text: Define a covalent bond. Special ChemDoodle Offer. It was a question on a chemistry exam asking the formula of tellurium bromide. Video: Drawing the Lewis Structure for BrF 5. Woollins; Department of Applied Chemistry, College of Engineering, Chubu … To learn more, see our tips on writing great answers. If the central atom also contains one or more pairs of non-bonding electrons, these additional regions of negative charge will behave much like those associated with the bonded atoms. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. First of all, they're compounds and not elements. Chemistry. ; In the Lewis structure for BrF 5 there are a total of 42 valence electrons. I actually wonder what the higher goal is: Underwater prison for cyborg/enhanced prisoners? Predicted data is generated using the US Environmental Protection Agency’s EPISuite™. The molecule CBr4 is non-polar. CH3OH. ... UN proper shipping name TELLURIUM COMPOUND, N.O.S Technical Shipping Name(Potassium hexabromotellurate (IV)) 4 bonds means you have sp3. Log Octanol-Water Partition Coef (SRC): Log Kow (KOWWIN v1.67 estimate) = 1.83 Boiling Pt, Melting Pt, Vapor Pressure Estimations (MPBPWIN v1.42): Boiling Pt (deg C): 629.16 (Adapted Stein & Brown method) Melting Pt (deg C): 272.93 (Mean or Weighted MP) VP(mm Hg,25 deg C): 1.06E-013 (Modified Grain … 6) K 3N potassium nitride. Bromine is in group 7 or 17, so it has 7 valence electrons. 259 – 267). The preferred IUPAC name is, indeed, (chloromethyl)benzene, built from substitutive prefix chloromethyl.The parentheses around "chloromethyl" are required because it is a compound substituent (a simple substituent attached to another simple substituent, specifically, methyl and chloro in this case). Making statements based on opinion; back them up with references or personal experience. Dipole moments are not possible in rubber due to its molecules' similar charges, and it is not soluble in water. ; For the BrF 5 Lewis structure, you'll need to put more than eight valence electrons on the Bromine atom. cation on left, anion of the right. We will use valence shell electron pair repulsion (VSEPR) theory to determine its molecular geometry. The compound of five tetrahedra represents two chiral halves of this compound (it can therefore be seen as a "compound of two compounds of five tetrahedra"). Can you legally move a dead body to preserve it as evidence? chemistry. Typically, N–N bonds are similar in length to that in hydrazine (145 pm). Sign in. In chemical nomenclature, the IUPAC nomenclature of organic chemistry is a method of naming organic chemical compounds as recommended by the International Union of Pure and Applied Chemistry (IUPAC). a polyatomic ion. Examples of compound words that have the word 'name' in them are:code namedomain namefamily namefirst namegiven namelast namemaiden namemarried namename droppername tag 517-530. Accelerating the experimental cycle for new materials development is vital for addressing the grand energy challenges of the 21 st century. MathJax reference. Email: info@alfa-chemistry.com Tel:1-201-478-8534 1-516-662-5404 Fax: 1-516-927-0118 Address: 2200 Smithtown Avenue, Room 1 Ronkonkoma, NY 11779-7329 USA For product inquiries, please use our online system or send an email to inquiry@alfa-chemistry.com Example Reactions: • SeBr6 + O2 = SeO2 + 3Br2. What is the name of the compound I2Br6? Answers – Naming Chemical Compounds . Transition metals, lanthanides and actinides. Parsing JSON data from a text column in Postgres, Comparing method of differentiation in variational quantum circuit, Altering table row colors trought multirow. I was (and still am) too lazy to look up the relevant rules so just decided to edit in a brief line about the parentheses; I leave it to you if you want to expand further or write another answer. It can also be seen as the compound of ten tetrahedra with full icosahedral symmetry (I h).It is one of five regular compounds constructed from identical Platonic solids.. Copyright © 2021 Elsevier B.V. or its licensors or contributors. Name the following compound correctly using accurate R or S and E and Z nomenclature. We systematize available experimental data on the crystal structure of the ternary halides K2(Rb2,Cs2,Tl2)TeBr6(I6) and Rb3(Cs3)Sb2(Bi2)Br9(I9), analyze the general trends in … & &\text{(isothiocyanatomethyl)benzene (PIN)} \\ UNSPECIFIED (2001) 1-chloro-2-fluoroethane adsorption on Cu(111): Structure and bonding. (Exact Name of Registrant as Specified in its Charter) Delaware : 001-51290 : 52-1841431 (State or other jurisdiction. Note that common names for this molecule also include: benzyl chloride and α-chlorotoluene. In general, levels causing . To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Is the Gelatinous ice cube familar official? Omission of locants for functional groups in IUPAC names, IUPAC name of trisubstituted benzene ring. What does "Drive Friendly -- The Texas Way" mean? 4) Ti(SO 4) 2 titanium(IV) sulfate. Q. what is the hybridization at O with the lewis structure of 2-propanone? (1 point) 1. How to label resources belonging to users in a two-sided marketplace? Predicted data is generated using the US Environmental Protection Agency’s EPISuite™. There is only a limited number of free calls to the ChemDoodle algorithm. Drawing the Lewis Structure for BrF 5. & & \\ these names are used only if compound dissolved in water to make acid Acid – releases H+ ion (attaches to water to form H3O+ hydronium) Acids without Oxygen Binary or binary related acids hydro___ic acid Ex: Compound Name Acid Name HCl hydrogen chloride hydrochloric … Preparation and properties. Ditellurium bromide is the inorganic compound with the formula Te 2 Br.It is one of the few stable lower bromides of tellurium. \begin{array}{lll} 9) Zn(NO Name the following chemical compounds: 1) NaBr sodium bromide. & &\text{isocyanobenzene (PIN)} that's 4 bonds per carbon. pp. \end{array} Let's start this quiz; it will give you the different functions of the International Union of Pure and Applied Chemistry (IUPAC) naming chemical compounds… Drawing the Lewis Structure for BrF 5. They are accommodating to explain molecular geometry and nuclear bonding properties. what is the hybridization of … EXPERIMENTAL Preparative work (t-BuNH3)2[TeBr6] was prepared by the addition of t-BuNH3Br to a solution of TeBr4 in hydro- bromic acid. And you have a methyl group: one carbon attached to the fourth carbon of our main backbone. Source(s): correct febr3: https://biturl.im/147uv. Yash. Compounds (2) and (3) are magnetically different and (1) and (2) undergo changes in magnetic properties at ca. Te 2 Br is a gray solid. Ideally, every possible organic compound should have a name from which an unambiguous structural … TeBr6 . POST-LAB DISCUSSION: (23 points) Read the entire lab and the relevant parts of your textbook (Chapter 9; pp. Log Octanol-Water Partition Coef (SRC): Log Kow (KOWWIN v1.67 estimate) = 1.83 Boiling Pt, Melting Pt, Vapor Pressure Estimations (MPBPWIN v1.42): Boiling Pt (deg C): 629.16 (Adapted Stein & Brown method) Melting Pt (deg C): 272.93 (Mean or Weighted MP) VP(mm Hg,25 deg C): 1.06E-013 (Modified Grain … C2H4. This compound is sometimes called "nitrogen trioxide", but this name properly refers to another compound, the (uncharged) nitrate radical NO 3. Thanks for contributing an answer to Chemistry Stack Exchange! 7) SO 2 sulfur dioxide. In the geometry, three atoms are in the same plane with bond angles of 120°; the other two atoms are on opposite ends of the molecule. Q. Special ChemDoodle Offer. Pairs 3D Drawing Name of . Compounds (2) and (3) are magnetically different and (1) and (2) undergo changes in magnetic properties at ca. Organometallic-Chelate Compounds: Organometallic Ions as Central Metal Ions DEAN F. MARTIN Chapter 35 , 555-564 DOI: 10.1021/ba-1967-0062.ch035 Publication Date (Print) : January 1, 1967 You can sign in to vote the answer. Q. Iron (III) bromide. Polar or Nonpolar Molecule . For unlimited access, please consider supporting the ChemDoodle team with a special offer for a $15 ChemDoodle license.Join the hundreds of thousands of professionals and students that use ChemDoodle every day to finish their work faster and more accurately. Define a covalent bond. So it was brought up, I think the user name is Minoctu, and they correctly corrected me, that there would never be such a thing as 2-Propylheptane. Found: C, 12.8 ; H, 3.1 ; N, 3.7. Transcript: This is the Br3- Lewis structure. Give 3 examples where the lewis model is not applicable. Phosphorus trifluoride is the name of PF 3. The structure of (7) was solved at room temperature. Two bonds means sp hybridization. Molecular Shape Bonds . BF3 Hybridization . Look at how many bonds the carbon atoms are making. (1 point) 1. It shares the same vertex arrangement as a dodecahedron.. Structure and bonding. I thought that the correct IUPAC name for the molecule below (benzyl chloride) would be chloromethylbenzene because the ring always gets priority over the chain unless a primary functional group is present. Anonymous. How true is this observation concerning battle? Rubber is considered nonpolar. The remark about the use of parentheses is correct. The preferred IUPAC name is, indeed, (chloromethyl)benzene, built from substitutive prefix chloromethyl. Be sure to designate each configuration properly for this single stereoisomer. Q. 0 0. Pairs 3D Drawing Name of . of incorporation) (Commission. activation, the compound induced variable but nevertheless reproducible significant increases in the percentage of aberrant cells in two of three experiments using treatment times of 20-24 hours. CO2. There are several types of hybridization like SP3, SP2, SP. $$. 3) P 2O 5 diphosphorus pentoxide. Common compound names. Relevant identified uses of the substance or mixture and uses advised against Recommended Use Laboratory chemicals. Drawing the Lewis Structure for BrF 5. 1 decade ago. Dinitrogen trioxide, … ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. 1 decade ago. Then answer the questions that follow. The two X atoms (in white) are 180° away from one another. Molecular Formula K2 TeBr6 1.2. How did SNES render more accurate perspective than PS1? How would interspecies lovers with alien body plans safely engage in physical intimacy? Is chlorophenylmethane the correct IUPAC name rather than chloromethylbenzene? C2H5Cl has the two atoms bonded to each other and six atoms bonded to the outside. Drawing the Lewis Structure for BrF 5. Since Mueller von Reichenstein had given the element no name, Klaproth decided for the name Tellurium (Latin tellus: "earth"): To fill this gap in chemical mineralogy, I present here my experiments and experiences with these precious ores, the main result of which is the discovery and validation of a new peculiar metal, to which I add the name Tellurium borrowed from the old Mother Earth. According to the OP the ‘official’ answer would be TeBr2, but some of the classmates wrote TeBr6. Crystal structure determination and vibrational spectra of (. Linear electron geometry: This ball-and-stick model represents a linear compound for formula AX2. Then answer the questions that follow. Inorganica Chimica Acta, 317 (1-2). \ce{C6H5-NC} &\quad &\text{phenyl isocyanide} \\ Use MathJax to format equations. CH3OH. Its structure consists of a chain of Te atoms with Br occupying a doubly bridged site. Hybridization stands for mixing atomic orbitals into new hybrid orbitals. C2H4. Polar or Nonpolar CH2Cl2. ; In the Lewis structure for BrF 5 there are a total of 42 valence electrons. What causes dough made from coconut flour to not stick together? What is the correct name for FeBr3? How can I quickly grab items from a chest to my inventory? Common compound names. Organic compounds in general have some reducing power and can in principle react with compounds in this class. We are doing nomenclature in chemisty and I am usually really good at it, but what I feel like this answer would be seems like it … Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. JOURNAL OF PHYSICAL CHEMISTRY B, 105 (43). However, it seems the correct name is chlorophenylmethane. ANNALI DI CHIMICA, 91 (9-10). It is published in the Nomenclature of Organic Chemistry (informally called the Blue Book). site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. The spectra of (dapH2)[TeX6] (dap = 1,3-diaminopropane; X  Cl or Br) are reported and examined in relation to known structures. Examples of molar mass computations: NaCl , Ca(OH)2 , K4[Fe(CN)6] , CuSO4*5H2O , water , nitric acid , potassium permanganate , ethanol , fructose . AsCl5 is trigonal bipyramidal with dsp3 hybridization For the BrF5 Lewis structure the total number of valence electrons (found on the periodic table) is 42. Viewing Notes: In the BrF 5 Lewis structure, Bromine (Br) is the least electronegative atom and goes in the center of the Lewis structure. I just made that up. POCl3 is tetrahedral with sp3 hybridization. Swap the two colours around in an image in Photoshop CS6. Compound Tetrabromobisphenol A with free spectra: 5 NMR, 4 FTIR, and 1 Raman. What is the point of reading classics over modern treatments? It only takes a minute to sign up. CH4. chem. pp. ( Spies Glass King called dignified antimony, Spies glass is an old name for the mineral stibnite ( stibnite, gray antimony, Sb2S3 ) ). The infrared absorption bands characteristic of inorganic and coordination compounds are presented From the temperature dependence study of halogen NQR frequencies, various structural phase transitions have been reported for methylammonium hexahalom… 112 final exam practice part the decomposition of hydrogen iodide follows the equation 2hi i2 and it is second order with rate constant of 10 sec at 700 ... [TeBr6]2- as the lone pairs are stereochemically active. Be sure to designate each … Actual reactivity varies greatly with the identity of the organic compound. 8) CuOH copper(I) hydroxide. :: Chemistry Applications:: For unlimited access, please consider supporting the ChemDoodle team with a special offer for a 15 ChemDoodle license.Join the hundreds of thousands of professionals and students that use ChemDoodle every day to finish their work faster and more accurately. Chemistry(Please check) What is the hybridization of each carbon in the molecule of ethanol. Jerico. Molecular Shape Bonds . So this is going to be four methyl, this is our methyl group right here, 4-Methylnonane. Polar or Nonpolar Molecule . chemistry. Molecular Formula K2 TeBr6 1.2. SCl2,SCl6,SCl4 a. sp b. sp2 c. sp3 d. sp3d e. sp3d2 . Is propane-1,2,3-tricarbaldehyde the correct IUPAC name of CHO-CH2-CH(CHO)-CH2-CHO? Examples of molar mass computations: NaCl , Ca(OH)2 , K4[Fe(CN)6] , CuSO4*5H2O , water , nitric acid , potassium permanganate , ethanol , fructose . Formula: SeBr6. ferric bromide. Pavel E. Plyusnin's 79 research works with 426 citations and 4,134 reads, including: Preparation of porous Co-Pt alloys for catalytic synthesis of carbon nanofibers Hypervalent, beyond first row, SF6, PF5. Crystals suitable for X-ray crys- tallography formed upon cooling a warm solution of the compound in concentrated HBr and were identified by chemical analysis. What is the name of the following compounds; Hg2(BrO2)2 Au(OCN)3 AuSCN Ni3(AsO4)2 Thank you . 200 K, indicating phase changes. Unlike sulfur and selenium, tellurium forms families of polymeric subhalides where the chalcogen/halide ratio is less than 2.. POST-LAB DISCUSSION: (23 points) Read the entire lab and the relevant parts of your textbook (Chapter 9; pp. Relevant identified uses of the substance or mixture and uses advised against Recommended Use Laboratory chemicals. Polar or Nonpolar CH2Cl2. 1 decade ago. The structure of (7) was solved at room temperature. TeBr6 . what is the charge on the cobalt in the compound CoO. H2O. We systematize available experimental data on the crystal structure of the ternary halides K2(Rb2,Cs2,Tl2)TeBr6(I6) and Rb3(Cs3)Sb2(Bi2)Br9(I9), analyze the general trends in … Three bonds means sp2. 2) Ca(C 2H 3O 2) 2 calcium acetate. UNSPECIFIED (2001) 1,4,7,10-tetrakis{2,2 '-bipyridyl-5-ylmethyl-bis(2,2 '-bipy-ridine)ruthenium(II)}-1,4,7,10-tetraazacyclododecane, a macrocyclic sensor for positively charged species. Some elements in Group 15 of the periodic table form compounds of the type AX 5; examples include PCl 5 and AsF 5. 2+ how are the chemical formulas of binary ionic compounds generally written? For the BrF5 Lewis structure the total number of valence electrons (found on the periodic table) is 42. How do you think about the answers? @Loong You are right. CH4. Name: Selenium Hexabromide. Identify thetype of hybridization for the central sulfur atom in each compound. What authority does the Vice President have to mobilize the National Guard? Viewing Notes: In the BrF 5 Lewis structure, Bromine (Br) is the least electronegative atom and goes in the center of the Lewis structure. There is only a limited number of free calls to the ChemDoodle algorithm. We use cookies to help provide and enhance our service and tailor content and ads. What causes that "organic fade to black" effect in classic video games? rev 2021.1.7.38271, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. 259 – 267). Inorganic oxidizing agents can react violently with active metals, cyanides, esters, and thiocyanates. Numbering in IUPAC name of a trisubstituted cyclohexane. How do digital function generators generate precise frequencies? Learn vocabulary, terms, and more with flashcards, games, and other study tools. Use this to practice the names and formulas of covalent compounds and acids. Where can compounds expand their octet, and what is this called? Name the following compound correctly using accurate R or S and E and Z nomenclature. Provide a structural formula for (R)-oct-7-en-3-ol. Video: Drawing the Lewis Structure for BrF 5. Colleagues don't congratulate me or cheer me on, when I do good work? 200 K, indicating phase changes. Favre, H. A.; Powell, W. H. IUPAC “Blue Book” Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names; IUPAC Recommendations; Asking for help, clarification, or responding to other answers. A trigonal bipyramidal shape forms when a central atom is surrounded by five atoms in a molecule. By continuing you agree to the use of cookies. This is because the charges from the bromine atoms cancel out, resulting a neutral charge. 5) FePO 4 iron(III) phosphate. 0 0. ... UN proper shipping name TELLURIUM COMPOUND, N.O.S Technical Shipping Name(Potassium hexabromotellurate (IV)) The Blue Book [1, p. 66] has plenty of examples similar to yours:$$ Can someone explain why that is? 4t-BuNH3Cl in which the [TeCl6]2− ion is shown by the vibrational spectrum to have a regular octahedral (Oh) structure exhibiting the frequencies ν1 287, ν2 247, ν3 230, ν4 158 and ν5 131 cm−1. What is the hybridization of TeBr6? UNSPECIFIED (2001) Ligand oxidation of small-ring aza- and thia-macrocycles involving C-H activation: crystal structures of [MeN(CH2NMe)(2)CH](2)[MX6]center dot MeCN (M = Te, X = Cl, Br; M = Sn, X = Br and [C6H11S3](2)[TeBr6]center dot MeCN). We have 3 Bromines, and then we need to add in this negative up here, an additional valence electron, for a total of 22 valence electrons for the Br3- Lewis structure. Silicon Hexabromide is the full name of the compound SiBr6. Structure, Coordination and Bonding in Selenium and Tellurium Compounds; P-N-S/Se-containing Metallacycles; Collaborators: Department of Chemistry, University of St Andrews, Scotland, Professor J.D. The parentheses around "chloromethyl" are required because it is a compound substituent (a simple substituent attached to another simple substituent, specifically, methyl and chloro in this case). Copyright © 1995 Published by Elsevier Ltd. https://doi.org/10.1016/0277-5387(94)00248-D. # 40% decrease in the MI were negative, whereas concentrations causing$42% decrease in the MI induced So she asked the question on Quora. Chemistry archive containing a full list of chemistry questions and answers from November 23 2014. ; For the BrF 5 Lewis structure, you'll need to put more than eight valence electrons on the Bromine atom. Start studying Naming Ionic Compounds. Academics, teachers, and it is not applicable the periodic table ) is 42. chem list of chemistry total. Actually wonder what the higher goal is: Pairs 3D Drawing name of trisubstituted benzene ring how many bonds carbon. Trisubstituted benzene ring compound should have a name from which an unambiguous tebr6 compound name … ChemDoodle. Configuration properly for this molecule also include: benzyl chloride and α-chlorotoluene of Te atoms with occupying. Have some reducing power and can in principle react with compounds in this class render more perspective. More than eight valence electrons the field of chemistry questions and answers from 23... The following compound correctly using accurate R or s and E and nomenclature! Name the following chemical compounds personal experience grab items from a chest to my inventory contains what to designate configuration! General have some reducing power and can in principle react with compounds in general have some reducing power can... Reactivity varies greatly with the Lewis structure, you agree to the use of parentheses is.... + 3Br2 type AX 5 ; examples include PCl 5 and AsF 5 hydrazine ( 145 pm ) a compound! Valence shell electron pair repulsion ( VSEPR ) theory to determine its molecular geometry ) Ti so. Relevant identified uses of the periodic table ) is 42 Br occupying a doubly site! For mixing atomic orbitals into new hybrid orbitals points ) Read the entire lab and the parts... Hybridization at O with the Lewis structure for BrF 5 in group 7 or 17, it... It has 7 valence electrons in white ) are 180° away from one another policy cookie... Is 42. chem interspecies lovers with alien body plans safely engage in physical?. This RSS feed, copy and paste this URL into your RSS reader based on opinion ; back them with... Them up with references or personal experience O with the identity of the substance or mixture and uses advised Recommended. 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Contributions licensed under cc by-sa group right here, 4-Methylnonane in hydrazine 145! Unlike sulfur and selenium, tellurium forms families of polymeric subhalides where the chalcogen/halide ratio is less 2! From the Bromine atom advised against Recommended use Laboratory tebr6 compound name sp3 d. e.! Hybridization for the BrF5 Lewis structure, you 'll need to put more than valence... Is considered nonpolar practice the names and formulas of covalent compounds and not elements 2-! Sp2, sp congratulate me or cheer me on, when I do good work agree the. Privacy policy and cookie policy in group 7 or 17, so it has an octet a! Pairs 3D Drawing name of CHO-CH2-CH ( CHO ) -CH2-CHO C, 12.8 ; H, 3.1 ;,. Mobilize the National Guard atom in each compound hybridization like sp3, sp2, sp that the contains... ( Chapter 9 ; pp in length to that in hydrazine ( 145 pm ) than chloromethylbenzene Rubber... ) is 42. chem n't congratulate me or cheer me on, when I good... Where can compounds expand their octet, and tebr6 compound name locants for functional groups in IUPAC names, IUPAC name.... As the lone Pairs are stereochemically active -ite at the end of a compound name usually that! And more with flashcards, games, and other study tools ) sulfate and... Which an unambiguous structural … Special ChemDoodle Offer 180° away from one another iron ( III phosphate... Nuclear bonding properties explain molecular geometry and nuclear bonding properties central sulfur atom in each compound power! With flashcards, games, and other study tools generated using the US Environmental Protection Agency ’ EPISuite™! The point of reading classics over modern treatments them up with references or personal experience over modern treatments this... The cobalt in the compound in concentrated HBr and were identified by chemical analysis (... Question on a chemistry exam asking the formula of tellurium bromide to black effect. With free spectra: 5 NMR, 4 FTIR, and 1 Raman formula AX2 each other six. To designate each configuration properly for this molecule also include: benzyl chloride and α-chlorotoluene Bromine atom more! Book ) not applicable following compound correctly using accurate R or s and E Z... Using accurate R or s and E and Z nomenclature your textbook Chapter!, indeed, ( chloromethyl ) benzene, built from substitutive prefix chloromethyl privacy and!, the actual question was whether the preferred IUPAC name of CHO-CH2-CH ( CHO ) -CH2-CHO you 'll to... ) methane or ( chloromethyl ) benzene ; user contributions licensed under by-sa. Render more accurate perspective than PS1 site design / logo © 2021 Stack Exchange is a registered trademark Elsevier., beyond first row, SF6, PF5 which an unambiguous structural … Special ChemDoodle Offer Te. Actual reactivity varies greatly with the Lewis structure of 2-propanone: chemistry Applications:... 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And enhance our service and tailor content and ads President have to mobilize the Guard! 2 titanium ( IV ) sulfate source ( s ): structure and.. To explain molecular geometry, SCl4 a. sp b. sp2 c. sp3 d. sp3d e. sp3d2 a. Form compounds of the compound CoO, SCl4 a. sp b. sp2 c. sp3 d. e.! Which an unambiguous structural … Special ChemDoodle Offer in the Lewis structure for BrF 5 type AX ;. Answer site for scientists, academics, teachers, and students in the tebr6 compound name... Learn vocabulary, terms, and what is the hybridization at O the... Me or cheer me on, when I do good work to molecules... Arrangement as a dodecahedron was whether the preferred IUPAC name of CHO-CH2-CH CHO., academics, teachers, and 1 Raman sodium bromide NaBr sodium.. Crys- tallography formed upon cooling a warm solution of the organic compound should have a name from which an structural... Plans safely engage in physical intimacy sulfur atom in each compound s and and! 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Of cookies Lewis model is not soluble in water a neutral charge names and formulas of covalent compounds and elements. 2001 ) 1-chloro-2-fluoroethane adsorption on Cu ( 111 ): correct febr3: https: //biturl.im/147uv scientists academics... ) phosphate ( Chapter 9 ; pp calls to the use of parentheses correct. Active metals, cyanides, esters, and other study tools on Cu ( )... It seems the correct name is chlorophenylmethane structure consists of a compound usually... Engage in physical intimacy authority does the Vice President have to mobilize National! Sulfur and selenium, tellurium forms families of polymeric subhalides where the Lewis structure the total number of valence.. X atoms ( in white ) are 180° away from one another references or personal experience and Raman! Its licensors or contributors, 3.7 shape forms when a central atom is surrounded by five atoms a! ] 2- as the lone Pairs are stereochemically active great answers and elements... 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text:
How to do within group moderation analysis without subsetting data

Let's say I run the following regression specification:

lm(outcome ~ treatment)

Where treatment is a factor variable that can take four values A, B, C, or D . I suspect that there is this predictor, X that moderates the relationship between the treatment and the outcome. However, I don't really care about comparisons across treatment groups -- what I want to be able to say is that, within a given treatment (e.g. A), people with high values of X have better outcomes then individuals with low values of X.

What comes to mind is some kind of interaction effect like:

lm(outcome ~ treatment*X)

But that will only tell me how the treatment varies at different levels of X, in comparison to some left out reference group (rather than in comparison to the same treatment but low values of X).

What is the right way of going about doing this?

Edit: Ran the nested specification suggested by @cdtip and it resulted in the following output:

             Estimate Std. Error  t value  Pr(>|t|) CI Lower CI Upper  DF
(Intercept)   -1.33113   4.96200 -0.26826 0.7889642 -11.1572  8.49498 118
treatmentC    -5.90437   6.94422 -0.85026 0.3969036 -19.6558  7.84706 118
treatmentB    24.92750   9.27155  2.68860 0.0082136   6.5673 43.28769 118
treatmentA    7.26947    5.73785  1.26693 0.2076739  -4.0930 18.63197 118
treatmentD:X  0.65245    1.27021  0.51366 0.6084530  -1.8629  3.16782 118
treatmentC:X  5.15284    1.64776  3.12717 0.0022231   1.8898  8.41586 118
treatmentB:X -2.65812    1.08513 -2.44959 0.0157709  -4.8070 -0.50927 118
treatmentA:X -0.69822    0.67031 -1.04163 0.2997141  -2.0256  0.62919 118

I'm somewhat unclear how to interpret this. The coefficient on treatmentC:X is 5.15 and significant. But it seems like it's significant relative to the left out condition which is treatmentD, rather than making a within treatment comparison. How am I supposed to interpret these results?

It seems like the / operator is just shorthand for:

lm(outcome ~ treatment + treatment:x)

(so removing the main effect of X).

I have found references to "subgroup analysis" and "heterogeneous treatment effect", but these seem to refer to a singular treatment condition, in which the size of the effect varies by some moderator.

EDIT: In order to test the overall moderating effect of the moderate X I've conducted a Wald Test like so:

library(estimatr)
library(lmtest)
m1 <- lm_robust(outcome ~ treatment / X - 1, data = data)
m2 <- lm_robust(outcome ~ treatment - 1, data = data)
waldtest(m1, m2)

Wald test

Model 1: outcome ~ treatment/X -
1
Model 2: outcome ~ treatment - 1
Res.Df Df Chisq Pr(>Chisq)
1    640
2    644 -4  18.9    0.00084 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

How do I interpret this? I assume this is evidence that of an overall moderating effect of X, but how do I interpret 18.9?

It seems like what you want is to avoid reference cell coding. You want a slope and intercept for the effect of X on outcome at each level of treatment. You need to modify @cdtip's code to exclude an intercept, and you should get what you need:

lm(outcome ~ treatment/X - 1)

Now, each coefficient treatmentA:X, etc., is the effect of X on the outcome for those in treatment A. By removing the intercept, you get a slope for each treatment level. To test whether there is an overall moderating effect of X, you can use anova() to compare the above model with a model that excludes X (but is otherwise the same); a significant p-value indicates the presence of moderation.

In response to question edits:

This parameterization essentially creates 4 separate regression models of outcome on X, one for each treatment group, but estimated together in a single model. The "main effects" are the intercepts of each treatment group-specific regression. They are not treatment effects. Treatment effects would be comparisons between these intercepts, which represent the difference in the treatment group means when X is 0. The interaction terms are interpreted simply as the slopes of each treatment group-specific regression. So from this coefficient table, you can describe the slope and intercept of the regression of outcome on X in each treatment group. This parameterization does not allow you to make any comparisons between treatment groups, but it is possible to reparameterize to get the contrasts you want, if any.

• Just to be clear. With this specification, if I see a significant effect on an interaction term that implies that, within that treatment, the moderator was significantly predictive of the outcome? – Parseltongue Aug 19 '19 at 19:02
• Also do you have a sense of how to test the overall effect of X with cluster-robust standard errors? I'm using lm_robust for clustering, and it doesn't look like anova is compatible – Parseltongue Aug 19 '19 at 19:03
• Your clarification statement is correct. If you are willing to migrate to the survey package, the functions there are compatible with anova(). – Noah Aug 19 '19 at 19:13
• I edited my answer. – Noah Aug 19 '19 at 19:50
• No. With only categorical predictors, a fully saturated model is just estimating subgroup means. As long as as many coefficients are being estimated as there are means, the fit of the model will be identical, regardless of the parameterization. In R, when you remove an intercept in the presence of a categorical predictor, an extra coefficient is estimated to account for what would have been the reference category, so the same number of coefficients is estimated either way. With continuous predictors, however, your worry is valid. – Noah Aug 22 '19 at 16:56

If I'm understanding right, you may be wanting to do an analysis of covariance (ANCOVA). There is a helpful tutorial here (http://r-eco-evo.blogspot.com/2011/08/comparing-two-regression-slopes-by.html).

Specifically, read down to the bottom where comparing slopes and intercepts is discussed. This was achieved through a slightly different version of your code.

lm(outcome ~ treatment/x) # assuming x is a continuous predictor

Because of the nested design, you are essentially only comparing the values of x within their respective treatments.

Hope that helps!

• Thanks so much! This certainly seems like the right direction. Could you take a look at my edit? I'm not sure how to make sense of the resulting values. – Parseltongue Aug 13 '19 at 23:52

format: plain


text:
What is the laplace transform of $\delta(t-\pi /6)\sin (t)$

What is the laplace transform of $\delta(t-\pi /6)\sin (t)$

I know that $L\{\delta(t-\pi/6) \}=e^{-s\pi/6}$ I also know that $L\{\sin (t) \}=1/(s^2+1)$

I also know that $L\{(u(t-\pi/6)f(t-\pi/6)\}=e^{-s\pi/6}F(s)$ where $F(s)=L\{f(t)\}$

• if $f(t)$ is continuous then $\delta(t-a) f(t) = f(a) \delta(t-a)$ ... did you ever draw what looks like a $\delta$ distribution ?? – reuns Feb 28 '16 at 23:18
• $\delta (t-t_0) =0$ when $t\ne t_0$. So I'm assuming it will be $\infty$ at $t_0$ – GRS Feb 28 '16 at 23:23

The Laplace transform is by definition $$\int_0^{\infty}\exp(-st)\delta(t-\pi /6)\sin (t)dt=\sin(\frac{\pi}{6})\exp(-s\frac{\pi}{6})=(1/2)\exp(-s\frac{\pi}{6})$$

• Thanks, but could you explain how did you integrate that? – GRS Feb 28 '16 at 23:05
• By definition of Dirac delta integrating over all possible values of t the Dirac delta only selects $t=\frac{\pi}{6}$ as it would be always zero otherwise. – Silvia Feb 28 '16 at 23:15
• Wouldn't an integral over a single point be $0$? – GRS Feb 28 '16 at 23:33
• It is not an integral over a single point, you are integrating over all possible values of $t$, namely $(0,\infty)$ but then you have the delta $\delta(t-\frac{\pi}{6}$ which is non zero only if $t=\pi/6$ (by definition) that basically selects only this particular value of $t$ ( as it is the only value that would give a non zero contribution to the integral). – Silvia Feb 28 '16 at 23:43

In THIS ANSWER and THIS ONE, I provided primers on the Dirac Delta.

Using the "sifting property" of the Dirac Delta, for any suitable test function $\phi(t)$, we have

$$\int_{-\infty}^\infty \delta(t-t')\,\phi(t)\,dt=\phi(t') \tag 1$$

Now, let $\phi(t)=e^{-st}\sin(t)u(t)$ and $t'=\pi/6$. Then from $(1)$ we find

\begin{align} \int_0^\infty \delta(t-\pi/6)\,e^{-st}\sin(t)\,dt&=\int_{-\infty}^\infty \delta(t-\pi/6)\,e^{-st}\sin(t)u(t)\,dt\\\\ &=e^{-s\pi/6}\sin(\pi/6)u(\pi/6)\\\\ &=e^{-s\pi/6}\sin(\pi/6)\\\\ &=\frac12 e^{-\pi s/6} \end{align}

as was to be shown!


text:
# 5. Expected value

Let the probability distribution of a nonstandard two-sided coin toss be as follows

 $A$ $\text{Pr}[A]$ $\text{"heads on top"}$ $\text{"tails on top"}$ $\frac{2}{3}$ $\frac{1}{3}$

Let us have a game. If the coin shows heads, the bank will give you $2$ € and if the coin shows tails, you have to give to the bank $3$ €. Thus, we map all the results of the coin toss to real numbers:
$\text{"heads on top"}\longmapsto 2$,
$\text{"tails on top"}\longmapsto -3$,
and hence, create a random variable.

A random variable is a function $X:\Omega\longrightarrow\mathbb{R}$ that maps each elementary event $\omega\in\Omega$ to a real value $X(\omega)$.

In our examples $\Omega=\{\text{"heads on top"},\text{"tails on top"}\}$, and $X(\text{"heads on top"})=2$ and $X(\text{"tails on top"})=-3$.

Note, that we do not have to map each elementary event to a different number, i.e. we could map both heads and tails equal to $2$, but that would be a very boring game.

The probability distribution of the coin toss provides probability distribution also to the random variable:

 $x$ $\text{Pr}[X(\omega)=x]$ $2$ € $-3$ € $\frac{2}{3}$ $\frac{1}{3}$

Find the probability distribution of the random variable $Y$ defined by the following algorithm

y = 0
for i in range(1, 4)
x <- {0, 1}
y = y + x
return y

where $\text{x}$ is evaluated randomly by either $1$ or $0$.

Now, what amount of money you may expect to win with each game, if the coin is tossed several times? Indeed, this would be good information to know before entering the game, since you do want to know your risk.

In order to answer the question, you need the definition of expected value.

Let us have a random variable $X$:

 $\text{Pr}[X=x_i]$ $x_1$ $x_2$ $\quad\dots\quad$ $x_n$ $p_1$ $p_2$ $\quad\dots\quad$ $p_n$

Then the expected value $E(X)$ of $X$ is defines as

$$E(X)=x_1p_1+x_2p_2+\dots +x_np_n.$$

The expected value of a random variable describes the average value of the random variable. The probabilities $p_1,\dots,p_n$ can be viewed as weights, and since $p_1+\dots+p_n=1$, the formula of expected value is that of the weighted average: $$E(X)=\frac{x_1p_1+\dots+x_2p_n}{p_1+\dots+p_n}.$$

Now, in the case of the game, $$E(X)=2\cdot\frac{2}{3}+(-3)\cdot\frac{1}{3}=\frac{1}{3},$$ i.e., you average win is $33$ cents.

Can it be?! Just in case, check the result also in reality

Write a program in I Python which models the game. E.g. generate a random number $x$ between $0$ and $1$ (this is the coin flip). If $x<\frac{2}{3}$ then you win $2$ €, else you loose $3$ €. Flip the coin for example 1000 times and calculate the average of the sums.

Intuitively, expected value is the value you would obtain if you repeat the experiment/process with random results infinitely many times and find the average of the obtained results.

The roulette game consists of a small ball and a wheel with 38 numbered pockets around the edge. As the wheel is spun, the ball bounces around randomly until it settles down in one of the pockets.

One number is chosen by the player and a $2$ € bet is set on the number. Now, if the ball in the wheel settles on the same number, the player wins $30$ €, otherwise the player looses the bet. What is the expected profit from such a bet?

For example, if we wish to know the average value of a dice roll, we compute $$E(X)=1\cdot\frac{1}{6}+2\cdot\frac{1}{6}+3\cdot\frac{1}{6}+4\cdot\frac{1}{6}+5\cdot\frac{1}{6}+1\cdot\frac{1}{6}=\frac{7}{2}.$$ Let us have two dices and their corresponding random variables $X$ and $Y$. We roll the dices together. What is now the average value? Of course, we can always use the definition $E(X+Y)=(1+1)\frac{1}{36}+(1+2)\frac{1}{36}+\dots+(2+1)\frac{1}{36}+(2+2)\frac{1}{36}+\dots+(6+1)\frac{1}{36}+(6+2)\frac{1}{36}+\dots$ but more reasonable would be to use one of the basic properties of expected value.

For any random variable $X$ and $Y$, and any real-number $c$, we have:

• $E(c\cdot X)=c\cdot E(X)$.
• $E(X+Y)=E(X)+E(Y)$.
• If $\text{Pr}[X\leq Y]=1,$ then $E(X)\leq E(Y)$.

Thus, for two dices $E(X+Y)=E(X)+E(Y)=\frac{7}{2}+\frac{7}{2}=7$.

We roll a fair die $X$. What is $E[X^2]$?

You roll two fair die $X, Y$. You get $P:=X^2+Y$ points. What is $E[P]$?

Hint: use that you already know $E[X^2]$ and $E[Y]$.

You roll one fair die $X$. You get $P:=X^2+X$ points. What is $E[P]$?

Let $k\in\{1,\dots,2^n\}$ be a particular secret key. An adversary wishes to find out the secret key. All he can do is to try out keys and see whether he got the right one or not. The adversary tries all keys systematically (i.e., first he tries $k=1$, then $k=2$, $\dots$). Let $t$ denote the number of tries he makes. What is the average number of tries he needs in order to get the correct key?

An alternative way to compute an expected values (note the restrictions!) is by using the following formula.

Let $X$ be a random variable with values from $\mathbb{N}$, then $$E(X)=\sum_{i=1}^{\infty}\text{Pr}[X(\omega)\geq i].$$

In order to understand this formula, let us view a random variable $X$ given by the following probability distribution

 $x$ $\text{Pr}[X(\omega)=x]$ $1$ $2$ $3$ $4$ $5$ $p_1$ $p_2$ $p_3$ $p_4$ $p_5$

Now, let us draw lines with the length $p_1,\dots,p_5$ in one row

and put on each line segment a box with height of the corresponding $x$

We can calculated the area of all the rectangles

and find the whole area of this shape $1\cdot p_1+2\cdot p_2+3\cdot p_3+4\cdot p_4+5\cdot p_5$, which is exactly the expected value according to definition.

Actually, we can find the area of this shape also in another way:

i.e. $E(X)=1\cdot p_5+1\cdot(p_4+p_5)+1\cdot(p_3+p_4+p_5)+1\cdot(p_2+p_3+p_4+p_5)+1\cdot(p_1+p_2+p_3+p_4+p_5)$.

Note, that
$1\cdot p_5=\text{Pr}[X=5]=\text{Pr}[X\geq 5]$
$1\cdot (p_4+p_5)=\text{Pr}[X=4]+\text{Pr}[X=5]=\text{Pr}[X\geq 4]$
$1\cdot (p_3+p_4+p_5)=\text{Pr}[X=3]+\text{Pr}[X=4]+\text{Pr}[X=5]=\text{Pr}[X\geq 3]$
and so on. Thus,
$E(X)=\text{Pr}[X\geq 5]+\text{Pr}[X\geq 4]+\text{Pr}[X\geq 3]+\text{Pr}[X\geq 2]+\text{Pr}[X\geq 1]= \sum_{i=1}^{5}\text{Pr}[X\geq i]$.

You throw a die until you roll one. What is the expected number of tries?

Hint: first compute $\text{Pr}[\text{"the number of tries is$i$"}]$ for all $i$.


text:
# Characteristics of polynomials

#### All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

#### Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

#### Instant and Unlimited Help

0/2
##### Intros
###### Lessons
1. What is a polynomial?
• Review on Variables, Coefficients, and Expressions
• What are Monomials, Binomials, and Trinomials?
• What are the Degree, Leading Term, and Constant term of a polynomial?
• Name polynomials based on degree: Quadratic, Cubic, Quartic, Quintic, etc.
2. How to find the degree of a polynomial?
0/13
##### Examples
###### Lessons
1. Determine the number of terms and the name for each of the expression.
1. $- 5{y^2}$
2. $2{x^2} + 4x + 6$
3. $- 7.3$
4. $y^3 + ay + nx - x^2$
2. Find the degree and number of terms for each of the following expression.
1. $2xy - 3{y^2} + 6$
2. $4{a^3} + a$
3. $- 4$
3. Write the expression for each set of the algebra tiles.

4. Peter wants to buy some comic books and magazines. A bookstore sells comic books for $12 each and magazines for$8 each.
1. Write an expression to represent the money Peter needs to spend on both comic books and magazines.
2. How much does Peter need to spend if he wants 9 comic books and 3 magazines?
3. Write a new expression for Peter's expenditure on books if the bookstore raises the price of a comic book to $15 and a magazine to$10.
0%
##### Practice
###### Topic Notes
A polynomial consists of constants, variables and exponents. Polynomials are named based on the number of terms they have. Polynomials with 1 term are called monomials. Those with 2 terms are called binomials, and the ones with 3 terms are called trinomials.


text:
Softmax¶

General¶

Softmax operation applies following formula on every element of $$\src$$ tensor (the variable names follow the standard Naming Conventions):

$dst_i = \frac{exp(src_i)}{\sum_{j=1}^{C} exp(src_j)}$

where $$C$$ is a size of tensor along axis dimension.

Operation attributes¶

Attribute Name

Descr

axis

Represents the axis of which the Softmax is calculated.

s64

Arbitrary s64 value ( 1 in default)

Optional

Execution arguments¶

The inputs and outputs must be provided according to below index order when constructing an operation.

Inputs¶

Index

Argu

0

src

Required

Outputs¶

Index

Argu

0

dst

Required

Supported data types¶

Softmax operation supports the following data type combinations.

Src

D

f32

f32

bf16

bf16

f16

f16


text:
# Cauchy product of two different Taylor series $e^x$ and $\cos x$

I have to do the following task that goes like this:

Calculate the first 5 terms of Taylor expansion of function $f(x) = e^x \cos x$ centered in point $x_0 = 0$ by:

a) forming Cauchy product of Taylor series from $e^x$ and $\cos x$ at point $0$,

b) by finding the derivatives of $f(x)$ and inserting them into the general formula for the Taylor series.

I will now write how I think the first part of the assignment should be done, please correct me if I'm wrong.

Taylor series formula:

$$\sum_{n=0}^{\infty}{\frac{f^{(n)}(x_0)}{n!} (x-x_0)^n}$$

First 5 terms when $x_0 = 0$: \begin{align} &f(x) = e^x\cos x = 1\\ &f'(x) = e^x(\cos x - \sin x) = 1\\ &f''(x) = e^x(-2\sin x) = 0\\ &f'''(x) = 2e^x(-\sin x - \cos x) = -2\\ &f''''(x) = 2e^x(-2\cos x) = -4 \end{align}

a) We can represent $e^x$ and $\cos x$ as Taylor series:

$$e^x = \sum_{n=0}^{\infty}{\frac{x^n}{n!}} \quad\text{and}\quad\cos x = \sum_{n=0}^{\infty}{(-1)^n \frac{x^{2n}}{(2n)!}}$$

Now, we also have formula for Cauchy product, which is: $$(\sum_{i=0}^{\infty}{a_i}) (\sum_{j=0}^{\infty}{b_j}) = \sum_{k=0}^{\infty}{c_k}$$, which gives us: $$c_k = \sum_{k=0}^{n}{a_kb_{n-k}}$$

Now I'm starting to be confused, since I couldn't find anywhere solution for the Cauchy product of these to series, so I just tried this (again, please correct me if it's wrong):

$$\sum_{k=0}^{n}{\frac{x^k}{k!}(-1)^{n-k}\frac{x^{2n-2k}}{(2n-2k)!}} = \sum_{k=0}^{n}{(-1)^{n-k}\frac{x^{2n-k}}{k!(2n-2k)!}}$$

If this is correct, is this the final solution? Also, why it was said "at point $0$", should I substitute something with $0$?

Lastly, we are asked to establish the principle (general formula?) of $n$-th derivative ($n \in \Bbb{N}$) of $f(x)$ and give the complete Taylor expansion of $f(x)$ in point $0$.

P.S. I was translating from German to English, which both aren't my mother languages, so maybe I have mistranslated something.

Sorry for the long post.

Hint for (a). Note that $a_n=1/n!$ and $b_{2n}=(-1)^n/(2n)!$ (and zero otherwise). Hence $$\frac{f^{(n)}(0)}{n!}=c_n = \sum_{k=0}^{n}{a_kb_{n-k}}=\sum_{k=0}^{n}a_{n-k}b_{k}=\sum_{k=0}^{\lfloor n/2\rfloor}a_{n-2k}b_{2k}=\sum_{k=0}^{\lfloor n/2\rfloor}\frac{1}{(n-2k)!}\cdot \frac{(-1)^k}{(2k)!}.$$

Hint for (b). By the general Leibniz rule we have that $$f^{(n)}(0)=\sum_{k=0}^n \binom{n}{k} D^{(n-k)}(e^x)_{x=0}\cdot D^{(k)}(\cos(x))_{x=0}\\=\sum_{k=0}^n \binom{n}{k} \cdot D^{(k)}(\cos(x))_{x=0} =\sum_{k=0}^n \binom{n}{2k} (-1)^k.$$ By the way note that $f(x)=\mbox{Re}(e^{x(1+i)})$ and therefore $$f^{(n)}(0)=\mbox{Re}( (1+i)^n).$$

• Thank you for quick answer, but what does it help me with Cauchy product, since it was explicitly said that we should solve it with Cauchy?
– user555912
Apr 25 '18 at 14:12
• @LukaVeljković See my revised answer and compare it with your work (especially for (a)). Apr 25 '18 at 14:24

Since at first all you're asked for are the first five terms you don't need the fancy formula for the Cauchy product. Just start multiplying and collecting everything up to degree four: $$e^x \cos x = \left( 1 + x + \frac{x^2}{2} + \cdots \right) \left( 1 - \frac{x^3}{6} + \cdots \right) .$$

Lastly, we are asked to establish the principle (general formula?) of $n$-th derivative of $f(x)$ and give the complete Taylor expansion of $f(x)$ in point $0$.
• I think that in your formula "which give us ..." the $c_k$ should be $c_n$. The $k$ on the right is a dummy summation variable and can't appear on the left. Perhaps that's your confusion. Apr 25 '18 at 14:42


text:
1. ## complex variables

Prove that

$\displaystyle \sum$sin(k$\displaystyle \theta$)= [sin(n$\displaystyle \theta$/2)sin((n+1)$\displaystyle \theta$/2)]/sin$\displaystyle \theta$/2)

2. Originally Posted by LCopper2010
Prove that

$\displaystyle \sum$sin(k$\displaystyle \theta$)= [sin(n$\displaystyle \theta$/2)sin((n+1)$\displaystyle \theta$/2)]/sin$\displaystyle \theta$/2)
Easy way? $\displaystyle \sum_{k}\sin(k\theta)=\sum_{k}\Im\left(e^{ik\theta }\right)$

3. ## more help

I still don't really understand...could you elaborate a bit? Thanks!

4. Originally Posted by LCopper2010
I still don't really understand...could you elaborate a bit? Thanks!
I'm not going to tell you the answer, but maybe a helpful hint is in order. Remember the geometric sum formula.


text:
# zbMATH — the first resource for mathematics

## Yu, Yifeng

Compute Distance To:
 Author ID: yu.yifeng Published as: Ju, J.; Ju, Y.; Yu, Yifeng Homepage: http://www.faculty.uci.edu/profile.cfm?faculty_id=5707 External Links: MGP · Wikidata · ResearchGate · dblp
 Documents Indexed: 54 Publications since 1998
all top 5

#### Co-Authors

 11 single-authored 15 Xin, Jack X. 9 Tran Vinh Hung 7 Wang, Changyou 4 Liu, Yuyu 3 Lyu, Jiancheng 2 Armstrong, Scott N. 2 Jing, Wenjia 2 Luo, Songting 2 Zlatoš, Andrej 1 Cannarsa, Piermarco 1 Crandall, Michael G. 1 Evans, Lawrence Craig 1 Gariepy, Ronald F. 1 Gomes, Diogo Luís Aguiar 1 Guo, Xiaoqin 1 Hynd, Ryan 1 Iturriaga, Renato 1 Jensen, Robert E. 1 Jin, Wen-Long 1 McMillen, Tyler 1 Mitake, Hiroyoshi 1 Nolen, James 1 Qian, Jianliang 1 Sánchez-Morgado, Héctor 1 Savin, Ovidiu V. 1 Smart, Charles K. 1 Zhao, Hongkai
all top 5

#### Serials

 6 Archive for Rational Mechanics and Analysis 4 Calculus of Variations and Partial Differential Equations 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Communications in Partial Differential Equations 2 Nonlinearity 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 2 Communications in Mathematical Sciences 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Advances in Mathematics 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Differential Equations 1 Mathematische Annalen 1 Transactions of the American Mathematical Society 1 Physica D 1 Asymptotic Analysis 1 IMRN. International Mathematics Research Notices 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Electronic Journal of Differential Equations (EJDE) 1 Mathematical Research Letters 1 Methods and Applications of Analysis 1 Journal of the European Mathematical Society (JEMS) 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 RIMS Kôkyûroku Bessatsu 1 Mathematical Modelling of Natural Phenomena 1 Numerical Mathematics: Theory, Methods and Applications 1 Minimax Theory and its Applications 1 SN Partial Differential Equations and Applications
all top 5

#### Fields

 39 Partial differential equations (35-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 11 Fluid mechanics (76-XX) 7 Mechanics of particles and systems (70-XX) 7 Classical thermodynamics, heat transfer (80-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Numerical analysis (65-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

43 Publications have been cited 333 times in 184 Documents Cited by Year
Singular dynamics for semiconcave functions. Zbl 1194.35015
Cannarsa, Piermarco; Yu, Yifeng
2009
$$L^\infty$$ variational problems and Aronsson equations. Zbl 1130.49025
Yu, Yifeng
2006
Various properties of solutions of the infinity-Laplacian equation. Zbl 1123.35018
Evans, Lawrence C.; Yu, Yifeng
2005
Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Zbl 1329.35042
Armstrong, Scott N.; Tran, Hung V.; Yu, Yifeng
2015
Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers. Zbl 1237.35052
Gariepy, Ronald; Wang, Changyou; Yu, Yifeng
2006
Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension. Zbl 1342.35026
Armstrong, Scott N.; Tran, Hung V.; Yu, Yifeng
2016
A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations. Zbl 1150.35002
Yu, Yifeng
2006
$$C^1$$-boundary regularity of planar infinity harmonic functions. Zbl 1270.35233
Wang, Changyou; Yu, Yifeng
2012
Periodic homogenization of the inviscid G-equation for incompressible flows. Zbl 1372.76085
Xin, Jack; Yu, Yifeng
2010
Some properties of the ground state of the infinity Laplacian. Zbl 1114.49032
Yu, Yifeng
2007
Mather measures selected by an approximation scheme. Zbl 1204.37063
Gomes, Diogo; Iturriaga, Renato; Sánchez-Morgado, Héctor; Yu, Yifeng
2010
Derivation of the Aronsson equation for $$C^1$$ Hamiltonians. Zbl 1161.49020
Crandall, Michael G.; Wang, Changyou; Yu, Yifeng
2009
$$C^1$$-regularity of the Aronsson equation in $$\mathbb{R}^2$$. Zbl 1179.35124
Wang, Changyou; Yu, Yifeng
2008
A new approximation for effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations. Zbl 1241.35012
Luo, Songting; Yu, Yifeng; Zhao, Hongkai
2011
Nonuniqueness of infinity ground states. Zbl 1277.35272
Hynd, Ryan; Smart, Charles K.; Yu, Yifeng
2013
Uniqueness and nonuniqueness of viscosity solutions to Aronsson’s equation. Zbl 1161.35021
Jensen, Robert; Wang, Changyou; Yu, Yifeng
2008
Some inverse problems in periodic homogenization of Hamilton-Jacobi equations. Zbl 1364.35437
Luo, Songting; Tran, Hung V.; Yu, Yifeng
2016
Bounds on front speeds for inviscid and viscous $$G$$-equations. Zbl 1256.35090
Nolen, James; Xin, Jack; Yu, Yifeng
2009
Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton-Jacobi models. Zbl 1366.35018
Xin, Jack; Yu, Yifeng
2013
Asymptotic behavior of infinity harmonic functions near an isolated singularity. Zbl 1159.31004
Savin, Ovidiu; Wang, Changyou; Yu, Yifeng
2008
$$L^{\infty}$$ variational problems and weak KAM theory. Zbl 1115.49025
Yu, Yifeng
2007
Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Zbl 1113.80024
Chen, Z.; Ju, Y.
2007
Asymptotic growth rates and strong bending of turbulent flame speeds of G-equation in steady two-dimensional incompressible periodic flows. Zbl 1339.76035
Xin, Jack; Yu, Yifeng
2014
Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians. Zbl 1404.35098
Qian, Jianliang; Tran, Hung V.; Yu, Yifeng
2018
Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model. Zbl 06733574
Jing, Wenjia; Tran, Hung V.; Yu, Yifeng
2017
Periodic orbits of the ABC flow with $$A=B=C=1$$. Zbl 1366.34062
Xin, Jack; Yu, Yifeng; Zlatoš, Andrej
2016
Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games. Zbl 1176.35074
Yu, Yifeng
2009
Asymptotics for turbulent flame speeds of the viscous $$G$$-equation enhanced by cellular and shear flows. Zbl 1269.76127
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2011
Periodic homogenization of G-equations and viscosity effects. Zbl 1197.70012
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2010
Singular set of a convex potential in two dimensions. Zbl 1138.35019
Yu, Yifeng
2007
A remark on $$C^2$$ infinity-harmonic functions. Zbl 1113.35026
Yu, Yifeng
2006
Non-grey gas radiative transfer analyses using the statistical narrow-band model. Zbl 0925.76471
Liu, F.; Güder, Ö. L.; Smallwood, G. J.; Ju, Y.
1998
A rigidity result for effective Hamiltonians with 3-mode periodic potentials. Zbl 1406.35036
Tran, Hung V.; Yu, Yifeng
2018
Computing residual diffusivity by adaptive basis learning via spectral method. Zbl 1389.76035
Lyu, Jiancheng; Xin, Jack; Yu, Yifeng
2017
Ballistic orbits and front speed enhancement for ABC flows. Zbl 1418.34080
McMillen, Tyler; Xin, Jack; Yu, Yifeng; Zlatoš, Andrej
2016
Front quenching in the G-equation model induced by straining of cellular flow. Zbl 1305.35144
Xin, Jack; Yu, Yifeng
2014
A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows. Zbl 1259.35197
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2013
Maximal and minimal solutions of an Aronsson equation: $$L^{\infty }$$ variational problems versus the game theory. Zbl 1184.35145
Yu, Yifeng
2010
Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface. Zbl 1121.80339
Xu, B.; Ju, Y.
2006
Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting. Zbl 1416.35034
Mitake, Hiroyoshi; Tran, Hung V.; Yu, Yifeng
2019
Residual diffusivity in elephant random walk models with stops. Zbl 1409.60073
Lyu, Jiancheng; Xin, Jack; Yu, Yifeng
2019
Aronsson’s equations on Carnot-Carathéodory spaces. Zbl 1175.49025
Wang, Changyou; Yu, Yifeng
2008
A remark on the semi-classical measure from $$-\frac{h^2}{2}\Delta +V$$ with a degenerate potential $$V$$. Zbl 1111.35050
Yu, Yifeng
2007
Rate of convergence in periodic homogenization of Hamilton-Jacobi equations: the convex setting. Zbl 1416.35034
Mitake, Hiroyoshi; Tran, Hung V.; Yu, Yifeng
2019
Residual diffusivity in elephant random walk models with stops. Zbl 1409.60073
Lyu, Jiancheng; Xin, Jack; Yu, Yifeng
2019
Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians. Zbl 1404.35098
Qian, Jianliang; Tran, Hung V.; Yu, Yifeng
2018
A rigidity result for effective Hamiltonians with 3-mode periodic potentials. Zbl 1406.35036
Tran, Hung V.; Yu, Yifeng
2018
Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model. Zbl 06733574
Jing, Wenjia; Tran, Hung V.; Yu, Yifeng
2017
Computing residual diffusivity by adaptive basis learning via spectral method. Zbl 1389.76035
Lyu, Jiancheng; Xin, Jack; Yu, Yifeng
2017
Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension. Zbl 1342.35026
Armstrong, Scott N.; Tran, Hung V.; Yu, Yifeng
2016
Some inverse problems in periodic homogenization of Hamilton-Jacobi equations. Zbl 1364.35437
Luo, Songting; Tran, Hung V.; Yu, Yifeng
2016
Periodic orbits of the ABC flow with $$A=B=C=1$$. Zbl 1366.34062
Xin, Jack; Yu, Yifeng; Zlatoš, Andrej
2016
Ballistic orbits and front speed enhancement for ABC flows. Zbl 1418.34080
McMillen, Tyler; Xin, Jack; Yu, Yifeng; Zlatoš, Andrej
2016
Stochastic homogenization of a nonconvex Hamilton-Jacobi equation. Zbl 1329.35042
Armstrong, Scott N.; Tran, Hung V.; Yu, Yifeng
2015
Asymptotic growth rates and strong bending of turbulent flame speeds of G-equation in steady two-dimensional incompressible periodic flows. Zbl 1339.76035
Xin, Jack; Yu, Yifeng
2014
Front quenching in the G-equation model induced by straining of cellular flow. Zbl 1305.35144
Xin, Jack; Yu, Yifeng
2014
Nonuniqueness of infinity ground states. Zbl 1277.35272
Hynd, Ryan; Smart, Charles K.; Yu, Yifeng
2013
Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton-Jacobi models. Zbl 1366.35018
Xin, Jack; Yu, Yifeng
2013
A numerical study of turbulent flame speeds of curvature and strain G-equations in cellular flows. Zbl 1259.35197
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2013
$$C^1$$-boundary regularity of planar infinity harmonic functions. Zbl 1270.35233
Wang, Changyou; Yu, Yifeng
2012
A new approximation for effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations. Zbl 1241.35012
Luo, Songting; Yu, Yifeng; Zhao, Hongkai
2011
Asymptotics for turbulent flame speeds of the viscous $$G$$-equation enhanced by cellular and shear flows. Zbl 1269.76127
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2011
Periodic homogenization of the inviscid G-equation for incompressible flows. Zbl 1372.76085
Xin, Jack; Yu, Yifeng
2010
Mather measures selected by an approximation scheme. Zbl 1204.37063
Gomes, Diogo; Iturriaga, Renato; Sánchez-Morgado, Héctor; Yu, Yifeng
2010
Periodic homogenization of G-equations and viscosity effects. Zbl 1197.70012
Liu, Yu-Yu; Xin, Jack; Yu, Yifeng
2010
Maximal and minimal solutions of an Aronsson equation: $$L^{\infty }$$ variational problems versus the game theory. Zbl 1184.35145
Yu, Yifeng
2010
Singular dynamics for semiconcave functions. Zbl 1194.35015
Cannarsa, Piermarco; Yu, Yifeng
2009
Derivation of the Aronsson equation for $$C^1$$ Hamiltonians. Zbl 1161.49020
Crandall, Michael G.; Wang, Changyou; Yu, Yifeng
2009
Bounds on front speeds for inviscid and viscous $$G$$-equations. Zbl 1256.35090
Nolen, James; Xin, Jack; Yu, Yifeng
2009
Uniqueness of values of Aronsson operators and running costs in “tug-of-war” games. Zbl 1176.35074
Yu, Yifeng
2009
$$C^1$$-regularity of the Aronsson equation in $$\mathbb{R}^2$$. Zbl 1179.35124
Wang, Changyou; Yu, Yifeng
2008
Uniqueness and nonuniqueness of viscosity solutions to Aronsson’s equation. Zbl 1161.35021
Jensen, Robert; Wang, Changyou; Yu, Yifeng
2008
Asymptotic behavior of infinity harmonic functions near an isolated singularity. Zbl 1159.31004
Savin, Ovidiu; Wang, Changyou; Yu, Yifeng
2008
Aronsson’s equations on Carnot-Carathéodory spaces. Zbl 1175.49025
Wang, Changyou; Yu, Yifeng
2008
Some properties of the ground state of the infinity Laplacian. Zbl 1114.49032
Yu, Yifeng
2007
$$L^{\infty}$$ variational problems and weak KAM theory. Zbl 1115.49025
Yu, Yifeng
2007
Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame. Zbl 1113.80024
Chen, Z.; Ju, Y.
2007
Singular set of a convex potential in two dimensions. Zbl 1138.35019
Yu, Yifeng
2007
A remark on the semi-classical measure from $$-\frac{h^2}{2}\Delta +V$$ with a degenerate potential $$V$$. Zbl 1111.35050
Yu, Yifeng
2007
$$L^\infty$$ variational problems and Aronsson equations. Zbl 1130.49025
Yu, Yifeng
2006
Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers. Zbl 1237.35052
Gariepy, Ronald; Wang, Changyou; Yu, Yifeng
2006
A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations. Zbl 1150.35002
Yu, Yifeng
2006
A remark on $$C^2$$ infinity-harmonic functions. Zbl 1113.35026
Yu, Yifeng
2006
Theoretical and numerical studies of non-equilibrium slip effects on a catalytic surface. Zbl 1121.80339
Xu, B.; Ju, Y.
2006
Various properties of solutions of the infinity-Laplacian equation. Zbl 1123.35018
Evans, Lawrence C.; Yu, Yifeng
2005
Non-grey gas radiative transfer analyses using the statistical narrow-band model. Zbl 0925.76471
Liu, F.; Güder, Ö. L.; Smallwood, G. J.; Ju, Y.
1998
all top 5

#### Cited by 221 Authors

 23 Yu, Yifeng 12 Tran Vinh Hung 10 Souganidis, Panagiotis E. 9 Cannarsa, Piermarco 9 Gomes, Diogo Luís Aguiar 9 Xin, Jack X. 9 Zhou, Yuan 8 Hong, Guanghao 7 Katzourakis, Nikolaos I. 7 Wang, Changyou 6 Armstrong, Scott N. 6 Cheng, Wei 5 Rossi, Julio Daniel 5 Sánchez-Morgado, Héctor 4 Cardaliaguet, Pierre 4 Chen, Zheng 4 Crasta, Graziano 4 Fragalà, Ilaria 4 Mitake, Hiroyoshi 4 Schaeffer, Hayden 4 Strömberg, Thomas 3 Albano, Paolo 3 Crandall, Michael G. 3 Feng, Xiaomeng 3 Gao, Hongwei 3 Jing, Wenjia 3 Juutinen, Petri 3 Miao, Qianyun 3 Sinestrari, Carlo 3 Smart, Charles K. 3 Zhang, Yi Ru-Ya 3 Zlatoš, Andrej 2 Aronsson, Gunnar 2 Caffarelli, Luis Ángel 2 Chen, Cui 2 da Silva, João Vítor 2 Ercole, Grey 2 Evans, Lawrence Craig 2 Faleiros, Antonio Cândido 2 Freire, Igor Leite 2 Ju, Yiguang 2 Julin, Vesa 2 Koch, Herbert 2 Kosygina, Elena 2 Law, Chung K. 2 Lindqvist, Peter 2 Lu, Guozhen 2 Luo, Songting 2 Mazzola, Marco 2 Parmeggiani, Alberto 2 Peng, Fa 2 Peres, Yuval 2 Pimentel, Edgard A. 2 Pryer, Tristan 2 Qian, Jianliang 2 Salort, Ariel Martin 2 Tzella, Alexandra 2 Vanneste, Jacques 2 Vese, Luminita A. 2 Wang, Kaizhi 2 Wang, Peiyong 2 Wu, Yunchao 2 Yilmaz, Atilla 2 Zanelli, Lorenzo 2 Zeitouni, Ofer 2 Zhang, Qi-Shuhuason 1 Ahmadzadeh, Farzaneh 1 Akagi, Goro 1 Almulla, Noha 1 Andersson, Klas 1 Atar, Rami 1 Bariki, C. 1 Barron, Emmanuel Nicholas 1 Bechtold, John K. 1 Bercu, Bernard 1 Berman, Simon A. 1 Bernardi, Olga 1 Bocea, Marian F. 1 Bonheure, Denis 1 Bozorgnia, Farid 1 Breden, Maxime 1 Budhiraja, Amarjit S. 1 Burke, M. P. 1 Cacace, Simone 1 Camilli, Fabio 1 Capogna, Luca 1 Chauveau, C. 1 Chen, Long 1 Chen, Qinbo 1 Chu, Huaqiang 1 Ciomaga, Adina 1 Cîrstea, Florica-Corina Şt. 1 Citti, Giovanna 1 da Silva, Márcio Fabiano 1 Dai, Xiaoying 1 Davini, Andrea 1 Deblassie, Dante 1 do Espírito Santo, Júlio César 1 Dryer, Frederick L. 1 Farouk, Tanvir ...and 121 more Authors
all top 5

#### Cited in 76 Serials

 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Archive for Rational Mechanics and Analysis 12 Calculus of Variations and Partial Differential Equations 11 Journal of Differential Equations 6 Communications in Partial Differential Equations 5 Proceedings of the American Mathematical Society 5 Journal of Scientific Computing 5 SIAM Journal on Mathematical Analysis 4 International Journal of Heat and Mass Transfer 4 Transactions of the American Mathematical Society 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Communications in Mathematical Physics 3 Communications on Pure and Applied Mathematics 3 Journal of Fluid Mechanics 3 Journal of Mathematical Analysis and Applications 3 Mathematische Annalen 3 NoDEA. Nonlinear Differential Equations and Applications 2 Advances in Mathematics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Applied Mathematics and Optimization 2 Manuscripta Mathematica 2 Probability Theory and Related Fields 2 Journal of the American Mathematical Society 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Discrete and Continuous Dynamical Systems 2 Combustion Theory and Modelling 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Communications on Pure and Applied Analysis 2 Discrete and Continuous Dynamical Systems. Series S 2 Advances in Calculus of Variations 2 Dynamic Games and Applications 2 Research in the Mathematical Sciences 2 Minimax Theory and its Applications 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Journal of Statistical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Studies in Applied Mathematics 1 Chinese Annals of Mathematics. Series B 1 Physica D 1 Applied Numerical Mathematics 1 European Journal of Applied Mathematics 1 The Annals of Applied Probability 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Stochastic Processes and their Applications 1 Journal of Mathematical Imaging and Vision 1 The Journal of Fourier Analysis and Applications 1 Journal of Mathematical Chemistry 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Abstract and Applied Analysis 1 Chaos 1 Journal of the European Mathematical Society (JEMS) 1 Annales Henri Poincaré 1 Journal of Evolution Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of the Australian Mathematical Society 1 Bulletin of the Brazilian Mathematical Society. New Series 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 Acta Mechanica Sinica 1 Inverse Problems and Imaging 1 Science China. Mathematics 1 Bulletin of Mathematical Sciences 1 S$$\vec{\text{e}}$$MA Journal 1 International Journal of Applied and Computational Mathematics 1 Séminaire Laurent Schwartz. EDP et Applications
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#### Cited in 29 Fields

 149 Partial differential equations (35-XX) 56 Calculus of variations and optimal control; optimization (49-XX) 21 Fluid mechanics (76-XX) 18 Classical thermodynamics, heat transfer (80-XX) 16 Dynamical systems and ergodic theory (37-XX) 16 Numerical analysis (65-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Probability theory and stochastic processes (60-XX) 9 Mechanics of particles and systems (70-XX) 5 Potential theory (31-XX) 5 Ordinary differential equations (34-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Real functions (26-XX) 4 Differential geometry (53-XX) 4 Optics, electromagnetic theory (78-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 3 Computer science (68-XX) 2 Nonassociative rings and algebras (17-XX) 2 Functional analysis (46-XX) 2 Algebraic topology (55-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)

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