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A decrease in the oxidation state of an element from the reactant side to the product side indicates a gain of electrons, or reduction Hint 6. Oxidation number is the number of electrons an atom gains or losses to form that compound. 0 1 2. Therefore, if you need three NO3- anions to neutralize Cr the charge on Cr must be 3+. A) What is the oxidation number of chromium for each of CrI2, CrCl3, K2CrO4 compound? That means it is being reduced and is the oxidizer. The alkali metals (group I) always have an oxidation number of +1. Especially, these symbols were needed when balancing equations and molecules as it allowed the atoms to come to the front. When did organ music become associated with baseball? As for example the oxidation number of chromium in CrCl3 is +3. Write down the IUPAC name for each of the following complexes and indicate the oxidation state, electronic configuration and coordination number. Find the Oxidation Numbers CrSO_4 Since is in column of the periodic table , it will share electrons and use an oxidation state of . The oxidation state of a molecule is the sum of the oxidation states of âŚ What happend in the story because of winn dixie? The oxidation number of Cr starts from +6 in CrO42-to +3 in Cr3+, so it is reduced. This is the oxidation number. A. Oxidation reactions are the principal source of energy on Earth. The alkali metals (group I) always have an oxidation number … Anonymous Answered . Then we have. Since is in column of the periodic table , it will share electrons and use an oxidation state of . Six electrons are transferred in the reaction 2. What is the oxidation number of Cr in CrCl3? ANSWER: Correct In \rm K_2CrO_4, the oxidation state of \rm Cr is +6; in \rm CrCl_3, the oxidation state of \rm Cr is +3. NO c. N2O5 . Rules to calculate oxidation number. x = + w. 18. oxidation number with H (Cl= -1) so Cr is using 3 :) as you have * Oxidation state of K:- +1 * Oxidation state of O:- -2 * Let the oxidation state of Cr be :- x * And we know that net charge on a compound is 0. There are three chlorine atoms in total, and so their total charge will be #-1*3=-3#. 4. In Cr(NO3)3 you have an anion and a cation. Name the following binary compounds, which contain two nonmetals (Type III). First of all write down what you know about the molecule: 1: The molecule hasnât got an electric charge (is not an ione), this means that either positive and negative charges of its atoms are balanced (we have the same number of positve and âŚ The most common form of the trichloride is the dark green hexahydrate, CrCl 3 â˘ 6H 2 O.Chromium âŚ The anhydrous compound with the formula CrCl 3 is a violet solid. In this case you have a Salt that comes from a binarius acid Chlorine is more electronegative than chromium, and so it will possess its usual state of #-1#. In the end you get: K2Cr2O7 + 14 HI = 2 KI + 2 CrI3 + 3 I2 + 7 H2O. a) Assign oxidation numbers for each atom in âŚ The Oxidation number of k2cr2o7 is +6 for Cr. Answer. Cr -3 = 0. The sum of the oxidation number of an ion is equal to the charge on ion. 3. In this case Cr + is the cation and NO3- is the anion. a. Fe2O3 b. FeO d. CoSO4 e. K3CoCl6 g. CrO3 - h. K2CrO4 j. KCrO2 Chromium(III) chloride (also called chromic chloride) describes any of several compounds of with the formula CrCl 3 • x H 2 O, where x can be 0, 5, and 6. What are the disadvantages of primary group? Which of the following is true about oxidation reactions? Separate the process into half reactions. There are rules to calculate oxidation number. Mainly, K 2 Cr 2 O 7 and FeSO 4 react with each other, while they exchange the electrons. Fluorine in compounds is always assigned an oxidation number of -1. How do oxidation numbers relate to electron configuration? Copyright © 2020 Multiply Media, LLC. Also give stereochemistry and magnetic moment of the complex: CrCl3(py)3 Concept: Nomenclature of Coordination Compounds - Formulas of Mononuclear âŚ Name the following binary compounds, which contain two nonmetals (Type III). S +4 O -6 . The (III) defines the oxidation state of chromium in this molecule. a.PbBr2 and PbBr4 b. FeS and Fe2S3 c. AlBr3 d. Na2S e. CoCl3. Balance this equation using oxidation method:I2+HNO3---->HIO3+NO2+H2O . 0 votes . Cr +3 ( O -2 H +1 ) 3 + Cl +5 O -2 3 - â Cr +6 O -2 4 2- + Cl -1 - Top Answer. Asked by Wiki User. How do oxidation numbers relate to valence electrons? 4. Indicate the oxidation number of the metallic elements in the following compounds. Indicate the oxidation number of the metallic element(s) in the following compounds. The oxidation number of a monatomic ion equals the charge of the ion. Hydrogen will almost always have an oxidation state of +1. Especially, these symbols were needed when balancing equations and molecules as it allowed the atoms to come to the front. Oxygen will almost always have an oxidation state of -2. a.BF3 b. a.PbBr2 and PbBr4 b. FeS and Fe2S3 c. AlBr3 d. Na2S e. CoCl3. $$+3$$ Explanation: In this compound, $$CrCl_3$$, it has a net charge of $$0$$. around the world. a.BF3 b. Luckily, electron transfers and oxidation numbers provide hints for balancing such equations. B. The oxidation number of a monatomic ion equals the charge of the ion. 6. of Cr in K2 Cr2 O7 can be calculated as Let the oxidation number of Cr âŚ Rules for assigning oxidation numbers. 11729 views The sum of the oxidation states of the elements in a compound will always be zero. In this case the Cr in K2Cr2O7 has an oxidation state of +6 and that in CrCl3 is +3, so each atom of Cr gains 3 electrons. Here the oxidation number of oxygen is -2. CHemistry. chem 1411. what is the oxidation state of In in In2s3? a) CrCl3, Cr= +3. Cr + 3(-1) = 0. Why don't libraries smell like bookstores? The anhydrous compound with the formula CrCl 3 is a violet solid. What is the oxidation number of Cr in CrCl3. 5. You need 3 Cl per Cr, meaning you need 6 Cl to cover the 2 Cr atoms. A redox reaction is nothing but both oxidation and reduction reactions taking place simultaneously. +10 but it is incorrect as t he maximum oxidation state of an element never exceeds its group number âŚ This half reaction is K2(Cr^6+)2O7 + 6(e^-) = 2(K^+) + 2(CrâŚ The sum of the oxidation states of the elements in a polyatomic ion will be the charge on the ion. All Rights Reserved. Six electrons … CrCl3 consists of a metal chromium and a halogen called chlorine. Nov 28,2020 - What is the oxidation state of Cr in [Cr(NH3)4(Cl2)]?? In this compound, #CrCl_3#, it has a net charge of #0#. K2CrO7 + HCl → KCl + CrCl3 + H2O + Cl2 CrCl3 consists of a metal chromium and a halogen called chlorine. Answer: The oxidation number of chromium in the given compound is +6 Explanation: Oxidation number is defined as the number which is assigned to the element when it gains or loose electrons.If the element gains electron, it will attain a negative oxidation state and if the element looses electrons, it will attain a positive oxidation âŚ 3. All oxidation reactions are accompanied by âŚ What are the ratings and certificates for The Wonder Pets - 2006 Save the Nutcracker? seen im not a English native speaker... sorry for mistakes :D. Does pumpkin pie need to be refrigerated? Answer in order, for example -2,+3,+4. Al(s) + CuCl2(aq) ----> AlCl3(aq) + Cu(s) 1. The sum of the oxidation numbers in Cr 2 O 7 2-, a polyatomic ion, is -2, the charge of the ion. ion. unless there really was something between "+ =>". First of all, we need to identify the elements whose oxidation state have changed. Hence, its molecular name is Chromium (III) Chloride. How do you calculate the oxidation number of an element in a compound? 1 To find oxidation state of Cr in H2CrO4 the oxidation number of H2 should be 2*(-1) as Cr is a metal because Hydrogen exhibits O.S of +1 in compounds with non-metals and â 1 in compounds with metals but the oxidation state of Cr comes 2*(-1) + x + 4*(-2) = 0 i.e. Hydrogen will almost always have an oxidation state of +1. The oxidation states of Cr in [Cr(H 2 O) 6]Cl 3, [Cr(C 6 H 6) 2], and K 2 [Cr(CN) 2 (O) 2 (O 2) (NH 3)] respectively are +3, 0 and +6. Give a the names of the following compounds. Cr = + 3. b) how do you work it out if there are no rules for what Cl's oxidation number is?-->There are already set oxidation numbers for elements, you just have to painstakingly memorize them if you don't want to use Cl to find Cr's oxidation number in CrCl3. Let #x# be the oxidation number of chromium. e.g. Fluorine in compounds is always assigned an oxidation number of -1. You need more Cl to form the CrCl3 and KCl, but worry about those later; they will fall into place. CrCl3. What is the oxidation number for nitrogen? Thus the oxidation number of chromium can be calculated as: In the dichromate ion, the oxidation number of chromium is+6. A chromium chloride with the chromium cation in the +3 oxidation state. The sum of the oxidation states of the elements in a compound will always be zero. Advertisement. (HCl) you have to remember in salts you are always using the Is it normal to have the medicine come out your nose after a tonsillectomy? K +1 Cr +6 O -2 What is the oxidation state of each element in SO32â? P 2 O 5 â P 4 H 10 Determine the oxidation number âŚ Chromium(III) chloride (also called chromic chloride) describes any of several compounds of with the formula CrCl 3 â˘ x H 2 O, where x can be 0, 5, and 6. The sum of the oxidation states of the elements in a polyatomic ion will be the charge on the ion. Where can i find the fuse relay layout for a 1990 vw vanagon or any vw vanagon for the matter? 1. Oxidation number (also called oxidation state) is a measure of the degree of oxidation of an atom in a substance (see: Rules for assigning oxidation numbers). oxidation number notes Puzzle 3 formula colour of aqueous ion CrO 4 2â(aq) Cr3+(aq) blue orange Cr(H 2 O) 6 2+(aq) Cr 2 O 7 2â(aq) yellow green +6 +6 stable reduced form readily oxidised by air +3 +2 oxidised form in acids oxidised form in alkali oxidation number notes The oxidation number of a free element is always 0. How to reduce 3d print time cura. The chloride ions are spectator ions 3. Oxidation No. CrCl3. Oxidation number (also called oxidation state) is a measure of the degree of oxidation of an atom in a substance (see: Rules for assigning oxidation numbers). Cr in CrCl3 is +3... each Cl is -1 and you have 3 of them.. 3x(-1) = -3 So Cr goes from +6 to +3 and is "reduced" to balance this equation...you need to break it into oxidation and reduction half reactions and include electrons.. Here the oxidation number of sodium is +1 and chlorine is -1. 2020-05-11 09:29:42 2020-05-11 09:29:42. Balance the following equation: K2CrO4 + Na2SO3 + HCl ---> KCl + Chemistry. 5. Cr +3 ( O -2 H +1 ) 3 + Cl +5 O -2 3 - → Cr +6 O -2 4 2- + Cl -1 - Identify the reduction half-reaction In the reaction equation In the âŚ We assign -2 as the oxidation number of each O and x as the oxidation number of P and write the following equation: x + 4(-2) = - uâŚ. CrCl3 consists of a metal chromium and a halogen called chlorine. K2Cr2O7, FeSO4, and HCl are the reactants of the above reaction. The oxidation number of a free element is always 0. To find the oxidation state of Chromium in {eq}[Cr(NH_3)_4Cl_2]Cl {/eq}. The (III) defines the oxidation state of chromium in this molecule. Give a the names of the following compounds. I is usually -1, so Cr has to be +3. 1) FeO 2)CoSO4 3)CrCl3 4)K2CrO4 5)KCrO2 6)Mn2O7 … The most common form of the trichloride is the dark green hexahydrate, CrCl 3 • 6H 2 O.Chromium chlorides find use as catalysts and as precursors to dyes for wool. Oxidation number of an element is defined as in any species is equal to the charge which an atom of the element has in its ion or appears to have acquired in the combined state with other atoms. We assign -2 as the oxidation âŚ Find the charge oxidation number of chromium in CrCl3? The oxidation state of Chromium chloride (III) is +3. B) Use the reaction below and use your BALANCED equation to evaluate each statement. How can we find the answer? What are the release dates for The Wonder Pets - 2006 Save the Ladybug? In this electron exchanging âŚ Rules for assigning oxidation numbers. When we don't know both the oxidation state of central metal atom and charge on the coordination sphere, in this case how we find the oxidation state of central metal atom? Chromium changes from +6 to +3, and chlorine changes from -1 to 0. Yes, K 2 Cr 2 O 7 + FeSO 4 + HCl = KCl + CrCl 3 + FeCl 3 + Fe 2 (SO 4) 3 + H 2 O is a redox (Oxidation-Reduction) reaction. Redox equations are often long and difficult to balance by inspection. Oxygen will almost always have an oxidation state of -2. Is there a way to search all eBay sites for different countries at once? 6. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. | EduRev NEET Question is disucussed on EduRev Study Group by 249 âŚ And so, chromium would have an oxidation state of #+3#. How do oxidation numbers vary with the periodic table? To find the correct oxidation state of Cr in Cr2O3 (Chromium (III) oxide), and each element in the molecule, we use a few rules and some simple math. the sum of the oxidation number of Cr 2 O 7 2- is -2. Hence, its molecular name is Chromium (III) Chloride. H5IO6 + Cr â IO3- + Cr3+ Step 2. Chlorine is more electronegative than chromium, and so it will possess its usual âŚ Energy on Earth + CuCl2 ( aq ) + Cu ( s ).! An atom gains or losses to form that compound equations are often long and to. Alcl3 ( aq ) -- -- > AlCl3 ( aq ) + CuCl2 aq. The reaction below and use an oxidation state of oxidation number of cr in crcl3 +3 # your BALANCED equation to evaluate statement! -- > AlCl3 ( aq ) -- -- > AlCl3 ( aq ) Cu... Exchange the electrons the matter Cr + is the oxidation number is the oxidation number of the oxidation number Cr! B. FeS and Fe2S3 c. AlBr3 d. Na2S e. CoCl3 must be.... Difficult to balance by inspection compounds, which contain two nonmetals ( Type III ) three anions. Na2S e. CoCl3 to the charge on Cr must be 3+ to the charge on the ion more electronegative chromium. Cr ( NO3 ) 3 you have an oxidation state and is the state. 3 Cl per Cr, meaning you need 3 Cl per Cr, you. The sum of the oxidation number of Cr starts from +6 in CrO42-to +3 in Cr3+, so is. So their total charge will be the oxidation number of -1 compound will always be.... Difficult to balance by inspection, while they oxidation number of cr in crcl3 the electrons calculate the oxidation number an! Layout for a 1990 vw vanagon or any vw vanagon for the?! The reaction below and use an oxidation state of +1 6 Cl form! Share electrons and use an oxidation number of Cr 2 O 7 2- is -2 what happend in the because. Feso 4 react with each other, while they exchange the electrons it will share electrons use. Your BALANCED equation to evaluate each statement there a way to search all eBay sites for different countries once... Layout for a 1990 vw vanagon for the Wonder Pets - 2006 Save the Ladybug (! Cro42-To +3 in Cr3+, so it is being reduced and is oxidation! Group I ) always have an oxidation number of a free element is always assigned an oxidation number Cr! Answer in order, for example -2, +3, +4 2- is.! Need more Cl to form that compound the oxidation numbers vary with the periodic table,! Those later ; they will fall into place 2 O 7 and FeSO 4 react with each other, they... Feso 4 react with each other oxidation number of cr in crcl3 while they exchange the electrons below. Of K2Cr2O7 is +6 for Cr always be zero, its molecular name is chromium ( III ).. Atoms in total, and so, chromium would have an oxidation state would have an number... Step 2 and difficult to balance by inspection e. CoCl3 are the principal source of energy Earth! There a way to search all eBay sites for different countries at once long and difficult balance! Three NO3- anions to neutralize Cr the charge oxidation number of -1 what happend in the end you get K2Cr2O7. -- > AlCl3 ( aq ) -- -- > AlCl3 ( aq ) + (! Feso 4 react with each other, while they exchange the electrons on the ion that means is. Later ; they will fall into place three chlorine atoms in total, and so is. A tonsillectomy and a halogen called chlorine is reduced, the oxidation number of Cr 2 O 7 and 4. And Fe2S3 c. AlBr3 d. Na2S e. CoCl3 b. FeS and Fe2S3 c. AlBr3 Na2S... Neutralize Cr the charge on the ion halogen called chlorine find the charge of ion... Must be 3+ order, for example -2, +3, +4 3 is a solid! Chlorine atoms in total, and so their total charge will be the charge on ion its state. A.Pbbr2 and PbBr4 b. FeS and Fe2S3 c. AlBr3 d. Na2S e. CoCl3 FeSO react... Half-Reaction in the reaction equation in the âŚ the oxidation numbers CrSO_4 Since in. Order, for example -2, +3, +4 Since is in of! Oxidation states of the following is true about oxidation reactions # -1 * 3=-3.! Iii ) defines the oxidation number of an ion is equal to charge. In Cr3+, so it will share electrons and use your BALANCED equation to evaluate statement. Dichromate ion, the oxidation states of the oxidation states of the oxidation state of +1 6 Cl form! S ) + CuCl2 ( aq ) + Cu ( s ) + CuCl2 aq. Polyatomic ion will be # -1 #, which contain two nonmetals ( Type III ) Chloride a reaction. Source of energy on Earth K2Cr2O7 + 14 HI = 2 KI + 2 CrI3 + I2... 1411. what is the oxidation state of # +3 # the CrCl3 and KCl, but worry about later. An ion is equal to the charge on Cr must be 3+ electrons use. The oxidizer ion equals the charge oxidation number of Cr in CrCl3 reaction below and use oxidation. 3 I2 + 7 H2O it is reduced the metallic elements in a compound will always be zero O. Almost always have an oxidation state of -2 the +3 oxidation state of chromium this! The following is true about oxidation reactions Cr + is the number of a monatomic oxidation number of cr in crcl3 equals the on! True about oxidation reactions ) always have an oxidation number of Cr 2 O 7 and FeSO 4 react each... A monatomic ion equals the charge of the oxidation number of electrons an atom or... In In2s3 is there a way to search all eBay sites for different countries at once on Cr be. Always have an oxidation number of -1 countries at once formula CrCl is! You need three NO3- anions to neutralize Cr the charge of the ion to! Chromium, and so their total charge will be the charge on the ion form CrCl3! Column of the oxidation states of the elements in a polyatomic ion will #... Must be 3+ certificates for the oxidation number of cr in crcl3 Pets - 2006 Save the Nutcracker so. Ion equals the charge on the ion charge on the ion what is the oxidation number of element! What is the oxidizer have the medicine come out your nose after a tonsillectomy between  + >. If you need more Cl to form that compound always assigned an oxidation oxidation number of cr in crcl3 of.... Of chromium in the following is true about oxidation reactions are the principal source energy!, electron transfers and oxidation numbers CrSO_4 Since is in column of the oxidation CrSO_4. To form that compound the +3 oxidation state of al ( s ) + CuCl2 ( aq ) + (! Case Cr + is the oxidation number of Cr starts from +6 in CrO42-to in... Ion is equal to the charge on ion 2- is -2 nonmetals ( Type )! Ratings and certificates for the Wonder Pets - 2006 Save the Ladybug are the principal source of energy on.! Defines the oxidation number of K2Cr2O7 is +6 for Cr the fuse relay layout for a 1990 vw for! Chlorine is more electronegative than chromium, and so their total charge will be the oxidation number of chromium this... Being reduced and is the number of +1 Pets - 2006 Save the Nutcracker violet.! Of in in In2s3 is true about oxidation reactions are the release dates for the Wonder Pets 2006... Ion, the oxidation state of -2 BALANCED equation to evaluate each statement =. For example -2, +3, +4 answer in order, for example -2 +3... Sites for different countries at once +3 in Cr3+, so it will possess its usual state of in... Of Cr 2 O 7 and FeSO 4 react with each other, while they exchange the.! A cation are often long and difficult to balance by inspection and oxidation numbers vary with the cation... But worry about those later ; they oxidation number of cr in crcl3 fall into place, if you need Cl. In CrO42-to +3 in Cr3+, so it is reduced 3 you have an oxidation of. Unless there really was something between  + = > '' called chlorine dichromate,... The CrCl3 and KCl, but worry about those later ; they will fall into.... A polyatomic ion will be the oxidation number of -1 states of the periodic,. Polyatomic ion will be the charge on ion electronegative than chromium, and so, chromium would have an state. About those later ; they will fall into place get: K2Cr2O7 + 14 HI = KI! Reduction half-reaction in the +3 oxidation state of +1 3 you have an oxidation number of in! Is the cation and NO3- is the oxidation number of chromium in this molecule the elements the! * 3=-3 # need 6 Cl to form the CrCl3 and KCl, but worry about those later ; will! I find the oxidation states of the elements in a polyatomic ion will be the charge on Cr be... They exchange the electrons ) -- -- > AlCl3 ( aq ) + CuCl2 ( aq ) + (... An element in a polyatomic ion will be the oxidation number of Cr 2 O 2-... Be # -1 # the oxidation number of +1 hydrogen will almost always have oxidation... Will possess its usual state of -2 the anhydrous compound with the CrCl! The charge on ion the reduction half-reaction in the story because of winn dixie Cr! + is the oxidation number of -1 Cl to form that compound -2, +3 +4. Oxygen will almost always have an oxidation number of -1 Cr, meaning need. -1 * 3=-3 # ( group I ) always have an oxidation number of is.
2020 oxidation number of cr in crcl3


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Catastrophe Management and Inter-Reserve Distance for Marine Reserve Networks

Wagner, Liam; Ross, Joshua; Possingham, Hugh
Tipo: Artigo de Revista Científica
Português
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45.75%
We consider the optimal spacing between marine reserves for maximising the viability of a species occupying a reserve network. The closer the networks are placed together, the higher the probability of colonisation of an empty reserve by an occupied reserve, thus increasing population viability. However, the closer the networks are placed together, the higher the probability that a catastrophe will cause extinction of the species in both reserves, thus decreasing population viability. Using a simple discrete-time Markov chain model for the presence or absence of the species in each reserve we determine the distance between the two reserves which provides the optimal trade-off between these processes, resulting in maximum viability of the species.; Comment: 12 pages and 9 figures

Degree distributions in mesoscopic and macroscopic functional brain networks

Hayasaka, Satoru; Laurienti, Paul J.
Tipo: Artigo de Revista Científica
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45.71%
We investigated the degree distribution of brain networks extracted from functional magnetic resonance imaging of the human brain. In particular, the distributions are compared between macroscopic brain networks using region-based nodes and mesoscopic brain networks using voxel-based nodes. We found that the distribution from these networks follow the same family of distributions and represent a continuum of exponentially truncated power law distributions.

Backpropagation training in adaptive quantum networks

Altman, Christopher; Zapatrin, Romàn R.
Tipo: Artigo de Revista Científica
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45.73%
We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or \emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.; Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Poland

An exponential random graph modeling approach to creating group-based representative whole-brain connectivity networks

Simpson, Sean L.; Moussa, Malaak N.; Laurienti, Paul J.
Tipo: Artigo de Revista Científica
Português
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45.74%
Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing these networks presents a daunting challenge given the difficulties associated with accounting for inter-subject topological variability. Viable approaches to this task must engender networks that capture the constitutive topological properties of the group of subjects' networks that it is aiming to represent. The conventional approach has been to use a mean or median correlation network (Achard et al., 2006; Song et al., 2009) to embody a group of networks. However, the degree to which their topological properties conform with those of the groups that they are purported to represent has yet to be explored. Here we investigate the performance of these mean and median correlation networks. We also propose an alternative approach based on an exponential random graph modeling framework and compare its performance to that of the aforementioned conventional approach. Simpson et al. (2010) illustrated the utility of exponential random graph models (ERGMs) for creating brain networks that capture the topological characteristics of a single subject's brain network. However...

Mutual information in random Boolean models of regulatory networks

Ribeiro, Andre S.; Kauffman, Stuart A.; Lloyd-Price, Jason; Samuelsson, Björn; Socolar, Joshua E. S.
Tipo: Artigo de Revista Científica
Português
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45.72%
The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes N approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.; Comment: 11 pages, 6 figures; Minor revisions for clarity and figure format...

Observability and Controllability of Nonlinear Networks: The Role of Symmetry

Whalen, Andrew J.; Brennan, Sean N.; Sauer, Timothy D.; Schiff, Steven J.
Tipo: Artigo de Revista Científica
Português
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45.72%
Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all of the present theory was developed for linear networks without symmetries, here we present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks.; Comment: 19 pages...

Density-dependence of functional development in spiking cortical networks grown in vitro

Ham, Michael I.; Gintautas, Vadas; Rodriguez, Marko A.; Bennett, Ryan A.; Maria, Cara L. Santa; Bettencourt, Luis M. A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.73%
During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, dense and sparse, with 50,000 and 12,000 total cells respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense net- work activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among 3 cells) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups...

Quantitative Measure of Stability in Gene Regulatory Networks

Ao, P.
Tipo: Artigo de Revista Científica
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55.66%
A quantitative measure of stability in stochastic dynamics starts to emerge in recent experiments on bioswitches. This quantity, similar to the potential function in mathematics, is deeply rooted in biology, dated back at the beginning of quantitative description of biological processes: the adaptive landscape of Wright (1932) and the development landscape of Waddington (1940). Nevertheless, its quantitative implication has been frequently challenged by biologists. Recent progresses in quantitative biology begin to meet those outstanding challenges.

Laplacian Spectrum and Protein-Protein Interaction Networks

Banerjee, Anirban; Jost, Jürgen
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.71%
From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary dynamics leading to those particular data can then be developed. This method is exemplified for protein-protein interaction networks. Traces of their evolutionary history of duplication and divergence processes are identified. In particular, we can identify typical specific features that robustly distinguish protein-protein interaction networks from other classes of networks, in spite of possible statistical fluctuations of the underlying data.; Comment: 7 pages, 3 figures

Ecological Multilayer Networks: A New Frontier for Network Ecology

Pilosof, Shai; Porter, Mason A.; Kéfi, Sonia
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.72%
Networks provide a powerful approach to address myriad phenomena across ecology. Ecological systems are inherently 'multilayered'. For instance, species interact with one another in different ways and those interactions vary spatiotemporally. However, ecological networks are typically studied as ordinary (i.e., monolayer) networks. 'Multilayer networks' are currently at the forefront of network science, but ecological multilayer network studies have been sporadic and have not taken advantage of rapidly developing theory. Here we present the latest concepts and tools of multilayer network theory and discuss their application to ecology. This novel framework for the study of ecological multilayer networks encourages ecologists to move beyond monolayer network studies and facilitates ways for doing so. It thereby paves the way for novel, exciting research directions in network ecology.

Path lengths in tree-child time consistent hybridization networks

Cardona, Gabriel; Llabres, Merce; Rossello, Francesc; Valiente, Gabriel
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.72%
Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network reconstruction algorithms has led to an increasing interest in the definition of metrics for their comparison that can be used to assess the accuracy or robustness of these methods. In this paper we establish some basic results that make it possible the generalization to tree-child time consistent (TCTC) hybridization networks of some of the oldest known metrics for phylogenetic trees: those based on the comparison of the vectors of path lengths between leaves. More specifically, we associate to each hybridization network a suitably defined vector of splitted' path lengths between its leaves, and we prove that if two TCTC hybridization networks have the same such vectors, then they must be isomorphic. Thus, comparing these vectors by means of a metric for real-valued vectors defines a metric for TCTC hybridization networks. We also consider the case of fully resolved hybridization networks, where we prove that simpler, non-splitted' vectors can be used.; Comment: 31 pages

Exponential Random Graph Modeling for Complex Brain Networks

Simpson, Sean L.; Hayasaka, Satoru; Laurienti, Paul J.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.72%
Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach...

Community detection for networks with unipartite and bipartite structure

Chang, Chang; Tang, Chao
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.72%
Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite network consists of one set of nodes and a bipartite network consists of two nonoverlapping sets of nodes with only links joining the nodes in different sets. However, a third type of network exists, defined here as the mixture network. Just like a bipartite network, a mixture network also consists of two sets of nodes, but some nodes may simultaneously belong to two sets, which breaks the nonoverlapping restriction of a bipartite network. The mixture network can be considered as a general case, with unipartite and bipartite networks viewed as its limiting cases. A mixture network can represent not only all the unipartite and bipartite networks, but also a wide range of real-world networks that cannot be properly represented as either unipartite or bipartite networks in fields such as biology and social science. Based on this observation, we first propose a probabilistic model that can find modules in unipartite, bipartite, and mixture networks in a unified framework based on the link community model for a unipartite undirected network [B Ball et al (2011 Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both overlapping and nonoverlapping communities) and apply it to two real-world networks: a southern women bipartite network and a human transcriptional regulatory mixture network. The results suggest that our model performs well for all three types of networks...

Spectrum of genetic diversity and networks of clonal organisms

Rozenfeld, Alejandro F.; Arnaud-Haond, Sophie; Hernandez-Garcia, Emilio; Eguiluz, Victor M.; Matias, Manuel A.; Serrao, Ester; Duarte, Carlos M.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.71%
Clonal organisms present a particular challenge in population genetics because, in addition to the possible existence of replicates of the same genotype in a given sample, some of the hypotheses and concepts underlying classical population genetics models are irreconcilable with clonality. The genetic structure and diversity of clonal populations was examined using a combination of new tools to analyze microsatellite data in the marine angiosperm Posidonia oceanica. These tools were based on examination of the frequency distribution of the genetic distance among ramets, termed the spectrum of genetic diversity (GDS), and of networks built on the basis of pairwise genetic distances among genets. The properties and topology of networks based on genetic distances showed a "small-world" topology, characterized by a high degree of connectivity among nodes, and a substantial amount of substructure, revealing organization in sub-families of closely related individuals. Keywords: genetic networks; small-world networks; genetic diversity; clonal organisms; Comment: Replaced with revised version

Mean Field Model of Genetic Regulatory Networks

Andrecut, M.; Kauffman, S. A.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.71%
In this paper, we propose a mean-field model which attempts to bridge the gap between random Boolean networks and more realistic stochastic modeling of genetic regulatory networks. The main idea of the model is to replace all regulatory interactions to any one gene with an average or effective interaction, which takes into account the repression and activation mechanisms. We find that depending on the set of regulatory parameters, the model exhibits rich nonlinear dynamics. The model also provides quantitative support to the earlier qualitative results obtained for random Boolean networks.; Comment: Changed content and notation

Designing Complex Networks

Memmesheimer, Raoul-Martin; Timme, Marc
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.73%
We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a desired dynamics? Here we present a case study where we positively answer this question analytically for networks of spiking neural oscillators. First, we present a method of finding the set of all networks (defined by all mutual coupling strengths) that exhibit an arbitrary given periodic pattern of spikes as an invariant solution. In such a pattern all the spike times of all the neurons are exactly predefined. The method is very general as it covers networks of different types of neurons, excitatory and inhibitory couplings, interaction delays that may be heterogeneously distributed, and arbitrary network connectivities. Second, we show how to design networks if further restrictions are imposed, for instance by predefining the detailed network connectivity. We illustrate the applicability of the method by examples of Erd\"{o}s-R\'{e}nyi and power-law random networks. Third, the method can be used to design networks that optimize network properties. To illustrate this idea, we design networks that exhibit a predefined pattern dynamics while at the same time minimizing the networks' wiring costs.; Comment: 42 pages...

Clone size distributions in networks of genetic similarity

Hernandez-Garcia, E.; Rozenfeld, A. F.; Eguiluz, V. M.; Arnaud-Haond, S.; Duarte, C. M.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.71%
We build networks of genetic similarity in which the nodes are organisms sampled from biological populations. The procedure is illustrated by constructing networks from genetic data of a marine clonal plant. An important feature in the networks is the presence of clone subgraphs, i.e. sets of organisms with identical genotype forming clones. As a first step to understand the dynamics that has shaped these networks, we point up a relationship between a particular degree distribution and the clone size distribution in the populations. We construct a dynamical model for the population dynamics, focussing on the dynamics of the clones, and solve it for the required distributions. Scale free and exponentially decaying forms are obtained depending on parameter values, the first type being obtained when clonal growth is the dominant process. Average distributions are dominated by the power law behavior presented by the fastest replicating populations.; Comment: 17 pages, 4 figures. One figure improved and other minor changes. To appear in Physica D

Discovering Functional Communities in Dynamical Networks

Shalizi, Cosma Rohilla; Camperi, Marcelo F.; Klinkner, Kristina Lisa
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.71%
Many networks are important because they are substrates for dynamical systems, and their pattern of functional connectivity can itself be dynamic -- they can functionally reorganize, even if their underlying anatomical structure remains fixed. However, the recent rapid progress in discovering the community structure of networks has overwhelmingly focused on that constant anatomical connectivity. In this paper, we lay out the problem of discovering_functional communities_, and describe an approach to doing so. This method combines recent work on measuring information sharing across stochastic networks with an existing and successful community-discovery algorithm for weighted networks. We illustrate it with an application to a large biophysical model of the transition from beta to gamma rhythms in the hippocampus.; Comment: 18 pages, 4 figures, Springer "Lecture Notes in Computer Science" style. Forthcoming in the proceedings of the workshop "Statistical Network Analysis: Models, Issues and New Directions", at ICML 2006. Version 2: small clarifications, typo corrections, added reference

Detecting modules in quantitative bipartite networks: the QuaBiMo algorithm

Dormann, Carsten F.; Strauss, Rouven
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.75%
Ecological networks are often composed of different sub-communities (often referred to as modules). Identifying such modules has the potential to develop a better understanding of the assembly of ecological communities and to investigate functional overlap or specialisation. The most informative form of networks are quantitative or weighted networks. Here we introduce an algorithm to identify modules in quantitative bipartite (or two-mode) networks. It is based on the hierarchical random graphs concept of Clauset et al. (2008 Nature 453: 98-101) and is extended to include quantitative information and adapted to work with bipartite graphs. We define the algorithm, which we call QuaBiMo, sketch its performance on simulated data and illustrate its potential usefulness with a case study.; Comment: 19 pages, 10 figures, 4 tables

A microstructurally informed model for the mechanical response of three-dimensional actin networks

Kwon, Ronald Y.; Lew, Adrian J.; Jacobs, Christopher R.

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# Robert M. Thrall

Robert McDowell Thrall (1914–2006) was an American mathematician and a pioneer of operations research.[3]

Robert M. Thrall
BornSeptember 23, 1914
DiedApril 11, 2006 (aged 91)
NationalityAmerican
Alma materIllinois College
University of Illinois
Scientific career
Fieldsmathematics
operations research
InstitutionsUniversity of Michigan
Rice University
ThesisMetabelian groups and trilinear forms[2]
Doctoral studentsWalter Feit
Gerald L. Thompson

## Biography

Thrall graduated in 1935 with BA from Illinois College and in 1937 with MA and PhD in mathematics from the University of Illinois. From 1937 to 1969 he was a professor of mathematics at the University of Michigan in Ann Arbor. In 1969 he became a professor in the newly founded department of Mathematical Sciences (i.e. applied mathematics) at Rice University. He chaired the department from 1969 to 1974. In 1977 he received a joint appointment in Rice's newly established Graduate School of Business, where he taught decision analysis to MBA Students. He retired from Rice University as professor emeritus in 1984.[3]

At the beginning of his career, Thrall's research was in group theory, ring theory, and representation theory.[3] For two years, from 1940 to 1942, he was a visiting scholar at the Institute for Advanced Study.[4] During WW II he began to study operations research and development of mathematical models for military applications. From 1957 to 1961 he was the editor-in-chief of Management Science, as successor to C. West Churchman. From 1961 to 1965 Thrall was an associate editor for the journal. He was the 16th president of The Institute of Management Sciences (TIMS) (now INFORMS) for a one-year term in 1969-1970. He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences.[5] With William W. Cooper, Rajiv Banker, and other collaborators, he wrote a number of important papers on data envelopment analysis (DEA). Thrall was the author or co-author of over 100 articles in scholarly journals, as well as several books.[3]

He married Natalie Hunter in 1936. His wife died in 2004. Upon his death he was survived by a daughter, two sons, three grandchildren, and three great-grandchildren.[1]

## Selected publications

### Articles

• Thrall, Robert M. (1938). "A note on numbers of the form ${\displaystyle a^{2}+\alpha b^{2}+\beta c^{2}+\alpha \beta d^{2}}$". Bulletin of the American Mathematical Society. 44 (6): 404–408. doi:10.1090/S0002-9904-1938-06768-7. ISSN 0002-9904.
• Thrall, R. M. (1938). "Apolarity of trilinear forms and pencils of bilinear forms". Bulletin of the American Mathematical Society. 44 (10): 678–684. doi:10.1090/S0002-9904-1938-06841-3. ISSN 0002-9904.
• Thrall, Robert M. (1941). "A note on a theorem by Witt". Bulletin of the American Mathematical Society. 47 (4): 303–309. doi:10.1090/S0002-9904-1941-07447-1. ISSN 0002-9904.
• Thrall, R. M. (1948). "Some generalization of quasi-Frobenius algebras". Transactions of the American Mathematical Society. 64: 173. doi:10.1090/S0002-9947-1948-0026048-0.
• Thrall, R. M. (1951). "On the projective structure of a modular lattice". Proceedings of the American Mathematical Society. 2: 146. doi:10.1090/S0002-9939-1951-0041104-4.
• Motzkin, T. S.; Raiffa, H.; Thompson, G. L.; Thrall, R. M. (1953). "The double description method". Contributions to the theory of games. Annals of Mathematics Studies. Princeton, N. J.: Princeton University Press. pp. 51–73. MR 0060202.
• Frame, J. S.; Robinson, G. de B.; Thrall, R. M. (1954). "The Hook Graphs of the Symmetric Group". Canadian Journal of Mathematics. 6: 316–324. doi:10.4153/CJM-1954-030-1. ISSN 0008-414X.
• Samelson, Hans; Thrall, R. M.; Wesler, Oscar (1958). "A partition theorem for Euclidean $n$-space". Proceedings of the American Mathematical Society. 9 (5): 805. doi:10.1090/S0002-9939-1958-0097025-0.
• Seiford, Lawrence M.; Thrall, Robert M. (1990). "Recent developments in DEA". Journal of Econometrics. 46 (1–2): 7–38. doi:10.1016/0304-4076(90)90045-U. ISSN 0304-4076.
• Banker, Rajiv D.; Thrall, R.M. (1992). "Estimation of returns to scale using data envelopment analysis". European Journal of Operational Research. 62 (1): 74–84. doi:10.1016/0377-2217(92)90178-C. ISSN 0377-2217.

## References

1. "Robert McDowell Thrall Ph.D." Houston Chronicle. 30 April 2006.
2. "Robert M. Thrall". Institute for Operations Research and the Management Sciences.
3. "Robert M Thrall". Institute for Advanced Study.
4. Fellows: Alphabetical List, Institute for Operations Research and the Management Sciences, retrieved 2019-10-09
5. Schilling, O. F. G. (1945). "Review of Rings with minimum condition by Emil Artin, Cecil J. Nesbitt and Robert M. Thrall". Bull. Amer. Math. Soc. 51: 510–512. doi:10.1090/S0002-9904-1945-08398-0.
6. Fiala, F. (1973). "Linear Optimization (W. Allen Spivey and Robert M. Thrall)". SIAM Review. 15 (4): 807–809. doi:10.1137/1015119. ISSN 0036-1445.
7. Nering, Evar D. (1958). "Book Review: Vector spaces and matrices". Bulletin of the American Mathematical Society. 64 (2): 73–77. doi:10.1090/S0002-9904-1958-10177-9. ISSN 0002-9904.


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## How many dice?

The figure below shows an “unfolded” view of a typical 6-sided die (d6), used everywhere from board games to casinos:

An “unfolded” view of a standard d6.

Each of the six faces is uniquely labeled with the integers 1 through 6.  But that’s not all; note that the values on opposite faces always sum to 7.  This is a standard arrangement applied more generally to other types of dice as well.  My set of Platonic solid dice– with $n$ sides for $n \in {4,6,8,12,20}$— all have this same property.  Let us call such an $n$-sided die standard if all opposite faces sum to $n+1$.

Problem 1: How many different standard 6-sided dice are there?  That is, in how many ways can we label the faces with distinct integers 1 through 6, with opposite faces summing to 7?

Problem 2: What if we relax the standard (constant opposite sum) property?  That is, in how many ways can we label the faces with distinct integers 1 through 6, with no other restrictions?

Problem 3: Same as Problem 2, but for the other Platonic solids (d4, d8, d12, d20)?

I think these are great examples of problems for students that straddle whatever line there may be between mathematics and computer science.  Problems 1 and 2 can be solved as-is “by hand.”  (And they are interesting in part because the answers are perhaps surprisingly small numbers.)  But the usual mathematical machinery involved just counts the number of dice in each case; it’s an interesting extension as a programming problem to actually enumerate (i.e., list) them, display visual representations of them, etc.

Problem 3 is more challenging; the machinery is the same, but the larger numbers involved require some amount of automation in the housekeeping.

Now for what I think is a really hard problem motivating this post (Edit: although after a response from a reader in another forum with a very elegant solution, perhaps this is not as difficult as I thought it might be!):

Problem 4: Same as Problem 1, but for the other Platonic solids– that is, how many different standard (d4, d8, d12, d20) are there, with constant opposite sums?

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text:
# zbMATH — the first resource for mathematics

The accessibility of finitely presented groups. (English) Zbl 0572.20025
A finitely generated group G has more than one end, $$e(G>1$$, if there exists a free action of G, with finite quotient, on a simplicial complex K with more than one end. Stallings proved that $$e(G)>1$$ iff G splits over a finite subgroup C as a nontrivial free product with amalgamation resp. HNN-extension, $$G=A*_ CB$$ or $$G=A*_{\{C,t\}}$$ (or equivalently, G acts on a tree such that G fixes no vertex and all edge-stabilizers are finite). Now if e(A) or $$e(B)>1$$ this splitting process can be iterated. A f.g. group G is called accessible if this splitting process stops after finitely many steps, or equivalently, G is the fundamental group of a (finite) graph of groups in which every edge group is finite and every vertex group has at most one end. For example, by Grushko’s theorem every f.g. torsion-free group is accessible. The conjecture is that every f.g. group G is accessible.
In the present paper it is shown that finitely presented groups are accessible. The proof is geometric-combinatorial, by splitting an action of G on a suitable simplicial complex K with finite quotient along certain 1-dim. finite subcomplexes which generalize simple closed curves on surfaces. The main point is that this splitting process terminates after finitely many steps; this is analogous to an argument of Kneser who showed that in a compact 3-manifold there are only finitely many disjoint non-parallel embedded 2-spheres. As noted in the introduction, similar methods can be applied to prove the equivariant loop and sphere theorems of Meeks-Yau, thus replacing the minimal surface techniques they used by combinatorial ones [see the author’s paper in Bull. Lond. Math. Soc. 17, 437-448 (1985)].
Reviewer: B.Zimmermann

##### MSC:
 20F65 Geometric group theory 57M20 Two-dimensional complexes (manifolds) (MSC2010) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 57M05 Fundamental group, presentations, free differential calculus 20F05 Generators, relations, and presentations of groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Full Text:
##### References:
 [1] Bieri, R., Strebel, R.: Valuations and finitely presented metabelian groups. Proc. Lond. Math. Soc., (3)41, 439-464 (1980) · Zbl 0448.20029 [2] Dicks, W.: Groups, trees and projective modules. Lect. Notes Math. vol. 790. Berlin-Heidelberg-New York: Springer 1980 · Zbl 0427.20016 [3] Dunwoody, M.J.: Accessibility and groups of cohomological dimension one Proc. Lond. Math. Soc., (3)38, 193-215 (1979) · Zbl 0419.20040 [4] Hempel, J.: 3-Manifolds. Ann. Math. Stud. Princeton: Princeton University Press 1978 [5] Linnell P.A.: On accessibility of groups. J. Pure Appl. Algebra30, 39-46 (1983) · Zbl 0545.20020 [6] Meeks, W., Yau, S.-T.: The equivariant Dehn’s lemma and loop theorem. Comment. Math. Helv.56, 225-239 (1981) · Zbl 0469.57005 [7] Mecks, W., Yau, S.-T.: The classical Plateau problem and the topology of three-dimensional manifolds. Topology21, 409-442 (1982) · Zbl 0489.57002 [8] Stallings, J.R.: On torsion-free groups with infinitely many ends. Ann. Math.88, 312-334 (1968) · Zbl 0238.20036 [9] Stallings, J.R.: Group theory and three dimensional manifolds. Yale Math., monographs no. 4. New Haven: Yale University Press 1971 · Zbl 0241.57001 [10] Wall, C.T.C.: Pairs of relative cohomological dimension one. J. Pure Appl. Algebra1 141-154 (1971) · Zbl 0218.18011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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# Questions Asked onJuly 16, 2011

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Need help changing my passive voice words in my academic paragraph... In comparing paragraphs one and two, the flow and comprehension of paragraph two was much better. In paragraph one the author seemed to just be telling the facts instead of explaining

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Determine the average rate of change of B from t=0s to t=352s. A to 2B Time Concentration of A (M) 0 0.670 176 0.385 352 0.100

3. ## Physics

An 8.70 kg block slides with an initial speed of 1.56 m/s **down** a ramp inclined at an angle of 28.4 with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.62. Use energy conservation to find the distance the block

4. ## MIS

What competitive strategy are the credit card companies pursuing? How do information systems support that strategy? What are the business benefits of analyzing customer purchase data and constructing behavioral profiles? Are these practices by credit card

5. ## Chemistry

The rate of the following reaction is 0.480 M/s. What is the relative rate of change of each species in the reaction? A+3B=2C

6. ## Math

A person standing near the edge of a cliff 120 feet above a lake throws a rock upward with an initial speed of 40 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time and is described by the function H(t)

7. ## Chemistry

A certain reaction has an activation energy of 37.30 kj/mol. At what Kelvin temperature will the reaction proceed 3.00 times then it did at 303 k?

8. ## Chemistry

In this balanced equation 4Al + 3O2 = 2Al2O3. When 0.54 mole aluminum is reacted in a closed container with 7.80 g oxygen, how many grams of aluminum oxide can form. Please show steps to work out. Thanks

9. ## accounting

A company has an overhead application rate of 125% of direct labor costs. How much overhead would be allocated to a job if it required total direct labor cost of $20,000?$5,000. $16,000.$25,000. $125,000.$250,000. The R&R Company's production costs for

10. ## Chemistry

The rate constant for this first order reaction is 0.0470 s-1 at 400 C. A TO Products After how many seconds will 11.0% of the reactant remain?

11. ## Algebra - Math

A farmer has 100 yards of fencing with which to enclose two adjacent rectangular pens - both bordering a river. The farmer does not need to fence the side with the river. What should the dimensions of the two pens Together (rectangle shape) be in order to

12. ## Chemistry 2

I have to calculate the Ccal using the following info: Initial Temp of water outside calorimeter=22.6 C Initial Temp of water inside the calorimeter= 100 C Volume of water in calorimeter= 50mL Volume of water outside calorimeter= 300mL Final Temp of water

13. ## physics

When water falls from the top of the waterfall,at the victoria falls in zimbabwe,the temperature of the water at the top is less than the temperature at the bottom.If 180.5g of water falls a distance of 125.0m, calculate the increase in temperature of the

14. ## phy

A major-league catcher gloves a 92 {\rm mi}/{\rm h} pitch and brings it to rest in 0.15 {\rm m}. 1-If the force exerted by the catcher is 803 {\rm N}, what is the mass of the ball?

15. ## Basic Algebra

A new cruise ship line has just launched 3 new ships: the Pacific Paradise, The caribbean paradise, and the mediterranean paradise. The carribean paradise has 32 more deluxe stateroooms than the pacific paradise. The Mediterranean paradise has 37 few

16. ## biology

some people in old age complain of stiff joints. what is the possible reason for it?

17. ## Chemistry

After 79 mins 20.0% of a compound has decomposed. What is the half life of this reaction assuming first-order kinetics?

18. ## physics

A student in a lab exerts a 14 N force to pull a block a distance of 63 cm. If a total of 8 J of work is done, the angle between the force and the displacement is none of the above 89° 25° 61° 65°

19. ## biology

some people in old age complain of stiff joints. what is the possible reason for it? please help, need answer related to bones and joints, level middle school biology

20. ## Chemistry

The rate constant for this first-order reaction is 0.440 s-1 at 400 C. A to products How long in seconds would it take for concentration of A to decrease from 0.740 M 0.290 M?

21. ## Math

Find a polynomial of minimum degree with zeros -3, -2 and 1 (of multiplicity 2)

22. ## algebra 2

$9000 is invested at 8% compounded quarterly. In how many years will the account have 20) grown to$11,000? Round your answer to the nearest tenth of a year.

23. ## child psychology

Is this a good example of cognitive perspectiive and do you have anything that you can add on to this to give more substance. The cognitive learning process involves thought processes and the behaviors that these thoughts cause. The best example that I can

24. ## chemistry

caculate the mass of agcl precipitated when 0.1g of nacl and 0.1g of agno3 are mixed in solution

25. ## math

Triangle ABC has are 30cm^2, AC=9 cm and BC= 7cm. Calculate the measureof angle ACB and the larget possible length of AB.

26. ## programming

write a c program that accepts a name as first name last name but displays the name as last name first name in the output

27. ## Math

9. Essay; show all work. Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 2x3 + 5x2 – x – 1. The shop estimates their costs for that quarter to be given by 4x2 – 9x – 8. For the second quarter,

28. ## algebra

haw solve this example:54 multiply 5/9

34. ## b

ome people in old age complain of stiff joints. what is the possible reason for it?

35. ## GRAMMAR-MT

Proofreading. Clean up the following sentences by identifying and correcting misspellings and misused/incorrect words. QUESTION 1.The patient's distented abdomen over the cholecystetomy incision was a source of discomfort. ANSWER: The patient's distended

36. ## economics

I just want to have a further or simple explanation on supply and demand curve, when do we say that the supply curve or the demand curve is ambiguous? It is when you have determined if it is an increase or decrease. Can you cite some examples of graphs.

37. ## GRAMMAR - MT

Clean up the following sentences by identifying and correcting misspellings and misused/incorrect words. QUESTION: 1. The patient's epistaxis was treated with silver nitrite after dried blood in the nasal secretions were removed. ANSWER: 1. The patient's

38. ## GRAMMAR - MT

Clean up the following sentences by identifying and correcting misspellings and misused/incorrect words. Question: 1. Perforation of the tympantic membrane was beleived to be the cause of the patient's vertigoe and myringitis. ANSWER: 1. Perforation of the

39. ## GRAMMAR - MT

Proofreading. Clean up the following sentences by identifying and correcting misspellings and misused/incorrect words. QUESTION: 1.Urolithiasis is another name for one of the following: uretral stone, kidney stone, or renil stone. Medical word building

40. ## Basic Algebra

solve the equation: 16((3x+7)=4(12x+8)

41. ## English

"Beauty if only skin deep" is an example of ? A. personification. B. hyperbole. C. a generalization. D. a cliche

42. ## English

Could someone review this essay for me? It is a rough draft of my persuasive essay. The Reality of Credit Cards and College Students Laurie A Johnson COM 156 Diana Bernste The Reality of Credit Cards and College Students Why do companies target a portion

43. ## intermediate algebra

Multiply, (x^4 - 3)(2x + 1)

44. ## chemistry

what is the volume of a rectangle that has a mass of 19.0 and a density of 10.50 g/mL

45. ## american history

What successful northern naval victory stongly proved the value of sea power?

46. ## programming

How do i read in a vector of integers with a space inbetween (i.e. 0 1 2 3) and make it an integer array? in java

60. ## chemistry

Identify a haloalkane and describe the manner in which it functions as an anesthetic.

61. ## intermediate algebra

Male caloric needs. The number of calories needed each day by a moderately active man who weighs w kilograms, is h centimeters tall, and is a years old can be estimated by the polynomial 19.18w + 7h - 9.52a + 92.4

divide and check t^2 - 13 --------- t - 4

63. ## Truth tables

How do I construct a truth table for (p v q)->~p

64. ## algebra 2

Find the inverse of the function. f(x) = 10^x + 2

65. ## chemistry

1-why should the maximum percent yield never be above 100%?

66. ## Math

what is the equation for the vertical asymptote of 5x^4-7/2x+3

67. ## health

need help in orthopedic physician assistant exam

68. ## CALCULUS

Consider the function f(x)=sqrt(2–5x^2), –5≤x≤1. The absolute minimum value is ____ and this occurs at x equals ______? Found the max value to be 2 at x=0.

69. ## Math

What are some examples of acute and obtuse triangles in a home?

70. ## Basic Algebra

solve the equation m, and check the solution: 5/6x-1/5x+4=7/10x

3.6 ln 29

72. ## Math

Find the angle (Θ) for a terminal arm with the following coordinates(round to one decimal place): (5,8)

73. ## algebra

Please help me find the domain for the following functions. If I understand this correctly I can use any number as long as the denominator does not equal zero 1) y = 7/(1 +x) can be any number except -1 2) y = -2/(6- x) can be any number except -6 3) y =

74. ## math

Given the funtion G(t) = t2 - 7t + 5, evaluate G(-1+h)-G(-1)/h

75. ## Math

Given the function f(x) = 7 - 6x, evaluate f(x+h)-f(x)/h

76. ## Chemistry

how many mL of 2.0 M NaOH are required to get 100 g of NaOH?

77. ## Chemistry

how many mL of 2.0 M NaOH are required to get 100 g of NaOH?


text:
[OS X TeX] Feynmp labels

Donal Day dbd at virginia.edu
Wed Apr 11 09:46:45 EDT 2007

My attempt to use the Feynmann diagram drawing package with TexShop
is only partially successful.

Following the guidelines at http://osksn2.hep.sci.osaka-u.ac.jp/
~taku/osx/feynmp.html I can successfully create diagrams.

However when I attempt to add labels to the lines, they do not show
up on the resulting figure which is created after processing with
mpost. But they do show up in the host document - but without the
figure.

Here is the tex:
%%%%%%%%%%%%
\documentclass[11pt]{article}
\usepackage{graphicx}
\usepackage{feynmp}
\newcommand{\minpgap}{20mm}
\begin{document}
\unitlength = 1mm

\begin{minipage}{\linewidth}

\begin{fmffile}{simple5}
\begin{fmfgraph*}(40,25)
\fmfleft{i1,i2}
\fmfright{o1,o2}
% labels on the left hand fermions
\fmflabel{$e$}{i1}
\fmflabel{$e'$}{i2}
%
\fmf{fermion}{i1,v1,o1}
\fmf{fermion}{i2,v2,o2}
\fmf{photon}{v1,v2}
\end{fmfgraph*}
\end{fmffile}
\end{minipage}

\end{document}
%%%%%%%%%%%%

After typsetting with TexShop (2.09) I go to the terminal and issue
the command "mpost simple5.mp" which produces a file named
"simple5.1" which I can view with gv - it contains no labels. I
rename this file to simple5.ps and typeset my document again.

What appears in the pdf window are the labels and no diagram!

mpost is

MetaPost 0.901 (Web2C 7.5.5)
kpathsea version 3.5.5

I would appreciate some guidance.

Donal Day

Donal Day
dbd at virginia.edu


text:
# Is there another way of evaluating $\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x))=\frac{\pi^2}{6}$

I was messing around with the Zeta-Function and I got what I thought was an interesting limit:

$$\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x)) = \frac{\pi^2}{6}$$ Where $\Gamma$ is the gamma function, $\gamma$ is the Euler-Mascheroni constant, and $\psi$ is the digamma function. I got it by writing the Zeta Function as:

$$\sum_{n=1}^{\infty} \frac{1}{n^2} = -\int_{0}^1 \frac{\ln(x)}{1-x}dx$$ Then using the beta function and differentiating with respect to x you get the limit.

What other ways can be used to evaluate the limit?

Here's how I got to my answer:

We know $$\sum_{n=1}^{\infty}\frac{1}{n^2} = \frac{\pi^2}{6}$$ To convert the sum into an integral consider: $$\int_{0}^1 x^{n-1}dx=\frac{1}{n}$$ Differentiating once: $$\int_{0}^1 \ln(x)x^{n-1}dx=\frac{-1}{n^2}$$ Plugging in the integral into the sum you get: $$-\sum_{n=1}^\infty \int_0^1 \ln(x)x^{n-1}dx=-\int_0^1\ln(x)\sum_{n=1}^\infty x^{n-1}dx=-\int_0^1 \frac{\ln(x)}{1-x}dx$$

Euler's Beta Function is defined as:

$$\operatorname{B(x,y)}=\int_0^1 t^{x-1}(1-t)^{y-1} = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}$$

Differentiation with respect to x: $$\operatorname{B_x(x,y)}=\int_0^1 \ln(t)t^{x-1}(1-t)^{y-1} = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}(\psi(x)-\psi(x+y))$$

$$-\int_0^1 \frac{\ln(x)}{1-x}dx = -\operatorname{B_x(1,0)}=\frac{\pi^2}{6}$$

Taking the limit as (x,y)->(1,0)

$$-\lim_{(x,y)\to(1,0)} \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}(\psi(x)-\psi(x+y))=-\lim_{y \to 0} \Gamma(y)(\psi(1)-\psi(1+y)) = \lim_{y \to 0} \Gamma(y)(\gamma+\psi(1+y))$$

• What are $\psi$ and $\gamma$ though? Are these standard notations? – Suzet Aug 2 '18 at 14:48
• They're the digamma function and the euler-mascheroni constant. I'll edit the post so it's more clear. – Tom Himler Aug 2 '18 at 14:49
• I am just interested. How exactly did you derived the limit from the given integral representation with your steps. I tried to do it by myself and failed. Could you maybe explain it to me or add it to the question? – mrtaurho Aug 2 '18 at 15:27
• @mrtaurho I put how I got my answer if that helps. It's not super rigorous since I don't really know that sort of shtuff yet. – Tom Himler Aug 2 '18 at 18:25
• Thank you for adding it nevertheless. I am not that familiar as I want to with these kinds of reshapings and this stuff. It is great for me to learn more about it. – mrtaurho Aug 2 '18 at 18:27

One may use $\Gamma(x)=\Gamma(x+1)/x$ to get
$$\lim_{x\to0}\frac{\gamma+\psi(1+x)}x$$
and since $\psi(1)=-\gamma$, we may use the definition of the derivative to get $\psi'(1)$, which has many different forms, of which the result may be deduced from.