{x} = e^{a\\ln x}$ is wrong. I assume you meant $\\displaystyle a^{x} = e^{x\\ln a}\\!$.\nIndeed. Thanks for catching that.\n\nAmazingly, if you calculate $\\displaystyle 3^{2}=e^{2\\ln3}$ on a simple TI calculator, it comes up with 9. Didn't expect that, after all the ten place intermediate decimals. Guess it was just a matter of rounding up the final number to ten places, which was 9.", null, "December 11th, 2017, 06:00 PM #8 Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 On the other hand, consider the function $\\displaystyle f(x)=x^{a}$ with definition: $\\displaystyle f(x)=x^{a}=e^{a\\ln x}$ What is $\\displaystyle f^{-1}(f(x))=x$? $\\displaystyle f^{-1}(x) = x^{\\frac{1}{a}}$ $\\displaystyle f^{-1}(x^{a})= (x^{a})^{\\frac{1}{a}}=(e^{a\\ln x})^{\\frac{1}{a}}=x$ To summarize, $\\displaystyle a^{x}$ and $\\displaystyle x^{a}$ are different functions of x with different inverses.", null, "December 11th, 2017, 06:13 PM #9\nMath Team\n\nJoined: Dec 2013\nFrom: Colombia\n\nPosts: 7,700\nThanks: 2682\n\nMath Focus: Mainly analysis and algebra\nQuote:\n Originally Posted by zylo", null, "To summarize, $\\displaystyle a^{x}$ and $\\displaystyle x^{a}$ are different functions of x with different inverses.\nPure genius. Who'd've thought it?", null, "December 12th, 2017, 08:23 AM #10 Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 126 Two ways of looking at $\\displaystyle \\ln_{a}x$ 1) Def: $\\displaystyle \\ln_{a}x$ is the power you have to raise a to to get x: $\\displaystyle a^{\\ln_{a}x}=x$ $\\displaystyle \\ln_{a}(a^{x}) = x$, power you have to raise a to to get a$\\displaystyle ^{x}$. 2) Def: $\\displaystyle \\ln_{a}x = f^{-1}(a^{x})$ $\\displaystyle \\ln_{a}(a^{x}) = x, f^{-1}(f(x))=x$ $\\displaystyle a^{\\ln_{a}x}=x, f(f^{-1}(x))=x$ Def 1 is what I will remember a week from now because that's what I learned. I like Def 2 as a development from first principles as in this thread.", null, "Tags lnx", null, "Thread Tools", null, "Show Printable Version", null, "Email this Page Display Modes", null, "Linear Mode", null, "Switch to Hybrid Mode", null, "Switch to Threaded Mode\n\n Contact - Home - Forums - Cryptocurrency Forum - Top", null, "", null, "", null, "", null, "", null, "", null, "", null, "" ]	[ null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/buttons/viewpost.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/buttons/viewpost.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/statusicon/user_offline.gif", null, "http://mymathforum.com/images/math/misc/11x11progress.gif", null, "http://mymathforum.com/images/math/buttons/printer.gif", null, "http://mymathforum.com/images/math/buttons/sendtofriend.gif", null, "http://mymathforum.com/images/math/buttons/mode_linear.gif", null, "http://mymathforum.com/images/math/buttons/mode_hybrid.gif", null, "http://mymathforum.com/images/math/buttons/mode_threaded.gif", null, "http://mymathforum.com/cron.php", null, "http://mymathforum.com/clear.gif", null, "http://mymathforum.com/clear.gif", null, "http://mymathforum.com/clear.gif", null, "http://mymathforum.com/clear.gif", null, "http://mymathforum.com/clear.gif", null, "http://mymathforum.com/clear.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7708021,"math_prob":0.9985619,"size":5181,"snap":"2019-43-2019-47","text_gpt3_token_len":1819,"char_repetition_ratio":0.20996717,"word_repetition_ratio":0.160221,"special_character_ratio":0.39181626,"punctuation_ratio":0.1617916,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99983114,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-21T06:05:20Z\",\"WARC-Record-ID\":\"<urn:uuid:00b4aa6c-c8b7-483d-987f-9e544e137e9a>\",\"Content-Length\":\"50265\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:001ebc25-1b0d-407b-bc81-22505370d68a>\",\"WARC-Concurrent-To\":\"<urn:uuid:5815fd1d-c00b-422e-8504-96f2c5b89738>\",\"WARC-IP-Address\":\"138.68.26.129\",\"WARC-Target-URI\":\"http://mymathforum.com/calculus/343053-lnx-e-x.html\",\"WARC-Payload-Digest\":\"sha1:4C54M64SPBEJIC7NOUHQOUJWSNUGSCJO\",\"WARC-Block-Digest\":\"sha1:BLNURSW2DMXRDD2YQMFBMOWKDUR7GUGD\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496670731.88_warc_CC-MAIN-20191121050543-20191121074543-00348.warc.gz\"}"}
https://planetmath.org/algebraicsumandproduct	[ "# algebraic sum and product\n\nLet $\\alpha,\\,\\beta$ be two elements of an extension field", null, "", null, "of a given field $K$. Both these elements are algebraic over $K$ if and only if both $\\alpha\\!+\\!\\beta$ and $\\alpha\\beta$ are algebraic over $K$.\n\nProof. Assume first that $\\alpha$ and $\\beta$ are algebraic", null, "", null, ". Because\n\n $[K(\\alpha,\\,\\beta):K]=[K(\\alpha,\\,\\beta):K(\\alpha)]\\,[K(\\alpha):K]$\n\nand both here are finite (http://planetmath.org/ExtendedRealNumbers), then $[K(\\alpha,\\,\\beta):K]$ is finite. So we have a finite field extension $K(\\alpha,\\,\\beta)/K$ which thus is also algebraic, and therefore the elements $\\alpha\\!+\\!\\beta$ and $\\alpha\\beta$ of $K(\\alpha,\\,\\beta)$ are algebraic over $K$. Secondly suppose that $\\alpha\\!+\\!\\beta$ and $\\alpha\\beta$ are algebraic over $K$. The elements $\\alpha$ and $\\beta$ are the roots of the quadratic equation$x^{2}-(\\alpha\\!+\\!\\beta)x+\\alpha\\beta=0$ (cf. properties of quadratic equation) with the coefficients in $K(\\alpha\\!+\\!\\beta,\\,\\alpha\\beta)$. Thus\n\n $[K(\\alpha,\\,\\beta):K]=[K(\\alpha,\\,\\beta):K(\\alpha\\!+\\!\\beta,\\,\\alpha\\beta)]\\,[% K(\\alpha\\!+\\!\\beta,\\,\\alpha\\beta):K]\\leqq 2[K(\\alpha\\!+\\!\\beta,\\,\\alpha\\beta):% K].$\n\nSince $[K(\\alpha\\!+\\!\\beta,\\,\\alpha\\beta):K]$ is finite, then also $[K(\\alpha,\\,\\beta):K]$ is, and in the finite extension (http://planetmath.org/FiniteExtension) $K(\\alpha,\\,\\beta)/K$ the elements $\\alpha$ and $\\beta$ must be algebraic over $K$.\n\n Title algebraic sum and product Canonical name AlgebraicSumAndProduct Date of creation 2013-03-22 15:28:03 Last modified on 2013-03-22 15:28:03 Owner pahio (2872) Last modified by pahio (2872) Numerical id 8 Author pahio (2872) Entry type Theorem Classification msc 11R32 Classification msc 11R04 Classification msc 13B05 Synonym sum and product algebraic Related topic FiniteExtension Related topic TheoryOfAlgebraicNumbers Related topic FieldOfAlgebraicNumbers" ]	[ null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null, "http://mathworld.wolfram.com/favicon_mathworld.png", null, "http://planetmath.org/sites/default/files/fab-favicon.ico", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7979835,"math_prob":0.9999366,"size":1240,"snap":"2021-04-2021-17","text_gpt3_token_len":320,"char_repetition_ratio":0.1553398,"word_repetition_ratio":0.011428571,"special_character_ratio":0.24758065,"punctuation_ratio":0.10526316,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000005,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-16T11:38:37Z\",\"WARC-Record-ID\":\"<urn:uuid:bf5b7bb6-84ec-4809-9c12-6d693f9b733b>\",\"Content-Length\":\"15649\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5d7759a4-7fb0-4e2e-b93b-66bfd3f2f615>\",\"WARC-Concurrent-To\":\"<urn:uuid:fa52e26f-f750-4258-b272-de5533de0b9a>\",\"WARC-IP-Address\":\"129.97.206.129\",\"WARC-Target-URI\":\"https://planetmath.org/algebraicsumandproduct\",\"WARC-Payload-Digest\":\"sha1:GRDH76JFRY45L2QLGRGRAWDZTTBNKSC7\",\"WARC-Block-Digest\":\"sha1:ET2QWDFHCAXF6DPYDY6O2J4AULYFNWTG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038056325.1_warc_CC-MAIN-20210416100222-20210416130222-00266.warc.gz\"}"}
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-4-section-4-1-properties-of-a-parallelogram-exercises-page-176/5	[ "## Elementary Geometry for College Students (6th Edition)\n\n(a) $QR = 6.4$ (b) $MP = 10.6$\n(a) The diagonals of a parallelogram bisect each other. Therefore the point R is the midpoint of $\\overline{QN}$ We can find $QR$: $QR = \\frac{QN}{2} = \\frac{12.8}{2} = 6.4$ (b) The diagonals of a parallelogram bisect each other. Therefore the point R is the midpoint of $\\overline{MP}$ We can find $MP$: $MP = 2\\times MR = (2)(5.3) = 10.6$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7806828,"math_prob":1.0000046,"size":396,"snap":"2022-27-2022-33","text_gpt3_token_len":147,"char_repetition_ratio":0.091836736,"word_repetition_ratio":0.3529412,"special_character_ratio":0.38636363,"punctuation_ratio":0.11363637,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000038,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-01T16:49:37Z\",\"WARC-Record-ID\":\"<urn:uuid:7e7c2ef9-daa5-445e-9f8e-45c9904b700d>\",\"Content-Length\":\"56046\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:798a0181-2066-4cf2-b882-7cd5ef544990>\",\"WARC-Concurrent-To\":\"<urn:uuid:93d5f46d-9eff-4dec-9494-b3a0ae7318e8>\",\"WARC-IP-Address\":\"34.228.46.14\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-4-section-4-1-properties-of-a-parallelogram-exercises-page-176/5\",\"WARC-Payload-Digest\":\"sha1:NDYJ64MOR2IACO4JCJ6PROEBADNSST3K\",\"WARC-Block-Digest\":\"sha1:T6K6VVEOPTRPQS3KA4PUJEU5SHC5XAJY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103943339.53_warc_CC-MAIN-20220701155803-20220701185803-00037.warc.gz\"}"}
https://wiki.workxpress.com/doku.php?id=expression%20function%20-%20hyperbolic%20sine&rev=1473877160&do=diff	[ "", null, "# Differences\n\nThis shows you the differences between two versions of the page.\n\n — expression function - hyperbolic sine [2016/09/14 14:19] (current) Line 1: Line 1: + ====== Hyperbolic Sine (Expression Function) ====== + ===== Purpose ===== + The Hyperbolic Sine function (SINH) is used to calculate the hyperbolic sine of an angle given in radians, degrees, or gradians. + + {{::sinh_initial.png?direct&600\|}} + + ===== Parameters ===== + The Hyperbolic Sine function has two parameters, the first of which is required: + + ==== Radians ==== + + Allowed Inputs: [[Field\|field]] value or number + + The first required parameter is the angle that the hyperbolic sine will be obtained from either use the use the [[Query Builder]] to choose a field that contains the value or use type a value to enter a number. + + ==== Angle Unit ==== + + Allowed Inputs: omitted, 'd', 'g' + + The second parameter of the Hyperbolic Sine function is the unit the angle is provided in. If the angle unit is omitted or not recognized then radians will be be used. For an angle provided in degrees use 'd'. For an angle provided in gradians use 'g'. If the angle unit needs to be dynamically stored in a field then the advanced expression builder will need to be used. + + + ===== Output ===== + + The output of the Hyperbolic Sine function is a number representing the horizontal run of an angle where in intersects with the unit hyperbola. + + ===== Example ===== + + For example SINH(0.5235987755983), SINH(30,'d'), and SINH(33.3333333333,'g') would result in \"0.547853473888\".\nexpression function - hyperbolic sine.txt · Last modified: 2016/09/14 14:19 (external edit)", null, "", null, "", null, "" ]	[ null, "https://wiki.workxpress.com/lib/tpl/arctic/images/logo.png", null, "https://wiki.workxpress.com/lib/tpl/arctic/images/fade-left.png", null, "https://wiki.workxpress.com/lib/tpl/arctic/images/fade-right.png", null, "https://wiki.workxpress.com/lib/exe/indexer.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.643914,"math_prob":0.9888071,"size":1718,"snap":"2020-24-2020-29","text_gpt3_token_len":467,"char_repetition_ratio":0.16452742,"word_repetition_ratio":0.042857144,"special_character_ratio":0.34167635,"punctuation_ratio":0.114285715,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99651575,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-04T11:14:48Z\",\"WARC-Record-ID\":\"<urn:uuid:7c9103a1-b390-4341-a6b7-88f21b165630>\",\"Content-Length\":\"21388\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f7cec046-a937-4358-9c93-4723b281de60>\",\"WARC-Concurrent-To\":\"<urn:uuid:cde0b631-798f-4161-9239-9947a4d5b44c>\",\"WARC-IP-Address\":\"104.196.129.10\",\"WARC-Target-URI\":\"https://wiki.workxpress.com/doku.php?id=expression%20function%20-%20hyperbolic%20sine&rev=1473877160&do=diff\",\"WARC-Payload-Digest\":\"sha1:Z3T2623GT2ADXSVWTEOSNIFJERIILLL5\",\"WARC-Block-Digest\":\"sha1:WS4LJWAPRKUH65WH3EF47M7ZBG7EQKWN\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655886121.45_warc_CC-MAIN-20200704104352-20200704134352-00170.warc.gz\"}"}
https://www.colorhexa.com/0d07d3	[ "# #0d07d3 Color Information\n\nIn a RGB color space, hex #0d07d3 is composed of 5.1% red, 2.7% green and 82.7% blue. Whereas in a CMYK color space, it is composed of 93.8% cyan, 96.7% magenta, 0% yellow and 17.3% black. It has a hue angle of 241.8 degrees, a saturation of 93.6% and a lightness of 42.7%. #0d07d3 color hex could be obtained by blending #1a0eff with #0000a7. Closest websafe color is: #0000cc.\n\n• R 5\n• G 3\n• B 83\nRGB color chart\n• C 94\n• M 97\n• Y 0\n• K 17\nCMYK color chart\n\n#0d07d3 color description : Strong blue.\n\n# #0d07d3 Color Conversion\n\nThe hexadecimal color #0d07d3 has RGB values of R:13, G:7, B:211 and CMYK values of C:0.94, M:0.97, Y:0, K:0.17. Its decimal value is 853971.\n\nHex triplet RGB Decimal 0d07d3 `#0d07d3` 13, 7, 211 `rgb(13,7,211)` 5.1, 2.7, 82.7 `rgb(5.1%,2.7%,82.7%)` 94, 97, 0, 17 241.8°, 93.6, 42.7 `hsl(241.8,93.6%,42.7%)` 241.8°, 96.7, 82.7 0000cc `#0000cc`\nCIE-LAB 26.562, 67.357, -92.338 11.997, 4.94, 61.946 0.152, 0.063, 4.94 26.562, 114.295, 306.109 26.562, -7.376, -105.267 22.226, 57.461, -149.691 00001101, 00000111, 11010011\n\n# Color Schemes with #0d07d3\n\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #cdd307\n``#cdd307` `rgb(205,211,7)``\nComplementary Color\n• #0767d3\n``#0767d3` `rgb(7,103,211)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #7307d3\n``#7307d3` `rgb(115,7,211)``\nAnalogous Color\n• #67d307\n``#67d307` `rgb(103,211,7)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #d37307\n``#d37307` `rgb(211,115,7)``\nSplit Complementary Color\n• #07d30d\n``#07d30d` `rgb(7,211,13)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #d30d07\n``#d30d07` `rgb(211,13,7)``\n• #07cdd3\n``#07cdd3` `rgb(7,205,211)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #d30d07\n``#d30d07` `rgb(211,13,7)``\n• #cdd307\n``#cdd307` `rgb(205,211,7)``\n• #080589\n``#080589` `rgb(8,5,137)``\n• #0a05a2\n``#0a05a2` `rgb(10,5,162)``\n• #0b06ba\n``#0b06ba` `rgb(11,6,186)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #0f08ec\n``#0f08ec` `rgb(15,8,236)``\n• #1c16f7\n``#1c16f7` `rgb(28,22,247)``\n• #342ef8\n``#342ef8` `rgb(52,46,248)``\nMonochromatic Color\n\n# Alternatives to #0d07d3\n\nBelow, you can see some colors close to #0d07d3. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #0734d3\n``#0734d3` `rgb(7,52,211)``\n• #0723d3\n``#0723d3` `rgb(7,35,211)``\n• #0712d3\n``#0712d3` `rgb(7,18,211)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #1e07d3\n``#1e07d3` `rgb(30,7,211)``\n• #2f07d3\n``#2f07d3` `rgb(47,7,211)``\n• #4007d3\n``#4007d3` `rgb(64,7,211)``\nSimilar Colors\n\n# #0d07d3 Preview\n\nThis text has a font color of #0d07d3.\n\n``<span style=\"color:#0d07d3;\">Text here</span>``\n#0d07d3 background color\n\nThis paragraph has a background color of #0d07d3.\n\n``<p style=\"background-color:#0d07d3;\">Content here</p>``\n#0d07d3 border color\n\nThis element has a border color of #0d07d3.\n\n``<div style=\"border:1px solid #0d07d3;\">Content here</div>``\nCSS codes\n``.text {color:#0d07d3;}``\n``.background {background-color:#0d07d3;}``\n``.border {border:1px solid #0d07d3;}``\n\n# Shades and Tints of #0d07d3\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, #000002 is the darkest color, while #efeefe is the lightest one.\n\n• #000002\n``#000002` `rgb(0,0,2)``\n• #010115\n``#010115` `rgb(1,1,21)``\n• #020128\n``#020128` `rgb(2,1,40)``\n• #04023b\n``#04023b` `rgb(4,2,59)``\n• #05034e\n``#05034e` `rgb(5,3,78)``\n• #060361\n``#060361` `rgb(6,3,97)``\n• #070474\n``#070474` `rgb(7,4,116)``\n• #080487\n``#080487` `rgb(8,4,135)``\n• #09059a\n``#09059a` `rgb(9,5,154)``\n``#0b06ad` `rgb(11,6,173)``\n• #0c06c0\n``#0c06c0` `rgb(12,6,192)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\n• #0e08e6\n``#0e08e6` `rgb(14,8,230)``\n• #110af7\n``#110af7` `rgb(17,10,247)``\n• #241df8\n``#241df8` `rgb(36,29,248)``\n• #3630f8\n``#3630f8` `rgb(54,48,248)``\n• #4943f9\n``#4943f9` `rgb(73,67,249)``\n• #5b56f9\n``#5b56f9` `rgb(91,86,249)``\n• #6e69fa\n``#6e69fa` `rgb(110,105,250)``\n• #807cfb\n``#807cfb` `rgb(128,124,251)``\n• #928ffb\n``#928ffb` `rgb(146,143,251)``\n• #a5a2fc\n``#a5a2fc` `rgb(165,162,252)``\n• #b7b5fd\n``#b7b5fd` `rgb(183,181,253)``\n• #cac8fd\n``#cac8fd` `rgb(202,200,253)``\n• #dcdbfe\n``#dcdbfe` `rgb(220,219,254)``\n• #efeefe\n``#efeefe` `rgb(239,238,254)``\nTint Color Variation\n\n# Tones of #0d07d3\n\nA tone is produced by adding gray to any pure hue. In this case, #6c6c6e is the less saturated color, while #0d07d3 is the most saturated one.\n\n• #6c6c6e\n``#6c6c6e` `rgb(108,108,110)``\n• #646377\n``#646377` `rgb(100,99,119)``\n• #5c5b7f\n``#5c5b7f` `rgb(92,91,127)``\n• #545288\n``#545288` `rgb(84,82,136)``\n• #4c4a90\n``#4c4a90` `rgb(76,74,144)``\n• #444298\n``#444298` `rgb(68,66,152)``\n• #3c39a1\n``#3c39a1` `rgb(60,57,161)``\n• #3431a9\n``#3431a9` `rgb(52,49,169)``\n• #2d29b1\n``#2d29b1` `rgb(45,41,177)``\n• #2520ba\n``#2520ba` `rgb(37,32,186)``\n• #1d18c2\n``#1d18c2` `rgb(29,24,194)``\n• #150fcb\n``#150fcb` `rgb(21,15,203)``\n• #0d07d3\n``#0d07d3` `rgb(13,7,211)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #0d07d3 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5476959,"math_prob":0.6637828,"size":3657,"snap":"2020-10-2020-16","text_gpt3_token_len":1690,"char_repetition_ratio":0.12455516,"word_repetition_ratio":0.011111111,"special_character_ratio":0.55646706,"punctuation_ratio":0.23809524,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98465073,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-23T23:46:02Z\",\"WARC-Record-ID\":\"<urn:uuid:9ed4a62c-b52a-4008-88f1-a3168a865ac0>\",\"Content-Length\":\"36211\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4e593ccb-0ad9-4d35-b20d-319b3e0429cd>\",\"WARC-Concurrent-To\":\"<urn:uuid:75acff9b-9114-4b80-a4d6-e6af9bccc98d>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/0d07d3\",\"WARC-Payload-Digest\":\"sha1:TO42KWCDLL7X3GVNJOLBU7VKT3Q7QVSM\",\"WARC-Block-Digest\":\"sha1:EWJFQ3CF3PVM5AWU3VQK57BJRKCF7YA3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145859.65_warc_CC-MAIN-20200223215635-20200224005635-00116.warc.gz\"}"}
http://icpc.njust.edu.cn/Problem/Hdu/5937/	[ "# Equation\n\nTime Limit: 2000/1000 MS (Java/Others)\n\nMemory Limit: 65536/32768 K (Java/Others)\n\n## Description\n\nLittle Ruins is a studious boy, recently he learned addition operation! He was rewarded some number bricks of $1$ to $9$ and infinity bricks of addition mark '+' and equal mark '='.\n\nNow little Ruins is puzzled by those bricks because he wants to put those bricks into as many different addition equations form $x + y = z$ as possible. Each brick can be used at most once and x, y, z are one digit integer.\n\nAs Ruins is a beginer of addition operation, $x$, $y$ and $z$ will be single digit number.\n\nTwo addition equations are different if any number of $x$, $y$ and $z$ is different.\n\n## Input\n\nFirst line contains an integer $T$, which indicates the number of test cases.\n\nEvery test case contains one line with nine integers, the $i^{th}$ integer indicates the number of bricks of $i$.\n\nLimits\n$1 \\leq T \\leq 30$\n$0 \\leq \\text{bricks number of each type} \\leq 100$\n\n## Output\n\nFor every test case, you should output 'Case #x: y', where x indicates the case number and counts from 1 and y is the result.\n\n## Sample Input\n\n3\n1 1 1 1 1 1 1 1 1\n2 2 2 2 2 2 2 2 2\n0 3 3 0 3 0 0 0 0\n\n## Sample Output\n\nCase #1: 2\nCase #2: 6\nCase #3: 2\n\nliuyiding\n\n## Source\n\n2016年中国大学生程序设计竞赛（杭州）" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.906579,"math_prob":0.9947877,"size":1080,"snap":"2020-24-2020-29","text_gpt3_token_len":270,"char_repetition_ratio":0.14405204,"word_repetition_ratio":0.0,"special_character_ratio":0.25462964,"punctuation_ratio":0.09589041,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958101,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T05:52:11Z\",\"WARC-Record-ID\":\"<urn:uuid:9eca1a02-f34a-4a9a-8c92-992ed6dcdf0d>\",\"Content-Length\":\"35284\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:41f3412d-af95-4daf-92d5-4dab5a55ef61>\",\"WARC-Concurrent-To\":\"<urn:uuid:06a9d1e2-1080-4494-aad9-f093ec06bcfa>\",\"WARC-IP-Address\":\"202.119.84.52\",\"WARC-Target-URI\":\"http://icpc.njust.edu.cn/Problem/Hdu/5937/\",\"WARC-Payload-Digest\":\"sha1:AGAG6ICNZUWTMELD7I6J2DIGUKJULFJX\",\"WARC-Block-Digest\":\"sha1:XM6JMPQZKSIOYRKVYNHRRIG4ANAAQ2SU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655878519.27_warc_CC-MAIN-20200702045758-20200702075758-00497.warc.gz\"}"}
https://or.stackexchange.com/questions/4374/linearization-of-the-shifted-copy-of-a-function	[ "# Linearization of the shifted copy of a function\n\nSuppose in a model I have the expression $$y_{1}(x) = 10 + 5 x^2$$ where $$x \\in [0,20]$$ is a continuous variable. In order to be able to use an MILP solver, I piecewise linearise $$z_{1} = x^2$$, by choosing $$\\{0,5,10,20\\}$$ as arbitrary values for $$x$$, as follows:\n\n$$x = 0 \\lambda_{1} + 5 \\lambda_{2} + 10 \\lambda_{3} + 20 \\lambda_{4} \\\\ z_{1} =0 \\lambda_{1} + 25 \\lambda_{2} + 100 \\lambda_{3} + 400 \\lambda_{4} \\\\ \\lambda_{1} + \\lambda_{2} + \\lambda_{3} + \\lambda_{4} = 1$$\n\nIn the same model, I have to deal with the function:\n\n$$y_{2}(x,d) = 20 + 5 (x-d)^2, d \\ge 0$$, $$d$$ is a variable\n\nIs there a way to express $$(x-d)^2$$ in a linearised form in terms of $$\\lambda_{1}, \\lambda_{2}, \\lambda_{3}, \\lambda_{4}$$?\n\nPlease consider that $$y_{1}(x)$$ could be any nonlinear function, the quadratic form stated here is just an example.\n\n• Is $d$ really a variable of the whole model, and not a parameter? (Asking as the function is $y_2(x)$ and not $y_2(x, d)$) Jun 13 '20 at 15:42\n• d is a decision variable. $y_{2}(x)$ should be written $y_{2}(x,d)$, you are right. Jun 13 '20 at 17:08\n• First, is $x$ constrained to $\\lbrace 0, 5, 10, 20\\rbrace$ in the model? (Your constraints imply this.) Next, is $d$ discrete, and if so can you enumerate the possible values of $d$. Jun 13 '20 at 21:23\n• The three equations $x= ...$ , $z_{1} = ...$ , $\\lambda_{1} + ...$ are supposed to piecewise linear approximate $x^2$ within [0,20]. The points $x=0$, $x=5$, $x=10$, $x=20$ are chosen arbitrarily for this example. $d$ is not discrete. The only constraint imposed on $d$ is $x-d \\ge 0.0$. Jun 13 '20 at 22:44\n• $(x-d)^2=x^2 - 2xd + d^2$ and then you can look at or.stackexchange.com/questions/180/… for the middle term.\n– PSLP\nJun 15 '20 at 6:53" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8152333,"math_prob":1.0000036,"size":820,"snap":"2021-43-2021-49","text_gpt3_token_len":302,"char_repetition_ratio":0.19975491,"word_repetition_ratio":0.0,"special_character_ratio":0.44878048,"punctuation_ratio":0.110497236,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000024,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-18T17:59:22Z\",\"WARC-Record-ID\":\"<urn:uuid:ec1a1ffd-b684-47b8-a8a3-b16de7969fbf>\",\"Content-Length\":\"153746\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:06fc94de-8d8f-4949-a3e1-312771c34bc4>\",\"WARC-Concurrent-To\":\"<urn:uuid:08888d36-9d8c-47db-af49-3bea0d8c7696>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://or.stackexchange.com/questions/4374/linearization-of-the-shifted-copy-of-a-function\",\"WARC-Payload-Digest\":\"sha1:GIVOMBG6W6GHFRD24W4F6URMHG23VJLG\",\"WARC-Block-Digest\":\"sha1:TAI2I5KEVCDEUDMAYHEAE7BT3B4JV2PM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585204.68_warc_CC-MAIN-20211018155442-20211018185442-00013.warc.gz\"}"}
https://www.comsol.com/blogs/solving-shallow-water-equations-with-equation-based-modeling/?setlang=1	[ "", null, "", null, "# Solving Shallow Water Equations with Equation-Based Modeling\n\nFebruary 21, 2017\n\nThe COMSOL Multiphysics® software includes many built-in physics equations and interfaces, but there may be times when you need to implement physics that aren’t part of the software to solve your modeling problem. You can use the flexibility of the COMSOL® software to add user-defined equations via equation-based modeling. Today, we discuss using equation-based modeling to solve a shallow water equation, which can be used to analyze coastal erosion.\n\n### Analyzing Coastal Erosion with Shallow Water Equations\n\nOn the shoreline, crashing waves and the continuous movement of the tides cause coastal erosion, a phenomenon that removes sediment from beaches and wears away land.", null, "A rock formation affected by coastal erosion. Image by John Nuttall — Own work. Licensed under CC BY 2.0, via Flickr Creative Commons.\n\nAlthough coastal erosion has benefits, such as creating sand for beaches, it also causes damage to seaside property and habitats. To help predict this damage, researchers can use shallow water equations to learn more about coastal erosion. These equations enable scientists to model oceanographic and atmospheric fluid flow, thereby predicting what areas will be affected by coastal erosion and other issues, such as polar ice cap melting and pollution.\n\nShallow water equations are beneficial compared to the Navier-Stokes equations, which may be problematic depending on how free surfaces are resolved and the scale of the modeling domain. Today, we highlight a tutorial that showcases how to solve shallow water equations using the power of equation-based modeling.\n\n### Solving Shallow Water Equations in COMSOL Multiphysics®\n\nIn this shallow water equation model, we can describe the physics by adding our own equations — a feature called equation-based modeling. We use the General Form PDE interface and two dependent variables to ensure that the modeling process is straightforward. This way, we can easily define expressions as model variables, which comes in handy when defining the initial wave profile.\n\nThis simple 1D model uses the Saint-Venant shallow water equations to study a wave settling over a variable bed as a function of time.\n\nThe 1D model featured here would require substantial work to convert into a 2D model for solving typical applications. This tutorial is therefore most useful as an example of the benefits of equation-based modeling.", null, "A vertical section of the fluid domain. Here, zf is the analytical expression for the seabed profile and zs is the water surface profile.\n\nThe model, which investigates shallow water in a channel, has constraints at both ends and uses a wave profile as the initial condition. In order to easily alter parameters like the wave amplitude and bed shape, we can use mathematical relations to represent the initial wave and bed shapes. Please note that the model has a difference in scale between the x– and y-directions, as seen in the plots below.\n\nPlots of the seabed profile (left) and a comparison of the initial water surface profile with the seabed profile (right).\n\nWe see that the flow develops hydraulic jump discontinuities over time, which can cause instability in the solution. To stabilize the solution, we can add an artificial viscosity that makes the cell Reynolds number of order unity. The hydraulic jumps are replaced with steep fronts that can be resolved on a grid.\n\nSwitching gears, let’s take a look at our results. After running the simulation for 60 seconds, we see results that show the water surface and seabed slope at 6 different times, from the start of the simulation to 15 seconds later.", null, "Plots of the seabed profile and water surface level at 3-second increments.\n\nThese results clearly indicate that the seabed topography influences the water surface elevation. This, in turn, affects the impact of coastal erosion.\n\nWe can share these custom results with others by creating and exporting an animation to help visualize our findings — something that is easy to do in COMSOL Multiphysics.\n\nAn animation of the simulation results.\n\nAs a next step, try this tutorial yourself by clicking on the button below." ]	[ null, "https://cdn.comsol.com/company/logo/comsol-logo-130x20.png", null, "https://cdn.comsol.com/wordpress/sites/1/2018/09/COMSOL_Blog_Header_General.png", null, "https://cdn.comsol.com/wordpress/2017/02/eroded-shoreline.jpeg", null, "https://cdn.comsol.com/wordpress/2017/02/vertical-section-of-fluid-domain.png", null, "https://cdn.comsol.com/wordpress/2017/02/seabed-profile-over-time-plotted-in-COMSOL-Multiphysics.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90772647,"math_prob":0.9577643,"size":4319,"snap":"2020-34-2020-40","text_gpt3_token_len":859,"char_repetition_ratio":0.13696408,"word_repetition_ratio":0.0029239766,"special_character_ratio":0.18522806,"punctuation_ratio":0.085413925,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9592753,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,5,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-12T00:27:25Z\",\"WARC-Record-ID\":\"<urn:uuid:6ea29f41-c547-4ca9-8f65-a3a0b0f342da>\",\"Content-Length\":\"94775\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f64717fe-02d8-4644-9e9d-9f05ce4af338>\",\"WARC-Concurrent-To\":\"<urn:uuid:50abc34e-8f90-4ba7-a0e8-7a3da026954c>\",\"WARC-IP-Address\":\"4.31.158.132\",\"WARC-Target-URI\":\"https://www.comsol.com/blogs/solving-shallow-water-equations-with-equation-based-modeling/?setlang=1\",\"WARC-Payload-Digest\":\"sha1:EK53SAXZXLGLTGKQKPNWGVMHS642DTQ3\",\"WARC-Block-Digest\":\"sha1:27LED62ZPDQFJ46VAQ4M3FUM6WZ7II3X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439738858.45_warc_CC-MAIN-20200811235207-20200812025207-00005.warc.gz\"}"}
https://www.physicsforums.com/threads/stress-tensor.90636/	[ "# Stress Tensor\n\nHello,\n\nPlease help me out here as I self study fluid mechanics. I ran into what they are calling a second order tensor quantity, which seems to be fancy words for a 3x3 matrix of sigmas and rhos, for shear and normal stress. They have a picture of a cube, with all the positive stresses indicated on it. Now they have a convention like sigma_xx or sigma_xy. I get that. I dont get the picture of the cube, though. Is it merely an illustration? See they start with the premise that you are looking locally at point C in space. And you make a plane of area deltaA, perpendicular to the x axis, then you find the shear and normal stress to the unit normal. Then they repeat for the other two orthogonal planes. Thats fine. Then the say there are an infinte number of planes that can pass through point C and have different shear values, FINE! Then they say that any stress can be found for any plane provided that you now know these three mutually perpendicular stress planes.......ok i kinda see what they mean, but im not tooo sure.....I could use some explaining on that point. Also, this damn box!? Is point C somewhere inside this box of dimensions dx,dy,dz?? Why is this thing now a box, I thought we just cared about flat planar areas that passed through point c? Is point C now surrounded by this box? Or is the box there just to explain to my stupid self the purpose of the x,y subsripts, becuase I have a feeling its going to be used as a local control surface for some reason.\n\n(This stuffs still great fun so far!", null, "Im just annoyed at the unclarity)\n\nAstronuc\nStaff Emeritus\nWell, stress (like pressure) is force/unit area, and one has three dimensions.\n\nWith three dimensions mutually orthogonal, each direction (dimension) has a surface associated with it formed by the other two dimensions. Thus the y,z-plane is perpendicular to x-direction, the x,z-plane to the y-direction, and the x,y-plane to the z-direction (in Cartesian cooridates). So with three dimensions there is an incremental volume (cube) with 6 faces (surface areas, planes) associated with the volume.\n\nThere are normal stress $\\sigma_{xx}, \\sigma_{yy}, and \\sigma_{zz}$ which act normal to a plane (surface) in tension or compression, and there are shear stress, e.g. $\\sigma_{xy} = \\tau_{xy}$ which acts parallel to a plane (surface). The $\\sigma_{xx}$ stress acts in the x-direction on the y,z plane (surface).\n\nI realize that astronuc, but my question was why the cube? I already know what the stresses and planes represnt, but im asking WHY are there 6 of them constructed the way they are?\n\nPerennialII\nGold Member\nTo satisfy the balance and equilibrium equations continuum mechanics is build upon in a 3D spatial description. That accounts for the 6 planes, the cube is a differential geometrical element.\n\nOk, and it is dx,dy,dz in dimension, but is it always true that dx,dy,dz are equal in magnitude? I dont see why they have to be, I have yet to run into a definition stating that they are.\n\nAstronuc\nStaff Emeritus\ncyrusabdollahi said:\nI realize that astronuc, but my question was why the cube? I already know what the stresses and planes represnt, but im asking WHY are there 6 of them constructed the way they are?\nAs PerennialII pointed out, a cube is an element in differential geometry, and it is the simplest volume element in Cartesian coordinates. What other volume element geometry would one propose?\n\nIf one used cylindrical or spherical coordinates (geometry) then one could use an annular or spherical volume segment.\n\nThe cube has 6 faces in 3D. In a static system, equal an opposing forces are applied on opposite faces of a volume element.\n\nPerennialII\nGold Member\nFollowing a typical differential geometric treatment their size is really not that much of an issue, the differential element under question being the smallest element in the continuum treatment's \"radar\", \"resolution\" etc. But if you think about the sizing of the different axes, nothing is gained by making them different sizes since it does not increase the \"information content\" of the solution of the problem (or its formulation)(ok, I'd say you could do it, but can't really see for what reason unless you'd be doing something really exotic, anisotropic, mixing different equilibrium concepts, material models etc., and even in such cases the basic formulation can be retained & formulated in a \"simple\" differential cube).\n\nVector base continuum non-cauchian theorem\n\nSymmetry of stress tensor ( ) is the start point of this survey. As we know in non-magnetic fields this symmetry is always valid and everybody has been accepting that for 200 years after Cauchy.\nWhile in quantum or discrete mechanics (statistical mechanics) it’s not evident. Also there are some continua situations, in them, that symmetry isn’t valid. So what is the reason of this difference? What is the problem?\n\nWhy a differential tetrahedron element is used? Nobody cares. But it’s the point because this element just differentiate the position not the orientation!\nAnd this result is not valid for any arbitrary volume, we will show the Cauchy principle is just a approximate solution of sigma. However we don’t know the exact one but it doesn’t matter.\n\nIn next we will try to find the most general shape for the relation. It’s just a claim to say vector form of equations is a valid shape for Cauchy–Riemann rules and we can’t prove it yet.\nWe will generate the conservative rule equations without assumption of linear mapping. And we show the computational cost advantages of vector base continuum in compare whit tensor.\nSome constitutive equations will be written in vector base form and we regenerate some well-known deformation such as navier-stockse\n\n#### Attachments\n\n• presentation.pdf\n1.7 MB · Views: 224" ]	[ null, "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94000894,"math_prob":0.93991745,"size":3168,"snap":"2021-31-2021-39","text_gpt3_token_len":725,"char_repetition_ratio":0.10493047,"word_repetition_ratio":0.9797297,"special_character_ratio":0.22632575,"punctuation_ratio":0.13980028,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9771588,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T20:03:51Z\",\"WARC-Record-ID\":\"<urn:uuid:cfe4c82c-1b15-4f27-9d8a-e9194a337bf3>\",\"Content-Length\":\"83049\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9c67787f-6e73-4e70-939a-6c2d19a290b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:c556c290-9690-4e06-a1f8-e937069270c9>\",\"WARC-IP-Address\":\"104.26.15.132\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/stress-tensor.90636/\",\"WARC-Payload-Digest\":\"sha1:4BBXB34LOOY6RKN5QM6WBIZFR77JXE2Z\",\"WARC-Block-Digest\":\"sha1:NSNU5V3E6H6E6XRP5QGEJN6FCNNJZWNR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056900.32_warc_CC-MAIN-20210919190128-20210919220128-00217.warc.gz\"}"}