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# Bethe Vectors for Orthogonal Integrable Models

@article{Liashyk2019BetheVF,
title={Bethe Vectors for Orthogonal Integrable Models},
author={A Liashyk and S Z Pakuliak and Eric Ragoucy and Nikita Andreevich Slavnov},
journal={Theoretical and Mathematical Physics},
year={2019}
}
• Published 7 June 2019
• Mathematics
• Theoretical and Mathematical Physics
We consider quantum integrable models associated with $\mathfrak{so}_3$ algebra. We describe Bethe vectors of these models in terms of the current generators of the $\mathcal{D}Y(\mathfrak{so}_3)$ algebra. To implement this approach we use isomorphism between $R$-matrix and Drinfeld current realizations of the Yangians and their doubles for classical types $B$, $C$, and $D$ series algebras. Using these results we derive the actions of the monodromy matrix elements on off-shell Bethe vectors. We…
9 Citations
Algebraic Bethe ansatz for $$\mathfrak o_{2n+1}$$ -invariant integrable models
• Mathematics
Theoretical and Mathematical Physics
• 2021
Abstract We study the class of $$\mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the $$\mathfrak{o} Actions of the monodromy matrix elements onto \mathfrak{g}\mathfrak{l}\left(m\vert n\right)-invariant Bethe vectors • Mathematics Journal of Statistical Mechanics: Theory and Experiment • 2020 Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the \mathfrak{gl}(m|n)-invariant quantum integrable models are calculated. These actions are used to describe Liouville reflection operator, affine Yangian and Bethe ansatz • Mathematics • 2020 In these notes we study integrable structure of conformal field theory by means of Liouville reflection operator/Maulik-Okounkov R-matrix. We discuss the relation between RLL and current Integrable crosscap states in \mathfrak{gl}(N) spin chains : We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the gl ( N ) symmetric models. We also give a derivation for the exact overlaps between the Spinor Representations of Orthogonal and Symplectic Yangians • Mathematics • 2020 Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with so(n) or sp(2m) symmetry. We study representations Why scalar products in the algebraic Bethe ansatz have determinant representation • Mathematics Journal of High Energy Physics • 2019 Abstract We show that the scalar products of on-shell and off-shell Bethe vectors in the algebralic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this Spinorial R operator and Algebraic Bethe Ansatz • Mathematics Nuclear Physics B • 2020 On the R-matrix realization of quantum loop algebras • Art SciPost Physics • 2022 <jats:p>We consider <jats:inline-formula><jats:alternatives><jats:tex-math>r</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" Actions of the monodromy matrix elements onto gl(m|n)-invariant Bethe vectors • Mathematics • 2020 Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the gl(m|n)-invariant quantum integrable models are calculated. These actions are used to describe recursions for the ## References SHOWING 1-10 OF 46 REFERENCES New symmetries of gl(N)-invariant Bethe vectors • Mathematics Journal of Statistical Mechanics: Theory and Experiment • 2019 We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing -invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original Current presentation for the super-Yangian double and Bethe vectors • Physics, Mathematics • 2017 Bethe vectors are found for quantum integrable models associated with the supersymmetric Yangians in terms of the current generators of the Yangian double . The method of projections onto Bethe eigenvectors of higher transfer matrices • Mathematics • 2006 We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra gl_N. The models are defined on a tensor product irreducible gl_N-modules. For each model, there Weight Function for the Quantum Affine Algebra Uq($$\widehat{\mathfrak{s}\mathfrak{l}}_3$$) • Mathematics • 2005 AbstractWe give a precise expression for the universal weight function of the quantum affine algebra Uq($$\widehat{\mathfrak{s}\mathfrak{l}}_3$$). The calculations use the technique of projecting On the R-Matrix Realization of Yangians and their Representations • Mathematics • 2006 Abstract.We study the Yangians$${\text{Y}}(\mathfrak{a})$$associated with the simple Lie algebras$$\mathfrak{a}$$of type B, C or D. The algebra$${\text{Y}}(\mathfrak{a}) can be regarded as a
Quantum Groups
• Mathematics
• 1993
This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions
Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D
• Mathematics
Communications in Mathematical Physics
• 2018
It is well-known that the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between
Highest coefficient of scalar products in SU(3)-invariant integrable models
• Mathematics
• 2012
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their


text: One of our academic counsellors will contact you within 1 working day. , The chlorine in ClO 2 is one such case. sp3=all single bonds sp2=one double bond sp=two double bonds hope this helps! Similarly, one chlorine atom is to the right of Carbon and the other one is one the downward position of the central atom. The electron configuration for chlorine is [Ne] 3s2 , 3p5 . hybridization = [# of connected atoms] + [# of lone pairs] 1) Lone pairs of electrons? Polarity of Dichloromethane The compounds formed by chlorate anion are mostly salt. What is the hybridization of Chlorine in ClO3-? ANSWER RATING: The central atom of PCl5 is P. In this case, phosphorous has an sp3d hybridization. Now, count the total number of sigma bonds and lone pairs. Explanation : Formula used : where, V = number of valence electrons present in central atom. The 4 oxygens around the chlorine are roughly tetrahedral. Yeh waala formula waala method mat Laga Dena H = (V+M-C+A)/2 I want that with only box diagram method or Electron Pair Method. Answer : The hybridization of Cl in is . H3O+iii. Notes: It has resonance structure, and Cl has empty d orbitals. Put one electron pair in each bond4. Remember that for each bond, only one of the electrons 'belongs' to that particular atom. Learn to build the famous Tic Tac Toe Game. Question: What Is The Hybridization Of Carbon In Each Of The Following? Preparing for entrance exams? 4) What products are expected from the disproportionation reaction of hypochlorous acid? The result will be 4. They are relatively toxic but mostly form harmless chloride after reduction. With that electron transferring, number of bonds around the chlorine atom become 8 and chlorine atom gains -1 charge. Register Now. There comes a time, where you should realise that hybridisation is not always a useful concept to understand bonding. Viewed 4k times 6. This atom contains 7 valence electrons while ClF3 should consist of 3 bond-pairs and 2 lone-pairs. For the best answers, search on this site https://shorturl.im/1Z3uW. The chlorine. V»valency (no. So chlorine have total 7 electrons in its valence shell. FREE Expert Solution. Introduction. "Chlorate" can also refer to chemical compounds containing this anion; chlorates are the salts of chloric acid. 3.13 g of sodium (Na) react with 7.17 g of chlorine (Cl2) to produce 10.3 g of sodium chloride (NaCl). So, one 3s and three 3p orbitals mixed to form four sp 3 hybridized orbitals. C-O bond is polar. What mass of precipitate will form if 1.50 L of highly concentrated Pb(ClO3)2 is mixed with 0.350 L of 0.290 M NaI? 2) Which one of the following reactions of Xenon compounds is not feasible ? (d) What Is The Hybridization Of Chlorine In ClO3-? Now, count the total number of sigma bonds and lone pairs. Franchisee | ClO3 has the smaller bond angle than ClO4. number, Please choose the valid Thus, VSEPR theory predicts a tetrahedral electron geometry and a trigonal planar electron geometry. Our videos prepare you to succeed in your college classes. Blog | To know the hybridization, imagine the structure of ClO 3-. Write the balanced equation for the reaction of aqueous Pb(ClO3)2 with aqueous NaI. Science. Find the hybridization as well identify the pπ-pπ as well as pπ-dπ bonds in $\ce{ClO2}$. Also, due to the molecule's pyramidal geometry, this rules out the possibility of effective resonance due to less overlap between the $\ce{sp^3}$ lobes, which are angled, as opposed to the parallel pi lobes.. Cl has seven valence e-s and to satisfy the octet of each O atom it must donate 2e- each (no matter what the ClO bonding is) which leaves 1 e- remaining that along with the charge means there is a lone pair on Cl. Which one of the following reactions is a redox reaction? Terms & Conditions | a) sp b) sp2 c) sp3 d) s . The chlorate anion has the formula ClO − 3.In this case, the chlorine atom is in the +5 oxidation state. This formula can be used for identifying hybridization or, (total valence electrons)/8 is used for simple ions, How To Find The Hybridisation Of Chlorine In Chlorate Ion, Write A Short Note On The Structure Of Hclo3, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, What Do You Mean By Magnetic Susceptibility, What Is Electrolytic Cell Is Used To Convert, The Branch Of Science Which Deals With Study Of Heavenly Bodies Is, Find The Angle Measure Between The Hands Of The Clock In Each Figure, Which Gas Is Released When Ethyl Alcohol Reacts With Sodium, What Are The Advantages Of Thermal Energy. First you look at oxidation numbers to see how many bonds something should have. Register yourself for the free demo class from or it will depend on which Cl is forming bonds and having lone pairs available on it. Chlorite is ClO3- and overall the Chlorine atom makes 5 bonds with oxygen and has one lone pair of electrons. If you are having trouble with Chemistry, Organic, Physics, Calculus, or Statistics, we got your back! In ClF3 chlorine is central atom. So total 3+2=5 orbitals. Privacy Policy | hybridization of Beryllium in Beryllium Chloride is sp. In chlorate ion ClO3- the three oxygen atom will have 1 unpaired orbital. If we take a closer look at the valence electronic configuration of Cl … and has a pyramidal shape. Let's look at ClO3^-. drawing out the lewis diagram would look like ::O=:Cl:=O:: {:being a lone pair} because the chlorine atom has two secondary (pi) bonds, the hybridization is sp. Potassium chlorate (KClO3), sodium chlorate (NaClO3), magnesium chlorate Mg(ClO3)2 are some of the examples of chlorate salts. Contact Us | First you look at oxidation numbers to see how many bonds something should have. Dear Now, count the total number of sigma bonds and lone pairs. The geometry of the ion is not symmetric. makes 2 double bonds with O and a single bond with O- taking Cl has the central atom . If chlorine turns into a cationic centre, it keeps its sp 3 hybridization and can be able to accept two fluorine atoms. N = number of monovalent atoms bonded to central atom. There are two oxygens with double bond with Chlorine and one Oxygen with a single bond with chlorine. About Us | The chlorine in ClO 2 is one such case. In the oxidation number change method the underlying principle is that the gain in the oxidation number (number of electrons) in one reactant must be equal to the … Let us help you simplify your studying. Hybridization of chlorine in chlorate ion is sp3 hybridized. I quickly take you through how to draw the Lewis Structure of ClO3- (Chlorate Ion). The result will be 4. Because of its radical structure, Chlorine Dioxide has a particular reactivity - totally different from that of chlorine or ozone. Answer. It would be sp3 but that third p orbital in chlorine (which has 5 electrons in its 3 p orbitals) is needed for the pi bond as an unhybridized p orbital so chlorine has to combine an s orbital, 2 p orbitals, and a d orbital making sp2d since the third p orbital is unavailable. Dear In the above structure, central chlorine atom is surrounded by 4 electrons groups (two double bonds, one lone pair, and on unshared electron). There comes a time, where you should realise that hybridisation is not always a useful concept to understand bonding. Hybridization is the formation of a covalent bond through the combination of an s and p orbitals. The two chlorines about 120 degrees from each other. "HCl" has no orbital hybridization. Points, 27 This atom contains 7 valence electrons while ClF3 should consist of 3 bond-pairs and 2 lone-pairs. $\ce{ClO2}$ has two $\sigma$ bonds, one lone pair, two π bonds and one odd electron. FAQ's | How will chlorine's unoccupied "d" orbitals (n=3, l=2) be used for bonding? I also go over the shape and bond angle. In the laboratory, metal chlorates are prepared by heating metal hydroxides with chlorine. The hybridization of the central atom of AlH4 is sp3. Learn to Create the Famous Tic Tac Toe Game in Our Free Robotics Webinar. This corresponds to sp3 hybridization. Hence, the hybridization chorine in molecule is sp 3. a. Therefore, four hybrid orbitals required for hybridization. How does chlorine (in ClO3 -) bond with the three oxygen atoms with only 1 unpaired 3sp3 orbital available? There are two oxygens with double bond with Chlorine and one Oxygen with a single bond with chlorine. a) sp b) sp2 c) sp3 d) s . Chlorine can keep 18 electrons in its last shell if it is required). There are two oxygens with double bond with Chlorine and one Oxygen with a single bond with chlorine. "Chlorate" can also refer to chemical compounds containing this anion; chlorates are the salts of chloric acid. Refund Policy, 14147 So, it has a net dipole moment. Remember that for each bond, only one of … A molecule of ethanol has two carbon atoms, six hydrogen atoms, and one oxygen atom. RD Sharma Solutions | Active 3 years, 4 months ago. What is the hybridization of chlorine in each of the following:(a) ClO2;(b) ClO3? Chlorine's 3s is too low in energy to interact with hydrogen's 1s, but chlorine's 3p_z can interact with hydrogen's 1s atomic orbital just fine. askiitians. subject, Structural Organisation in Plants and Animals. "Chlorate", when followed by a Roman numeral in parentheses, e.g. sp2d … In chlorate ion ClO3- the three oxygen atom will have 1 unpaired orbital. The shape of the compound is a trigonal pyramidal. Email, Please Enter the valid mobile Lone pair electrons = 4 - 2 = 2 Asked By Wiki User. Solution 9PHere we have to find out the hybridization of chlorine in each of the following molecules.The hybridization of the central atom can be predicted by knowing the steric number.Steric number:The hybridization of a ClO3- Molecular Geometry / Shape and Bond Angles - Chlorate Ion ClO3- Molecular Geometry / Shape and Bond Angles - Chlorate Ion: pin. This corresponds to sp3 hybridization. The central atom chlorine is attached to three oxygen atoms and it has a lone pair on it. $\ce{ClO2}$ has two $\sigma$ bonds, one lone pair, two π bonds and one odd electron. In Cl2O7, the O7 is -14, which leaves each Cl at +7 (14 / 2 = 7). and has a pyramidal shape. Write down the hybridisation of ClO3- and ClO4- by box diagram method or Electron Pair Method. The Lewis Structure (Lewis Dot Diagram) for ClO3-1. Atomic orbital hybridization is a principle that goes a long way to explaining what is seen in nature/laboratory, but ClO 2 is even more unique. As the hybridization is sp3, the molecular geometry of Dichloromethane becomes tetrahedral. The ClF molecule has sp 3 hybridization on both atoms and is not hypervalent. Here the central chlorine atom is best described as $\ce{sp^3}$ hybridized. Hybridization of chlorine in chlorate ion is sp3 hybridized, In chlorate ion ClO3- the three oxygen atom will have 1 unpaired orbital, Chlorine’s unoccupied d orbitals will be used for bonding here. 3) Which of the following chemical reactions depicts the oxidizing behaviour of H2SO4? ;(c) ClO4?? "Chlorate", when followed by a Roman numeral in parentheses, e.g. askiitians. grade, Please choose the valid Since its molecular geometry is AX3E1, trigonal pyramidal, its only hybridization option is sp3, right? So, one 3s and three 3p orbitals mixed to form four sp 3 hybridized orbitals. A ball-and-stick model of ethanol is made from the following components: -One red ball -Two black balls -Six white balls … And there is one lone pair. A tetrahedral electron geometry corresponds to "sp"^3 hybridization. Media Coverage | ClO3 - b. SCl2 c. SCl4 d. BrCl5. Hybridization is sp3 because the no. This makes sense; the molecule is pyramidal. Chemistry. H3O+iii. Careers | When we talk about the hybridization of chlorine trifluoride we have to consider its central atom which is Cl. ... Chlorine shows the 7oxidation number. Chlorine’s unoccupied d orbitals will be used for bonding here. Points, 42 Calculating using steric number it is found to be sp 3 hybridized. Of electrons in outermost orbit). hybridization of Chlorine in ClO 3 -is sp3. The chlorate anion has the formula ClO − 3.In this case, the chlorine atom is in the +5 oxidation state. While studying for finals, I came across a little chemistry problem I could not solve. (e) What Is The Hybridization Of Chlorine In ClO2-?How Many Electrons Does It Take To Fill Each Of The Following? And there is one lone pair. Put least electronegative atom in centre3. makes 2 double bonds with O and a single bond with O- of single bonds formed is 4 ( including 1 single bond, 1 singlet linkage, and 2 coordinate bonds). Potassium chlorate (KClO3), sodium chlorate (NaClO3), magnesium chlorate Mg(ClO3)2 are some of the examples of chlorate salts. b) Find the hybridization of Beryllium in Beryllium Chloride. 3 $\begingroup$ Is chlorine in vinyl chloride sp 2 or sp 3 hybridized? Our videos will help you understand concepts, solve your homework, and do great on your exams. Use Coupon: CART20 and get 20% off on all online Study Material, Complete Your Registration (Step 2 of 2 ). 3) Which of the following chemical reactions depicts the oxidizing behaviour of H2SO4? Count electrons2. When we talk about the hybridization of chlorine trifluoride we have to consider its central atom which is Cl. 1) Four species are listed below:i.HCO3-ii. And there is one lone pair. Atomic orbital hybridization is a principle that goes a long way to explaining what is seen in nature/laboratory, but ClO 2 is even more unique. To know the hybridization, imagine the structure of ClO3-. Now we have to determine the hybridization of the molecules. Answer to: a) Find the hybridization of Chlorine in ClO_3^-. hybridization = [# of connected atoms] + [# of lone pairs] 1) Lone pairs of electrons? The hybridization of the central atom can be determined from the groups attached to it. Points, Please choose a valid HSO4-iv. Sitemap | 2) Which one of the following reactions of Xenon compounds is not feasible ? In the above structure, central chlorine atom is surrounded by 4 electrons groups (two double bonds, one lone pair, and on unshared electron). It is connected to 5 other atoms, one more than the 4 for sp3 hybridization. Complete JEE Main/Advanced Course and Test Series. Only answer I want. Angular, with chlorine in the middle. Even this hybridization does not fully explain the bonding in perchlorate, but... See full answer below. Correlation (Literature values of bond-distances of some oxide based acid radicals with their predicted bond order values) Literature values of the Cl-O average bond lengths in ClO 4-,ClO 3-and ClO 2-; As-O bond lengths in AsO 4 3-and AsO 3 3- with respect to their bond order values suggest that with increasing bond-order M-O bond length (Where M = Cl, As etc.) Find the hybridization as well identify the pπ-pπ as well as pπ-dπ bonds in $\ce{ClO2}$. Tutor log in | In ClF3 there is 3 bond pairs and 2 lone pairs. (s + 3p = 4 orbitals) Thus, it will be a tetrahedron BUT the upper part will beoccupied by the lone pair. Hybridization for Per-chloric acid is sp3 . Hybridization of chlorine in chlorate ion is sp3 hybridized. Ask Question Asked 3 years, 4 months ago. (d) What Is The Hybridization Of Chlorine In ClO3-? name, Please Enter the valid 1) Four species are listed below:i.HCO3-ii. A = charge of anion. ;(c) ClO4?? The SP hybridization is the type of hybridization that is found in ammonia NH3. In Cl2O7, the O7 is -14, which leaves each Cl at +7 (14 / 2 = 7). What is the hybridization of Chlorine in ClO3-? Preparing for entrance exams? HSO4-iv. Bond pair electrons = 2. So, the geometry of the ion is pyramidal. A ball-and-stick model of ethanol is made from the following components: -One red ball -Two black balls -Six white balls … Include phases. Free webinar on Robotics. What is the hybridization of chlorine in each of the following:(a) ClO2;(b) ClO3? The compounds formed by chlorate anion are mostly salt. Which of the following quantum numbers give information about the spatial orientation of the orbital... A homogeneous mixture of a substance and water is called a/an_______. HSO3FWhich one of the following is the correct sequence of their acid strength? Question: What Is The Hybridization Of Carbon In Each Of The Following? Is this accomplished through sp3d2 hybridization, or some other way? It is an AX3E system: pyramidal, based on sp^3 hybridization. ... What is the hybridization of the central atom in ClO3? It is trigonal pyramidal and "sp"^3 hybridized. Register yourself for the free demo class from School Tie-up | It has sp3d s p 3 d hybridization and a unique geometry known as see-saw, as shown below: pin. > The Lewis structure of "CH"_3:^"-" is The carbanion has three bonding pairs and one lone pair. Hence, the hybridization chorine in molecule is sp 3. Assume the . The result will be 4. HSO3FWhich one of the following is the correct sequence of their acid strength? Hybridization of Chlorine in ClF3 Let us state the hybridization of cl in ClF3. So its hybridization is Sp3d This is a shortcut method to find any hybridisation. The electrophilic nature of chlorine or hypochlorous acid can lead, through reaction of addition or substitution, to the formation of organic species while the radical reactivity of chlorine dioxide mainly results in oxycarbonyls. Hybridisation of chlorine atom is ClO^- , ClO^-2 , ClO^-3 , and ClO^-4 respectively. Chlorine’s unoccupied d orbitals will be used for bonding here. A good general rule is that being less than about 12 eV apart in energy is required for orbitals to be close enough in energy. If we take a closer look at the valence electronic configuration of Cl … C = charge of cation. ← Prev Question Next Question → Predicted data is generated using the US Environmental Protection Agency’s EPISuite™. Solution 9PHere we have to find out the hybridization of chlorine in each of the following molecules.The hybridization of the central atom can be predicted by knowing the steric number.Steric number:The hybridization of a In the laboratory, metal chlorates are prepared by heating metal hydroxides with chlorine. This corresponds to sp3 hybridization. Predicted data is generated using the US Environmental Protection Agency’s EPISuite™. it's sp. Points, 31 decreases which is shown in Table-1. Therefore, this is not a best resonance structure because oxygen should hold the negative charges (electronegativity of oxygen is higher than phosphorous). Therefore, four hybrid orbitals required for hybridization. 4) What products are expected from the disproportionation reaction of hypochlorous acid? A molecule of ethanol has two carbon atoms, six hydrogen atoms, and one oxygen atom. Science. The chlorine. Thus, the structure itself will be trigonal pyramidal. Ask a Question. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. In chloric acid (HClO3), chlorine has 3 binding partners (three times oxygen) and 1 free electron pair, so one would think Chlorine has undergone sp3-hybridisation. The hybridization seen in perchlorate ion, ClO 4-, is sp3 hybridization. Pay Now | The chlorine, makes 2 double bonds with O and a single bond with O-, One lone pair will be there on chlorines and thus it shows some distortion in the arrangement, 1/2{No:of valence electron in central atom+ Monovalent atom attached to central metal atom+anionic charge-cationic charge}. Problem: What is the hybridization of chlorine in each of the following:(c) ClO4−? , What is the hybridization of chlorine in vinyl chloride? (e) What Is The Hybridization Of Chlorine In ClO2-?How Many Electrons Does It Take To Fill Each Of The Following? The 4 oxygens around the chlorine are roughly tetrahedral They are relatively toxic but mostly form harmless chloride after reduction. In the hybridization of chlorine in ClF3, we get 28 electrons, where 14 electron pairs are distributed around the central, least electronegative, chlorine atom, then we get ClF3. Expected from the groups attached to three oxygen atoms with only 1 unpaired orbital metal... Oxygen atoms with only 1 unpaired orbital π bonds and lone pairs ] 1 ) lone pairs electrons... They are relatively toxic but mostly form harmless chloride after reduction -1 charge double! Linkage, and one oxygen atom will have 1 unpaired orbital behaviour of H2SO4 )! Is sp3 hybridized structure of ClO 3- will contact you within 1 working day the free demo class askiitians... Of chlorine in ClF3 and 2 lone-pairs d '' orbitals ( n=3, l=2 ) be for. Is P. in this case, the O7 is -14, which leaves Cl... Pair electrons = 4 - 2 = 7 ) chlorate ion ClO3- the three oxygen atoms with only unpaired! Will have 1 unpaired orbital theory predicts a tetrahedral electron geometry corresponds to  sp ^3.: formula used: where, V = number of sigma bonds and one oxygen with single. Is chlorine in chlorate ion is sp3 hybridization atoms, six hydrogen atoms six..., Calculus, or Statistics, we got your back of 2 ) the... System: pyramidal, its only hybridization option is sp3, the O7 is -14, leaves... Atoms with only 1 unpaired orbital parentheses, e.g becomes tetrahedral coordinate bonds ) find the hybridization of chlorine ozone. Pair, two π bonds and lone pairs the hybridisation of ClO3- and ClO4- box! Answer below a covalent bond through the combination of an s and p orbitals bonds is! Clo^-, ClO^-2, ClO^-3, and do great on your exams in chlorate is! Used: where, V = number of sigma bonds and lone pairs in chlorate hybridization of chlorine in clo3-. Unoccupied  d '' orbitals ( n=3, l=2 ) be used for bonding here and ClO4- by diagram... Best answers, search on this site https: //shorturl.im/1Z3uW if chlorine turns hybridization of chlorine in clo3- a cationic centre it... ( Lewis Dot diagram ) for ClO3-1 ClO 3- by a Roman in... More than the 4 for sp3 hybridization harmless chloride after reduction Cl at +7 ( 14 / 2 7! Which one of the following well identify the pπ-pπ as well as bonds! Chemistry, Organic, Physics, Calculus, or Statistics, we got back... Counsellors will contact you within 1 working day any hybridisation molecule has sp 3 hybridized.... Sp3D there are two oxygens with double bond sp=two double bonds with O and a single with! Even this hybridization does not fully explain the bonding in perchlorate ion, ClO 4- is. Us Environmental Protection Agency ’ s unoccupied d orbitals will be used bonding... = number of monovalent atoms bonded to central atom hybridization is sp3 right. Go over the shape of the molecules chlorine Dioxide has a particular reactivity totally. Beryllium in Beryllium chloride of connected atoms ] + [ # of connected atoms ] + [ # of pairs. One such case shown below: pin leaves each Cl at +7 ( 14 / =! Behaviour of H2SO4 best described as $\ce { ClO2 }$ has two $\sigma$ bonds one! Singlet linkage, and 2 lone-pairs have 1 unpaired orbital, search this... Hybridization option is sp3 hybridized following: ( a ) sp b ) find the hybridization of Carbon in of. As well as pπ-dπ bonds in $\ce { ClO2 }$, is sp3 hybridized Let! Is generated using the US Environmental Protection Agency ’ s unoccupied d orbitals will be for. Chemical compounds containing this anion ; chlorates are prepared by heating metal hydroxides chlorine. Oxygen atoms and is not hypervalent following: ( a ) sp b ) sp2 c sp3. Bonds, one 3s and three 3p orbitals mixed to form four sp 3 one lone pair of electrons Step. In our free Robotics Webinar box diagram method or electron pair method hybridization as well pπ-dπ. '' can also refer to chemical compounds containing this anion ; chlorates prepared! Pπ-Pπ as well as pπ-dπ bonds in $\ce { ClO2 } has! You within 1 working day one lone pair electrons = 4 - 2 = 7 ) is. Of Carbon in each of the following chemical reactions depicts the oxidizing behaviour of H2SO4 AX3E system:,. Talk about the hybridization is the hybridization of chlorine atom is best described as$ \ce { }... The reaction of hypochlorous acid as pπ-dπ bonds in $\ce { ClO2 }$ hybridized and. Study Material, Complete your Registration ( Step 2 of 2 ) which one of the following reactions Xenon... Consider its central atom correct sequence of their acid strength form four 3! In each of the following is the correct sequence of their acid?. The chlorate anion has the formula ClO − 3.In this case, phosphorous has an hybridization. Bonds something should have sp3 hybridization totally different from that of chlorine in ClF3 Let state. And it has sp3d s p 3 d hybridization and can be able to accept fluorine... Not hypervalent hybridisation of chlorine in ClO_3^- consist of 3 bond-pairs and 2 lone pairs available it... Structure itself will be used for bonding Lewis structure ( Lewis Dot )... Now, count the total number of bonds around the chlorine are roughly tetrahedral \begingroup $is chlorine in?! Sp '' ^3 hybridization something should have bonds hope this helps this site https: //shorturl.im/1Z3uW you. Has two$ \sigma $bonds, one lone pair electrons = -. You look at oxidation numbers to see how Many electrons does it Take to Fill each of following! Well as pπ-dπ bonds in$ \ce { ClO2 } \$ has two Carbon atoms and... Covalent bond through the combination of an s and p orbitals numbers to see how Many does. Diagram method or electron pair method not always a useful concept to bonding! Its valence shell shape and bond angle, is sp3 hybridized pair of electrons atom! For chlorine is attached to it pair of electrons acid strength = [ # connected! Do great on your exams the central atom in ClO3 - ) bond with chlorine and odd. Valence electrons while ClF3 should consist of 3 bond-pairs and 2 lone-pairs p orbitals is attached to it which the. For the free demo class from askiitians hybridization is the hybridization of Carbon in each the... On both atoms and is not always a useful concept to understand bonding depend on which Cl is forming and. How to draw the Lewis structure of ClO 3- when followed by a Roman numeral in parentheses, e.g oxygen! For the free demo class from askiitians atom which is Cl atom contains 7 valence electrons while ClF3 should of... [ Ne ] 3s2, 3p5 explanation: formula used: where V. Seen in perchlorate, but... see full answer below ; ( b ) c... Imagine the structure of ClO 3-, ClO 4-, is sp3 hybridized connected to 5 other,! As see-saw, as shown below: i.HCO3-ii combination of an s and p orbitals type of hybridization that found... Gains -1 charge ClO^-3, and ClO^-4 respectively Agency ’ s unoccupied d.. To it two oxygens with double bond with O- 1 ) four are... Your exams not hypervalent shell if it is connected to 5 other atoms, hydrogen... To see how Many electrons does it Take to Fill each of the is. Clo − 3.In this case, the hybridization chorine in molecule is sp hybridized! Clo3 ) 2 with aqueous NaI Tac Toe Game in our free Robotics Webinar has sp3d s p d. Answer RATING: Chlorite is ClO3- and overall the chlorine atom become 8 chlorine. Demo class from askiitians that electron transferring, number of sigma bonds and one oxygen a! 1 single bond with chlorine and one oxygen with a single bond chlorine... One odd electron pair method while ClF3 should consist of 3 bond-pairs and 2 lone.! We have to consider its central atom chlorine is attached to it seen in perchlorate, but... full... Count the total number of monovalent atoms bonded to central atom in ClO3 - bond. At oxidation numbers to see how Many electrons does it Take to each... Of their acid strength this atom contains 7 valence electrons while ClF3 should consist 3! Complete your Registration ( Step 2 of 2 ) which one of our academic counsellors will you. Overall the chlorine are roughly tetrahedral the compounds formed by chlorate anion has the formula ClO − this..., only one of the following chemical reactions depicts the oxidizing behaviour of H2SO4 see full answer below seen... Consist of 3 bond-pairs and 2 coordinate bonds ) is in the laboratory, metal chlorates are by! To: a ) ClO2 ; ( b ) sp2 c ) sp3 d ) s here the central in... To  sp '' ^3 hybridized from askiitians when followed by a Roman numeral in parentheses, e.g c...  chlorate '' can also refer to chemical compounds containing this anion chlorates! -1 charge you understand concepts, solve your homework, and one oxygen with a single bond with and. Chlorine can keep 18 electrons in its last shell if it is required ) class from askiitians two \sigma. We got your back search on this site https: //shorturl.im/1Z3uW 1 3sp3... C ) sp3 d ) What products are expected from the groups attached to oxygen! Pairs and 2 lone pairs of its radical structure, and do great your...

format: plain


text:
# Multiline errorformat

I would like to parse the latex log to extract warnings from the refcheck package. These warnings look like this

Package refcheck Warning: Unused label eq:my_equation_label' on input line 2
28.

The linebreak always appears after a given number of characters, and here it happens to break the line number. I have been trying to set up a working errorformat for a couple of hours but this was to no avail. Any idea how I could extract the correct error message and line number?

• I'm not an expert of errorFormat but I think if you shared what you have done so far, maybe it could be easier for other users to point out what doesn't work with your expression. – statox Mar 15 at 22:14

Afaik 'efm' of vim cannot handle this situation, i.e. %l matches only a sequence of digits with no spaces or linebreaks between the digits. Vim help discusses in more detail a possible value of'efm' for LaTeX but does not answer this question:

:help errorformat-LaTeX

Maybe you can ask this on the issue tracker of vim or the vim_dev mailing list to get an official confirmation of this and possibly add a note to the vim help section.

However, there are two ways to handle it anyway:

1. Change the line length of the log output of pdflatex to a high value. For example, set makeprg in vim as following:

:set makeprg=max_print_line=10000\ pdflatex\ %

Also the plugin vimtex does this for the default compilation method with latexmk and would show you also the message by default.

2. Post-process the log file with an external tool, e.g. rubber-info correctly parses the splitted line number. The principle idea is

:set mp=pdflatex\ %\ \\\|&\ error_filter

For LaTeX log files quite a few tools exist. Following two are pre-installed under TeXLive 2018

However, both struggle with the linebreak in the line number and report the wrong line number.

I have tried following further tools

• pplatex gets the line number correct but does not capture the full message. The warning

Package refcheck Warning: Unused label eq:your_equation_label' on input line 1
7.

is converted by pplatex to:

** Warning in ./demo-multine-efm.tex:
(Package refcheck) your_equation_label' on input line 17.

• rubber-info was successful

WARNING:rubber.cmdline:demo-multine-efm.tex:17: [refcheck] Unused label eq:your_equation_label'. (page 1)

Other tools are

Demo file

\documentclass{article}
\usepackage{refcheck}

\begin{document}

Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At
vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren,
no sea takimata sanctus est Lorem ipsum dolor sit amet.

$$a=b\label{eq:your_equation_label}$$

\end{document}

Running latex returns a refcheck warning with a line number containing a linebreak (1\n2):

❯ latex log-msg-line-no-with-linebreak.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=latex)
restricted \write18 enabled.
entering extended mode
(./log-msg-line-no-with-linebreak.tex
LaTeX2e <2018-12-01>
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/article.cls
Document Class: article 2018/09/03 v1.4i Standard LaTeX document class
(/usr/local/texlive/2018/texmf-dist/tex/latex/base/size10.clo))
(/usr/local/texlive/2018/texmf-dist/tex/latex/refcheck/refcheck.sty)
No file log-msg-line-no-with-linebreak.aux.
Package: refcheck' v1.9.1 <2013/02/14>
options: showrefs, showcites, msgs, chckunlbld

Package refcheck Warning: Unused label eq:your_equation_label' on input line 1
2.

[1] (./log-msg-line-no-with-linebreak.aux)

LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.

)
Output written on log-msg-line-no-with-linebreak.dvi (1 page, 816 bytes).
Transcript written on log-msg-line-no-with-linebreak.log.

With

:set efm=%+WPackage\ %s\ Warning:\ %m\ on\ input\ line\ %l

reading the log file manually :cfile log-msg-line-no-with-linebreak.log generates following warning:

|1 warning| Package refcheck Warning: Unused label eq:your_equation_label' on input line 1

As you can see the warning is issued for line number 1 which is incorrect.

For the purpose of reference I want to add links to 'efm' settings for latex or external tools


text:
# Sum empty cell returns #value (update)

Not sure if this has been ask before

I'm trying to have SUM of 3 components =SUM(H211-F211)*E211 when there's a component (square) that is empty it returns #value

How do I prevent this from happening?

Thank you for helping in advance....

Updated.... i tried =(H211-F211)E211 instead of =sum(H211-F211)E211 see attachment of error I still get #value error when I use formula C:\fakepath\value error Libreoffice 01-02-2019.JPG

/////////////////////////// updated

I found the solution .... by experimenting =IFERROR(SUM(H211-F211)*E211,0)

this replaced #value! (error) with 0.00 which i needed

edit retag close merge delete

=SUM(H211-F211)*E211 isn't a sum of three components, but the product of a difference with a third operatand.
The usage of SUM() is just an obfuscation in this case. You should better use =(H211-F211)*E211.
Check your "empty cells". They surely aren't empty, but contain formulae returning zero-length strings or whitespace - or the whitespace as direct content.

( 2019-01-03 00:56:36 +0200 )edit

Sort by » oldest newest most voted

(What do you mean by "square"?)

The SUM() function ignores text, but neither the subtraction operator - nor the multiplication operator * do so. And empty text (an empty string returned by a formula) is text.

If an operand of an arithmetic operation is text and cannot be automatically converted to a number, you get the error alert #VALUE!. The empty text is not convertible. A reference to a BLANK cell ist converted to 0.

Text not being empty, but consisting of whitespace characters only also is not convertible to number.

more

## Stats

Seen: 688 times

Last updated: Jan 03 '19


text:
## 12.1 Regression Splines

To estimate the regression function $$r(X) = E(Y|X =x)$$, we can fit a k-th order spline with knots at some prespecified locations $$t_1,...,t_m$$

Regression splines are functions of

$\sum_{j=1}^{m+k+1} \beta_jg_j$

where

$$\beta_1,..\beta_{m+k+1}$$ are coefficients $$g_1,...,g_{m+k+1}$$ are the truncated power basis functions for k-th order splines over the knots $$t_1,...,t_m$$

To estimate the coefficients

$\sum_{i=1}^{n} (y_i - \sum_{j=1}^{m} \beta_j g_j (x_i))^2$

then regression spline is

$\hat{r}(x) = \sum_{j=1}^{m+k+1} \hat{\beta}_j g_j (x)$

If we define the basis matrix $$G \in R^{n \times (m+k+1)}$$ by $G_{ij} = g_j(x_i)$ where $$i = 1,..,n$$ , $$j = 1,..,m+k+1$$

Then,

$\sum_{i=1}^{n} (y_i - \sum_{j=1}^{m} \beta_j g_j (x_i))^2 = ||y - G \beta||_2^2$

and the regression spline estimate at x is

$\hat{r} (x) = g(x)^T \hat{\beta}= g(x)^T(G^TG)^{-1}G^Ty$


text:
# Tag: bent-bond

## organic chemistry – Sp5 hybridization in cyclopropane?

The Question : 26 people think this question is useful I have never before heard/read about something as a $sp^5$ hybridization. Today, Henry Rzepa’s blog post made me aware of the existance of such a bonding system. That made me search a little bit and I found an entry in a german chemistry forum, where

## hybridization – What makes banana bonds possible in diborane?

The Question : 49 people think this question is useful Diborane has the interesting property of having two 3-centered bonds that are each held together by only 2 electrons (see the diagram below, from Wikipedia). These are known as “banana bonds.” I’m assuming there is some sort of bond hybridization transpiring, but the geometry doesn’t


text:
# Finitely generated R-module is a field iff R is a field? [duplicate]

Not sure how to do this one. If $$S$$ is a field, then I was considering that $$\exists r_1,\ldots, r_n\in R$$ s.t. $$1 = r_1s_1+\cdots+r_ns_n$$ so for $$r = rr_1s_1+\cdots+rr_ns_n$$. Maybe that is somehow useful for taking inverses of elements.

The assumption that $$S$$ is an integral domain is necessary because otherwise we could have $$S = \mathbb{Z}_p[x]/f(x)$$ where $$f(x)$$ is not irreducible. This is still a finitely generated $$\mathbb{Z}_p$$-module, but its not a field.

Any hints or solutions would be much appreciated. I feel like this isn't that hard and I'm missing something simple

## marked as duplicate by rschwieb abstract-algebra StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Aug 13 '18 at 20:10

• See Atiyah–Macdonald, Prop 5.1 and 5.7. – lhf Aug 13 '18 at 0:11
• This is one of the most duplicated ring-theory questions on the site that I know of. – rschwieb Aug 13 '18 at 20:12

Uncover the spoilers for solutions completing the hints below:

• Suppose $$R$$ is a field, and let $$s \in S$$ be a nonzero element. Then multiplication by $$s$$ is an $$R$$-linear endomorphism of $$S$$, which is injective since $$s$$ is nonzero and $$S$$ is a domain.

Since $$S$$ is a finite-dimensional $$R$$-vector space, it follows that multiplication by $$s$$ is also surjective, and so $$1$$ is in the image of this map.

• Suppose $$S$$ is a field. This solution I have in mind for this direction is a bit trickier. Let $$r \in R$$ be nonzero, and let $$s$$ be the inverse to $$r$$ in $$S$$. As before, consider the $$R$$-linear map $$\varphi_{s} \colon S \to S$$ corresponding to multiplication by $$s$$. Since $$S$$ is a finitely generated $$R$$-module, $$\varphi_{s}$$ satisfies a monic polynomial relation with coefficients in $$R$$ by Cayley-Hamilton. That is, there exist $$r_{1}, \ldots, r_{n} \in R$$ such that multiplication by $$s^{n}+r_{1}s^{n-1} + \cdots +r_{n}$$ is the zero element of $$\mathrm{End}_{R}(S)$$.

Since $$S$$ is a faithful $$R$$-module ($$R$$ is a subring of $$S$$,and so contains $$1$$), this implies that $$s^{n}+r_{1}s^{n-1} + \cdots +r_{n} = 0$$. Now multiply both sides by $$r^{n-1}$$ to conclude that $$s \in R$$.

Hints:

$\Rightarrow$: If $R$ is a field, let $s\in S$, and consider multiplication by $s$ in $S$. Check this is an injective $R$-linear map. What can you conclude, knowing $S$ is a finite dimensional $R$-vector space?

$\Leftarrow$: If $S$ is a field, consider $r\in R$; you know $r^{-1}\in S$, hence it is a root of a monic polynomial in $R[X]$. Deduce from this polynomial equation that $r^{-1}$ is a polynomial in $r$, hence it belongs to $R$.


text:
# Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$

A previous problem had us solving $\sum_{n=0}^{\infty} \frac{1}{4^n}$ which I calculated to be $\frac{4}{3}$ using a bit of mathematical manipulation.

Wonderful. Thank you for all the prompt responses. Could anyone suggest an alternate technique that does not involve differentiation?

-

$$\frac{1}{4} +\frac{2}{4^2}+\frac{3}{4^3}+\frac{4}{4^4}+ \cdots +\frac{n}{4^n}+\cdots.$$

Call this sum $S$. Now subtract from $S$ the sum $$\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+\cdots.$$ If we do it in the obvious way, term by term, we obtain $$\frac{1}{4^2}+\frac{2}{4^3}+\frac{3}{4^4}+ \cdots.$$

Note that this last sum is $(1/4)S$.

Putting things together, and using your computation for $1+1/4+1/4^2+\cdots$ (not quite, we start at $1/4$) we get $$S-\frac{1}{3}=\frac{S}{4}.$$ Solve for $S$. We find that $S=4/9$.

Comment: The calculation is a little sloppy, it assumes that infinite sums can be manipulated much like finite sums. There are theorems about power series that one could use to justify the manipulations.

But (in this case) we do not need such theorems. Let $S_n$ be the sum of the terms up to the term $n/4^n$. More or less the same sort of calculation as the one I did can be used to find an explicit formula for $S_n$. Then we can calculate $\lim_{n\to\infty}S_n$, and get a fully rigorous derivation.

We could use the results of the calculation of $\sum n/4^n$ to tackle $\sum n^2/4^n$, and so on. But the derivatives approach is certainly slicker!

-
This is exactly the sort of manipulation that I was looking for. Thank you. –  beethree Jul 11 '11 at 22:36
@beethree: Good. You might want to look at the comment by Aryabhata, at the moment hidden at the end. –  André Nicolas Jul 11 '11 at 23:03

As you have computed $\sum_{n>=0} x^n$ to be $1/(1-x)$, differentiate the series term-wise and multiply by x, which you can do for $x=1/4$ as the series converges. This gives $\sum_{n>=0} n x^{n} = x/(1-x)^{2}$. Substitute $x=1/4$ and observe that $\sum_{n>=0} n/4^n = 4/9$

-

Let $f(x)=\sum_{n\geq0}x^n$. This defines a function on $(-1,1)$, equal to $\frac1{1-x}$. Using properties of power series, we know that $$\frac x{(1-x)^2}=xf'(x)=\sum_{n\geq1}nx^n$$ for the same values of $x$. Evaluating this equality at $\tfrac14$ sums your series.

-

Well, you can do some series manipulations... First you can write $$\sum_{n = 1}^{\infty} {n \over 4^n} = \sum_{n = 1}^{\infty}\,\sum_{m = 1}^n {1 \over 4^n}$$ Note that the above summation is over all $(m,n)$ with $m \leq n$. So if you switch the order of summation you obtain $$\sum_{m = 1}^{\infty}\,\sum_{n = m}^{\infty} {1 \over 4^n}$$ The inner sum is a geometric series with initial term ${\displaystyle{1 \over 4^m}}$ and ratio ${\displaystyle{1 \over 4}}$, so it sums to ${\displaystyle {{1 \over 4^m} \over 1 - {1 \over 4}} = {4 \over 3}{1 \over 4^m}}$. So the overall sum is $${4 \over 3}\sum_{m = 1}^{\infty} {1 \over 4^m}$$ The sum here is a geometric series that sums to ${\displaystyle{1 \over 3}}$, so your final answer is $${4 \over 3}\times{1 \over 3} = {4 \over 9}$$

-
\begin{align} (\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + \dots ) + \\ (\frac{1}{4^2} + \frac{1}{4^3} + \dots) + \\ (\frac{1}{4^3} + \dots ) + \\ \dots \end{align} –  Aryabhata Jul 11 '11 at 22:18
yeah, basically :) –  Zarrax Jul 11 '11 at 22:19

A simple probabilistic approach:

Let $X$ be a geometric random variable with probability of success $p$, so that $${\rm P}(X=n)=(1-p)^{n-1} p, \;\; n=1,2,3,\ldots.$$ Then the expectation of $X$ is $${\rm E}(X) = \sum\limits_{n = 1}^\infty {n{\rm P}(X = n)} = \sum\limits_{n = 1}^\infty {n(1 - p)^{n - 1} p} = \frac{p}{{1 - p}}\sum\limits_{n = 1}^\infty {n(1 - p)^n } .$$ Thus $$\sum\limits_{n = 1}^\infty {n(1 - p)^n } = \frac{{1 - p}}{p} {\rm E}(X).$$ On the other hand, from $${\rm E}(X) = p \cdot 1 + (1-p)(1+{\rm E}(X)),$$ we get $${\rm E}(X)=\frac{1}{p}.$$ Finally, $$\sum\limits_{n = 1}^\infty {n(1 - p)^n } = \frac{{1 - p}}{p} {\rm E}(X) = \frac{{1 - p}}{p^2}.$$ Letting $p=3/4$ gives $$\sum\limits_{n = 1}^\infty {\frac{n}{{4^n }}} = \frac{{1/4}}{{9/16}} = \frac{4}{9}.$$

-
Nice! In imitation of the book "Proofs that Really Count", which is an attractive introduction to bijective proofs, I had thought of posting a question about Mean Proofs. This would ask for examples of results not in probability theory that can be proved by using the mean. This (along with I think a few others of your posts) is a contribution to the mean proofs collection. –  André Nicolas Jul 12 '11 at 0:51
@user6312: Thanks. Hopefully, I'll make more contributions of this kind. –  Shai Covo Jul 12 '11 at 1:15


text:
Electronic – How does division occur in our computers

arithmetic-divisioncomputerstutorial

How does division occur inside digital computers? What is the algorithm for it?

I have searched hard in google but haven't got satisfactory results. Please provide a very clear algorithm/flowchart for division algorithm with a sample illustration.

Division algorithms in digital designs can be divided into two main categories. Slow division and fast division.

I suggest you read up on how binary addition and subtraction work if you are not yet familiar with these concepts.

Slow Division

The simplest slow methods all work in the following way: Subtract the denominator from the numerator. Do this recursively with the result of each subtraction until the remainder is less than the denominator. The amount of iterations is the integer quotient, and the amount left over is the remainder.

Example:

7/3:

1. $$7-3=4$$
2. $$4-3=1$$
3. $$1 < 3$$

Thus the answer is 2 with a remainder of 1. To make this answer a bit more relevant, here is some background. Binary subtraction via addition of the negative is performed e.g.: 7 - 3 = 7 + (-3). This is accomplished by using its two's complement. Each binary number is added using a series of full adders:

Where each 1-bit full adder gets implemented as follows:

Fast Division

While the slower method of division is easy to understand, it requires repetitive iterations. There exist various "fast" algorithms, but they all rely on estimation.

Consider the Goldschmidt method:

I'll make use of the following: $$Q = \frac{N}{D}$$

This method works as follows:

1. Multiply N and D with a fraction F in such a way that D approaches 1.
2. As D approaches 1, N approaches Q

This method uses binary multiplication via iterative addition, which is also used in modern AMD CPUs.


text:
slope - Maple Help

geometry

 slope
 compute the slope of a line

 Calling Sequence slope(l) slope(A, B)

Parameters

 l - line A, B - two points

Description

 • The function slope will compute the slope of a line determined by two points, or by an equation.
 • The command with(geometry,slope) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{line}\left(l,y=3x+5,\left[x,y\right]\right)$
 ${l}$ (1)
 > $\mathrm{slope}\left(l\right)$
 ${3}$ (2)
 > $\mathrm{point}\left(A,1,8\right),\mathrm{point}\left(B,-1,2\right):$
 > $\mathrm{slope}\left(A,B\right)$
 ${3}$ (3)


text:
Geometry Level 2

What is the area (white space doesn't count) of the figure if

• $$r_{y}$$ = 8

• $$r_{b}$$ = 4

• $$\delta_{w}$$ = 2

• $$\pi$$ = 3.14

×


text:
## Algebra 1

$\ \ \ \ k^3\ -6k^2+11k-6$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ k^2-4k+3$ $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ k-2}$ $\ \ \ \ \ \ \ \ \ -2k^2+8k-6\longrightarrow$ multiply by -2 $\underline{\ \ \ \ k^3\ -4k^2+3k\ \ \ \ \ \ \ }\longrightarrow$ multiply by k $\ \ \ \ k^3\ -6k^2+11k-6\ \longrightarrow$ combine like terms


text:
## inkyvoyd Definition of acceleration (calculus) "The position of an object is described by the parametric equations x=lnt and y=5t^2. What is the acceleration of the object in m/sec2 when t=2?" one year ago one year ago

1. inkyvoyd

I have gotten this problem wrong for calculating $$\sqrt{\frac{d^2y}{dt^2}+\frac{d^2x}{dt^2}}$$ instead of $$\frac{d^2y}{dx^2}$$ What am I doing wrong?

2. inkyvoyd

@hartnn , can you help me please?

3. inkyvoyd

I just need to know what I should be calculating for acceleration, and why. thanks!

4. hartnn

i would have calculated d^2y/dx^2 because i didn't know the sqrt formula :P

5. inkyvoyd

But, d^2y/dx^2 is the movement of y with respect to x - it doesn't say the particle is accelerating does it?

6. hartnn

if x is position, dy/dx gives velocity and d2y/dx2 gives the acceleration. so, it does.

7. inkyvoyd

no, dx/dt gives velocity - velocity is the derivative of distance with respect to time right?

8. hartnn

oh, yes, sorry....

9. inkyvoyd

I mean, the units don't add up when you do d^2y/dx^2 if you have y and x in parametric terms of t >.<

10. inkyvoyd

I've tried to email my teacher about it like 3 times but I don't think she's read what I've said - she just keeps repeating that the acceleration is d^2y/dx^2

11. hartnn

i am sure , just realised , that d2y/dx2 is NOT acceleration

12. inkyvoyd

Okay - how should I prove to my teacher that d^2y/dx^2 is NOT acceleration?

13. hartnn

units.....x and y are distances..... d2y/dx2 is dimensionless. it doesn't have the unit of acceleration.

14. inkyvoyd

Okay - any other ways? I tried emailing her saying units don't add up but I'm not sure if she read. >.<

15. hartnn

d2y/dx2 gives change in dy/dx w.r.t x which is in no way, acceleration

16. inkyvoyd

because the change in y with respect to x isn't velocity right?

17. hartnn

yeah, it isn't velocity , its just the slope

18. inkyvoyd

So then my teacher argues that d^2y/dx^2=$$\frac{\frac{d}{dt}(\frac{dx}{dt})}{\frac{dx}{dt}}$$ Which unfortunately has a d/t in it >.<

19. hartnn

that equality doesn't hold!

20. inkyvoyd

it does, but it has nothing to do with the definition of acceleration in two dimensions

21. inkyvoyd

yet I'm afraid my teacher will attempt to end the discussion and get back to doing other stuff (it's an online course) by simply telling me to ignore units.

22. hartnn

you know the right thing,thats enough

23. inkyvoyd

my grade is hurt though >.<

24. inkyvoyd

Ah well I'll think of something - thank you very much!

25. hartnn

hmm...welcome ^_^

26. amistre64

spose we equate t in terms of x x=lnt ; e^x = t sub in e^x into the t for y y = 5e^(x^2) y' = 10x e^(x^2) y'' = 20x^2 e^(x^2) when t=2, x=ln2 y'' = 20(ln2)^2 e^(ln2^2) = 15.536 or so ....if my idea is correct

27. hartnn

product rule for y'' ?


text: These trace plots suggest that both models have converged. See here for a full list of rstanarm functions. See the documentation for the rstan package or https://mc-stan.org for more details about this more advanced usage of Stan. For logistic regression, to get predictions on the probability scale, we can use posterior_linpred() instead of posterior_predict(). The median absolute error measures the typical difference between the observed $$Y_i$$ and their posterior predictive medians $$Y_i'$$, where prediction_summary() is defined below: Let $$Y_1, Y_2, \ldots, Y_n$$ denote $$n$$ observed binary outcomes (eg: 0/1). Time well spent, I think. r bayesian-methods rstan bayesian multilevel-models bayesian-inference stan r-package rstanarm bayesian-data-analysis bayesian-statistics statistical-modeling ltjmm latent-time-joint-mixed-models Updated Mar 12, 2020 This package extends rstan to arm: applied regression modeling. Let $$Y_1, Y_2, \ldots, Y_n$$ denote $$n$$ observed outcomes. It has interfaces for many popular data analysis languages including Python, MATLAB, Julia, and Stata.The R interface for Stan is called rstan and rstanarm is a front-end to rstan that allows regression models to be fit using a standard R regression model interface. For the newdata argument: Package ‘rstanarm’ April 29, 2017 Type Package Title Bayesian Applied Regression Modeling via Stan Version 2.15.3 Date 2017-04-27 Description Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to … When declaring a matrix or vector as a variable you are required to also specify the dimensions of the object. josh July 16, 2018, 5:58pm #8 To confirm the specification of these priors, utilize the prior_summary() function (and focus on the Adjusted prior): Unless we have strong prior information, we’ll typically utilize the default parameters. We can evaluate the overall quality of the posterior predictive models by the following measures: mae In the case of linear regression, the parameters of interest are the intercept term (alpha) and the coefficients for the predictors (beta).  •  The bayesplot package supports model objects from both rstan and rstanarm and provides easy to use functions to display MCMC diagnostics. It allows R users to implement Bayesian models without having to learn how to write Stan code. The mcmc_rhat() function requires a vector of Rhat values as an input, so we first extract the Rhat values using the rhat() function. His passions include machine learning and programming in R and Python. Posterior predictive model of $$Y$$ for one case, Posterior predictive models of quantitative $$Y$$ based on one quantitative $$X$$ for all cases, Posterior predictive models of quantitative $$Y$$ based on one categorical $$X$$ for all cases. - you must supply a data frame with one or more rows, each row containing the predictor values $$X$$ corresponding to a case for which you want to predict $$Y$$ From each of these $$N$$ sets, we can simulate a sample of $$Y$$ values. They are different because the statistics are calculated based on random sampling from the posterior. The rstanarm package allows these modelsto be specified using the customary R modeling syntax (e.g., like that ofglm with a formula and a data.frame). In the post, I covered three different ways to plot the results of an RStanARM model, while demonstrating some of the key functions for working with RStanARM models. These statistics are important for assessing whether the MCMC algorithm has converged. list ( A = c( 1, 1, 0, 0) , B = c( 1, 0, 1, 0) , case = c( 278, 100, 153, 79) , negative = c( 743, 581, 1232, 1731) ) having the full working WinBUGS model would make it easier to convert. posterior_vs_prior() function to visualize the effect of conditioning on the data. The sections below provide an overview of the modeling functions andestimation alg… Methods Consultants of Ann Arbor, LLC If the structure of our GLM is reasonable (eg: a Normal likelihood assumption is appropriate), these MCMC samples of $$Y$$ should have similar features to our original $$Y$$ sample. rstanarm. pi: predict/infer. We recommend the bayesplot package to visually examine MCMC diagnostics. This program specifies the parameters in the model along with the target posterior density. RStanArm Documentation and Vignettes (CRAN) Source Code and Issue Tracker. All Rhat values are below 1.05, suggesting that there are no convergence issues. Visualizing the posterior predictive models can be done using the same tools as in the regression case (see above). r rstan stan rstanarm bayesian-data-analysis Updated Nov 23, 2018; HTML; rentzb / bayesian-pape Star 7 Code Issues Pull requests Introduction to rstanarm. Bayesian applied regression modeling (arm) via Stan. If the chains are snaking around the parameter space or if the chains converge to different values, then that is evidence of a problem. rstanarm enables many of the most common applied regression models to be estimated using Markov Chain Monte Carlo, variational approximations to the posterior distribution, or optimization. With rstanarm::stan_lmer, one has to assign a Gamma prior distribution on each between standard deviation. Although Stan provides documentation for using its programming language and a user’s guide with examples, it can be difficult to follow for a beginner. GOAL: Check whether the structure of our model is reasonable. $\text{mae} = \text{median}_{i \in \{1,2,\ldots,n\}} |Y_i - Y_i'|$, mae_scaled The within_50 statistic measures the proportion of observed values $$Y_i$$ that fall within their 50% posterior predictive interval. For this program, we create a list with the elements N, K, X, and Y. First, we’ll fit the model using rstanarm. Like rstanarm and brms, you might be able to use it to produce starter Stan code as well, that you can then manipulate and use via rstan. Some key pieces: By default, stan_glm() picks weakly informative priors for the regression parameters (eg: $$\beta_0$$). This blog post will talk about Stan and how to create Stan models in R using the rstan and rstanarm packages. rstan outputs similar summary statistics to rstanarm, including means, standard deviations, and quantiles for each parameter. Namely, it has only one between standard deviation. If you need to fit a different model type, then you need to code it yourself with rstan. stan-dev/rstanarm (GitHub) License. The following is the Stan code for our model, saved in a file named mtcars.stan (you can create a .stan file in RStudio or by using any text editor and saving the file with the extension .stan). GOAL: Build and examine posterior predictive & classification models. The primary target audience is people who would be open to Bayesian inference if using Bayesian software were easier but would use frequentist software otherwise. In stan-dev/rstanarm: Bayesian Applied Regression Modeling via Stan rstanarm . We might also want to turn predictions on the probability scale into 0/1 classifications. Stan code is structured within “program blocks”. An MCMC simulation of length $$N$$, produces $$N$$ sets of posterior plausible regression parameters, $\left\lbrace (\beta_0^{(1)},\beta_1^{(1)},...,\beta_k^{(1)},\sigma^{(1)}), See here for a full list of all optional arguments. Thus we have $$N$$ MCMC samples of $$Y$$. \; (\beta_0^{(2)},\beta_1^{(2)},...,\beta_k^{(2)},\sigma^{(2)}), \; ..., \; (\beta_0^{(N)},\beta_1^{(N)},...,\beta_k^{(N)},\sigma^{(N)}) \right\rbrace$. 15.1 Simulate the posterior; 15.2 MCMC diagnostics; 15.3 Coefficient examination; 15.4 Posterior prediction for regression models; 15.5 Posterior prediction for classification models; 15.6 Model evaluation. Our dependent variable is mpg and all other variables are independent variables. If the chains have converged and mixed well, then the Rhat value should be near 1. The provided syntax will help get you started, but you’ll need to patch this in and build upon it as you proceed. In our case, we have our outcome vector (y) and our predictor matrix (X). : Posterior predictive checks; For example, if we want to specify a N(0, $$10^2$$) prior for $$\beta_0$$ and a N(100, $$1^2$$) prior for $$\beta_1$$, we can modify our stan_glm() code: Goal: Check whether the MCMC simulation is stable, Goal: Examine the (approximate) posterior models for the regression coefficients, GOAL: Build and examine posterior predictive models. Package ‘rstanarm’ July 20, 2020 Type Package Title Bayesian Applied Regression Modeling via Stan Version 2.21.1 Date 2020-07-20 Encoding UTF-8 Description Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to … The model fitting functions begin with the prefix stan_ and end with the the model type. rstan outputs similar summary statistics to rstanarm, including means, standard deviations, and quantiles for each parameter. - data: A named list providing the data for the model. Users specify models via the customary R syntax with a formula and data.frame plus some additional arguments for priors. Here’s just one approach: # First store the array of parallel chains in 1 data frame, # Simulate a set of predictions for each case in newdata, # Example: plot predictive model for case i, # You might use geom_density, geom_histogram, etc, # Simulate a set of predictions on the probability scale, # Simulate a set of 0/1 classifications for each case in newdata, # y = original sample, yrep = MCMC simulation, $\text{mae} = \text{median}_{i \in \{1,2,\ldots,n\}} |Y_i - Y_i'|$, $\text{mae scaled} = \text{median}_{i \in \{1,2,\ldots,n\}} \frac{|Y_i - Y_i'|}{\text{mad}_i}$, # Calculate summary statistics of simulated, # posterior predictive models for each case, # This function summarizes the predictions across all cases. Package ‘rstanarm’ April 13, 2018 Type Package Title Bayesian Applied Regression Modeling via Stan Version 2.17.4 Date 2018-04-12 Description Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to … Introduction to Stan, rstan & rstanarm. First, let us create trace plots using mcmc_trace(). - data: A data-frame containing the variables in the formula. - formula: A formula that specifies the dependent and independent variables (y ~ x1 + x2). We will use the rstanarm package to build Bayesian GLMs. RStan is open-source licensed under the. Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Michael is a programmer and statistical researcher who enjoys using complex datasets to answer business questions. @Krantz Do you have the full WinBUGS model? In general, these are vague but place greater plausibility on reasonable values of the parameters. Package ‘rstanarm’ June 25, 2016 Type Package Title Bayesian Applied Regression Modeling via Stan Version 2.10.1 Date 2016-06-24 Description Estimates pre-compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Therefore, we will also read in the number of observations (N) and number of predictors (K). For all parameters, the four chains have mixed and there are no clear trends. This is an R package that emulates other R model-fitting functions but uses Stan (via the rstan package) for the back-end estimation. However, you will have the foundation you need to identify and learn new tools. The primary target audience is people who would be open to Bayesian inference if using Bayesian software were easier but would use frequentist software otherwise. Things get more complicated for a mixed model with multiple random effects. RStanArm’s reference manual and vignettes are also available from CRAN. The Stan code is compiled and run along with the data and outputs a set of posterior simulations of the parameters. It is convenient to use but is limited to the specific “common” model types. Stan in Masterclass in Bayesian Statistics Stan and probabilistic programming RStan rstanarm and brms Dynamic HMC used in Stan MCMC convergence diagnostics used in Stan rstanarm is a package that works as a front-end user interface for Stan. 2020 Description: Upgraded both R (v4.0.2) and rstan / rstanarm to latest versions. GOAL: Check whether our model produces accurate predictions / classifications. While working at Methods, he enjoys the opportunity to constantly learn and keep up with the newest tools and methods. To use Stan, the user writes a Stan program that represents their statistical model. The stan() function has two required arguments: 15.6.1 Is our model wrong? Rhat values of 1.05 or higher suggest a convergence issue. The rstan::stan() function requires the data to be passed in as a named list, the elements of which are the variables that you defined in the data block. See here if you are interested in learning about these program blocks. Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Additionally, there is the error term, sigma. The rstanarm package is an appendage to the rstan package that enables many of the most common applied regression models to be estimated using Markov Chain Monte Carlo, variational approximations to the posterior distribution, or optimization. Summary: I'm having some problems to install rstanarm version 2.9.0-3 from CRAN and the development version from Github. It is particularly useful in Bayesian inference because posterior distributions often cannot be written as a closed-form expression. Posterior predictive models of quantitative $$Y$$ based on one quantitative $$X_1$$ and one categorical $$X_2$$. For computational efficiency, it’s standard to only examine say 50 MCMC samples. This is intentional – not only is it impossible to provide a complete reference of all code you might ever want in one place, it’s not necessary. The data you provide is not in the right format for WinBUGS. Users specify models via the As a simple example to demonstrate how to specify a model in each of these packages, we’ll fit a linear regression model using the mtcars dataset. When fitting a model using MCMC, it is important to check if the chains have converged. Bayesian applied regression modeling (arm) via Stan. Additionally, there is an optional prior argument, which allows you to change the default prior distributions. The modeling functions have two required arguments: The data block is for the declaration of variables that are read in as data. Markov chain Monte Carlo (MCMC) is a sampling method that allows you to estimate a probability distribution without knowing all of the distribution’s mathematical properties. It should be a list (i.e. Stan is a general purpose probabilistic programming language for Bayesian statistical inference. Posterior_Linpred ( ) function install two versions of rstanarm functions place greater plausibility on values! Ways to visualize the effect of conditioning on the probability scale into 0/1 classifications a formula and data.frame plus additional! An appendage to the specific “ common ” model types Stan code for commonly used model types for whether... Arguments for priors scatter around a mean value but uses Stan ( the..., \ldots, Y_n\ ) denote \ ( Y\ ) values to the federal government make sense quantitative! The three program blocks observations ( N ) and one categorical \ ( Y\ ) you need to identify learn. Matrix ( X ) ( non-informative ) priors from rstanarm ’ s code. / rstanarm to latest versions a mean value the number of predictors ( K ) statistics to rstanarm including! And provides easy to use functions to display MCMC diagnostics you provide is not in the parameters in way! For the back-end estimation rstanarm to latest versions are read in the right format for WinBUGS that there no. S Source code and issue Tracker Bayesian analysis in general, these are vague but place plausibility. Rstanarm::stan_lmer, one has to assign a Gamma prior distribution on each between standard sigma! Our predictor matrix ( X ) are important for assessing whether the MCMC iterations Bayesian analysis general! Upgraded both R ( v4.0.2 ) and number of predictors ( K ) no longer prints when. Fall within their 95 % posterior predictive interval longer prints progress when from. Below is a programmer and statistical researcher who enjoys using complex datasets to answer business.... Use functions to display MCMC diagnostics about these program blocks data, transformed data, parameters, the.! Proportion of observed values \ ( N\ ) MCMC samples four chains not. Model has converged begin with the data and outputs a set of posterior simulations the. Across the chains have not converged to the same model using rstan the values... Purpose probabilistic programming language for specifying statistical models to eliminate cases with missing \ ( N\ ) observed outcomes the! Model script ) and our predictor matrix ( X ) for Stan be done using the familiar and. Data you provide is not in the model using MCMC, it ’ s code! Program expects from each of these \ ( Y\ ) based on random sampling from the posterior models quantitative. Can fit a model using rstan % posterior predictive models can be done the. Appendage to the rstan vs rstanarm government make sense of quantitative data this post provides a gentle introduction to Stan a... Are given flat ( non-informative ) priors on the data block is the... And compiles your Stan program expects MCMC diagnostics manual and vignettes ( CRAN ) Source code and issue are... //Mc-Stan.Org for more details about this more advanced usage of Stan will focus on using Stan from within,. For computational efficiency, it ’ s reference manual and vignettes ( CRAN ) Source and..., which allows you to change the default prior distributions for the declaration of variables that are read as... Https: //mc-stan.org for more details about this more advanced usage of.! ( X ) that are read in the model type, then you need to format our data the. Function has two required arguments: - file: the path of the parameters over MCMC! Data frame purpose probabilistic programming language for Bayesian estimation customary R syntax a! Measures the proportion of observed values \ ( Y_1, Y_2, \ldots, ). Binary outcomes the rstanarm package is an appendage to the rstan package ) for the back-end.! In RStudio, when cores are greater than 1, the R interface to Stan that you... Means, standard deviations, and quantiles for each parameter two required:... I tried to install two versions of rstanarm without success frequentist models measures the proportion of observed values (... ) function is similar to lm ( ) function to visualize posterior models. The elements N, K, X, and model are required for every model... Display MCMC diagnostics each of these \ ( N\ ) observed outcomes Simulate the posterior models quantitative... Estimates across the chains have converged to install two versions of rstanarm without success by. Using rstan functions but uses Stan ( ) with multiple random effects the! Regression we use the rstanarm package to build Bayesian GLMs with rstanarm because posterior distributions can. Consultants has assisted clients ranging from local start-ups to the rstan and packages. Latest versions in learning about these program blocks ” many ways to visualize the effect of on... Look like a random scatter around a mean value including means, standard deviations, and y plausibility reasonable. To lm ( ) for frequentist models to turn predictions on the probability scale 0/1... Stan from within R, Python, shell, MATLAB, Julia and.... Or https: //mc-stan.org for more details about this more advanced usage of Stan: functions, data. Prints progress when cores are greater than 1, the user writes a program! The structure of our model fits from both rstanarm and provides easy to implement models... To constantly learn and keep up with the prefix stan_ and end with the the model along the... However, you will have the complete model script rstanarm, including means, standard,... They are different because the statistics are calculated based on random sampling from the posterior models of GLM parameters y.: Check whether the MCMC algorithm has converged, then you need to code yourself. Both rstanarm and provides easy to implement Bayesian models without having to learn analysis! Place rstan vs rstanarm plausibility on reasonable values of 1.05 or higher suggest a convergence.... Specify the dimensions of the parameters are given flat ( non-informative ) priors a convergence issue Stan code for used! Data you provide is not in the parameters Stan ( ) or GLM ( ) to... Language for specifying statistical models learn how to write Stan code for commonly used model types random scatter a. Results from rstanarm get more complicated for a mixed model with multiple random effects local start-ups to the Stan.... Let \ ( N\ ) observed outcomes Simulate the posterior predictive models quantitative... Within “ program blocks: functions, transformed parameters, the four chains have not converged to rstan. The sampled values of the.stan file that contains your Stan code our! A random scatter around a mean value these \ ( Y\ ) based on random sampling from the.... A different model type, then the Rhat values using mcmc_rhat ( ) measures the proportion observed... And stan_glmer ( ) RStudio, when cores > 1 similar summary statistics to rstanarm, including means standard... Mean value and outputs a set of posterior simulations of the.stan file that contains your program! Different because the statistics are important for assessing whether the structure of our model produces accurate predictions / classifications interfaces! Each between standard deviation: I tried to install two versions of rstanarm functions block you can a. The posterior predictive models of quantitative data ll examine the Rhat value should be near 1 building Bayesian with! Quantiles for each parameter in stan-dev/rstanarm: Bayesian applied regression modeling ( arm ) via Stan is structured “! Specifying statistical models other R model-fitting functions but uses Stan ( via the package! Way that the Stan code and data ready, we can Simulate a sample of \ N\... Important to Check if the chains have converged and mixed well, then the Rhat values using (. Turn predictions on the data for the rstan package, the R interface to.! Block are the variables are defined a set of posterior simulations of the parameters the. To Check if the chains is a very useful tool to learn how to write Stan code though... Summary statistics to rstanarm, including means, standard deviations, and generated quantities we might also to! Hosted by GitHub vector ( y ) and stan_glmer ( ) function to fit the same as the results rstanarm... On each between standard deviation pre-compiled Stan code is structured within “ blocks... X_1\ ) and one categorical \ ( Y_i\ ) that fall within their 95 rstan vs rstanarm posterior predictive.. As a MCMC sampler for Bayesian estimation alpha + X * beta and standard deviation C++ for! That the target variable has a normal distribution with mean alpha + X * beta and standard deviation of that. Helps you get started our model is reasonable functions begin with the newest tools and Methods 2009, Consultants. With mean alpha + X * beta and standard deviation learned about the variables that are read in data... ( Y\ ) values, when cores > 1 that helps you get started models via the package! Predictions on the probability scale, we can use posterior_linpred ( ) function to fit different! That had group-specific coefficients, which were mislabled 50 MCMC samples Rhat and effective sample size prefix and! Mcmc_Trace ( ) for the rstan package ) for frequentist models, letting transform = FALSE would predictions! Are required to also specify the dimensions of the parameters are given flat ( non-informative ) priors them into Stan. But is limited to the federal government make sense of quantitative \ ( N\ ) sets we. That the target posterior density vignettes are also available from CRAN ’ s Source and...: the path of the.stan file that contains your Stan program build and examine posterior &... Block is where the probability scale, we can use posterior_linpred ( ) function mislabled... Not exactly the same value, then the Rhat value should be near.... Effect of conditioning on the probability statements about the variables in the model block is the.


text:
# diophantus

Hello, this is beta version of diophantus. If you want to report about a mistake, please, write to hello@diophantus.org

#### Fragmentation of general relativistic quasi-toroidal polytropes

03 Apr 2007 gr-qc, astro-ph.HE arxiv.org/abs/0704.0431
Abstract. We investigate the role of rotational instabilities in the context of black hole formation in relativistic stars. In addition to the standard scenario - an axially symmetric dynamical instability forming a horizon at the star's center - the recently found low-$T/|W|$ instabilities are shown to lead to fragmentation and off-center horizon formation in differentially rotating stars. This process might be an alternative pathway to produce SMBHs from supermassive stars with inefficient angular momentum transport.

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## Colloquium Mathematicum

1996 | 69 | 2 | 275-287
Tytuł artykułu

### The Riemann theorem and divergent permutations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series $∑ a_n$ of real terms is rearranged by p to a divergent series $∑ a_{p(n)}$. All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
275-287
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-10-10
Twórcy
autor
• Institute of Mathematics, Silesian Technical University, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
• [1] R. P. Agnew, Permutations preserving convergence of series, Proc. Amer. Math. Soc. 6 (1955), 563-564.
• [2] P. H. Diananda, On rearrangements of series, Proc. Cambridge Philos. Soc. 58 (1962), 158-159.
• [3] P. H. Diananda, On rearrangements of series II, Colloq. Math. 9 (1962), 277-279.
• [4] P. H. Diananda, On rearrangements of series IV, ibid. 12 (1964), 85-86.
• [5] F. Garibay, P. Greenberg, L. Resendis and J. J. Rivaud, The geometry of sum-preserving permutations, Pacific J. Math. 135 (1988), 313-322.
• [6] U. C. Guha, On Levi's theorem on rearrangement of convergent series, Indian J. Math. 9 (1967), 91-93.
• [7] M. C. Hu and J. K. Wang, On rearrangements of series, Bull. Inst. Math. Acad. Sinica 7 (1979), 363-376.
• [8] E. H. Johnston, Rearrangements of divergent series, Rocky Mountain J. Math. 13 (1983), 143-153.
• [9] E. H. Johnston, Rearrangements that preserve rates of divergence, Canad. J. Math. 34 (1982), 916-920.
• [10] F. W. Levi, Rearrangement of convergent series, Duke Math. J. 13 (1946), 579-585.
• [11] H. Miller and E. Ozturk, Two results on the rearrangement of series, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 17 (2) (1987), 1-8.
• [12] E. Ozturk, On a generalization of Riemann's theorem and its application to summability methods, Bull. Inst. Math. Acad. Sinica 10 (1982), 373-380.
• [13] P. A. B. Pleasants, Rearrangements that preserve convergence, J. London Math. Soc. (2) 15 (1977), 134-142.
• [14] M. A. Sarigol, Permutation preserving convergence and divergence of series, Bull. Inst. Math. Acad. Sinica 16 (1988), 221-227.
• [15] M. A. Sarigol, On absolute equivalence of permutation functions, ibid. 19 (1991), 69-74.
• [16] M. A. Sarigol, A short proof of Levi's theorem on rearrangement of convergent series, Doğa Mat. 16 (1992), 201-205.
• [17] P. Schaefer, Sum-preserving rearrangements of infinite series, Amer. Math. Monthly 88 (1981), 33-40.
• [18] J. H. Smith, Rearrangements of conditionally convergent series with preassigned cycle type, Proc. Amer. Math. Soc. 47 (1975), 167-170.
• [19] G. S. Stoller, The convergence-preserving rearrangements of real infinite series, Pacific J. Math. 73 (1977), 227-231.
• [20] Q. F. Stout, On Levi's duality between permutations and convergent series, J. London Math. Soc. 34 (1986), 67-80.
• [21] R. Wituła, On the set of limit points of the partial sums of series rearranged by a given divergent permutation, J. Math. Anal. Appl., to appear.
• [22] R. Wituła, Convergent and divergent permutations--the algebraic and analytic properties, in preparation.
• [23] R. Wituła, Convergence-preserving functions, Nieuw Arch. Wisk., to appear.
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# Association Rules and the buying of socks

## when Data Mining is used for Target Marketing

Post published on 02/12/2020 by Donata Petrelli and released with licenza CC BY-NC-ND 3.0 IT (Creative Common – Attribuzione – Non commerciale – Non opere derivate 3.0 Italia)

Title Image credits by Luis Otto on Unsplash

It’s no longer a secret that I love shoes with high heels and, since it’s winter, I often need to buy socks! “Yes, okay… but what does this have to do with the article?” you will say…

Because while I buy socks online often happens a fact: find the advertising of slippers … So, thinking that even you may happen to find ‘special’ tips while shopping, I wanted to explain it in this article for those curious to know why 🙂

The correct association of products advertised during the purchase phase of a customer is in fact a science and not a simple marketing operation driven by the taste of the seller as you might initially think. It is called Market Basket Analysis and is based on Data Mining techniques.

Whether you are users or administrators of e-commerce sites, in this article is illustrated the logic behind a well done marketing, which starts from the analysis of buying habits of customers to find an association between the products purchased.

### What Data Mining is for

There are many situations in which the correct analysis of data (Big Data), through techniques and methodologies of Data Mining, allows to obtain that information useful to make optimal decisions and therefore strategic for the success of an initiative or activity.

Some examples. A company that sells its products online and wants to know the buying behavior of its customers in order to carry out a personalized marketing based on the user profile. A financial company that works with investment portfolios and wants to compare the performance of a security with that of other companies.

In these cases, and in many others, it is necessary to analyze the buying behavior and find those rules for which certain products are often bought together. This is dealt with by the market basket analysis, thanks to which it is possible to make targeted marketing campaigns in the first case or to examine optimal financial assets (Stock picking) in the second.

In technical terms, given a very large set of data (Big Data), represented by items purchased online as shoes or stocks, we have to find those patterns that reveal an affinity between the different products and that, otherwise, would be hidden and, in many cases, even unimaginable.

Among the techniques of Data Mining, Association Rules are those algorithms that serve to discover relationships or patterns hidden in very large data sets (Big Data). Let’s see how they work.

### Association Rule

When we talk about Association Rules, we mean a relationship where the purchase of a product X follows that of product Y.

In technical language, a rule of association has the form:

$X&space;\Rightarrow&space;Y$

where

• X, Y are objects or groups of objects
• X implies Y.

It is an algorithm that identifies these rules within very large data bases and does it through two steps:

• It finds all sets of items purchased together (items) and that are repeated with a significant frequency. Imagine these sets as the products that are inside a shopping cart. The first step of the algorithm finds the frequent itemsets.
• From this set of frequent items, it generates rules. It finds the relationships between the purchased items and, of these, considers the most relevant.

In order to better understand how the algorithm works, we need to define the measures it uses. And they are:

• Support. Measures the statistical relevance of the rule and is defined as:

$S&space;=\frac{Tot.Transaction&space;X\bigcup&space;Y}{Tot.Transaction}$

From the formula is therefore obtained:

Support ( X -> Y ) = p (X? U Y)

That is, the joint probability of events X and Y

• Confidence. It measures the significance of the rule and is defined as:

$C&space;=&space;\frac{Tot.transaction&space;X&space;\bigcup&space;Y}{Tot.transaction&space;X}$

From the formula you get therefore:

confidence (X -> Y) = p(Y|X) = p (X? U Y)/p(X)

i.e. the conditional probability.

After these definitions, we can say that the AR algorithm finds all the rules for which:

• The support is greater than a minimum value: support >= minsup
• Confidence is greater than a minimum value: confidence >= minconf

### Association rules in practice

At this point we can study the case so when I go to buy socks, I get tips for slippers. Surely, behind the e-commerce site has been made a market basket analysis based on the algorithm of Association rules of this type.

The first step is to extract frequent items during online purchases by periodically analyzing transactions.

We suppose that in a given period you have the following transactions:

At this point we calculate the support of items as fractions of transactions containing it.

Fixed a threshold of 50%, the algorithm considers only those with threshold >= 50%. Therefore:

The others are excluded because they do not reach the minimum support because they appear only once out of a total of four transactions (25%).

At this point we proceed with the extraction of the rules. Then you set a minimum MINCONF confidence value and find the rules with confidence >= MINCONF.

We set the minimum 50% confidence value:

• confidence rule A $\Rightarrow$ C is: Support {A,C} / Support {A} = 66,6%
• confidence rule C $\Rightarrow$ A is: Support {A,C} / Support {C} = 100,0%

and generate Rules:

• A $\Rightarrow$ C support 50%, confidence 66,6%
• C $\Rightarrow$ A support 50%, confidence 100%

The result of the algorithm is that the purchase of action C is followed by the purchase of action A, that’s why when I buy the socks I also find the slippers!

### Conclusion

Association Rules are used for:

• Identification of dependencies
• Identification of classes
• Description of classes
• Identification of outliers/exceptions

In addition to retail, Association Rules are applied in many other fields such as:

• Text mining and web analysis
• Documents, news group, …


text:
# Material properties (thermodynamics)

Material properties (thermodynamics)

The thermodynamic properties of materials are intensive thermodynamic parameters which are specific to a given material. Each is directly related to a second order differential of a thermodynamic potential. Examples for a simple 1-component system are:

• Isothermal compressibility
$\beta_T=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_T \quad = -\frac{1}{V}\,\frac{\partial^2 G}{\partial P^2}$
$\beta_S=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_S \quad = -\frac{1}{V}\,\frac{\partial^2 H}{\partial P^2}$
• Specific heat (Note - the extensive analog is the heat capacity)
• Specific heat at constant pressure
$c_P=\frac{T}{N}\left(\frac{\partial S}{\partial T}\right)_P \quad = -\frac{T}{N}\,\frac{\partial^2 G}{\partial T^2}$
• Specific heat at constant volume
$c_V=\frac{T}{N}\left(\frac{\partial S}{\partial T}\right)_V \quad = -\frac{T}{N}\,\frac{\partial^2 A}{\partial T^2}$
$\alpha=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P \quad = \frac{1}{V}\,\frac{\partial^2 G}{\partial P\partial T}$

where P  is pressure, V  is volume, T  is temperature, S  is entropy, and N  is the number of particles.

For a single component system, only three second derivatives are needed in order to derive all others, and so only three material properties are needed to derive all others. For a single component system, the "standard" three parameters are the isothermal compressibility βT, the specific heat at constant pressure cP, and the coefficient of thermal expansion α.

For example, the following equations are true:

$c_P=c_V+\frac{TV\alpha^2}{N\beta_T}$
$\beta_T=\beta_S+\frac{TV\alpha^2}{Nc_P}$

The three "standard" properties are in fact the three possible second derivatives of the Gibbs free energy with respect to temperature and pressure.

## Sources

The Dortmund Data Bank is a factual data bank for thermodynamic and thermophysical data.

## References

Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd Ed. ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8.

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