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# Pogil Stoichiometry How Do Chemists Use Balanced Chemical Equations Answer Key
Concept introduction: The acidic or basic character of a salt is estimated. Chemistry 11 Stoichiometry Review Package March 10, 2017 b) Given the following scenario, define which is the limiting reagent and which is the excess reagent: a 1L solution containing 0. Because we know the identity of both the reactants and the product, we can write the reaction as follows: Key Takeaway. This worksheet has 10 short. Remember that "H2O" means. In Cooking we measure ingredients. The larger the K a of an acid, the larger the concentration of $\text{H}_3\text{O}^{+}$ and A − relative to the concentration of the nonionized acid, HA. Data and Results. 00-g sample of a compound containing carbon, hydrogen and nitrogen is analyzed by com-. Chem 30 worksheets Chem 30 worksheets. Get Free Mole Ratio Pogil Answers computing formula mass work, Work on. Balance the following redox reaction. If a reaction's stoichiometry (balanced chemical equation) is not known, chemists determine it experimentally by measuring an _____ that indicates a chemical reaction has taken place. 1 How is a balanced equation like a recipe? A balanced chemical equation provides the same kind of quantitative information that a recipe does. Similarly, chemists classify chemical equations according to their patterns to help predict products of unknown but similar chemical reactions. combination of elements, and encouraged others to pursue chemistry as a quantitative science? 5. 4 How to Write Balanced Chemical Equations 7. We calculate moles with 22. Composition stoichiometry deals with the mass relationship of elements in compounds. A chemical equation that isn't balanced is called a skeleton equation. +! Abalanced-chemical-equation!isarepresentationofa!chemical!reaction! using!the!chemical!formulas!ofthereactants!and!products. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. Also, lend a little guidance on what equations to use for the remaining problems. Chapter 3 Stoichiometry 3-3 3. Finally, convert moles of product to mass. 1) Write a balanced equation for the reaction. Ecological Succession: Nature's Great Grit Discover a process that truly demonstrates nature's grit: ecological succession!EXAMPLE to support your answer. This outcome-based lab requires the students to pre-. The reactants of the equation are typically on the left-hand side of the equation and the products are on the right-hand side, which gives the equation its basic structure. - Closer: Go over number 1 with the class before the end of the period. n 3, thus (n)(n 1) (3)(2) 6 mole ratios 7. Everyday Stoichiometry. - ACTIVITY: Balancing Chemical Equations - pHeT Balancing - Balancing Equations WS 3 - Study for quiz. The answer will appear below; Always use the upper case for the first character in the element name and the lower case for the second character. Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. The larger the K a of an acid, the larger the concentration of $\text{H}_3\text{O}^{+}$ and A − relative to the concentration of the nonionized acid, HA. Determine the known quantity 3. We'll look at Determining the Mole Ratio Determining the mole ratios of a balanced chemical equation for stoichiometry. HS Chemistry POGIL Activity Topic: Stoichiometry. Term In terms of what quantities can you interpret a balanced chemical equation?. Oxidation numbers are assigned to elements using these rules: Rule 1: The oxidation number of an element in …. Chemical Equations #1 - Balancing Chemical Equations #2 - Types of Reactions Chemical Equations #3 - Predicting Products Answer Keys to All Chemical Equations homework #1-3 Balancing Equations - Virtual Modeling / Phet sim link Unit 6 Study Guide (& limited key) Rocket Lab files: PPT: Rocket Lab intro Rocket contest rubric. We will learn about the different kinds of bonds, ways chemists draw bonds and molecules, and how the type of chemical bonding affects the bulk properties of a material. Mole Calculation Worksheet – Answer Key What are the molecular weights of the following compounds? 1) NaOH 22. Use the "Atom Key" to find the chemical symbol for each element. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. Writing and balancing chemical equations is an essential skill for chemistry students, who must learn to predict the products of a reaction when given only the reactants. Chemists classify chemical reactions in order to organize the numerous numbers of Predict products and write complete balanced chemical equations for the following reactions: 1. a chemical reaction involving three substances. Chemical Bonding. Students draw Lewis Dot structures and balance chemical equations. ISBN-10: 0-195-11599-1, ISBN-13: 978-0-495-11599-1 This student workbook is designed to support Process Oriented Guided Inquiry Learning (POGIL) with activities that promote a student-focused active classroom. 2A + 3B ( 5C + 4D. The octet rule, Lewis structures, and valence-shell-electron-pair repulsion (VSEPR) theory are then introduced as early efforts to describe the stability and structures of. 500 M silver nitrate are added to 100. About This Product: This Mini-POGIL activity works great as an introduction to ionic bonding, a review of previously taught material, or as a reinforcement activity. Order of operations pemdas practice work, Stoichiometry 1 work and key, Answer key. HS Chemistry POGIL Activity Name: Date: Basic Stoichiometry Why? In this activity we will address the question: How do I convert between moles of different chemical species in a given reaction? Model 1 2A + 3B 5C + 4D 2 mol A produces 5 mol C 4 mol A produces 10 mol C 3 mol B produces 4 mol D 6 mol B produces 8 mol D. Not grams, kilograms, or liters—but moles. Learn vocabulary, terms, and more with flashcards, games, and other study tools. My point to the class today is that if you can articulate how to do something, you will actually be more likely to truly learn the skill because putting what you know into words uses a different set of skills and a different part of the brain. Balance the chemical reaction equation. 022 × 10^ 23 atoms. For each example, we'll do it two ways. KEY Chemistry: Energy and Stoichiometry Directions: Solve each of the following problems. pdf KEY_HW_Solution Stoichiometry. Chapter 20 Section 2 Guided Reading The New Frontier Answer Key, Chapter 18 Solutions Chemistry Guided Reading Answers, guided reading activity Determining the Mole Ratio Determining the mole ratios of a balanced chemical equation for stoichiometry. One major hurdle to use of technology in the classroom is the ability for students to engage with and successfully use all the tools at their disposal is that students may not know how to use the tools already. 13 V: a) The mass of the iron electrode increases during discharge. What a chemical equation tells you?. Solved Stoichiometry How Do Chemists Use Balanced C. The combustion of propane (C 3 H 8) produces 248 kJ of energy per mole of propane burned. Typical Approach to Stoichiometry Very algorithmic grams A --> moles A--> moles B--> grams B Based on factor-label, unit cancelling, dimensional analysis Fosters "plug-n-chug" solution Approach can be used without much conceptual understanding Disconnected from balanced equation and physical reaction Relies exclusively on computation. For example, the reaction of mercury with oxygen to produce mercuric oxide would be expressed by the equation. 4 L at STP, and use molar. The key to most chemistry problems (real and academic) is the MOLE! That is how elements and compounds combine, and from the balanced equations of their reactions, we can convert the molar quantities into measured quantities like masses or volumes. Chemists use balanced equations to allow them to manipulate chemical reactions in a quantitative manner. Mole Calculation Worksheet – Answer Key What are the molecular weights of the following compounds? 1) NaOH 22. In this sense, data plays a central role in instruction. Combustion Analysis 5 13. videos on Avogadro's Number and the mole. Answer: The ambiguity can be removed by using exponential notation. Financial accounting 11th edition answer key pdf; Comment faire pousser un jacaranda pdf; Team of rivals doris kearns goodwin pdf; Estimating in building construction 8th edition pdf; Dont let the pigeon drive the bus free pdf; How to covert multpile pdf into one with sopda pdf; Insight oriented therapy techniques pdf; Dr seuss books pdf free. There is one Cl atom on the left and two Cl atoms on the right. The balanced equation will appear above. CHEM1001 Worksheet 4: Moles and Stoichiometry Model 1: Balancing Chemical Equations Chemical equations specify how chemical reactions occur - the reactants used, the products formed and the amounts of each. php on line 143 Deprecated: Function create_function() is deprecated in. After you've got a balanced equation, you can use the coefficients to build mole-mole conversion factors. 50% of quiz grade from in-class questions. How many moles of nitrogen would be needed to make 10. Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1. Molar Mass Mole Ratio Molar Volume Molar Mass NH 3 14. Stoichiometry. To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. Then calculate the number of moles of [Au(CN) 2] − present by multiplying the volume of the solution by its concentration. Some Types of Chemical Reactions. In this activity, you will be introduced to simple stoichiometry. 3 Oxidation-Reduction Reactions 1. 3 The Chemical Equation 7. videos on Avogadro's Number and the mole. Balance the following equation with the SMALLEST WHOLE NUMBER COEFFICIENTS possible. The molecular weight of O2 is 32 Pogil the mole answer key Pogil the mole answer key. Molecular Orbitals in Chemical Bonding. A balanced reaction equation contains the same number of each type of atom on both sides of the reaction arrow. The study of the chemical behavior of gases was part of the basis of perhaps the most fundamental chemical revolution in history. If a reactant is in excess, why do we not worry about the mole ratios involving Answers 1. Most often, stoichiometry calculations deal with the mass or volumes. Balancing Chemical Equations Worksheet Answer Key from chemistry unit 7 worksheet 4 answers , source:pinterest. French nobleman Antoine Lavoisier, widely regarded as the "father of modern chemistry," changed chemistry from a qualitative to a quantitative science through his work with gases. A balanced equation is necessary for the mole ratio! 2 Step Example Mole to Mole: Using the tips you just learned about to solve a stoichiometry problem, answer each of these. section, see Equation Stoichiometry Problems with Mixtures on our Web site. HS Chemistry POGIL Activity Page 7 Basic Stoichiometry On your own 1. The smaller answer is the limiting reactant! STOICHIOMETRY Theoretical Yield STOICHIOMETRY: Solutions Ch. A We first use the information given to write a balanced chemical equation. Chemistry 100. Chemistry 11 Stoichiometry Review Package March 10, 2017 b) Given the following scenario, define which is the limiting reagent and which is the excess reagent: a 1L solution containing 0. where the concentrations are those at equilibrium. 1 Grade School Volcanoes, Automobiles, and Laundry Detergents 7. Objectives: 1. You have learned about chemical equations and the techniques used in order to balance them. So, oxygen is already balanced. Not grams, kilograms, or liters—but moles. 00 moles of hydrogen? c. Define ionic bond. BarCharts - CHEMISTRY Equations & Answers (Quick Study: Academic) [2006 version] All of this information also included in CHEMISTRY Spiral Bound Easel (ISBN-13: 978-1423225751) Basic Skills: (Calculator Survival) (How to do Word Problems) (How to Work with Units) (How to Use equations for Data Conversion) (How to use a Conversion Factor). 500 M silver nitrate are added to 100. Campbell); (2) "Curriculum Innovation in School Chemistry " (R. Atestanswers. Users can search by subject and grade level. POGIL- Stoichiometry How do chemists use balanced chemical equations? Why? Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. PhET, based at the University of Colorado at Boulder, offers over four dozen chemistry-based simulations. Students investigate reactions which produce a gas, form a precipitate, and cause a color change. A balanced reaction equation contains the same number of each type of atom on both sides of the reaction arrow. Applying Conversion Factors to Stoichiometry Now you're ready to use what you know about conversion factors to solve some stoichiometric problems in chemistry. What is the Law of Conservation of Matter? AfÅ 7. The role of stoichiometry in real-world applications is important to note, so that it does not seem to be simply an exercise done only by chemists. Balancing Chemical Equations - Answer Key Balance the equations below: 1) 1 N 2 + 3 H 2 2 NH 3 2) 2 KClO 3 2 KCl + 3 O 2 3) 2 NaCl + 1 F 2 2 NaF + 1 Cl 2 4) 2 H 2 + 1 O 2 2 H 2 O 5) 1 Pb(OH) 2 + 2 HCl 2 H 2 O + 1 PbCl 2 6) 2 AlBr 3 + 3 K 2 SO 4 6 KBr + 1 Al 2 (SO 4) 3 7) 1 CH 4 + 2 O 2 1 CO. The molecular formula contains information on the actual number of atoms of each element in the molecule where C3H8 or C6H18. The chemical substance is O 2. The number of particles (atoms, molecules, or other objects) in one. 2A + 3B ( 5C + 4D. The cards cover the basic principle of what a balanced chemical equation means. The octet rule, Lewis structures, and valence-shell-electron-pair repulsion (VSEPR) theory are then introduced as early efforts to describe the stability and structures of. For each experiment in Model 2, determine the relationship between the independent and dependent variables, and write an algebraic expression for the relationship using variables that relate to those in the experiment (P internal, V, T or n). Review Questions 1. 1080/09500690210145738 [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). These kinds of mole conversion factors tell you how much of any given product you get by reacting any given amount of. Key is included at the end of the document. Pogil Chemistry Batteries Answer Key Batteries Pogil Answer - petitionsgofossilfreeorg POGIL CHEMISTRY BATTERIES ANSWER KEY LIBRARYDOC66 PDF Justify your answer The relationship is a direct linear proportion The slope of the line graphed would be constant When another hour is added, an additional 805 g of silver is collected 3 When the time and. 022 x 1023 O. Solved Stoichiometry How Do Chemists Use Balanced C. Chapter 12: Section 1 - The Arithmetic of Equations. KEY Chemistry: Energy and Stoichiometry Directions: Solve each of the following problems. The reactants of the equation are typically on the left-hand side of the equation and the products are on the right-hand side, which gives the equation its basic structure. Use the equations that have been added (Combined Gas Law, Avagadro's Law, Gay-Lussac's Law) to answer the questions on the back of the packet. Use the laws of conservation of mass number and charge to determine the identity of X in equations below. Stoichiometry is the measure of elements. The 2020 POGIL Writers' Retreat will provide an opportunity for individuals or small teams to spend focused time on developing, writing, and improving POGIL activities with the mentorship of experienced POGIL author coaches. Chemistry 100. 3 mol B produces 4 mol D 6 mol B produces 8 mol D. ” • This is different from the actual yield, the amount one actually produces and measures. Balancing Chemical Equations Word Problems Worksheets: Balancing Chemical Equations Worksheets 1. Example: The fireworks that brighten the sky each Fourth of July are based on the reaction between magnesium and oxygen to form magnesium oxide. This is why it is called a "skeleton" equation. A We first use the information given to write a balanced chemical equation. Hank does his best to convince us that chemistry is not torture, but is instead the amazing and beautiful science of stuff. answer lies in chemical equations. In your classroom work in chemistry, you will learn a great deal of the information that has been gathered by scientists about matter. Note the use of 32. A chemical formula is an easy way to tell what atoms are present in a compound. Unit 4 Stoichiometry. The only downside to using skeleton equations as opposed to balanced equations is that skeleton equations don't tell you the quantity of 'stuff' that reacts. There is one Na on the left and one Na on the right. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way. Notice that the Cl-ions drop out, as they are spectator ions and do not participate in the actual redox reaction. We'll see Polar & Non-Polar Molecules: Crash Course Chemistry #23 PLEASE WATCH WITH ANNOTATIONS ON! SOME INACCURACIES IN GRAPHICS ARE NOTED AND CORRECTED IN. Some Types of Chemical Reactions. C) Practice Writing Chemical Formulas. Mole Ratios Stoichiometry Some of the worksheets for this concept are Stoichiometry practice work, Stoichiometry work 1 answers, Co, Chemistry computing formula mass work, Work on moles and stoichiometry, Chem 115 pogil work, Chapter 13 stoichiometry, Moles stoichiometry answers key Title: Microsoft Word - 8-10a,b Mole-Mass Problems wkst-Key. SPENCER GEORGE M. One major hurdle to use of technology in the classroom is the ability for students to engage with and successfully use all the tools at their disposal is that students may not know how to use the tools already. Solved Stoichiometry How Do Chemists Use Balanced C. Stoichiometry. Students have been known to sometimes forget to write the subscript of 2 on a diatomic element (H 2, N 2, O 2, F 2, Cl 2, Br 2, I 2) 3) Construct two molar ratios and set them equal to each other: First molar ratio is from the coefficients of the balanced chemical equation. Weighing is often easier than counting! Model 1: The Balanced Equation How can the coefficients in a chemical equation be interpreted? Consider the reaction: 1 cuC12 +2 2 + 1 cu Key. Laboratory Manual Chemistry: Matter and Change vii How to Use This Laboratory Manual Chemistry is the science of matter, its properties, and changes. Any stoichiometry problem will likely need to work through the mole unit at some point, especially if you are working with a balanced chemical reaction. Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Answers Key Questions & Exercises 1. 500 moles AgNO 3 1 moles Ag 2 CrO 4 331. Gruner Veltliner Osterreichs Trendsetter Und Seine Winzer Im Portrat Wein Pur Islamic Patterns An Analytical And Cosmological Approach Human Factors In Alarm Design. The following Stoichiometry Road Map gives a summary of how to use stoichiometry to calculate moles, masses, volumes and particles in a chemical reaction with limiting and excess reactants. uonenba UI saouv)sqns JO. The combustion of propane (C 3 H 8) produces 248 kJ of energy per mole of propane burned. Stoichiometry is the study of the quantitative relationships or ratios between two or more substances undergoing a physical change or chemical change (chemical reaction). A skeleton equation isn't a wrong way to look at a reaction; it tells you what reacts to produce what. BarCharts - CHEMISTRY Equations & Answers (Quick Study: Academic) [2006 version] All of this information also included in CHEMISTRY Spiral Bound Easel (ISBN-13: 978-1423225751) Basic Skills: (Calculator Survival) (How to do Word Problems) (How to Work with Units) (How to Use equations for Data Conversion) (How to use a Conversion Factor). Student must balance and determine the type of reaction. 3 The Chemical Equation 7. Balancing Chemical Equations Practice Problems. There is one Cl atom on the left and two Cl atoms on the right. Calculate the molar mass of atoms, ions, molecules, and formula units. You can balance a chemical equation by adjusting the coefficients that precede reactant and product compounds within the equation. First and foremost, chemical equations are not balanced in terms of grams; they are balanced in terms of moles. Do both CO2 and NaCl have the same type of elements (metal or non-metal) connected together? What is different about the CO2 particle model and the NaCl particle model (charges? connections of particles? etc…)No, CO2 has only non-metal elements connected to non-metal elements. Do not depend on answer keys to do your homework. balanced chemical equation. Any stoichiometry problem will likely need to work through the mole unit at some point, especially if you are working with a balanced chemical reaction. Ferrer-Vinent, M. We will learn about the different kinds of bonds, ways chemists draw bonds and molecules, and how the type of chemical bonding affects the bulk properties of a material. Figuring this out involves a type of balanced equation and the sort of calculations you would do for a chemical reaction. Name:_____ Date: _____ Period:_____ POGIL- Stoichiometry How do chemists use balanced chemical equations? Why? Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. 400 M potassium chromate? 2 AgNO 3(aq) + K 2 CrO 4(aq) Ag 2 CrO 4(s) + 2 KNO 3(aq) 0. 8: The student can translate among reaction energy profile representations, particulate representations, and symbolic representations (chemical equations) of a chemical reaction occurring in the presence and absence of a catalyst. 4 Mass Relationships in Chemical Equations. In the "Application Phase," learners use the invented concept to verify and modify their ideas. The semester begins with fundamentals related to stoichiometry, chemical reactions, solution chemistry, and gas properties, with an emphasis on quantitative problem solving. 7 we saw how ions are formed by losing electrons to make cations or by gaining electrons to form anions. Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Solved Stoichiometry How Do Chemists Use Balanced C. 11 provides a general outline of the various computational steps associated with many reaction stoichiometry calculations. Always use units and box your final answer. Combustion Analysis 5 13. Deprecated: Function create_function() is deprecated in /www/wwwroot/centuray. Because we know the identity of both the reactants and the product, we can write the reaction as follows: Key Takeaway. The stoichiometry of. When a chemical equation is balanced it means that equal numbers of atoms for each element involved in the reaction are represented on the reactant and product sides. It is a super technical-sounding word that simply means using ratios from the balanced equation. It Stoichiometry - Chemistry for Massive Creatures: Crash Course Chemistry #6 Chemists need stoichiometry to Crash Course Chemistry #6 Chemists need stoichiometry to make the scale of chemistry more. Stoichiometry - (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. 0 and not 16. Data and Results. Mole Ratios POGIL Part 2 Tutorial! Recorded with https://screencast-o-matic. Let us consider a more complicated example. To solve stoichiometry problems, you must first do two very important things. What IS stoichiometry? 41. In the process of mixing elements in during chemical reactions the precision of measures of the reactants determines the expected outcomes of products. Chemists use symbols and formulae to represent elements and compounds. Answer the following stoichiometry-related questions: 12) Write the balanced equation for the reaction of acetic acid with aluminum hydroxide to form water and aluminum acetate: 13) Using the equation from problem #12, determine the mass of aluminum acetate that can be made if I do this reaction with 125 grams of acetic acid. Define ionic bond. First, write a balanced equation for this reaction. There are two steps in writing a. You should see that you are given TWO or more reactants, and you are probably asked about a product. The voltaic cell can be recharged by A. There is one Na on the left and one Na on the right. Remember that "H2O" means. In this bonding worksheet, students give the valence electrons for given elements. Writing and balancing chemical equations is an essential skill for chemistry students, who must learn to predict the products of a reaction when given only the reactants. The coefficients in the balanced chemical equations help you. Solved Stoichiometry How Do Chemists Use Balanced C. For each experiment in Model 2, determine the relationship between the independent and dependent variables, and write an algebraic expression for the relationship using variables that relate to those in the experiment (P internal, V, T or n). The key to this instructional approach is that the learner derives the concept from their observations of the behavior of a chemical system. Chemists use symbols and formulae to represent elements and compounds. In a balanced chemical equation, the coefficients may be used to represent m/mole-ratios-pogil-answer-key/ read more. CK-12 Chemistry Concepts - Intermediate Answer Key Chapter 12: Stoichiometry 12. This is performed by measuring the Latent Heats involved with these. Not grams, kilograms, or liters—but moles. The decomposition of hydrogen peroxide is spontaneous; it would occur no matter what over a period of time. 1 How do chemists use balanced chemical equations? Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. Chemical reactions must be balanced, or in other words, must have the same number of various atoms in the products as in the reactants. a chemical reaction involving three substances. The easiest way to obtain the mole-to-mole ratios would be to simply balance the chemical equations for these reactions. POGIL- Stoichiometry How do chemists use balanced chemical equations? This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way Look at the purpose of the POGIL on the front page and answer the question. A chemical equation is a written symbolic representation of a chemical reaction (The symbols are the elemental letter or letters representing that element). This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way. 01 g/mol + (3 x 1. Answer keys for homework assignments are listed below. Chemical bonds are the glue that hold molecules together. You can balance a chemical equation by adjusting the coefficients that precede reactant and product compounds within the equation. Mole Ratios POGIL Part 2 Tutorial! Recorded with https://screencast-o-matic. Chapter 6: Chemical Change. 6 POGIL™ Activities for High School Chemistry 20. 13 V: a) The mass of the iron electrode increases during discharge. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way. Catalysts are incredibly useful and sometimes vital in chemistry because they are able to significantly change the rate of the reaction without interacting with the reaction itself. Download File PDF Chemistry Pogil Answers chemical equations according to their Chemical - LTHS Answers On this page you can read or download biochemistry basics pogil answer key in PDF format. BODNER LYMAN H. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Answer the following stoichiometry-related questions: 12) Write the balanced equation for the reaction of acetic acid with aluminum hydroxide to form water and aluminum acetate: 13) Using the equation from problem #12, determine the mass of aluminum acetate that can be made if I do this reaction with 125 grams of acetic acid. A balanced reaction equation contains the same number of each type of atom on both sides of the reaction arrow. 1 Introduction to Stoichiometry, Ch 9. To solve stoichiometry problems, you must first do two very important things. The reduction potentials of. Always use units and box your final answer. The following Stoichiometry Road Map gives a summary of how to use stoichiometry to calculate moles, masses, volumes and particles in a chemical reaction with limiting and excess reactants. Chemical GA11. 4 How to Write Balanced Chemical Equations 7. Show your work, including proper units, to earn full credit. ; Draw Lewis structures for ionic compounds. The excess reagent is present in more than a sufficient amount to react. 6 Precipitation Reactions: Reactions in Aqueous Solution That Form a Solid 7. Round each of the following numbers to four significant figures, and express the result in scientific notation: a. Solve problems involving the relationship between the number of particles, the amount of substance in moles, and the mass in grams. Concept introduction: The acidic or basic character of a salt is estimated. Chemical reactions must be balanced, or in other words, must have the same number of various atoms in the products as in the reactants. I begin by interpreting one of the balanced chemical equations from the Do Now. Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc. Pogil Molarity Answer Key 2 Molarity pogil explains how to perform mole to mole conversions from a balanced chemical equation. Mole Ratios 3 7. 12) Write the balanced equation for the reaction of acetic acid with aluminum hydroxide to form water and aluminum acetate: 3 C 2 H 3 O 2 H + Al(OH) 3 Al(C 2 H 3 O 2) 3 + 3 H 2 O 13) Using the equation from problem #1, determine the mass of aluminum acetate that can be made if I do this reaction with 125 grams of acetic acid and 275 grams of. 50% of quiz grade from in-class questions. 2 mol A produces 5 mol C 4 mol A produces 10 mol C. $\endgroup$ - LordStryker Apr 16 '14 at 14:45. 5) of oxygen in half to 1. pdf KEY_HW_Solution Stoichiometry. 5 Aqueous Solutions and Solubility: Compounds Dissolved in Water 7. Solved Stoichiometry How Do Chemists Use Balanced C. Objectives: 1. Financial accounting 11th edition answer key pdf; Comment faire pousser un jacaranda pdf; Team of rivals doris kearns goodwin pdf; Estimating in building construction 8th edition pdf; Dont let the pigeon drive the bus free pdf; How to covert multpile pdf into one with sopda pdf; Insight oriented therapy techniques pdf; Dr seuss books pdf free. 400 M potassium chromate? 2 AgNO 3(aq) + K 2 CrO 4(aq) Ag 2 CrO 4(s) + 2 KNO 3(aq) 0. Remember that "H2O" means. HS Chemistry POGIL Activity Page 10 Basic Stoichiometry HS Chemistry POGIL Activity T opi c : Stoichiometry Basic Stoichiometry - KEY Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1 2A + 3B → 5C + 4D 2 mol A produces 5 mol C 4 mol A produces 10 mol C. We can use each half-reaction to balance the charges. Essential Knowledge 3. The 2020 POGIL Writers' Retreat will provide an opportunity for individuals or small teams to spend focused time on developing, writing, and improving POGIL activities with the mentorship of experienced POGIL author coaches. In this lesson, we will look into some examples of stoichiometry problems. This is called. The reactant chemical(s) are given on the. Do both CO2 and NaCl have the same type of elements (metal or non-metal) connected together? What is different about the CO2 particle model and the NaCl particle model (charges? connections of particles? etc…)No, CO2 has only non-metal elements connected to non-metal elements. Then determine moles of a product formed from that much reactant based on the balanced equation (I usually use a mass that gives a simple, but fractional number of moles such as 0. The decomposition of hydrogen peroxide is spontaneous; it would occur no matter what over a period of time. Balance the chemical equation if needed 2. Download File PDF Chemistry Pogil Answers chemical equations according to their Chemical - LTHS Answers On this page you can read or download biochemistry basics pogil answer key in PDF format. HS Chemistry POGIL Activity Topic: Stoichiometry. The purpose of a chemical equation is to express this relation in terms of the formulas of the actual reactants and products that define a particular chemical change. Essential Knowledge 3. Access the answers to hundreds of Stoichiometry questions that are explained in a way that's easy for you to understand. Finally, convert moles of product to mass. Mole Calculation Worksheet – Answer Key What are the molecular weights of the following compounds? 1) NaOH 22. 1 Grade School Volcanoes, Automobiles, and Laundry Detergents 7. I note that in the expression 2 H 2 O + O 2 --> 2 H 2 O 2 there is a ratio of 2:1:2. Oxidation numbers are assigned to elements using these rules: Rule 1: The oxidation number of an element in …. 3: Critical Writing Name_____ Class_____ Date_____ Thoroughly answer the question below. You have learned about chemical equations and the techniques used in order to balance them. 2) Convert all amounts of products and/or. Chemical reactions must be balanced, or in other words, must have the same number of various atoms in the products as in the reactants. answer lies in chemical equations. 00 grams/mol 2) H 3 PO 4. Mole Ratios POGIL Part 2 Tutorial! Recorded with https://screencast-o-matic. In this sense, data plays a central role in instruction. Saturday 5/24 Final Exam Review Learning Targets Covered by Exam Acid-Base Stoichiometry Chemical Reactions Chemical Names and Formulas Covalent Bonding Friday 5/23 2020 Final Review Short Answer Key. Name four major categories of stoichiometry problems. POGIL Exercise on Chapter 5. If you don't see any interesting for you, use our search form on bottom ↓. Periodic Table, Balancing Chemical Equations, Writing Balanced Equations, Stoichiometry, School Chemistry, Chemistry & Physics Experiments, High School Chemistry, General Chemistry I, General Chemistry II and Organic Chemistry, examples and step by step solutions. You should use answer keys as a tool, not to plagiarize. Safety precautions are detailed. a chemical reaction involving three substances. Compare: Co - cobalt and CO - carbon monoxide; To enter. POGIL Activities for AP* Chemistry Flinn Scientific and the POGIL. Create your own sandwich and then see how many sandwiches you can make with different amounts of ingredients. Steps to solving Stoichiometry 1. Students use the provided diagram and key to answer questions which guide them through many key concepts in ionic bonding, including:-. But the only practical use for N A is to have a more convenient way of expressing the huge numbers of the tiny particles such as atoms or molecules that we deal with in chemistry. 4 How to Write Balanced Chemical Equations 7. [Filename: Ch5-Chemical Reactions in Solutions. answer lies in chemical equations. 1a Avogadro's Number The mole (abbreviated mol) is the unit chemists use when counting numbers of atoms or molecules in a sample. Reaction types are given in a sidebar. What IS stoichiometry? 41. Laboratory Manual Chemistry: Matter and Change vii How to Use This Laboratory Manual Chemistry is the science of matter, its properties, and changes. When balanced, the equation indicates that ___ moles of O 2 are required for each mole of C 3H 8. Weather experts use patterns to predict dangerous storms so people can get their families to safety. Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc. The charges don't match yet so this is not a balanced equation. 022 x 1023 O. 1) Write a balanced equation for the reaction. Figuring this out involves a type of balanced equation and the sort of calculations you would do for a chemical reaction. Chemists use symbols and formulae to represent elements and compounds. This is called Stoichiometry- (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. They allow chemists to do things such as balance redox (reduction/oxidation) equations. 3 mol B produces 4 mol D 6 mol B produces 8 mol D. The final answer is provided on the worksheet so students can verify their answers, but the answer key shows the work required to arrive at the final answer. 1549899516197 Ws Model 1 Mole To Pdf Name Date Period. When balanced, the equation indicates that ___ moles of O 2 are required for each mole of C 3H 8. Admittance into the 2020 Writers' Retreat will be decided via an Application process. Chem 30 worksheets Chem 30 worksheets. The octet rule, Lewis structures, and valence-shell-electron-pair repulsion (VSEPR) theory are then introduced as early efforts to describe the stability and structures of. Examples: Fe, Au, Co, Br, C, O, N, F. Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1. Some Types of Chemical Reactions. Answer; How do chemists use balanced chemical equations? Chemists use balanced chemiscal equations as a basis to calculate how much reactant is needed or how mush product will be formed in a reaction. First, write a balanced equation for this reaction. Chemists use balanced equations to allow them to manipulate chemical reactions in a quantitative manner. POGIL Exercise on Chapter 5. Use the mole ratio from the balanced chemical equation in Model 1, N 2 (g) + 3H 2 (g) → 2NH 3 (g), to solve the following problems. The chemical substance is O 2. PDF Format stoichiometry with these practice problems! In this video, we go over how to convert Balancing Chemical Equations Practice Problems Equation balancing will make sense! Here, we will do a bunch of practice problems for balancing chemical. What is stoichiometry? the calculations of quantities in chemical reactions : In terms of what quantities can you intercept a balanced chemical. This is why it is called a "skeleton" equation. Qualitative analysis is a method used for identification of ions or compounds in a sample. Balancing Chemical Equations Practice Problems Equation balancing will make sense! Here, we will do a bunch of practice problems for balancing chemical equations. traversee du haut languedoc histoire geographie education civique e et toc six epigraphes antiques piano francais epreuve ecrite le guide des techniques d animation. pdf KEY_HW_Solution Stoichiometry. Our intention is that these Mole Ratio Worksheet Answer Key images gallery can be a direction for you, give you more references. Solved Stoichiometry How Do Chemists Use Balanced C. KEY Chemistry: Energy and Stoichiometry Directions: Solve each of the following problems. particles (atoms, molecules, formula units), moles, and mass 8. When balanced, the equation indicates that ___ moles of O 2 are required for each mole of C 3H 8. com › … › Chemistry › Chemical Equations › Stoichiometry To solve stoichiometry problems, you must first do two very important things. Choose your answers to the questions and click 'Next' to see the next set of questions. Gas stoichiometry chem worksheet 14-5 answer key. We calculate moles with 22. Chemistry Solutions: Featured Simulations Each issue of Chemistry Solutions, the periodical of. sgsacpuís 1 ppov,N JO cfHç + Od ppe oyoqdsoqd + aprxoauad sn-10Hdsoqdup. Political analysts use patterns to predict election outcomes. While it may not seem all that "chemical," stoichiometry is a concept that. 00 u, so a mole of O2 would have a mass of 32. What does it mean to have a chemical equation that is "balanced"? 8. POGIL Activities for AP* Chemistry Flinn Scientific and the POGIL. Lead (II). Weather experts use patterns to predict dangerous storms so people can get their families to safety. Chapter 12: Section 1 - The Arithmetic of Equations. PhET, based at the University of Colorado at Boulder, offers over four dozen chemistry-based simulations. Balancing an unbalanced equation is mostly a matter of making certain mass and charge are balanced on the reactants and products side of the reaction arrow. 8: The student can translate among reaction energy profile representations, particulate representations, and symbolic representations (chemical equations) of a chemical reaction occurring in the presence and absence of a catalyst. 00 g and would contain 6. Chemistry students routinely use skeleton equations in order to balance the equations for chemical reactions. Materials and Procedure. Top of fractions is multiply. Units are important! 5. Throughout the chapters, David presents two features that reinforce the. Ferrer-Vinent, M. We will cover electronegativity, Lewis dot structures, VSEPR, bond hybridization, and ionic, covalent, and metallic bonds. It is important to reiterate that balanced chemical equations are balanced in terms of moles. 10] 9S1 dOiS saaoqv. Basic Stoichiometry - KEY. Pogil Molarity Answer Key 2 Molarity pogil explains how to perform mole to mole conversions from a balanced chemical equation. International Journal of Science Education, 25(3), 351 – 372. The role of stoichiometry in real-world applications is important to note, so that it does not seem to be simply an exercise done only by chemists. This gives us the final balanced equation of. Describe the mole concept. Review, quiz, or play games with these Chemistry Task Cards Set that feature stoichiometry and mole problems! There are 60 questions in all, so you can pick and choose which questions you want your students to use. Did you need balanced chemical combustion equations to find the empirical formula of your unknowns in Model 3? 14. In addition, students look at chemical equations and start to make clearer connections to the idea that bonds are broken and formed during chemical reactions. Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Then calculate the number of moles of [Au(CN) 2] − present by multiplying the volume of the solution by its concentration. (b) How is this equation different from the equations in the model? e uaJ I son frha__ í€acfani S 1 3. 2 molecules. The octet rule, Lewis structures, and valence-shell-electron-pair repulsion (VSEPR) theory are then introduced as early efforts to describe the stability and structures of. Balance the following equation with the SMALLEST WHOLE NUMBER COEFFICIENTS possible. B From the balanced chemical equation, use a mole ratio to calculate the number of moles of gold that can be obtained from the. +! Abalanced-chemical-equation!isarepresentationofa!chemical!reaction! using!the!chemical!formulas!ofthereactants!and!products. What a chemical equation tells you?. Solved Stoichiometry How Do Chemists Use Balanced C. C) Practice Writing Chemical Formulas. Always use units and box your final answer. Review Questions 1. The role of stoichiometry in real-world applications is important to note, so that it does not seem to be simply an exercise done only by chemists. For you to be successful in this class you will need to do your own work and ask questions when you need clarification. I note that in the expression 2 H 2 O + O 2 --> 2 H 2 O 2 there is a ratio of 2:1:2. Each of the quiz questions will follow the same pattern: first classify the reaction type, then balance the equation, and finally solve a stoichiometry problem based on the balanced equation. Chapter 12: Section 1 - The Arithmetic of Equations. We know how to do this by simply using the molar mass of Cl 2 as a conversion factor. But, chemistry is not just information. Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. pogil_high_school_chemistry_teacher_copy. Chemists use balanced equations to allow them to manipulate chemical reactions in a quantitative manner. Identify the unknown quantity (the thing that is being asked for) 4. HS Chemistry POGIL Activity Page 10 Basic Stoichiometry HS Chemistry POGIL Activity T opi c : Stoichiometry Basic Stoichiometry - KEY Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1 2A + 3B → 5C + 4D 2 mol A produces 5 mol C 4 mol A produces 10 mol C. Scroll down the page for more examples and solutions. See more ideas about High school chemistry, Chemistry worksheets, Chemistry teacher. Stoichiometry - (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. 2H₂(g) + O₂(g) → 2H₂O(g) The mole ratio between O₂ and H₂O is #(1 mol O₂)/(2 mol H₂O)#. The smaller answer is the limiting reactant! STOICHIOMETRY Theoretical Yield STOICHIOMETRY: Solutions Ch. 1 Everyday Stoichiometry Practice Check the answers with the answer key at the bottom of the page. Lesson 1: Representing Chemical Equations and Stoichiometry This lesson should be implemented at the beginning of the stoichiometry unit when balancing equations are introduced. If a reaction's stoichiometry (balanced chemical equation) is not known, chemists determine it experimentally by measuring an _____ that indicates a chemical reaction has taken place. 1 How do chemists use balanced chemical equations? Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Chapter 12: Section 1 - The Arithmetic of Equations. Similarly, chemists classify chemical equations according to their patterns to help predict products of unknown but similar chemical reactions. n 3, thus (n)(n 1) (3)(2) 6 mole ratios 7. Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. Rayne ; JCE, 2015, I. In Cooking we measure ingredients. Problems get successively harder as you do the sheet. We'll look at Determining the Mole Ratio Determining the mole ratios of a balanced chemical equation for stoichiometry. Notice that the Cl-ions drop out, as they are spectator ions and do not participate in the actual redox reaction. For example, the reaction of mercury with oxygen to produce mercuric oxide would be expressed by the equation. Though I had used a version of the decomposition of sodium bicarbonate lab in our stoichiometry unit for years, with consistent results, what the ADI book provided was a surprisingly different and more creative approach. Units are important! 5. So, oxygen is already balanced. The Foundations of Chemistry. In a balanced chemical equation, the coefficients may be used to represent m/mole-ratios-pogil-answer-key/ read more. If 6 mol A are reacted, how many mol D are formed? Explain as a group how you calculated this answer and show your work. The use of chemical literature for teaching and learning was heavily encouraged in tertiary education (for example JCE, 1993, H. 3 mol B produces 4 mol D 6 mol B produces 8 mol D. 0 x 10 1 g or 1. pdf KEY_HW_Solution Stoichiometry. HS Chemistry POGIL Activity Topic: Stoichiometry. Steps to solving Stoichiometry 1. KEY Chemistry: Energy and Stoichiometry Directions: Solve each of the following problems. At the center of stoichiometry is the mole. One mole is an amount of a substance that contains 6. The word derives from the Greek words: stoicheion (meaning "element") and metron (meaning "to measure"). This section should include all of the information required to answer the three pre-lab questions. Although water is a reactant in the reaction, it is the solvent as well, so we do not include [H 2 O] in the equation. 3 mol B produces 4 mol D 6 mol B produces 8 mol D. HS Chemistry POGIL Activity Page 7 Basic Stoichiometry On your own 1. Chemical Reactions: Precipitation, Acid-base, Gas-forming and Redox 5. Reaction types are given in a sidebar. The decomposition of hydrogen peroxide is spontaneous; it would occur no matter what over a period of time. 01 g/mol + (3 x 1. Use this activity to introduce or reinforce these principles. The combustion of propane (C 3 H 8) produces 248 kJ of energy per mole of propane burned. The order of 5 questions will be random, so students should not have the same order of questions as a peer. The reduction potentials of. Everyday Stoichiometry. Students are developing and using models (SEP 2) in order to fully understand conservation of matter--in order for a chemical reaction to make products, the atoms needed must have come from somewhere. Fansler The Arithmetic of Equations Objectives: Interpret balanced chemical equations in terms of interacting moles, representative particles, masses, and gas volume at STP - The Story So Far o We have learned chemical symbols, charges, how to put together a. Mole Ratios 3 7. Answer keys for homework assignments are listed below. 2 Real-World Applications of Equation Stoichiometry Goals To explain why chemists sometimes deliberately use a limited amount of one reactant (called the limiting reactant) and excessive amounts of others. Then determine moles of a product formed from that much reactant based on the balanced equation (I usually use a mass that gives a simple, but fractional number of moles such as 0. We'll see Polar & Non-Polar Molecules: Crash Course Chemistry #23 PLEASE WATCH WITH ANNOTATIONS ON! SOME INACCURACIES IN GRAPHICS ARE NOTED AND CORRECTED IN. There is one Cl atom on the left and two Cl atoms on the right. Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1. Which Balanced Chemical Equation Best Represents the Thermal Decomposition of Sodium Bicarbonate? 1. Chemistry can tell us how three tiny particles - the proton, neutron and. Stoichiometry Theoretical Yield • The theoretical yield is the amount of product that can be made – In other words itʼs the amount of product possible from stoichiometry. Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc. found online for almost every single POGIL Pogil answer key chemistry Pogil answer key chemistry Currently, there is a significant amount of discussion on teaching list serves about the frustration of people posting answer keys online and students checking Moles & Stoichiometry Answers Key Questions & Exercises Chem 115 POGIL Worksheet - Week 4. Chemists classify chemical reactions in order to organize the numerous numbers of Predict products and write complete balanced chemical equations for the following reactions: 1. Because we know the identity of both the reactants and the product, we can write the reaction as follows: Key Takeaway. Weighing is often easier than counting! Model 1: The Balanced Equation How can the coefficients in a chemical equation be interpreted? Consider the reaction: 1 CuCl 2 + 2 Ag 2 AgCl + 1 Cu. HS Chemistry POGIL Activity Name: Date: Basic Stoichiometry Why? In this activity we will address the question: How do I convert between moles of different chemical species in a given reaction? Model 1 2A + 3B 5C + 4D 2 mol A produces 5 mol C 4 mol A produces 10 mol C 3 mol B produces 4 mol D 6 mol B produces 8 mol D. Why? In this activity we will address the question: How do I convert between different chemical species in a given reaction? Model 1. A balanced reaction equation contains the same number of each type of atom on both sides of the reaction arrow. The smaller answer is the limiting reactant! STOICHIOMETRY Theoretical Yield STOICHIOMETRY: Solutions Ch. POGIL Exercise on Chapter 5. Solve problems involving the relationship between the number of particles, the amount of substance in moles, and the mass in grams. ( 1 ) Balanced chemical reaction equation on a mole basis. Decide which conversion factors are needed. B From the balanced chemical equation, use a mole ratio to calculate the number of moles of gold that can be obtained from the. Use your understanding of common chemical reactions to predict the products for the follow- ing reactions. Answer the following stoichiometry-related questions: 12) Write the balanced equation for the reaction of acetic acid with aluminum hydroxide to form water and aluminum acetate: 13) Using the equation from problem #12, determine the mass of aluminum acetate that can be made if I do this reaction with 125 grams of acetic acid. x 10 1 g or 1. This is performed by measuring the Latent Heats involved with these. Write a balanced equation for the combustion of propane, C 3H 8. Examples of qualitative tests would include ion precipitation reactions (solubility tests) or chemical reactivity tests. The mole allows a chemist to find what masses of substances to use in a reaction. Figuring this out involves a type of balanced equation and the sort of calculations you would do for a chemical reaction. that portion of chemistry dealing with numerical relationships in chemical reactions; the calculation of quantities of substances involved in chemical equations mole ratio a conversion factor derived from the coefficients of a balanced chemical equation interpreted in terms of moles. The weight can be expressed as 12. Qualitative analysis is a method used for identification of ions or compounds in a sample. Mole ratios are used as conversion factors between products and reactants in stoichiometry calculations. Choose your answers to the questions and click 'Next' to see the next set of questions. There is one Na on the left and one Na on the right. 12) Write the balanced equation for the reaction of acetic acid with aluminum hydroxide to form water and aluminum acetate: 3 C 2 H 3 O 2 H + Al(OH) 3 Al(C 2 H 3 O 2) 3 + 3 H 2 O 13) Using the equation from problem #1, determine the mass of aluminum acetate that can be made if I do this reaction with 125 grams of acetic acid and 275 grams of. Molar Mass Mole Ratio Molar Volume Molar Mass NH 3 14. Home - Thousand Islands CSD. In a chemical reaction, one or more reactants are transformed into products:. The reactants are displayed on the left side of the equation and the products are shown on the right, with the separation of either a single or double arrow that signifies the direction of the reaction. A chemical formula is an easy way to tell what atoms are present in a compound. PDF Format stoichiometry with these practice problems! In this video, we go over how to convert Balancing Chemical Equations Practice Problems Equation balancing will make sense! Here, we will do a bunch of practice problems for balancing chemical. 8: The student can translate among reaction energy profile representations, particulate representations, and symbolic representations (chemical equations) of a chemical reaction occurring in the presence and absence of a catalyst. Ingel and A. Using a balanced chemical equation to calculate amounts of reactants and products is called stoichiometry. In this bonding worksheet, students give the valence electrons for given elements. 1a Avogadro's Number The mole (abbreviated mol) is the unit chemists use when counting numbers of atoms or molecules in a sample. Hit the ENTER key, you should see the result "4" Now we are ready to talk about balancing equations. So to use the balanced chemical equation to relate an amount of Cl 2 to an amount of AlCl 3, we need to convert the given amount of Cl 2 into moles. Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Mikulecky, Chris Hren. Download File PDF Chemistry Pogil Answers chemical equations according to their Chemical - LTHS Answers On this page you can read or download biochemistry basics pogil answer key in PDF format. The semester begins with fundamentals related to stoichiometry, chemical reactions, solution chemistry, and gas properties, with an emphasis on quantitative problem solving. 20 x 10 2 g if we have a confidence level extending to 3 sig figs. Mole Calculation Worksheet – Answer Key What are the molecular weights of the following compounds? 1) NaOH 22. answer key understanding psychology, Select Readings Elementary Student Answer Determining the Mole Ratio Determining the mole ratios of a balanced chemical equation for stoichiometry. Mole Ratios Worksheet Answer Key Pogil Beside that, we also come with more Stoichiometry work 1 answers, Co, Chemistry Page 7/20. A Check the chemical equation to make sure it is balanced as written; balance if necessary. Apr 7, 2020 - Explore karencellis's board "Chemistry" on Pinterest. This is an agreed simple means to specifically get guide by on-line. Flashcards. The excess reagent is present in more than a sufficient amount to react. Financial accounting 11th edition answer key pdf; Comment faire pousser un jacaranda pdf; Team of rivals doris kearns goodwin pdf; Estimating in building construction 8th edition pdf; Dont let the pigeon drive the bus free pdf; How to covert multpile pdf into one with sopda pdf; Insight oriented therapy techniques pdf; Dr seuss books pdf free. Use k as a proportionality constant in each equation. Name:_____ Date: _____ Period:_____ POGIL- Stoichiometry How do chemists use balanced chemical equations? Why? Chemists use balanced chemical equations as a basis to calculate how much reactant is needed or product is formed in a reaction. Chemical Formulas and Composition Stoichiometry. The molecular formula contains information on the actual number of atoms of each element in the molecule where C3H8 or C6H18. pdf KEY_HW_Solution Stoichiometry. Figure 2 provides a general outline of the various computational steps associated with many reaction stoichiometry calculations. Stoichiometry - (stoi-key-ah-meh-tree) Another way of looking at it is using the mole ratio from the balanced equation and information about one compound in the reaction to determine information about. Use uppercase for the first character in the element and lowercase for the second character. The chemical substance is O 2. What does it mean to have a chemical equation that is "balanced"? 8. Stoichiometry is the calculation of quantitative relationships of the reactants and products in chemical reactions. This gives us the final balanced equation of. 2 mol A produces 5 mol C 4 mol A produces 10 mol C. 2H₂(g) + O₂(g) → 2H₂O(g) The mole ratio between O₂ and H₂O is #(1 mol O₂)/(2 mol H₂O)#. Starting with a balanced chemical equation, we make use of the proportional nature of chemical reactions to calculate the amount of reactant needed at the start or predict the amount of product that will be produced. Most often, stoichiometry calculations deal with the mass or volumes. CH 4 (g) + 2 O 2 (g) CO 2 (g) + 2 H 2 O (g) Stoichiometry Anatomy of a Chemical Equation Coefficients are inserted to balance the equation. Unit 8: Reactions-Key Regents Chemistry '14-'15 Mr. Determine the oxidation states of the species involved. Basic Stoichiometry - KEY. Weather experts use patterns to predict dangerous storms so people can get their families to safety. Pogil stoichiometry answer key pdf Sign In. HS Chemistry POGIL Activity Name: Date: Basic Stoichiometry Why? In this activity we will address the question: How do I convert between moles of different chemical species in a given reaction? Model 1 2A + 3B 5C + 4D 2 mol A produces 5 mol C 4 mol A produces 10 mol C 3 mol B produces 4 mol D 6 mol B produces 8 mol D. x 10 1 g or 1. Atestanswers. 500 M silver nitrate are added to 100. 400 M potassium chromate? 2 AgNO 3(aq) + K 2 CrO 4(aq) Ag 2 CrO 4(s) + 2 KNO 3(aq) 0. During our stoichiometry unit, I wanted my students to take part in an engaging investigation. POGIL Exercise on Chapter 5. 022 x 1023 O. You could not lonesome going next ebook hoard or library or borrowing from your contacts to get into them. I was never taught in school to use matrices to balance my equation in stoichiometry. gives more information about a chemical reaction because it includes the symbols and formulae of the substances involved. Chemistry ionic puzzle piece activity answer key Chemistry ionic puzzle piece activity answer key. Examples and practice problems of solving equation stoichiometry questions with gases Gas stoichiometry chem worksheet 14-5 answer key. Unit 8: Reactions-Key Regents Chemistry '14-'15 Mr. First, write a balanced equation for this reaction. The weight can be expressed as 12. Regardless of the details, all these calculations share a common essential component: the use of stoichiometric factors derived from balanced chemical equations. A We first use the information given to write a balanced chemical equation. 2 x 10 2 g if we wish to quote unambiguously to 2 sig figs, and 12. 5) of oxygen in half to 1. In a chemical reaction, one or more reactants are transformed into products:. In the equation, A and. Chemical Reactions 7. Gas stoichiometry chem worksheet 14-5 answer key. Use these 50 task cards to give your students practice in doing stoichiometry calculations in your high school chemistry course. answer lies in chemical equations. For each example, we'll do it two ways. You should use answer keys as a tool, not to plagiarize. 1: Students can translate among macroscopic observations of change, chemical equations, and particle views. Target Stoichiometry Lab Mole Relationships and the Balanced Equation Introduction A simple decomposition reaction of sodium bicarbonate (baking soda) presents the opportunity for students to test their knowledge of stoichiometry, factoring labels, and the mole concept. Do the same with chemical reactions. There is one Na on the left and one Na on the right. 0 and not 16.
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2020-10-27 23:12:52
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https://dsp.stackexchange.com/questions/21752/sampling-of-a-band-limited-analog-signal-dft-and-aliasing
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# Sampling of a band-limited analog signal: DFT and aliasing
I saw this question on one of the sites related to DFT:
The analog signal $x(t)$ is band-limited to $40\textrm{ Hz}$. Suppose the signal is sampled at the rate of $100\textrm{ samples/second}$ and that at this rate $200\textrm{ samples}$ are collected. Then $200$ zeros are appended to the $200\textrm{ samples}$ to form a $400$-point vector. Then the $400$-point DFT of this vector is computed to get $X[k]$ for $0 \leq k \leq 399$.
1. Which DFT coefficients are free of aliasing?
2. The DFT coefficient $X[50]$ represents the spectrum of the analog signal at what frequency $f$? (Give your answer in $\textrm{Hz}$).
1. All of the DFT coefficients are free of aliasing. The sampling rate is more that twice the maximum signal frequency.
2. The DFT bin width is $100/400$ or $0.25\textrm{ Hz}$. The $50^{\rm th}$ DFT coefficient corresponds to the frequency $50$ times $0.25\textrm{ Hz}$ or $12.5\textrm{ Hz}$
I'm not really sure if this is right because when you append zeros you are upsampling and the sampling rate becomes $400\textrm{ Hz}$. So when you take a $400$-point DFT the bins are seperated by $1\textrm{ Hz}$.
Please let me know if I am right or not. If I am wrong please explain the answer to me.
Jose.
• That is incorrect. When you append zeros you are not up-sampling your signal. Sampling rate is always the same, you only change the spacing of frequency bins and interpolating samples between them. – jojek Feb 26 '15 at 9:22
The provided answers are correct. Appending zeros is not upsampling and therefore the sampling rate is still $R_\mathrm{s}=100\, \text{Samples/s}$. Accordingly, the frequency spacing after taking the N-DFT is $f_\mathrm{d}=(R_\mathrm{s}/N)=0.25\, \text{Hz}$.
Upsampling can be achieved by inserting $N_\mathrm{U}$ zeros after every sample followd by lowpass filtering.
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2019-02-22 05:18:09
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|
https://socratic.org/questions/how-do-you-differentiate-g-x-x-3-sqrt-4-x-using-the-product-rule
|
How do you differentiate g(x) =x^3 sqrt(4-x) using the product rule?
Apr 23, 2018
$g ' \left(x\right) = 3 {x}^{2} \sqrt{4 - x} - \frac{{x}^{3}}{2 \sqrt{4 - x}}$
Explanation:
$\text{Given "y=f(x)h(x)" then}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = f \left(x\right) h ' \left(x\right) + h \left(x\right) f ' \left(x\right) \leftarrow \textcolor{b l u e}{\text{product rule}}$
$f \left(x\right) = {x}^{3} \Rightarrow f ' \left(x\right) = 3 {x}^{2}$
$h \left(x\right) = \sqrt{4 - x} = {\left(4 - x\right)}^{\frac{1}{2}}$
$\text{differentiate using the "color(blue)"chain rule}$
$\Rightarrow h ' \left(x\right) = \frac{1}{2} {\left(4 - x\right)}^{- \frac{1}{2}} \times \frac{d}{\mathrm{dx}} \left(4 - x\right)$
$\textcolor{w h i t e}{\Rightarrow h ' \left(x\right)} = - \frac{1}{2 \sqrt{4 - x}}$
$\Rightarrow g ' \left(x\right) = - \frac{{x}^{3}}{2 \sqrt{4 - x}} + 3 {x}^{2} \sqrt{4 - x}$
Apr 23, 2018
$\implies g ' \left(x\right) = \frac{\left(24 - 7 x\right) {x}^{2}}{2 \sqrt{4 - x}}$
Explanation:
We are given:
$g \left(x\right) = {x}^{3} \sqrt{4 - x}$
We apply the product rule as follows:
$g ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[{x}^{3}\right] \sqrt{4 - x} + {x}^{3} \frac{d}{\mathrm{dx}} \left[\sqrt{4 - x}\right]$
Simplifying:
$g ' \left(x\right) = \left[3 {x}^{2}\right] \sqrt{4 - x} + {x}^{3} \left[- \frac{1}{2} \frac{1}{\sqrt{4 - x}}\right]$
$g ' \left(x\right) = 3 {x}^{2} \sqrt{4 - x} - \frac{{x}^{3}}{2 \sqrt{4 - x}}$
$g ' \left(x\right) = 3 {x}^{2} \sqrt{4 - x} \cdot \frac{2 \sqrt{4 - x}}{2 \sqrt{4 - x}} - \frac{{x}^{3}}{2 \sqrt{4 - x}}$
$g ' \left(x\right) = \frac{6 {x}^{2} \left(4 - x\right)}{2 \sqrt{4 - x}} - \frac{{x}^{3}}{2 \sqrt{4 - x}}$
$g ' \left(x\right) = \frac{24 {x}^{2} - 6 {x}^{3} - {x}^{3}}{2 \sqrt{4 - x}}$
$g ' \left(x\right) = \frac{24 {x}^{2} - 7 {x}^{3}}{2 \sqrt{4 - x}}$
$\implies \textcolor{b l u e}{g ' \left(x\right) = \frac{\left(24 - 7 x\right) {x}^{2}}{2 \sqrt{4 - x}}}$
Apr 23, 2018
g'(x) = 3x^2sqrt(4-x) - x^3/(2sqrt(4-x)
Explanation:
We can use the product rule with the form;
$g ' \left(x\right) = u ' v + v ' u$
Where we let one term equal to $u$ and the other equal to $v$.
Here;
Let color(blue)(u = x^3
$u$ would have to be differentiated by multiplying the term by the initial power and decreasing the power by one;
$u ' = 3 \cdot {x}^{3 - 1}$
$u ' = 3 {x}^{2}$
And we can do the same for $v$;
Let color(blue)(v = sqrt(4-x)
Just like $u$, $v$ would also have to be differentiated. We can start by changing the square root to the power of $\frac{1}{2}$ to make it easier;
$v = {\left(4 - x\right)}^{\frac{1}{2}}$
By using chain rule;
$v ' = \frac{1}{2} \cdot {\left(4 - x\right)}^{\frac{1}{2} - 1} \cdot \left(4 - x\right) '$
$v ' = - \frac{1}{2} \cdot {\left(4 - x\right)}^{- \frac{1}{2}}$
$v ' = - \frac{1}{2} \cdot \frac{1}{\sqrt{4 - x}}$
color(blue)(v' = -1/(2sqrt(4-x))
Now we can substitute these equations in blue into the equation from the start;
$g ' \left(x\right) = u ' v + v ' u$
$g ' \left(x\right) = 3 {x}^{2} \cdot \sqrt{4 - x} - \frac{1}{2 \sqrt{4 - x}} \cdot {x}^{3}$
g'(x) = 3x^2sqrt(4-x) - x^3/(2sqrt(4-x)
|
2019-07-22 14:28:25
|
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|
https://lambdageeks.com/thermal-diffusivity/
|
# Thermal diffusivity | It’s all Important Facts and FAQs
## Thermal diffusivity definition
Thermal diffusivity is defined as the ratio of conducted heat to heat stored in material per unit volume.
## Unit of Thermal diffusivity
The unit of thermal diffusivity is given as m2/s
## Thermal diffusivity formula
The equation of thermal diffusivity is given by,
Where,
α is thermal diffusivity,
k is thermal conductivity (w/mK)
𝛒 is the density of the material (kg / m3)
Cp is the specific heat (J/ kg k)
## Thermal diffusivity of water
The thermal diffusivity of water changes with temperature and pressure. If we consider atmospheric pressure condition, then the thermal conductivity values with temperature are given as below table.
## Thermal diffusivity of air
The thermal diffusivity of air with temperature change is shown in the above table. Generally , the thermal diffusivity of gas is more than liquid in practice. we will study is more in next topic.
## Thermal diffusion
Thermal diffusion of substance is the relative motion of the molecules due to temperature gradient.
## Thermal diffusivity of aluminium
Thermal diffusivity of aluminium material is given as 9.7 * 10-5 m2/s
## Flash method Thermal diffusivity
The flash method is used to determine the thermal diffusivity of the material. The short duration radiant energy pulse is passed through the sample. The laser or light flash lamp source is used for radiant energy. The piece will absorb the emitted energy. The process is repeated for the sample. Due to this emitted radiation, there is a temperature increase of the material sample. The infrared temperature detector records this increase in temperature.
The duration of the measured signal is calculated. The thermal diffusivity will be found from the following equation.
Where L is the sample thickness,
t/2 is the half time,
we can find thermal diffusivity, specific heat, and density using the flash method.
The schematic diagram of the flash method is shown in the figure below
## How to measure Thermal diffusivity
The thermal diffusivity can be measured using the flash method as discussed above. in this method, the short energy pulse is radiated one end, and temperature rise is calculated on the other end.
## Thermal conductivity and thermal diffusivity
To differentiate between thermal conductivity and thermal diffusivity, consider two materials having the same thermal conductivity but with different thermal diffusivity. Both will permit the same rate of heat flow in the steady-state condition. At the start of the heat transfer process, the material with higher thermal diffusivity will reach a steady-state first compared to other material since it retains less heat energy. Heat energy penetrates fast through this material, but after getting a steady-state, the rate of heat flow will be the same. Also, remember that the material having less thermal diffusivity takes more time to reach the steady state.
## Thermal diffusivity measurement techniques
There are mainly three types of thermal diffusivity measurement techniques.
• Flash method
• Thermal wave interferometry
• Thermographic method
## Thermal diffusivity of asphalt
The thermal diffusivity of the asphalt (Ah-70) is 0.123 mm2/s,
Asphalt (Ah-90) 0.128 mm2/s
## Thermal diffusivity of rubber
The thermal diffusivity of the rubber material is in the range of 0.089-0.13 mm2/s
## Thermal diffusivity values
Thermal diffusivity values for various materials are given in the table below. The values are changes with properties like temperature. These values are given for standard temperature and pressure.
## Thermal diffusivity symbol
The symbol of thermal diffusivity is α
## The highest Thermal diffusivity is of
The highest thermal diffusivity is of pure silver 165.63 mm2 / s
## Thermal diffusivity of sand
Thermal diffusivity of dry sand varied from 0.6 * 10-7 to 7.0 * 10-7 m2/s.
## Thermal diffusivity heat transfer
There are three modes of heat transfer conduction, convection and radiation. Heat conduction is dependent on main two properties. One is thermal conductivity and thermal diffusivity. Thermal conductivity is well-known property, but thermal diffusivity is not well known. It defines the rate of heat transfer through a given medium.
The rate of heat transfer is faster is the thermal diffusivity is higher. Thermal diffusivity is balancing between the medium of heat transfer and heat storage.
## The Thermal diffusivities for gases are generally
The thermal diffusivities of gases substance are found more than liquid substance
## Thermal diffusion coefficient
It is one of physical parameter which describes the dependency of mass diffusion flow of the mixture. In other words, the thermal diffusion coefficient is the ratio of a temperature gradient to the absolute temperature.
## Thermal diffusion meaning
Thermal diffusion of substance is the relative motion of the molecules due to temperature gradient.
## Glass Thermal diffusivity
The thermal diffusivity of glass is 0.34 * 10-6 m2/s at normal atmospheric condition.
## Stainless steel Thermal diffusivity
The thermal diffusivity of stainless steel at 100 °C is 4.55 *10-6 m2/s
## Thermal diffusion ratio
The thermal diffusion ratio is the ratio of the thermal diffusion coefficient to the concentration coefficient.
## Thermal diffusivity of gas vs liquid
The thermal diffusivities of gases substance are found more than liquid substance
## Which material has the highest Thermal diffusivity
The most increased thermal diffusivity is of pure silver 165.63 mm2 / s
## Application of Thermal diffusivity
The conduction heat transfer in any apparatus requires the study of thermal diffusivity. The industries are using the analysis of thermal diffusivity to optimize the heat transfer rate.
If we take a particular example, then insulation is one example. In insulation, the thermal diffusivity of the material is minimum so that it can resist maximum heat flow.
We are using computers, laptops and other electronic gadgets. Do you know what the method to extract heat from devices is? Yes, it’s Heat sinks.
Heat sink requires higher thermal diffusivity to transfer faster heat from any gadgets.
An increase in heat transfer in any electronics degrades its performance. The higher thermal diffusivity material should be used to improve its performance in that case.
## Thermal diffusivity of concrete
The thermal diffusivity of the concrete is 0.75 *10 -6 m2/s
## What is the physical significance of thermal diffusivity?
Thermal diffusivity can be defined as the ratio of the thermal conductivity of the substance to the heat storage capacity of the substance.
The ratio defines the generated heat gets diffused out at a specific rate. The higher value of thermal diffusivity indicates that the time required for heat diffusion is less. The study of the equation of thermal diffusivity can be possible by the higher value of thermal conductivity or the lower value of heat capacity.
\alpha = \frac{k}{\rho \cdot Cp}
Thermal diffusivity is helpful for more intransient heat transfers. In steady-state heat transfer, the thermal conductivity is enough to study.
## Why is the thermal diffusivity of gas greater than liquid even though the thermal conductivity of the liquid is greater than gases?
Thermal diffusivity means the ability of a material to transfer heat and store the heat at an unsteady state. A faster heat transfer can be possible if the thermal diffusivity is higher. The lower thermal diffusivity of material means the storage of heat in it.
Gas possesses low volumetric heat capacity because of low density. Due to low volumetric heat capacity, the value of thermal diffusivity is high.
Liquid possesses a high heat capacity compare to gas; hence thermal diffusivity is lower in the liquid.
## What is the order of thermal diffusivity for solid, liquid, and gas?
The order of thermal diffusivity in solid, liquid and gas as shown below,
Gas > Liquid > Solid
## Momentum diffusion
It can be considered the kinematic viscosity of the fluid, i.e. the ability of the fluid to flow the momentum. Momentum diffusion is occurred by shear stress in a fluid. Shear stress causes a random and any direction movement of molecules.
## Thermal diffusion
It can be defined as thermal conductivity divided by the multiplication of density and specific heat capacity (when the pressure is constant). It measures the heat transfer rate for a given material from the hot side to the cool side. It is predictive analogous to whether a given material is “cool to the touch.”
## How is the Prandtl number related to kinematic viscosity and thermal diffusivity?
The Prandtl Number is dimensionless. It can be given as the ratio of momentum diffusivity (it is kinematic viscosity as explained above) to thermal diffusivity.
It can be formulated in equation as,
Pr = Prandtl number
V= momentum diffusivity ( m2/s )
α = Thermal diffusivity ( m2/ s )
## Thermal diffusivity is the _________
(a) Dimensionless parameter (b) Function of heat (c) Physical property of the material
(d) All of the above
## Thermal diffusivity of a material is __________________?
(a) directly proportional with thermal conductivity (k)
(b) inversely proportional with the density of a material
(c) inversely proportional with specific heat
(d) all of the above
(e) none of the above
## Find the wrong statement: Specific heat of a material ______________.
(a) Constant for a material (b) Heat capacity per unit mass
(c) Extrinsic property (d) Has units as J/kg-K.
(a) m/h
(b) m²/h
(c) m/hk
(d) m²/hk
(a) True
(b) False
(a) Rubber
(c) Iron
(d) Concrete
(a) Rubber
(c) Aluminum
(d) Iron
|
2021-06-15 19:56:14
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|
http://mathhelpforum.com/number-theory/184216-elliptic-curve.html
|
1. ## Elliptic Curve
Hi I was wondering how you would find the number of points with integer coordinates on an elliptic curve E.
In particular for the given curve E:y^2 = x^3 + 17, how many points with integer coordinates can you find on E.
2. ## Re: Elliptic Curve
Here are two points,P $_1$(-1,4), P $_2$(2,5)
Which can be easily verified by substituting them into E.
3. ## Re: Elliptic Curve
Found some more points, (-2,3), (4,9), (8,23), (43,282), (52,375) So we have a total of 7 points.
Maybe someone could lend a hand by implementing
for i in range(-3,n):
x = sqrt(i^3 + 17)
if x == int
print i,x
To see if there are any more values, (I tried to put this code into SAGE but doesn't seem to work, could anyway tell me why not, and how I could get it working?) I will ask my computer science friend if not =)
Cheers guys
4. ## Re: Elliptic Curve
Originally Posted by liedora
Found some more points, (-2,3), (4,9), (8,23), (43,282), (52,375) So we have a total of 7 points.
My guess is that there are quite a lot more, for example (5234,378661). Maybe there are infinitely many.
5. ## Re: Elliptic Curve
Oooh I skimmed past the first 10000 points, must of missed that one, good job. Did you write a program for that? The gap seems to be getting very large between the points, will be interesting to how many more there are! Any idea how to write a program in SAGE that would find such points?
Thanks for taking an interest!
6. ## Re: Elliptic Curve
This is a famous example. See for example the exercises in Silverman & Tate. It has finitely many points, but it's not easy to show (I don't know how to do it).
7. ## Re: Elliptic Curve
Have run it up to x=10000000 and still no more values... But how on earth do you prove its finite!!
8. ## Re: Elliptic Curve
Originally Posted by liedora
Oooh I skimmed past the first 10000 points, must of missed that one, good job. Did you write a program for that?
No, I just used the fact that if you have two integer points on the curve such that the line joining them has integer-valued gradient, then that line will meet the curve at a third such point. The line joining (43,–282) and (52,375) has gradient 73, and meets the curve again at (5234,378661).
That is a neat technique for finding such points, but of course it is not going to help in proving that there are only finitely many of them.
Edit. I just came across this reference to a theorem of Siegel. It also states that the eight integer solutions to y^2=x^3+17 are the only ones with y>0.
|
2017-02-27 14:01:08
|
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|
http://sandordargo.com/blog/2019/08/14/stl-alogorithms-tutorial-part-5-copy-operations
|
In this next part of the big STL algorithm tutorial, we will discover all the modifying sequence operations whose name start with copy:
• copy
• copy_n
• copy_if
• copy_backward
## copy
There is no big surprise about the goal of std::copy. It takes the elements of the input range and copies them to the output. Let here be an example:
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6};
auto copiedNumbers = std::vector<int>{};
std::copy(inputNumbers.begin(), inputNumbers.end(), copiedNumbers.begin());
for (auto number : copiedNumbers) {
std::cout << number << "\n";
}
return 0;
}
So what do you think? Will our copy operation be successful?
No, it won’t be! Instead, we are facing a core dump caused by a segmentation fault. The reason is that there is simply not enough space in copiedVectors. Its size is zero and there is no automatic expansion of the vector unless you use the corresponding API (like push_back()).
So we have two options to choose from.
1) We can make sure that the output vector has a big enough size for example by declaring it with the size of the input like this:
auto copiedNumbers = std::vector<int>(inputNumbers.size());
• copiedNumbers will be populated with the default constructed objects. Okay, in our example we use integers, but imagine if we use a big vector of custom objects that are more costly to build.
• There is another issue. What if the size of the input changes between you create copiedNumbers and you actually call the copy algorithm? Still the same segmentation fault.
2) Instead, you can use an inserter which is an inserter iterator and as its name suggests it will help you to add new elements to the output vector. You can use it like this:
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6};
auto copiedNumbers = std::vector<int>{};
std::copy(inputNumbers.begin(), inputNumbers.end(), std::back_inserter(copiedNumbers));
for (auto number : copiedNumbers) {
std::cout << number << "\n";
}
return 0;
}
Please note that we used std::back_inserter in our example that always inserts new elements at the end of its target. Just like push_back, but that’s someone you cannot use in algorithms as it is related to a specific container, it’s not an inserter iterator.
A particular problem you might think off is that our output container is empty in the beginning and it grows and grows. In how many steps? We can’t really know in advance that’s an implementation detail of the compiler you are using. But if your input container is big enough, you can assume that the output operator will grow in multiple steps. Resizing your vector might be expensive, it needs memory allocation, finding continuous free areas, whatever.
If you want to help with that, you might use std::vector::reserve, which will reserve a big enough memory area for the vector so that it can grow without new allocations. And if the reserved size is not enough, there won’t be a segmentation fault or any other issue, just a new allocation.
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6};
auto copiedNumbers = std::vector<int>{};
copiedNumbers.reserve(inputNumbers.size());
std::copy(inputNumbers.begin(), inputNumbers.end(), std::back_inserter(copiedNumbers));
for (auto number : copiedNumbers) {
std::cout << number << "\n";
}
return 0;
}
What we could observe is that copy doesn’t insert new elements on its own, but it overwrites existing elements in the output container. It can only insert if an inserter iterator is used.
## copy_n
copy took its inputs by a pair of iterators. One marked the beginning of the input range and one the end. But what if you want to copy let’s say 5 elements. Easy-peasy, you can still use copy:
std::copy(inputNumbers.begin(), inputNumbers.begin()+5, std::back_inserter(copiedNumbers));
Pointer arithmetics work well on iterators, so you are free to do this. But you have a more elegant way, you can use copy_n and then you need only the first iterator:
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6};
auto copiedNumbers = std::vector<int>();
copiedNumbers.reserve(inputNumbers.size());
std::copy_n(inputNumbers.begin(), 5, std::back_inserter(copiedNumbers));
for (auto number : copiedNumbers) {
std::cout << number << "\n";
}
return 0;
}
Otherwise copy_n has the same characteristics as copy.
## copy_if
Let’s say you only want to copy certain elements of a list. For example only the even numbers? What can you do? You can simply call copy_if and pass your condition in the form of a unary predicator. What can it be? It can be a function object, a function pointer or simply a lambda expression. Due to its simplicity, I stick to lambdas:
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6};
auto copiedNumbers = std::vector<int>();
copiedNumbers.reserve(inputNumbers.size());
std::copy_if(inputNumbers.begin(), inputNumbers.end(), std::back_inserter(copiedNumbers), [](int i) { return i % 2 == 0; });
for (auto number : copiedNumbers) {
std::cout << number << "\n";
}
return 0;
}
## copy_backward
The last algorithm for today is copy_backward. This algorithm copies elements from the input range but starting from the back going towards the beginning.
Does it produce a reversed order compared to the input? No, it doesn’t. It keeps order. So why does this copy_backward exists? What is its use?
You have an input range of {1, 2, 3, 4, 5, 6, 7} and you want to copy the part {1, 2, 3} over {2, 3, 4}. To make it more visual:
{1, 2, 3, 4, 5, 6, 7} => {1, 1, 2, 3, 5, 6, 7}
So we try to use copy and the output container is the same as the input.
You might try this code:
#include <iostream>
#include <algorithm>
#include <vector>
int main () {
auto inputNumbers = std::vector<int>{1, 2, 3, 4, 5, 6, 7};
std::copy(std::begin(inputNumbers), std::begin(inputNumbers)+3, std::begin(inputNumbers)+1);
for (auto number : inputNumbers) {
std::cout << number << "\n";
}
return 0;
}
The output might be different compared to what you expected - it depends on your expectation and compiler:
1
1
1
1
5
6
7
So what happened?
First, the first number (inputNumbers.begin()) is copied over the second one (inputNumbers.begin()+1). So 2 is overwritten by 1. Then the second number (inputNumbers.begin()+1) is getting copied to the third (inputNumbers.begin()+2) position. But by this time, the second number is 1, so that’s what will be copied to the third. And so on.
(It is possible that you’re using a compiler that is smart enough to overcome this issue)
std::copy_backward will help you to not to have this issue. First, it will copy the last element of your input range and then it will one by one towards the first element, keeping the relative order in the output. Use copy_backward when you copy to the right and the input range is overlapping with the output one.
## Conclusion
Today, we had a peek into the algorithms that start with the copy prefix. They are not all the copy algorithms, but the rest (like reverse_copy, unique_copy) I decided to fit in other parts.
Maybe the most important thing to remember that if you don’t want to rely on your compiler smartness’ and your input and output containers are the same, you have to think wise whether you should use copy or copy_backward.
Next time we’ll start learning about the move and swap and their friends. Stay tuned!
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2020-03-30 23:15:00
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http://math.stackexchange.com/questions/880703/question-about-path-method-for-multivariable-limits
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# Question about path method for multivariable limits
I have to prove that the limit $$\lim\limits_{(x,y) \to (0,0)}\dfrac{x^2}{x+y}$$ does not converge.
This is fairly 'easy' to do, but while I was doing it I came across some doubts. I took the limit $(x,y)\to(0,0)$ when $y=mx$. In this case, the function approches zero as x approaches zero.
Then I tried to approximate it with a curve. But none of the curves $y=x^{n}$ worked, so I did $y=x^2-x$ and then took the limit, which is $1$.
My question is, can I do that? I mean, the only condition that, as far as I know, I have to check, is that the path have to include the point (0,0), but is that the only condition? I know it may be a silly question, but I've never find any theorem regarding the path method and I want to be sure that I'm not messing things up.
I'm sorry if the redaction is a bit messy, It's been a while since I write something in English, please, if you don't understand something I wrote, ask me. Thanks!
-
$m=-1$, i.e. $y=-x$, for your first condition shows the limit does not exist – Adam Hughes Jul 28 '14 at 16:48
@AdamHughes That path is not within the domain of the function... – Lessa121 Jul 28 '14 at 16:51
I mean, how do you procede when you set $y=-x$? – Lessa121 Jul 28 '14 at 16:53
It doesn't particularly matter if you're not allowing that, I suppose. Your choice of $y=x^2-x$ is a good one, that will show the limit does not exist because you get different results from different paths. I've also included a general counterexample in my answer, below, in case you are still a bit leery about the "two different limits" approach. – Adam Hughes Jul 28 '14 at 16:56
@LunaSage What you have done in the original post is perfectly acceptable. – apnorton Jul 28 '14 at 17:01
Aside from showing that two limits differ as you do for $y=x$ and $y=x^2-x$, you can also do this in one fell swoop:
Let $y=x^3-x$, then you get
$$\lim_{(x,y)\to (0,0)}{x^2\over x^3}$$
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2016-05-31 06:11:11
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https://encyclopediaofmath.org/wiki/Trace_on_a_C*-algebra
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# Trace on a C*-algebra
$A$
An additive functional $f$ on the set $A ^ {+}$ of positive elements of $A$ that takes values in $[ 0, + \infty ]$, is homogeneous with respect to multiplication by positive numbers and satisfies the condition $f ( xx ^ {*} ) = f ( x ^ {*} x)$ for all $x \in A$. A trace $f$ is said to be finite if $f ( x) < + \infty$ for all $x \in A ^ {+}$, and semi-finite if $f ( x) = \sup \{ {f ( y) } : {y \in A, y \leq x, f( y) < + \infty } \}$ for all $x \in A ^ {+}$. The finite traces on $A$ are the restrictions to $A ^ {+}$ of those positive linear functionals $\phi$ on $A$ such that $\phi ( xy) = \phi ( yx)$ for all $x, y \in A$. Let $f$ be a trace on $A$, let $\mathfrak N _ {f}$ be the set of elements $x \in A$ such that $f ( xx ^ {*} ) < + \infty$, and let $\mathfrak M _ {f}$ be the set of linear combinations of products of pairs of elements of $\mathfrak N _ {f}$. Then $\mathfrak N _ {f}$ and $\mathfrak M _ {f}$ are self-adjoint two-sided ideals of $A$, and there is a unique linear functional $\phi$ on $\mathfrak M _ {f}$ that coincides with $f$ on $\mathfrak M _ {f} \cap A ^ {+}$. Let $f$ be a lower semi-continuous semi-finite trace on a $C ^ {*}$- algebra $A$. Then the formula $s ( x, y) = \phi ( y ^ {*} x)$ defines a Hermitian form on $\mathfrak N _ {f}$, with respect to which the mapping $\lambda _ {f} ( x): x \mapsto xy$ of $\mathfrak N _ {f}$ into itself is continuous for any $x \in A$. Put $N _ {f} = \{ {x \in \mathfrak N _ {f} } : {s ( x, x) = 0 } \}$, and let $H _ {f}$ be the completion of the quotient space $\mathfrak N _ {f} /N _ {f}$ with respect to the scalar product defined by the form $s$. By passing to the quotient space and subsequent completion, the operators $\lambda _ {f} ( x)$ determine certain operators $\pi _ {f} ( x)$ on the Hilbert space $H _ {f}$, and the mapping $x \mapsto \pi _ {f} ( x)$ is a representation of the $C ^ {*}$- algebra $A$ in $H _ {f}$. The mapping $f \mapsto \pi _ {f}$ establishes a one-to-one correspondence between the set of lower semi-continuous semi-finite traces on $A$ and the set of representations of $A$ with a trace, defined up to quasi-equivalence.
#### References
[1] J. Dixmier, "$C ^ { * }$ algebras" , North-Holland (1977) (Translated from French)
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2023-04-01 04:22:23
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http://docs.dit.io/en/latest/measures/multivariate/deweese.html
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# DeWeese-like Measures¶
Mike DeWeese has introduced a family of multivariate information measures based on a multivariate extension of the data processing inequality. The general idea is the following: local modification of a single variable can not increase the amount of correlation or dependence it has with the other variables. Consider, however, the triadic distribution:
In [1]: from dit.example_dists import dyadic, triadic
Class: Distribution
Alphabet: ('0', '1', '2', '3') for all rvs
Base: linear
Outcome Class: str
Outcome Length: 3
RV Names: None
x p(x)
000 1/8
022 1/8
111 1/8
133 1/8
202 1/8
220 1/8
313 1/8
331 1/8
This particular distribution has zero coinformation:
In [3]: from dit.multivariate import coinformation
Out[4]: 0.0
Yet the distribution is a product of a giant bit (coinformation $$1.0$$) and the xor (coinformation $$-1.0$$), and so there exists within it the capability of having a coinformation of $$1.0$$ if the xor component were dropped. This is exactly what the DeWeese construction captures:
$\ID{X_0 : \ldots : X_n} = \max_{p(x'_i | x_i)} \I{X'_0 : \ldots : X'_n}$
In [5]: from dit.multivariate import deweese_coinformation
Out[6]: 1.0
DeWeese version of the total_correlation, dual_total_correlation, and caekl_mutual_information are also available, and operate on an arbitrary number of variables with optional conditional variables.
## API¶
deweese_coinformation(*args, **kwargs)
Compute the DeWeese coinformation.
Parameters: dist (Distribution) – The distribution of interest. rvs (iter of iters, None) – The random variables of interest. If None, use all. crvs (iter, None) – The variables to condition on. If None, none. niter (int, None) – If specified, the number of optimization steps to perform. deterministic (bool) – Whether the functions to optimize over should be deterministic or not. Defaults to False. rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’. val – The value of the DeWeese coinformation. float
deweese_total_correlation(*args, **kwargs)
Compute the DeWeese total correlation.
Parameters: dist (Distribution) – The distribution of interest. rvs (iter of iters, None) – The random variables of interest. If None, use all. crvs (iter, None) – The variables to condition on. If None, none. niter (int, None) – If specified, the number of optimization steps to perform. deterministic (bool) – Whether the functions to optimize over should be deterministic or not. Defaults to False. rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’. val – The value of the DeWeese total correlation. float
deweese_dual_total_correlation(*args, **kwargs)
Compute the DeWeese dual total correlation.
Parameters: dist (Distribution) – The distribution of interest. rvs (iter of iters, None) – The random variables of interest. If None, use all. crvs (iter, None) – The variables to condition on. If None, none. niter (int, None) – If specified, the number of optimization steps to perform. deterministic (bool) – Whether the functions to optimize over should be deterministic or not. Defaults to False. rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’. val – The value of the DeWeese dual total correlation. float
deweese_caekl_mutual_information(*args, **kwargs)
Compute the DeWeese caekl mutual information.
Parameters: dist (Distribution) – The distribution of interest. rvs (iter of iters, None) – The random variables of interest. If None, use all. crvs (iter, None) – The variables to condition on. If None, none. niter (int, None) – If specified, the number of optimization steps to perform. deterministic (bool) – Whether the functions to optimize over should be deterministic or not. Defaults to False. rv_mode (str, None) – Specifies how to interpret rvs and crvs. Valid options are: {‘indices’, ‘names’}. If equal to ‘indices’, then the elements of crvs and rvs are interpreted as random variable indices. If equal to ‘names’, the the elements are interpreted as random variable names. If None, then the value of dist._rv_mode is consulted, which defaults to ‘indices’. val – The value of the DeWeese caekl mutual information. float
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2019-04-19 10:50:44
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https://cs.stackexchange.com/questions/66025/modified-sutherland-hodgeman-algorithm
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# Modified Sutherland Hodgeman Algorithm
I'm familiar with applying the sutherland hodgeman algorithm for convex polygons(and even concave polygons with a slight modification) against convex clipping windows.
However, if I am to modify the sutherland hodgeman algorithm in such a way that I can clip a concave polygon against a concave window, is that possible?
My question is precisely this:
It's a question that has come in my exam and the only thing I thought of was using the Weiler Atherton algorithm, but that's no amendment to the Sutherland Hodgman approach and is a different algorithm altogether.
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2020-05-25 22:06:50
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https://alpynepyano.github.io/healthyNumerics/posts/secret-of-confidential-interval-python.html
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# HealthyNumerics
HealthPoliticsEconomics | Quant Analytics | Numerics
# BasicStats: The secret of the CI
Some more and interesting explanations can be found here: - http://hamelg.blogspot.ch/2015/11/python-for-data-analysis-part-23-point.html
import numpy as np
import pandas as pd
import scipy.stats as sst
import matplotlib.pyplot as plt
import random
import math
### Generate a population
We generate a population with 250'000 members
np.random.seed(10)
population_ages1 = sst.poisson.rvs(loc=18, mu=35, size=150000)
population_ages2 = sst.poisson.rvs(loc=18, mu=10, size=100000)
population_ages = np.concatenate((population_ages1, population_ages2))
pd.DataFrame(population_ages).hist(bins=58, range=(17.0,76.0), figsize=(15,6))
plt.show()
## Numerical evaluation of the CI
### Confidential intervals of the means of several samples of the same population
• We take 100 times a random sample with 10000 elements from the population that has 250'000 elements
• For each sample we determin the mean and it's confidence intervall:
• with the z-critical value (0.975 e.g.) we determin the margins of error (meo)
• the confidence interval for a singele sample is [mean-meo, mean+moe]
• This procedure is designed to ascert that 95% of the samples have sample confident intervalls that include the parameter (here the mean) of the population
• This is the meaning of the 95% confidence intervall
• The invers closure: "The parameter has a probability of 95% to lie within the CI" , is not correct
sample_size = 1000 # size of 1 sample
Nsamp = 100 #number of experiments we run
np.random.seed(123)
intervals = []
sample_means = []
#--- statistics of the population--
pop_mean = population_ages.mean() # mean of the population
pop_stdev = population_ages.std() # standard deviation of the population
#---- z-value and margin of errors---
z_critical = sst.norm.ppf(q = 0.975) # z-critical value*
margin_of_error = z_critical * (pop_stdev/math.sqrt(sample_size)) # remains constant !
for samp in range(Nsamp):
#--- take a sample and calculate the mean ---
sample = np.random.choice(a= population_ages, size = sample_size)
sample_mean = sample.mean()
sample_means.append(sample_mean)
#--- caluclate the margins and the confidence interval ---
confidence_interval = (sample_mean - margin_of_error,
sample_mean + margin_of_error)
intervals.append(confidence_interval)
#### Evaluation, Grafics
intv = np.array(intervals)
above = intv[intv[:,0]>pop_mean]
below = intv[intv[:,1]<pop_mean]
print(); print('Number of samples with CI above mean of population : ', len(above))
print('Number of samples with CI below mean of population : ', len(below)); print()
with plt.style.context('fivethirtyeight'):
plt.figure(figsize=(25,6))
plt.errorbar(x=np.arange(0.1, Nsamp, 1), y=sample_means,
yerr=[(top-bot)/2 for top,bot in intervals],
fmt='o',ms=8, markerfacecolor='k');
plt.hlines(xmin=0, xmax=Nsamp,y = pop_mean,
linewidth=2.0, color="red", label="mean of population");
plt.title("Means with CI of "+str(Nsamp)+" samples of the population", fontsize=25, fontweight='bold')
plt.legend(loc='upper center',prop={'size': 20})
plt.show()
Number of samples with CI above mean of population : 2
Number of samples with CI below mean of population : 1
### Confidential interval of the mean of a single sample
If you know the standard deviation of the population, the margin of error is equal to:
$$z*\frac{\sigma}{\sqrt{n}}$$
where - σ (sigma) is the population standard deviation, - n is sample size, and - z is a number known as the z-critical value.
Note, that the standard deviation of the population is in most applications not known. So the standard deviation of the sample will be used instead usually, provided the sample has at least 30 elements (more than 100 would be nicer)..
The z-critical value is the number of standard deviations you'd have to go from the mean of the normal distribution to capture the proportion of the data associated with the desired confidence level. For instance, we know that roughly 95% of the data in a normal distribution lies within 2 standard deviations of the mean, so we could use 2 as the z-critical value for a 95% confidence interval (although it is more exact to get z-critical values with stats.norm.ppf().).
np.random.seed(10)
#--- take a sample---
sample_size = 1000
sample = np.random.choice(a= population_ages, size = sample_size)
sample_mean = sample.mean()
#--- statistics of the population--
pop_mean = population_ages.mean() # mean of the population
pop_stdev = population_ages.std() # standard deviation of the population
#--- confidence interval of the mean of the sample
z_critical = sst.norm.ppf(q = 0.975) # Get the z-critical value*
margin_of_error = z_critical * (pop_stdev/math.sqrt(sample_size))
confidence_interval = (sample_mean - margin_of_error,
sample_mean + margin_of_error)
print("Mean of sample :", sample_mean)
print("Mean of population :", pop_mean)
print("Diff meanPop - meanSmpl:",pop_mean - sample_mean)
print("St_dev of population :", pop_stdev)
print("z-critical value :", z_critical)
print("sst.norm.ppf(q=0.025) :", sst.norm.ppf(q=0.025))
print("margin of error :", margin_of_error)
print("Confidence interval :", confidence_interval)
Mean of sample : 42.523
Mean of population : 43.002372
Diff meanPop - meanSmpl: 0.479372
St_dev of population : 13.2291465474
z-critical value : 1.95996398454
sst.norm.ppf(q=0.025) : -1.95996398454
margin of error : 0.819935931173
Confidence interval : (41.703064068826833, 43.342935931173173)
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2019-08-24 18:27:33
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https://www.physicsforums.com/threads/scaling-in-dis.270130/
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# Scaling in DIS
1. Nov 7, 2008
### blue2script
Hi all!
I am just wondering why scaling in DIS is approximately realized for the middle (Bjorken-) x-values and not e.g. for the high or low x-values? Is there any depicitive reason?
Thanks for the ideas!
Blue2script
2. Nov 7, 2008
### vanesch
Staff Emeritus
Scaling comes about in the parton model of a hadron, where the hadron is simply seen as an almost unbound "bag" of "partons" (quarks and gluons). The bjorken -x is then nothing else (at least in the relativistic approximation of all-massless particles) of the longitudinal momentum fraction of the "hit" parton on the "whole".
As such, the interaction cross section of a particle with a hadron should factorize in a "form factor" (the probability to have a parton with fraction x of the momentum) and an "elementary cross section" which is nothing else but the interaction cross section of the incoming particle and the "free parton".
For the small x values, what happens is in fact that there are higher-order QCD diagrams in which the "original parton" presents itself as another one. That's a bit as in the case of an electron, there's a cloud of virtual e+/e- pairs around it (vacuum polarization), and at small enough scale, the interaction can be not with the original electron, but, say, with a positron of this "cloud". In the same way, an initial up quark can couple through a higher-order QCD diagram with, say, an anti-up quark with the incoming particle.
There are "evolution equations", the Altarelli-Parisi equations, which use higher-order QCD diagrams to change the quark density at a certain energy into a quark density at another energy. There have been corrections to this, which have to do with 'diffractive effects', which can be seen as scattering on "bound states" within the hadron.
I have to say that I don't really know what gives scaling violations at high x. All this is from memory from 10 years ago...
3. Nov 7, 2008
### cygnus2
Well, I can give you a simple reason why there are scaling violations in the structure functions. As it happens in the naive parton model, in the infinite momentum frame the quarks are taken to be non-interacting with each other. Further, all their momentum is considered to be longitudinal. However, there is always the case where the quark can emit a gluon and acquire a momentum in the transverse direction. Moreover, the maximum momentum of the gluon that it can emit is limited by the momentum carried by the quark itself, which is $x$ times the total momentum of the proton. When you calculate this process, youy get log(x) scaling violations.
4. Nov 7, 2008
### blue2script
Hi cygnus2 and vanesh! Thanks for your replies! I think I got the idea now, so let me try to summarize:
The behavior of the x-Q^2-dependence is:
1) for low x-values the density of the partons increases with increasing Q^2
2) in mid-x values the density of the partons stays constant (scaling)
3) for high-x values the density of the partons decreases with increasing Q^2
The x-value is the fraction of momentum the parton posses.
Reason:
1) If the x-value is low, the momentum of the quark is low. The cross section to emit a gluon of low moment (say, half of the quark momentum) is relatively high. That means, we will rather not find a quark with momentum fraction x but three quarks (a pair created from the gluon) with roughly the same, low momentum x/3. Then, if we probe the cloud with a high momentum transfer, we will eventually see the three quarks separately leading to a high scattering probability at low-momentum quarks-> we see a high density at low momentum.
3) If the x-value is high, the quark as a high momentum fraction. It will radiate mainly low-momentum gluons keeping itself most of the momentum. Thus, the original quark dominates the cloud and, making many experiments, we will most often see quarks at the top line of momentum whereas the low-momentum quarks are suppressed.
2) Since it lies in the middle of 1) and 3) there should be some intermediate range where the density is constant
Hope one can understand the point of my argumentation. It may be a bit confusing. If so, just tell me and I will try to clear it up.
Is this the right interpretation? Thanks again for all upcoming comments!
Blue2script
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2017-08-19 00:43:53
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|
http://palicinfo.rs/5wrtzp/fe27d1-pie-chart-class-8-notes
|
The data can be grouped using the frequency distribution table. For thorough revision of pie charts and other data handling topics, explore our study materials like practice tests and ICSE Class 8 Maths sample papers. Q03. Calculate the total 3. Pie charts are different types of data presentation. The above figure is a double bar graph. An Experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. Q9. Q03. A circle is divided in sectors. Probability is the likelihood of occurrence of an event. An event is a set of outcomes of an experiment. Class VIII Math Notes for Data Handling. The chart is divided into 5 parts. The pie chart is an important type of data representation. Convert into percentages 5. Chapter 5 of Class 8 Maths, Data handling deals with organising data and grouping the data. 50%. CBSE Notes for Class 7 Computer in Action – Charts in Microsoft Excel 2013. Class width or size = upper limit – lower limit. Class 8 Maths Data Handling: Drawing a pie chart: Drawing a pie chart. This data is presented in the form of a circle. For creating a pie chart the following steps needs to be followed: Each sector in the pie chart is proportional to the amount spent for that particular activity or item. Here we have given NCERT Class 8 Maths Notes Chapter 5 Data Handling. To know more about Data handling, visit here. Class 8 Video | EduRev sample questions with examples at the bottom of this page. In a grouped frequency distribution a large amount of raw data is represented by making groups or class intervals and obtain a frequency distribution of the number of observations falling in each group. Experimental or empirical probability: $$P(E)=\frac{number\;of\;trials\;where\;the\;event\;occurred}{total\;number\;of\;trials}$$ Pie Charts RS Aggarwal Class 8 Solutions Ex 23A Q1. Q4. The circle is divided into sectors. The above data can be represented as a frequency distribution table as: Here, 60-70, 70-80, 80-90, 90-100 are the class intervals. These solutions for Pie Charts are extremely popular among Class 8 students for Math Pie Charts Solutions come handy for quickly completing your homework and preparing for exams. How to Draw a Pie Chart. There are segments and sectors into which a pie chart is being divided and each of these segments and sectors forms a certain portion of the total(in terms of percentage). Chapter 5 Data Handling Class 8 Revision Notes is prepared Studyrankers experts faculty according to the latest exam pattern released by CBSE. Frequency is the number of times that a particular observation/event occurs. For Study plan details. Looking for Information; Organising Data; Grouping Data; Circle Graph or Pie Chart Size of each sector is proportional to the activity or information it represents. You more than likely think of the delicious dessert with a flaky crust and the filling of your choice. 10:00 AM to 7:00 PM IST all days. or own an. Donut! All questions and answers from the Rs_aggarwal_(2018) Book of Class 8 Math Chapter 24 are provided here for you for free. Example: The following pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. However, if a coin is tossed ten times its not necessary that we will get a head five times and a tail five times. Representation of data. Solution: Table to find the central angle of each sector. Data handling is referred to the procedure done to organize the information provided in order to perform mathematical operations on them. Class 8 Video | EduRev Summary and Exercise are very important for perfect preparation. You can see some How to Draw Pie Charts? Class 8 How to Draw Pie Charts? Need assistance? A pie graph/pie chart is a specialized graph used in statistics. When we toss a coin we get only one outcome either a head or a tail. So there are more than twice as many pets in form 7GI. Multiple bar graphs is a bar graph which is used for comparing more than one kind of information. It contains different segments and sectors in which each segment and sectors of a pie chart forms a certain portion of the total(percentage). Tally marks are used to represent and count data. Hours in % In fraction. The horizontal axis represent the class intervals. Learn how to draw a pie chart correctly with our revision notes. It shows the proportion of each group at a glance. When the outcomes of an experiment are equally likely, the probability of an event is given by: To know more about Experimental Probability, visit here. The table shows the colours preferred by a group of people. Firefly Moonshine Apple Pie Flavor Whisky (1 x 0.75 l) 20,99€ 6: Whiskey and Apple Pie: 16,98€ 7: Whiskey Pie [Explicit] 1,29€ 8: Live at the Whiskey a Gogo 69: 9,44€ 9: Favorite Things Tacos Naps Tequila: Journal Notebook To Write In - Funny Taco and Tequila Book with Pie Chart (Pie Chart Series - Tacos Naps Tequila, Band 1) 6,45€ 10 Class 8 Maths Data Handling. Markdownish syntax for generating flowcharts, sequence diagrams, class diagrams, gantt charts and git graphs. The total value of the pie is always 100%. If the table is present with data, convert it into percentage as below. Overview Installation Change Log. In the class interval 60-70, 60 is the lower limit and 70 is the upper limit. If the total marks obtained by the students were 540, answer the following questions. Pie charts are also known as circle graphs. Hence, it should be used when you want to compare individual categories with the whole. To know more about Tally Marks, visit here. To know more about Pie Charts, visit here. $$P(E)=\frac{number\;of\;outcomes\;that\;make\;an\;event}{total\;number\;of\;outcomes\;of\;the\;experiment}$$ In tally marks, one vertical line is made for each count for the first four numbers and the fifth number is represented by a diagonal line across the previous four. After collection of data, it is necessary to represent data in a precise manner so that it is easily understood. Hallo und Herzlich Willkommen auf unserer Webpräsenz. Your email address will not be published. 93,98,87,65,75,77,67,88,67,97,72,73,75,90. Download free printable worksheets for CBSE Class 8 with important topic wise questions, students must practice the NCERT Class 8 worksheets, question banks, workbooks and exercises with solutions which will help them in revision of important concepts of Class 8. CBSE Class 8 Maths Notes Chapter 5 Data Handling Pdf free download is part of Class 8 Maths Notes for Quick Revision. Pie Charts ,Data Handling - Get topics notes, Online test, Video lectures, Doubts and Solutions for CBSE Class 8 on TopperLearning. Getting 1, 2, 3, or getting even numbers when a die is rolled is an event. Finally, calculate the degrees Therefore, the pie chart formul… For example, we can organise raw data using Frequency distribution table, Bar graphs etc. You will also love the ad-free experience on Meritnation’s Rs_aggarwal_(2018) Solutions. Pie chart panel for grafana. A Histogram is a type of bar diagram, where: To know more about Histogram, visit here. 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2021-02-26 10:39:23
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https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.centrality.edge_betweenness_centrality.html
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# edge_betweenness_centrality#
edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None)[source]#
Compute betweenness centrality for edges.
Betweenness centrality of an edge $$e$$ is the sum of the fraction of all-pairs shortest paths that pass through $$e$$
$c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}$
where $$V$$ is the set of nodes, $$\sigma(s, t)$$ is the number of shortest $$(s, t)$$-paths, and $$\sigma(s, t|e)$$ is the number of those paths passing through edge $$e$$ [2].
Parameters
Ggraph
A NetworkX graph.
kint, optional (default=None)
If k is not None use k node samples to estimate betweenness. The value of k <= n where n is the number of nodes in the graph. Higher values give better approximation.
normalizedbool, optional
If True the betweenness values are normalized by $$2/(n(n-1))$$ for graphs, and $$1/(n(n-1))$$ for directed graphs where $$n$$ is the number of nodes in G.
weightNone or string, optional (default=None)
If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight. Weights are used to calculate weighted shortest paths, so they are interpreted as distances.
seedinteger, random_state, or None (default)
Indicator of random number generation state. See Randomness. Note that this is only used if k is not None.
Returns
edgesdictionary
Dictionary of edges with betweenness centrality as the value.
betweenness_centrality
edge_load
Notes
The algorithm is from Ulrik Brandes [1].
For weighted graphs the edge weights must be greater than zero. Zero edge weights can produce an infinite number of equal length paths between pairs of nodes.
References
1
A Faster Algorithm for Betweenness Centrality. Ulrik Brandes, Journal of Mathematical Sociology 25(2):163-177, 2001. https://doi.org/10.1080/0022250X.2001.9990249
2
Ulrik Brandes: On Variants of Shortest-Path Betweenness Centrality and their Generic Computation. Social Networks 30(2):136-145, 2008. https://doi.org/10.1016/j.socnet.2007.11.001
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2022-05-28 05:31:41
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http://mathandmultimedia.com/2010/01/13/geogebra-sliders-tranformation/
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# GeoGebra Tutorial 7 – Sliders and Rotation
This is the seventh tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, please read the GeoGebra Essentials Series.
In the Graphs and Sliders posts (click here and here ), we have discussed how to use number sliders. In this tutorial, we use the Angle slider to rotate a triangle in order to show that its angle sum is 180 degrees. This is the same GeoGebra worksheet shown in my Parallel Lines and Transversals post, but we will change some of the labels. Although this tutorial is the seventh of the GeoGebra Tutorial Series.
Figure 1 – Rotated triangles using sliders.
Construction Overview
The construction will start by drawing line AB and constructing triangle ABC using the Polygon tool. Afterwards, we reveal the interior angle measures of the triangle and create two angle sliders namely $\alpha$ and $\beta$. Next, we rotate the triangle 180 clockwise about the midpoint of BC producing triangle A’B’C’ (see Figure 1-B). We then repeat the process, and rotate triangle A’B’C’ 180 degrees clockwise about the midpoint of A’C’ to produce A’’B’’C’’.
Part I – Constructing Triangle ABC
1.) Open GeoGebra and select Geometry from the Perspectives menu. 2.) Click the Line through Two Points tool, and click two distinct locations on the Graphics view to construct line AB. 3.) If the labels of the points are not displayed, click the Move tool, right click each point and click Show label from the context menu. 4.) Click the New Point tool and construct a point C not on line AB. 5.) Display the name of the third point. GeoGebra would automatically name it C, otherwise right click and rename it C. 6.) Click the Polygon tool and click the points in the following order: point A, point B, point C, and click again on point A to close the polygon. Your drawing should look like Figure 1. Figure 2 – Triangle ABC on line AB. 7.) Move the vertices of the polygon. What do you observe? 8.) Now we construct two angle sliders $\alpha$ and $\beta$. To do this, click the Slider tool, and click on the Graphics view. 9.) In the Slider dialog box (see Figure 3), choose the Angle radio button, and then leave the name angle as $\alpha$. In the Interval tab, choose 0° as minimum, 180° as maximum and 1°, and then click the Apply button when finished. Figure 3 – The Slider dialog box 10.) Using steps 8-9, create another slider with the same specifications shown in Figure 3 and name it $\beta$. You can find the Greek letters by pressing the $\alpha$ button located at the right of the text box. 11. ) We reveal the angle measures of the interior angles of the triangle, the change the colors of the angle symbols (green sectors). To do this, click the Angle tool and then click the interior of triangle ABC. 12.) We now hide the measures of the angles. To do this, right click each angle symbol and uncheck Show label from the context menu. 13. We set angle colors: angle A red, angle B blue and angle C green. To change the color of the angle symbol of angle A, right click the angle symbol (not point A) and click Object Properties from the context menu to display the Preferences window. 14. In the Preferences window, click the Color tab and choose the color you want from the color palette then click the Close button. 15. Change the color of angle B to blue and leave angle C as is. Your drawing should look line Figure 1-A after step 15.
Part II – Rotating the Triangle
We already have the sliders ready. The next thing that we will do is to rotate the triangle. The idea is to create a rotation point. Our choice would be the midpoint of BC. That is because if we rotate ABC by 180 degrees producing A’B’C’, angle A’C’B’ will be adjacent to angle ABC (see Figure 1-B). This is also the idea when we rotate A’B’C producing A’’B’’C’’.
.
1.) To construct D, the midpoint of BC, click the Midpoint or Center tool, and click side BC (the segment, not the points). 2.) Note that we want ABC to rotate around D $\alpha$ degrees clockwise. To do this, choose Rotate around a Point by Angle tool, click the interior of the triangle and click point D to reveal the Rotate Object dialog box. 3.) In the Rotate Object around Point by Angle dialog box, change the measure of the angle to $\alpha$, choose the clockwise radio button, and then click the OK button. Figure 4 – The Rotate Dialog Box 4.) Now move slider $\alpha$. What do you observe? 5.) Adjust slider $\alpha$ to 90 degrees, and show the labels of the vertices of the rotated triangle. (Refer to Part I – Step 3). 6.) While the triangle is still rotated 90 degrees, click the Angle tool and click the interior of triangle A’B’C’. Hide the labels of the angles symbols. 7.) Change the colors of the angle measures. Refer to Part I – Steps 13 through 15. Be sure that angle A and A’ have the same color, B and B’ have the same color, and C and C’ have the same color. Your drawing should look like the drawing in Figure 6. Figure 5 – The Rotated Triangle
Part III – Creating the Third Triangle
The idea of creating the third triangle is basically the same as that of creating the second triangle, so I will just enumerate the steps and left the construction as an exercise.
1. Get the midpoint of A’C’. (Refer to Part II Step 1)
2. Rotate triangle A’B’C’ $\beta$ degrees clockwise around the midpoint of A’C’. (Refer to Part II – Steps 2 – 3).
3. Reveal the labels of the vertices of the third triangle which is A’’B’’C’’. (Refer to Part II – Step 5 and Part I – Step 3).
4. Reveal the angle symbols of triangle A’’B’’C’’. (Refer to Part I – Step 11)
5. Hide the labels of the angle symbols, and change the colors of the angle symbols of triangle A’’B’’C’’. (Refer to Part I – Step 13-15)
The explanation of the theory behind this construction is in my Parallel Lines and Transversal post.
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3. Gavin
Very good. Thanks very much!
4. you are welcome, Gavin.
5. Sir, your website is very educational. i would like to know how long it takes to do something like the Sum of the angles of a triangle in GeoGebra.
• Well, it’s not that long. Three to 5 minutes maybe. Well, that actually depends on your GeoGebra skill. Try following the tutorials from Tutorial 1 though 5. Once you get the hang of it, it wouldn’t take that long.
6. Thanks a lot. That’s a wonderful tutorial. We all (regular visitors as well as one timers) appreciate your hard work and the time you spend preparing all these tutorials.
Carry on the good work.
• Thank you Sohael.
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9. Mickey D
Thanks again.
When I rotate teh triangles, the red/blue/green colours of the angle indicators are not maintained – i get 3 green ones again.
Perhaps because of the upgrade to Geogebra 4.
Not a problem – but I thought I’d mention it in case you intend to redo this lesson.
Really enjoying the tutorials – even though for classes i have produced more complex work already, this is a good way to make sure I am learning everything. Thanks
• Mickey D
Whoops – I posted that faster than I meant – all the praise remains, and the angle colour point is irrelevant as it is covered in your original text (now I have read further)!!
• Guillermo Bautista
@Mickey D.
Thank you.
You have to changed the colors of the angles of the rotated triangle manually. I’m not sure if I have mentioned it in the tutorial. I will check it as soon as possible.
10. Kelsey
Is there anyway to get the angle measures to show up in spreadsheet?
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2015-07-04 08:24:41
|
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|
https://ncatlab.org/nlab/show/A-infinity-algebra
|
# nLab A-infinity-algebra
Contents
### Context
#### Higher algebra
higher algebra
universal algebra
# Contents
## Idea
An $A_\infty$-algebra is a monoid internal to a homotopical category such that the associativity law holds not as an equation, but only up to higher coherent homotopy.
## Definition
###### Definition
An $A_\infty$-algebra is an algebra over an operad over an A-∞ operad.
## Realizations
### In chain complexes
Let here $\mathcal{E}$ be the category of chain complexes $\mathcal{Ch}_\bullet$. Notice that often in the literature this choice of $\mathcal{E}$ is regarded as default and silently assumed.
An $A_\infty$-algebra in chain complexes is concretely the following data.
A chain $A_\infty$-algebra is the structure of a degree 1 coderivation
$D : T^c V \to T^c V$
on the reduced tensor coalgebra $T^c V = \oplus_{n\geq 1} V^{\otimes n}$ (with the standard noncocommutative coproduct, see differential graded Hopf algebra) over a graded vector space $V$ such that
$D^2 = 0 \,.$
Coderivations on free coalgebras are entirely determined by their “value on cogenerators”, which allows one to decompose $D$ as a sum:
$D = D_1 + D_2 + D_3 + \cdots$
with each $D_k$ specified entirely by its action
$D_k : V^{\otimes k} \to V \,.$
which is a map of degree $2-k$ (or can be alternatively understood as a map $D_k : (V[1])^{\otimes k}\to V[1]$ of degree $1$).
Then:
• $D_1 : V\to V$ is the differential with $D_1^2 = 0$;
• $D_2 : V^{\otimes 2} \to V$ is the product in the algebra;
• $D_3 : V^{\otimes 3} \to V$ is the associator which measures the failure of $D_2$ to be associative;
• $D_4 : V^{\otimes 4} \to V$ is the pentagonator (or so) which measures the failure of $D_3$ to satisfy the pentagon identity;
• and so on.
One can also allow $D_0$, in which case one talks about weak $A_\infty$-algebras, which are less understood.
There is a resolution of the operad $\mathrm{Ass}$ of associative algebras (as operad on the category of chain complexes) which is called the $A_\infty$-operad; the algebras over the $A_\infty$-operad are precisely the $A_\infty$-algebras.
A morphism of $A_\infty$-algebras $f : A\to B$ is a collection $\lbrace f_n\rbrace_{n\geq 1}$ of maps
$f_n : (A[1])^{\otimes n}\to B[1]$
of degree $0$ satisfying
$\sum_{0\leq i+j\leq n} f_{i+j+1}\circ(1^{\otimes i}\otimes D_{n-i-j}\otimes 1^{\otimes j}) = \sum_{i_1+\ldots+i_r=n} D_r\circ (f_{i_1}\otimes\ldots f_{i_r}).$
For example, $f_1\circ D_1 = D_1\circ f_1$.
#### Rectification
###### Theorem
If $A$ is a dg-algebra, regarded as a strictly associative $A_\infty$-algebra, its chain cohomology $H^\bullet(A)$, regarded as a chain complex with trivial differentials, naturally carries the structure of an $A_\infty$-algebra, unique up to isomorphism, and is weakly equivalent to $A$ as an $A_\infty$-algebra.
More details are at Kadeishvili's theorem.
###### Remark
This theorem provides a large supply of examples of $A_\infty$-algebras: there is a natural $A_\infty$-algebra structure on all cohomologies such as
etc.
### In Topological space
An $A_\infty$-algebra in Top is also called an A-∞ space .
#### Examples
Every loop space is canonically an A-∞ space. (See there for details.)
#### Rectification
###### Theorem
Every $A_\infty$-space is weakly homotopy equivalent to a topological monoid.
This is a classical result by (Stasheff, BoardmanVogt). It follows also as a special case of the more general result on rectification in a model structure on algebras over an operad (see there).
### In spectra
A-∞ operadA-∞ algebra∞-groupA-∞ space, e.g. loop spaceloop space object
E-k operadE-k algebrak-monoidal ∞-groupiterated loop spaceiterated loop space object
E-∞ operadE-∞ algebraabelian ∞-groupE-∞ space, if grouplike: infinite loop space $\simeq$ ∞-spaceinfinite loop space object
$\simeq$ connective spectrum$\simeq$ connective spectrum object
stabilizationspectrumspectrum object
algebraic deformation quantization
dimensionclassical field theoryLagrangian BV quantum field theoryfactorization algebra of observables
general $n$P-n algebraBD-n algebra?E-n algebra
$n = 0$Poisson 0-algebraBD-0 algebra? = BD algebraE-0 algebra? = pointed space
$n = 1$P-1 algebra = Poisson algebraBD-1 algebra?E-1 algebra? = A-∞ algebra
## References
A survey of $A_\infty$-algebras in chain complexes is in
• Bernhard Keller, A brief introduction to $A_\infty$-algebras (pdf)
Classical articles on $A_\infty$-algebra in topological spaces are
• Jim Stasheff, Homotopy associativity of H-spaces I , Trans. Amer. Math. Soc. 108 (1963), p. 275-292.
A brief survey is in section 1.8 of
• Martin Markl, Steve Shnider, James D. Stasheff, Operads in algebra, topology and physics, Math. Surveys and Monographs 96, Amer. Math. Soc. 2002.
The 1986 thesis of Alain Prouté explores the possibility of obtaining analogues of minimal models for $A_\infty$ algebras. It was published in TAC much later.
Last revised on February 17, 2017 at 07:20:31. See the history of this page for a list of all contributions to it.
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2019-04-24 08:45:09
|
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|
https://tex.stackexchange.com/questions/347121/beamer-tikz-pgf-using-a-variable-math-calculations-as-part-of-a-file-na
|
Beamer / TIKZ / PGF: Using a Variable (Math / Calculations) as Part of a File Name for an External File
I want to indicate the progress of a beamer presentation using external pictures.
Let's say we are at slide 24 out of 200 slides then I want to display a picture called 12.png (24/200 = 12 %) on the current slide.
I am already able to manage to calculate the percentage of the progress but I can't use \pgfmathresult (\pgfmathprintnumber[precision=0]{\pgfmathresult}, which in my MWE gives the progress percentage of the current slide) as part of a file name (error ! Missing \endcsname inserted.).
I use the calc library of tikz/pgf to do the calculations.
In the MWE I input an external tex file in order to emulate inserting a picture.
\documentclass{beamer}
\usepackage{filecontents}
\begin{filecontents}{33.tex}
File with name \texttt{33.tex}.
\end{filecontents}
\begin{filecontents}{67.tex}
File with name \texttt{67.tex}.
\end{filecontents}
\begin{filecontents}{100.tex}
File with name \texttt{100.tex}.
\end{filecontents}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\pgfmathprintnumber[precision=0]{\pgfmathresult}\,\%
\end{description}
%
\input{33.tex}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\pgfmathprintnumber[precision=0]{\pgfmathresult}\,\%
\end{description}
%
\input{67.tex}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\pgfmathprintnumber[precision=0]{\pgfmathresult}\,\%
\end{description}
%
\input{100.tex}
\end{frame}
\end{document}
When you first compile the document then \inserttotalframenumber is 1 (One). So if you are on slide 3 (Three) then the current progress percentage is 300 (slide 3 out of 1). Therefore I use the min function to restrict the result of the calculation to be 100 at maximum.
Related
• Are you sticking to pgfmath... calculations? – user31729 Jan 4 '17 at 19:59
• @ChristianHupfer I do not. I just thought that pgf/tikz will be modern (state of the art) and easy to use. – Dr. Manuel Kuehner Jan 4 '17 at 20:08
• \pgfmathresult does not survive the group, that's the point – user31729 Jan 4 '17 at 20:09
• @ChristianHupfer Ok. As I said - I do not need to use pgfmath. Thanks for the help by the way. – Dr. Manuel Kuehner Jan 4 '17 at 20:10
This exploits expl3 features of easy calculation and storing values into a property list, the \prop_item:Nn command is expandable, whereas the expansion content of \pgfmathresult does not survive the description environment group, it will show 0.0 most likely.
The wrapper command \retrievepercentage is expandable as well then and can be used as argument to \input in order to generate the corresponding filename.
\documentclass{beamer}
\usepackage{filecontents}
\begin{filecontents}{33.tex}
File with name \texttt{33.tex}.
\end{filecontents}
\begin{filecontents}{67.tex}
File with name \texttt{67.tex}.
\end{filecontents}
\begin{filecontents}{100.tex}
File with name \texttt{100.tex}.
\end{filecontents}
\usepackage{tikz}
\usepackage{xparse}
\usetikzlibrary{calc}
\ExplSyntaxOn
\int_new:N \l_beamer_percentage_int
\prop_new:N \g_beamer_percentage_prop
\NewDocumentCommand{\getpercentage}{}{%
\prop_gput:NnV \g_beamer_percentage_prop {percentage} { \l_beamer_percentage_int }
}
\newcommand{\retrievepercentage}{%
\prop_item:Nn \g_beamer_percentage_prop {percentage}
}
\ExplSyntaxOff
\begin{document}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\getpercentage%
\retrievepercentage
\end{description}
%
\input{\retrievepercentage.tex}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\getpercentage%
\retrievepercentage
\end{description}
%
\input{\retrievepercentage.tex}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent]
\getpercentage%
\retrievepercentage
\end{description}
\input{\retrievepercentage.tex}
\end{frame}
\end{document}
Details of the solution.
As explained above, \pgfmathresult will not keep the result being stored in the description environment since this is TeX group.
A possible bypass would use an \xdef - based approach, say \xdef\foo{\pgfmathresult} which is a globally expanded definition, i.e. \foo will contain the value of \pgfmathresult at definition time.
I tried another strategy to calculate the result of the percentage with expl3 (the upcoming (;-)) LaTeX 3 format)
Let's look into the code...
\int_new:N \l_beamer_percentage_int
defines a new integer 'variable' (internally it is a TeX count register)
\prop_new:N \g_beamer_percentage_prop
defines a property list, which is something like expl3's version of a hash-table or array, i.e. key names can be defined and a value assigned to it.
evaluates (\fp_eval:n) the floating point (fp) expression with min(...) which looks equal basically to the pgfmath approach. After evaluation it is converted ('truncated') to an integer value, which is stored to the \l_beamer_percentage_int with \int_set:Nn.
The set-operation is not expandable, it can not be used in expansion chains, e.g. like in the generation of the filenames as requested here, but storing the value to property list is a possible way with
\prop_gput:NnV \g_beamer_percentage_prop {percentage} { \l_beamer_percentage_int }
this means: Globally put (gput) the Value (V) of \l_beamer_percentage_int into the list named \g_beamer_percentage_prop and assign it to key percentage.
Finally, calling the command \prop_item:Nn \g_beamer_percentage_prop {percentage} is the slower but expandable version of getting the stored value.
I refer to the description of texdoc interface3 for the details about the name conventions used in expl3.
• Thanks. Can you give me a resource hint where I can read about stuff like \prop and so on? It would be perfect if the solution also would work with \beamer@startpageofappendix (see tex.stackexchange.com/questions/141157). – Dr. Manuel Kuehner Jan 4 '17 at 21:07
• @Dr.ManuelKuehner texdoc.net/pkg/interface3 – Joseph Wright Jan 4 '17 at 21:09
• Better to use xparse to make a protected outer layer than using \newcommand :) – Joseph Wright Jan 4 '17 at 21:09
• It works perfectly. Can you elaborate the code a little bit? It all looks very unfamiliar to me :). – Dr. Manuel Kuehner Jan 5 '17 at 15:20
• @Dr.ManuelKuehner: No, not this way. You would overwrite the property value each time you're using retrievepercentage because \getpercentage recalculates the value again -- the values of the input for computing the percentage are lost outside however – user31729 Jan 7 '17 at 15:21
You can define an expandable command:
\begin{filecontents}{33.tex}
File with name \texttt{33.tex}.
\end{filecontents}
\begin{filecontents}{67.tex}
File with name \texttt{67.tex}.
\end{filecontents}
\begin{filecontents}{100.tex}
File with name \texttt{100.tex}.
\end{filecontents}
\documentclass{beamer}
\usepackage{xparse}
\ExplSyntaxOn
\DeclareExpandableDocumentCommand{\percentageofpresentation}{}
{
}
\ExplSyntaxOff
\begin{document}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent] \percentageofpresentation
\end{description}
%
\InputIfFileExists{\percentageofpresentation.tex}{}{NOT YET COMPUTED}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
\item[Progress in Percent] \percentageofpresentation
\end{description}
%
\InputIfFileExists{\percentageofpresentation.tex}{}{NOT YET COMPUTED}
\end{frame}
%% Start of Frame
\begin{frame}
\frametitle{Frame Title}
%
\begin{description}
|
2019-10-14 01:04:47
|
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|
http://eprint.iacr.org/2005/275/20050817:232701
|
Cryptology ePrint Archive: Report 2005/275
Explicit Construction of Secure Frameproof Codes
Dongvu Tonien and Reihaneh Safavi-Naini
Abstract: $\Gamma$ is a $q$-ary code of length $L$. A word $w$ is called a descendant of a coalition of codewords $w^{(1)}, w^{(2)}, \dots, w^{(t)}$ of $\Gamma$ if at each position $i$, $1 \leq i \leq L$, $w$ inherits a symbol from one of its parents, that is $w_i \in \{ w^{(1)}_i, w^{(2)}_i, \dots, w^{(t)}_i \}$. A $k$-secure frameproof code ($k$-SFPC) ensures that any two disjoint coalitions of size at most $k$ have no common descendant. Several probabilistic methods prove the existance of codes but there are not many explicit constructions. Indeed, it is an open problem in [J. Staddon et al., IEEE Trans. on Information Theory, 47 (2001), pp. 1042--1049] to construct explicitly $q$-ary 2-secure frameproof code for arbitrary $q$.
In this paper, we present several explicit constructions of $q$-ary 2-SFPCs. These constructions are generalisation of the binary inner code of the secure code in [V.D. To et al., Proceeding of IndoCrypt'02, LNCS 2551, pp. 149--162, 2002]. The length of our new code is logarithmically small compared to its size.
Category / Keywords: combinatorial cryptography, fingerprinting codes, secure frameproof codes, traitor tracing
Publication Info: International Journal of Pure and Applied Mathematics, Volume 6, No. 3, 2003, 343-360
Date: received 16 Aug 2005, last revised 17 Aug 2005
Contact author: dong at uow edu au
Available format(s): PDF | BibTeX Citation
Note: This is the revised version of the paper published in International Journal of Pure and Applied Mathematics, volume 6 no. 3, 2003, 343-360.
Short URL: ia.cr/2005/275
[ Cryptology ePrint archive ]
|
2016-09-28 13:06:21
|
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|
https://quantumcomputing.stackexchange.com/questions/7007/performing-a-measurement-in-the-standard-computational-basis-of-a-three-qubit-sy
|
# Performing a measurement in the standard computational basis of a three qubit system on two qubits
I often see written "and then we perform measurement in the standard computational basis" but I'm a little fuzzy on what this means as it's never stated what type of measurement we're supposed to take.
Firstly I know what the standard computational basis is and secondly I know that (usually) measurement is take using projective operators.
What I mean is , say we're given some circuit with three qubits for instance and in the circuit at the end is written the measurement symbol on the first and second wire but not the last then how do we know what projective operators to use ( I'm assuming that we have to use a complete set of measurement operators to get a full measurement ). There is no one complete set of measurement operators it all depends on what type of measurement you want to perform so in this case should we perform projective measurement on the end state with all of :
$$P_0 \otimes P_0\otimes I\\ \vdots\\ P_1 \otimes P_1\otimes I$$
Or
$$P_0 \otimes P_0\otimes P_0\\ \vdots\\ P_1 \otimes P_1\otimes P_1$$
Because I would assume that we use the first given that the circuit requires measurement on just the first two but then what becomes of the third qubit if we don't project as we would in the second set I listed. Its wavefunction won't collapse if we don't measure it so do we just discard it if the measurement is not stated for it? Otherwise, what do we do?
P.S. A little bit of a side note but if we want to perform a measurement in say, for example, the bell basis, then do we just take the density operator of the 4 bell states and treat them as projection operators?
How you perform the projection is exactly what you would normally do. If $$|\psi\rangle$$ is a 3-qubit state, you calculate, for example, the probability of getting the 00 result: $$p_{00}=\langle\psi|P_0\otimes P_0\otimes I|\psi\rangle,$$ and the state after measurement is $$\frac{P_0\otimes P_0\otimes I|\psi\rangle}{\sqrt{p_{00}}}.$$ You do not discard the third qubit. It does collapse somewhat - for example, had your initial state been $$(|000\rangle+|111\rangle)/\sqrt2$$, you get the 00 answer with probability 1/2, and the final state is $$|000\rangle$$.
• @bhapi Yes, unless you've already found that $\sum_ip_i=1$ for all the probabilities you've already calculated, because then you know all others have 0 probability. – DaftWullie Aug 14 at 8:59
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2019-11-17 15:50:08
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https://photonsphere.org/posts/2016-09-21-tongue.html
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# Tongue
A do-it-yourself i18n library for Clojure and ClojureScriptTongue (by Nikita Prokopov).
# From its documentation
Tongue is very simple yet capable:
• Dictionaries are just Clojure maps.
• Translations are either strings, template strings or arbitrary functions.
• It comes with no built-in knowledge of world locales. It has all the tooling for you to define locales yourself though.
• Pure Clojure implementation, no dependencies.
• Can be used from both Clojure and ClojureScript.
In contrast with other i18n solutions relying on complex and limiting string-based syntax for defining pluralization, wording, special cases etc, Tongue lets you use arbitrary functions. It gives you convenience, code reuse and endless possibilities.
As a result you have a library that handles exaclty your case well with as much detail and precision as you need.
# Earlier i18n posts
My earlier i18n related posts Lightweight i18n using DataScript and Lightweight i18n using re-frame are totally obsoleted by the Tongue library and should only be read for their amusement value (and perhaps some DataScript and re-frame background information).
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2020-12-05 17:44:50
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https://mathematica.stackexchange.com/questions/125759/callout-how-to-add-to-graphs
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# Description of Problem
Mathematica recently added Callout as a new labeling option. While I am preferential to using Tooltip, if one has to use the image in a presentation, it is nice to have labels. Further, while Placed allows one to designate where the label goes in respect to the vertex, I find that it does not exactly do so in a way that is easy to read - especially if some verticies are close together.
# Question
So how can one use Callout with Graph option VertexLabels to get a clean labeling of a directed graph?
Example:
A basic graph
simpleGraph = {1 \[DirectedEdge] 2, 2 \[DirectedEdge] 3, 3 \[DirectedEdge] 1, 1 \[DirectedEdge] 4, 4 \[DirectedEdge] 2};
Default labels
Graph[simpleGraph, VertexLabels -> "Name"]
Using Placed works
Graph[simpleGraph, VertexLabels -> Placed["Name", Above]]
Using Callout does not work
Graph[simpleGraph, VertexLabels -> Callout["Name", Above]]
Graph[{1 \[DirectedEdge] 2, 2 \[DirectedEdge] 3, 3 \[DirectedEdge] 1, 1 \[DirectedEdge] 4, 4 \[DirectedEdge] 2}, VertexLabels -> Callout[{1, 2, 3, 4}, {1, 2, 3, 4}, Above]]
# Example of Desired Output
Because this image is wide, we will just zoom up at one part of it
Ideal:
I know making a automated label function that minimizes textual overlap with vertices is hard, but hopefully there is a way to at least get text to not overlap.
Sample graph to practice on:
exampleGraph={17835 \[DirectedEdge] 17848, 17848 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 17845, 17845 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 5779, 5779 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 3931, 3931 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 3870, 3870 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 3554, 3554 \[DirectedEdge] 20967,
17835 \[DirectedEdge] 3403, 3403 \[DirectedEdge] 20967,
20967 \[DirectedEdge] 12657, 12657 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 9038, 9038 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 5779, 5779 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 3870, 3870 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 3637, 3637 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 3554, 3554 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 3367, 3367 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 1390, 1390 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 560, 560 \[DirectedEdge] 17835,
20967 \[DirectedEdge] 482, 482 \[DirectedEdge] 17835};
# An unsatisfying approach
Alternatively, a footnote like style would also be ok, e.g. a vertex has a number, and below the graph a table of number name pairs appears...
Functions
getVerticies[edgeList_] := Module[{vertexList = {}},
Table[AppendTo[
vertexList, {edgeList[[i]][[1]], edgeList[[i]][[2]]}], {i, 1,
Length[edgeList]}];
Return[DeleteDuplicates[Flatten[vertexList]]]
]
makeVertexLabels[vertexList_, labelList_] :=
Return[Table[
vertexList[[i]] -> Placed[labelList[[i]], Center], {i, 1,
Length[vertexList]}]];
makeEdgeLabels[edgeList_, labelList_] :=
Return[Table[
edgeList[[i]] -> Placed[labelList[[i]], "Middle"], {i, 1,
Length[edgeList]}]];
Variables
simpleGraph = {1 \[DirectedEdge] 2, 2 \[DirectedEdge] 3,
3 \[DirectedEdge] 1, 1 \[DirectedEdge] 4, 4 \[DirectedEdge] 2};
listOfVertexNames = {"One", "Fish", "Two", "Fish"};
listOfEdgeNames = {"Red", "Fish", "Blue", "Fish", "Octupus"};
Graph
Graph[simpleGraph,
VertexLabels ->
makeVertexLabels[getVerticies[simpleGraph],
Range[Length[getVerticies[simpleGraph]]]],
EdgeLabels ->
makeEdgeLabels[simpleGraph, Range[Length[simpleGraph]]]]
Table
verticies =
Prepend[Table[
Range[Length[getVerticies[simpleGraph]]][[i]] ->
listOfVertexNames[[i]], {i, 1, Length[listOfVertexNames]}],
"Verticies"]
edges = Prepend[
Table[Range[Length[simpleGraph]][[i]] -> listOfEdgeNames[[i]], {i,
1, Length[listOfEdgeNames]}], "Edges"]
Grid[{{Column[verticies]}, {Column[edges]}}, Alignment -> Left,
BaselinePosition -> Top]
Downsides: 1) I don't know how to guarantee that the vertex numbers fit inside the verticies. 2) nor do I know how to offset the edge labels sightly. 3) Requires more space for publications (because of the table), which means the graph has to be smaller.
• The simple answer is that Callout doesn't work with graphs. You have to implement such a display yourself. You can write to Wolfram and suggest adding the functionality. Sep 7 '16 at 9:49
• This is just personal opinion, but I find that your excessive use of headers and boldface harms the readability of your questions. I could skim them faster if you only highlighted what is truly important. Sep 7 '16 at 9:50
• @Szabolcs I followed your advise about quesiton layout. So how would one do that.... Sep 7 '16 at 10:13
• It depends on how nice you want it to look ... can you give a mock-up example? If it's sophisticated enough to make it worth doing, I don't expect it to be easy. I assume you want more than placing the label in a fixed position relative to the vertex and connecting it to the vertex with a line. It's a good question, just not easy to implement (in my opinion; maybe someone will surprise us) Sep 7 '16 at 10:18
• You could make the labels themselves graph nodes and set different styles on them. Use some force directed layout and try to enforce a minimal internode distance using its options. Finally verify that the positions are reasonable in the result. This might be worth a try for certain kinds of graphs. I am assuming that you don't just want to connect the label and node with a line, but you also want smart positioning (which Callout usually does). Sep 7 '16 at 12:15
One possible way is to ListPlot the vertex coordinates of the Graph object and Show the graph and list plot together:
gr=Graph[exampleGraph];
lp=ListPlot[Callout@@@Transpose[{GraphEmbedding[gr], VertexList[gr]}],
Axes->False, PlotStyle->None];
Show[gr, lp]
However ... without finer control on the Callout parameters, this is not much better than using VertexLabels->"Name":
Graph[exampleGraph, VertexLabels->"Name"]
Using labels as VertexShapeFunction gives a better picture:
Graph[exampleGraph, ImageSize -> 500, VertexShapeFunction -> "Name"]
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2021-09-21 12:02:58
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https://www.transtutors.com/questions/costing-questions-mal-de-mer-ltd-a-manufacturer-makes-and-sells-a-product-which-80085.htm
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# Costing questions: Mal de Mer Ltd, a manufacturer makes and sells a product which
1. Mal de Mer Ltd, a manufacturer makes and sells a product which has a variable cost of $30 and which sells for$40. The fixed cost is $700.00. If the quality of the product is x units, write the cost function (C ) and the revenue function (R) for the manufacturer. Which is the breakeven point for the manufacturer? 2. The ultrasonic technology company makes and sells two models of stereo systems; the basic model, CD20, and the advanced model, CD90. Each CD20 model makes a contribution of £25 and each CD90 model £30. It takes 150 minutes of production time and 30 minutes of assembly time for each CD20 and 120 minutes of production time and 40 minutes for assembly of CD90. Currently there is a maximum of 240 hours per week available in the production department and 60 hours in the assembly department. Let x units of CD20 and y units of CD90 to be produced. 3. The profit function is given by P= 2X² + 60X – 250, where X units is the quantity and P the total profit. Find the maximum profit and the number of units where the maximum profit occurs. Sketch the curve of the profit function. 4. A firm borrows$10000 from the bank at 8.5% per annum compounded semi-annually. If no reply merits are made, how much is owed after 4 years? 5. A company buys a computer for $125,000 and house it in a specially constructed suite at a cost of$20,000. (a) If the computer depreciates at 30% (reducing balance) and the suite appreciates at 6% (compound), what is the book value of suite and computer after 5 years? (b) Taking computer and suite together and using the reducing balance method, what is the overall depreciation rate? 6. A machine that costs $100,000 is expected to have life of 5 years and then a scrap value of$15000. If its expected net returns are year 1 $20000; year 2$50000; year 3 $35000; year 4$35000; year 5 \$35000, and projects of this type are expected to return at least 18% comment on whether the machine should be purchased. 7. Using the project in question 6, obtain also the NPV for a cost of interest of 10% and thus estimate the Internal Rate of Return.
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2018-12-16 12:29:58
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https://www.quantopian.com/posts/tackling-overfitting-via-cross-validation-over-quarters
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Tackling overfitting via cross-validation over quarters
Overfitting is probably the biggest potential pitfall in algorithmic trading. You work on a factor or algorithm that looks pretty good, you have some ideas to improve it so that it looks even better. Excitedly, you turn the algorithm on only to be dismayed when the out-of-sample performance doesn't look nearly as good as your backtest. We at Quantopian certainly observe this pattern a lot when evaluating algorithms for inclusion in the fund. If you want your algorithm to do well in the contest, you need to be very careful in this regard.
In this notebook you will learn a simple technique to detect if you overfit your factor or not, by splitting your data into odd and even quarters.
64
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Notebook previews are currently unavailable.
Disclaimer
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21 responses
@Thomas, Thanks for your work on this, it helps!
I looked this over a few times, and while I think I understand the concepts and the code, I'm not sure I understand the results...basically why the results are so different IN THIS CASE for the train vs the test...so here are some questions:
1. Holding out every other quarter is a potentially biased decision itself, as it could introduce some time-of-year bias(e.g. Even(Jan-Mar,July-Sept) vs. Odd(Apr-June, Oct-Dec)). So is the difference due to time-of-year bias?
2. OTOH...the two Quantile statistics metrics are close, whereas the Returns Analysis are not...what's up with that?
Even Quantiles Statistics
min max mean std count count %
1 -1.730268 -0.325803 -1.203210 0.267923 36123 20.019730
2 -1.025159 0.279893 -0.430024 0.295982 36072 19.991465
3 -0.415741 0.960416 0.336761 0.289696 36064 19.987031
4 0.371067 1.353257 0.993832 0.176791 36072 19.991465
5 1.063428 1.731804 1.474874 0.140226 36106 20.010308
Even Returns Analysis
10D
Ann. alpha 0.059
beta -0.113
Mean Period Wise Return Top Quantile (bps) 14.221
Mean Period Wise Return Bottom Quantile (bps) -27.574
Mean Period Wise Spread (bps) 41.794
Odd Quantiles Statistics
min max mean std count count %
1 -1.729265 -0.360678 -1.210830 0.260762 35387 20.023086
2 -1.059931 0.304455 -0.452029 0.292576 35328 19.989702
3 -0.439530 0.929758 0.318451 0.292419 35326 19.988570
4 0.288471 1.349952 0.983764 0.190968 35328 19.989702
5 1.074236 1.731799 1.477151 0.141219 35362 20.008940
Odd Returns Analysis
10D
Ann. alpha -0.008
beta -0.081
Mean Period Wise Return Top Quantile (bps) -7.183
Mean Period Wise Return Bottom Quantile (bps) 13.801
Mean Period Wise Spread (bps) -20.985
3. Bottom line, I don't know at this point whether the factor is flawed, as you suggest or there is an error in the way I'm looking at it.
Certainly, I can try and split the train-test sets temporally using other than odd/even quarters and see what happens(e.g. random quarters)...or I can try and explain why the statistics for a simple factor like momentum are so non-continuous...any ideas gladly taken!
alan
Can someone also demonstrate in backtest form?
Hi Thomas,
I think this is a novel idea and quite a stringent stress test of overfitting, so I thought I'd give it a test drive with an algo I have been working on lately. Cloned your notebook and keep same dates and replace the simple momentum factor with my alpha combination factor. Of course, I wouldn't want to giveaway my secret sauce, so I just cut and paste the relevant stats,
TRAINING
Quantiles Statistics
min max mean std count count %
factor_quantile
1 -2.726328 -0.827215 -1.470242 0.434959 34728 20.035539
2 -0.944471 -0.161090 -0.534089 0.188538 34643 19.986500
3 -0.281707 0.387344 0.064343 0.163708 34656 19.994000
4 0.274276 0.933425 0.609198 0.159646 34638 19.983615
5 0.844164 2.635445 1.333821 0.343627 34667 20.000346
Returns Analysis
10D
Ann. alpha 0.061
beta -0.229
Mean Period Wise Return Top Quantile (bps) 6.621
Mean Period Wise Return Bottom Quantile (bps) -20.563
Mean Period Wise Spread (bps) 27.184
Information Analysis
10D
IC Mean 0.020
IC Std. 0.112
Risk-Adjusted IC 0.178
t-stat(IC) 1.720
p-value(IC) 0.089
IC Skew 0.135
IC Kurtosis -0.087
TEST
Quantiles Statistics
min max mean std count count %
factor_quantile
1 -2.725484 -0.791198 -1.465107 0.425436 34006 20.029096
2 -0.932438 -0.143606 -0.539442 0.188026 33952 19.997291
3 -0.296662 0.372270 0.058329 0.165776 33933 19.986100
4 0.289199 0.920854 0.607867 0.159483 33949 19.995524
5 0.854588 2.642809 1.341129 0.345461 33943 19.991990
Returns Analysis
10D
Ann. alpha 0.021
beta -0.217
Mean Period Wise Return Top Quantile (bps) -5.305
Mean Period Wise Return Bottom Quantile (bps) 4.986
Mean Period Wise Spread (bps) -10.292
Information Analysis
10D
IC Mean 0.004
IC Std. 0.123
Risk-Adjusted IC 0.033
t-stat(IC) 0.312
p-value(IC) 0.755
IC Skew 0.188
IC Kurtosis -0.541
Turnover Analysis
10D
Quantile 1 Mean Turnover 0.281
Quantile 2 Mean Turnover 0.435
Quantile 3 Mean Turnover 0.481
Quantile 4 Mean Turnover 0.459
Quantile 5 Mean Turnover 0.319
10D
Mean Factor Rank Autocorrelation 0.762
I am not a big user of AlphaLens but understand the concepts and the stats. It seems to me that the results shows a case of not overfitting, at least on a 10 day forward returns. Would appreciate your comments and feedback, thanks.
It would be of interest to know how Q's lo beta, low vol market neutral algos have weathered the minor storm in the past few weeks. The FT reports some fairly poor performance from Long / Short hedge funds in general. It would be nice to think that all your hard work has paid off and that your shorts balanced out your longs or so that at least you have suffered a less than market decline.
Equally, I assume Q will have at least run its algos against the 2007/8 crisis.
In a market crash, what exactly does "market neutral" entail?
Let me clarify: Thomas, if the market were to decline 50% over the next two months, how would you hope your fund would perform? Not because I have any view on the matter but merely because I am putting together one or two algos based on fundamentals which I may or may not submit. Out of interest I willl run them through the 2007/8 period. How should I expect / hope my algo would behave?
How would YOU wish such an algo to behave in such conditions?
Cross validation over quarters may need to spread its wings rather more widely than looking at the past two years of bull markets?
Incidentally the platform seems to have come on leaps and bounds since I last took a serious look at it. Zipline and its related software is indeed a formidable weapon. You pipeline tutorials are excellent - a far remove from the days pipeline was first introduced.
Hi @Thomas,
Really great NB - thank you for putting it together and sharing it. Will help me quite a bit in my research.
I have a few questions as well:
1. Would training on even quarters every year be prone to 'over-training' on seasonal trends (e.g. sell-in-May, the January effect, etc), and if so, is there a better way of dividing up the training and testing sets?
2. I 'tweaked' your simple_momentum factor (quite a bit) to get the below figures on the 'training set' (all else in the NB is the same); I haven't run the 'testing set' yet.
Returns Analysis
10D
Ann. alpha 0.055
beta -0.032
Mean Period Wise Return Top Quantile (bps) 18.806
Mean Period Wise Return Bottom Quantile (bps) -20.839
Mean Period Wise Spread (bps) 39.645
Information Analysis
10D
IC Mean 0.026
IC Std. 0.080
Risk-Adjusted IC 0.320
t-stat(IC) 3.084
p-value(IC) 0.003
IC Skew 0.232
IC Kurtosis 0.682
Before I run and look at the 'testing set' output, how much 'variance tolerance' should I accept before I call it 'overfit'? For example, if I set my p-value cutoff on the 'testing set' to <0.05, I may say that this factor model is 'overfit' if the p-value is above 0.05 on the test set, correct?
However, if I do get a p-value of below 0.05 on the test set, how much variance of the below figures should I be able to 'tolerate' before I call the model 'overfit?':
• Mean IC
• Ann. Alpha
• Mean Period Wise Spread (bps)
@Alan:
1. I'll answer that below with Joakim's question.
2. The quantile statistics are not what you want to look at there. Those just tell how much data is in your quantiles and what range the quantiles cover, not what is actually happening to the stock returns. The way I constructed my factor here (ranking and then zscoring) the quantile stats are pretty meaningless because I know that by construction I will get uniform quantiles over a specific range. The thing to look for instead are the performance metrics like Alpha which is positive for even but negative for odd quarters. Same for mean IC. The mean returns of the quantiles is also nicely going from negative to positive for even but all over the place for odd.
3. As outlined in 2 it is bad, you want a factor that works rather evenly across time. Although that is very hard in general, if you find that your factor only works on the time-period you looked at but not your testing set, it's a pretty strong sign you overfit.
@Blue Seahawk: [How would one do that in a backtest?]
I don't think it's currently possible to do this in a backtest, unfortunately. However, I would treat the backtest just as a last step where you already know your factor works from the research env and alphalens. The backtest then is mainly to make sure it's not killed by turnover or has some other undesirable things like high exposures. Ideally you'd spend 90% time in research designing the factor and then when you're done run a single backtest to make sure it also works when actually placing trades. If you don't want to do that, you can just leave out the last 2 years when you run backtests and only test that time-period once at the very end. Personally I'm quite excited about the aspect that the factset fundamentals enforce a 1-year hold-out period we can use to evaluate the strategy over.
@James Villa: [Tried it on his own factor]
Thanks for trying this out! I think you already know this and just wanted to test it out, which is great, but I'll say it anyway: I guess you developed that factor already beforehand which renders this test less meaningful because you already tweaked it on the test-set - it can only be used once. Even then though, the factor doesn't seem to be significant (p-value) in either period. The mean returns of the top and bottom quantile also seems to flip in train and test which also is not a good sign.
@Zenothestoic: [Does being market neutral pay off for corrections like we just experienced?]
This is definitely a market period for which market-neutral was developed. In theory, the market tanks but because you are well hedged your portfolio should not be influenced. Those periods can even be especially lucrative because that's when opportunities open up. So I would hope that our fund would do especially well if the market were to drop 50%. Unfortunately, it seems that for most funds that hasn't been true in this most recent correction: https://twitter.com/robinwigg/status/1055802622739968000?s=21
Thanks for feedback, I agree that the tools have improved a lot, and even more good stuff is coming :).
@Joakim
Would training on even quarters every year be prone to 'over-training' on seasonal trends (e.g. sell-in-May, the January effect, etc), and if so, is there a better way of dividing up the training and testing sets?
This is similar to Alan's question above. I think the key thing to ask there is whether you designed your factor to exploit any of these effects. If it does exploit seasonal patterns than this type of testing might not be the right choice. However, if that's not the case there is no good reason it should behave in this way. Probabilistically speaking, the probability that the factor is overfit is much higher in that case. Finally, would you even want a factor that only works in these certain time-periods? We certainly wouldn't. Having said all that, you could also sample your quarters randomly if it's a concern, or flip every year from even to odd.
I 'tweaked' your simple_momentum factor (quite a bit) to get the below figures on the 'training set' (all else in the NB is the same); I haven't run the 'testing set' yet.
Thank you, that is excellent. Yes, this looks like it could be a great factor just from looking at the stats, which makes it an even better example. I like your proposal of also looking for p < .05 for the test set performance.
@all
One question a few of you touch on is how to actually say one way or the other. Certainly if the factor performance goes from positive to negative between train and test it should be rather obvious, but what if it's not as clear cut? What if it's still positive but maybe not quite as much. This is something I haven't done too much thinking / experimenting with yet, so I hope I will have a better answer at some point. For now, probably the simplest thing which sounds very reasonable is to require the p-value to be < 0.05 in both periods, as suggested by Joakim.
Hi Thomas,
Thanks for your feedback. As I mentioned, I'm not a big user of AlphaLens mainly because metrics like t-stats and p-values are based on assumptions that the time series are stationary with normal distributions and are measured as such. For financial time series, I don't think these assumptions hold true and that is why I really don't pay much attention to those metrics. The novelty of your idea in splitting training and testing of factors (tweaked or untweaked) between odd and even quarters in a "no more excuses" outcome. Having said this, I actually just look at one metric, Ann. Alpha. What I want to know is if the factor will make money on both the even and odd quarters , formatted as train and test. If it does, chances are the factor is not overfitted, provided one has a long enough dataset to analyze. I'm just an ordinary Joe with a simple mind that just looks at the bottom line. I still see the utilty of your routine and for me, it is a validation mechanism.
@James: Yeah, p-values are less than ideal here, although we do report other statistics to say how non-normal the data is (skew, kurtosis). Using Ann. Alpha should work just as well but I would set a predefined threshold before evaluating on the test set and being self-disciplined about the outcome.
Thanks @Thomas,
I decided I was done 'training' the factor, so ran the 'test set' to see how overfit it might be (see below). Looks like it was quite overfit? So, now that I've looked at the test set data, I should 'throw away' this factor (since it was overfit) and try something quite different? Unless I've held out more data that I could test on again?
One thing I find very strange is the Turnover Analysis. I didn't include it earlier, but it was all 0.0 for all the quantile's mean Turnover, and 1.0 for AutoCorrelation in the 'training set' (see very bottom). I didn't include it earlier because I thought that might be 'normal' for a Momentum type factor with 10D holding period. However, the result from the 'test set' was quite different, which seems quite odd to me and makes me a bit suspicious...
Returns Analysis (Test set)
10D
Ann. alpha 0.009
beta -0.045
Mean Period Wise Return Top Quantile (bps) 0.821
Mean Period Wise Return Bottom Quantile (bps) 2.573
Mean Period Wise Spread (bps) -1.751
Information Analysis (Test set)
10D
IC Mean 0.007
IC Std. 0.083
Risk-Adjusted IC 0.081
t-stat(IC) 0.769
p-value(IC) 0.444
IC Skew 0.011
IC Kurtosis -0.462
Turnover Analysis (Test set)
10D
Quantile 1 Mean Turnover 0.604
Quantile 2 Mean Turnover 0.729
Quantile 3 Mean Turnover 0.722
Quantile 4 Mean Turnover 0.741
Quantile 5 Mean Turnover 0.557
10D
Mean Factor Rank Autocorrelation 0.365
Turnover Analysis (Training set)
10D
Quantile 1 Mean Turnover 0.0
Quantile 2 Mean Turnover 0.0
Quantile 3 Mean Turnover 0.0
Quantile 4 Mean Turnover 0.0
Quantile 5 Mean Turnover 0.0
10D
Mean Factor Rank Autocorrelation 1.0
@Joakim: Yes, quite overfit. Personally I would expect most ideas not to work but can be made to look good by tweaking. Now, however, you can tell when you're fooling yourself quicker and work on more promising ideas instead.
And yes, the turnover issue looks very weird so I investigated. Turns out the turnover calculation is wrong here due to a bug (https://github.com/quantopian/alphalens/issues/323) and can thus not be trusted. The factor is doing the right thing, it's just not shown correctly.
Unfortunately not all ideas however good will work all the time. We have seen this very clearly over the years where fashion seems to dictate which factors will lead to out-performance in different periods. All things are driven by fundamentals at the end of the day but look at the varying fortunes of value stocks over time.
Yes, most things will turn out to be temporary fads or curve fit anomalies. What we can count on in the very long term is increasing earnings per share coupled with a strong balance sheet to drive share price. Which in turn depends on a robust economy in the geographical area or areas where the company makes its sales.
Without those two fundamental factors (or three including the general economy) you can forget long term share price appreciation.
As regards Long / Short, the big question I have is "was Alfred Jones right?"
In fundamental terms those stocks with good earnings increases and strong balance sheets should outperform those with the reverse. In the long term.
It would be foolish however to imagine they will do so every quarter or year. I suspect it would also be over optimistic to expect a long short model built on such principals to retain a lack of correlation to the general market in a crash where the baby is inevitably thrown out with the bathwater.
But I will use your excellent platform to attempt to prove myself incorrect.
@Zenothestoic: For the long term, I'm with you, but for shorter time-periods you would expect cognitive biases like herd behavior, loss aversion etc to be present, no?
Thomas
I agree that it is over the long term that value holds out. I agree that in the shorter term other factors can reign supreme for a while. The problem is that benefiting from such shorter term factors then becomes a matter of of luck or "market timing" - the latter two may amount to the same thing.
In the long term long short / market neutral may have great validity if based on the correct fundamental factors. It may be as good as Alfred Jones thought it was; in theory at least.
And of course "short term" can seem a long time in the context of a traditional career span of say 25 years. Take the success of the commodity trend followers who had a good run for many year before (perhaps) their trade was spoiled by sheer weight of competition.
Of course short term can also be just that - a couple of years. Take the guys who profited so handsomely but so briefly from the Big Short. Atradis went from a small player to the biggest hedge fund manager in Singapore. Its managers made hundreds of millions from fees. But they turned out to be a one trick pony and their fund lost 60% one year after the crisis and closed.
I think your aims at Q are entirely correct in a sense. You are looking to eschew short term-ism and are looking to run with something you hope makes sense "forever". In bull and bear markets. I have never been comfortable with leverage but leaving that aside it may be you are creating something with as much long term utility as the basic stock index. Hats off to you.
So in a way it all depends on what type of investor you are. If you are a pension fund, even 25 years may be short term. If you are a hedge fund manager looking to profit personally from a quick buck for a few years from management and performance fees then it makes sense to be short term. IF you are lucky. If your strategy hits the right market at the right time.
And of course it may be that you are looking to patch together or use many shorter term factors in your long short trading which, in aggregate, you hope will give longevity. But in that case there is the age old question of when to abandon a strategy.
At least if you know the strategy/ factor is in tune with the very long term, it may go out of fashion temporarily but you are pretty sure it holds over the long and very long term.
I hope this makes sense. As ever I fear my rambling tends almost more towards philosophy than day to day investment.
Thanks @Thomas,
I'm curious if you've tested the NB on a factor that is 'known' (or at least very unlikely) not to be overfit? E.g. perhaps the ExtractAlpha factor?
If not, how can we be sure that the NB is working as intended? I'm only asking because I tend to get 'too good' results on the 'train set' and 'too bad' results on the 'test set' on all factors I've tested so far. Perhaps they are all overfit, but how can I be sure that the NB actually does work as intended on factors that are not overfit?
Just a suggestion, but a good QA process might be to write a test case (with expected results) for both a factor that is 'known' to be overfit, and another test case for a factor that is 'known' to not be overfit, and then compare the actual test results with the expected results in each test case?
@Joakim: I have not. If you use this test on existing factors it's more of a stability test, rather than an overfitting on. Remember, it's only a test-set if you haven't used it before. Something that we know works well, like ExtractAlpha, will do well in this test but be useless because the author had access to the time-period in our testing set. It is a bit surprising though that all your factors seem to fail that test. At the least, if you pass in factors that you already developed using the whole time period, performance on train and test should be similar (or rather, random as to which set it performs better on).
I think you provided the perfect test case above where you tweaked my factor to where it looked great on train but then failed on test.
@Thomas,
Rightio, fair enough. I actually only tried the NB on two of my factors (both of which I had used most of this period to 'train' them), and got a bit depressed (and gave up) when they both failed the 'test set'.
However, I just tried on two other factors (also 'trained' and 'known' to work quite well during this period) and they both passed the 'test set' with flying colors (roughly 10D Mean IC of 0.03 with p-value of 0.001 for both of them, both during the 'train' and 'test' sets). This makes me 'trust' that the NB does indeed work as intended (even though both factors were already 'trained' on the full period).
Thanks again for the NB and taking the time to answer my questions. It will help me quite a bit when researching and testing new factors going forward.
Hi Thomas,
If we analyzed the factor year over year from training to test wouldn't our conclusion be different than that presented in the notebook. I am assuming the odd and even quarters in a year probably average out (when summed together) to some kind of medium'ish metric for all years in AL.
Would be helpful to know how Quantopian sees the difference between overfitting that you are tackling in this thread and hypothesis testing that you referred to in this thread Alternative Test For Overfitting
Thanks.
Leo
Sorry, another question. In the attached notebook are you testing a hypothesis (a definition of momentum) or illustrating an overfit factor. The reason I am asking the question is because, I didn't see any of the steps in the notebook that can be considered as overfitting as defined in this post portfolio structure and overfitting although you have mentioned that one could try to improve the factor. It appears the raw factor itself is predictive only in some quarters and one cannot make any conclusions with confidence about any improvements to the factor as having overfit if the factor is not predictive to start with in the test set and highly predictive in the training set without any changes.
Leo: The idea is that you iteratively improve the factor on the train set (this is implicit in the NB). By doing so it will probably start to look pretty good, but you might have just overfit. Then you run it on testing and if it doesn't do as well there, you know that you overfit. The factor is just for illustrative purposes.
Thomas, thanks for clarifying that the factor is for illustrative purposes.
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2019-04-18 14:28:29
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https://paperswithcode.com/paper/image-compressive-sensing-recovery-using
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# Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization
30 Apr 2014Jian ZhangChen ZhaoDebin ZhaoWen Gao
From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance... (read more)
PDF Abstract
No code implementations yet. Submit your code now
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2020-09-24 18:46:39
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https://adunumdatum.org/post/kepass2-kpscript-installation-on-linux/
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# KeePass2 KPScript Installation on Linux
I recently wrote about extending the functionality of the KeePass2 password manager to allow the creation of CSV files from KeePass2 password database files. KeePass2 has a wide variety of functionality built in, and has a straightforward GUI.
GUI = Graphical User Interface
It also comes with an extension, called kpscript, that adds a robust CLI.
CLI = Command-Line Interface
Installing KPScript in Linux was confusing to me, so I’m posting quick instructions here, hoping that they might be useful to someone coming to this site from a search engine in the future.
These instructions are derived from a working PKGBUILD for Arch Linux by Jonathan Liu in the Arch User Repository (AUR). I’ve expanded them to work for other Linux distributions, as well; I tested the instructions in openSUSE 13.1, but they should work anywhere. They might even work in Mac OSX.
# Initial information-gathering
1. Having installed KeePass through your distro. repository, run which keepass in a terminal to see where the keepass program file is stored on your system. In openSUSE 13.1, the location is /usr/bin/keepass.
2. If you use that location and run cat with it (e.g., cat /usr/bin/keepass), you’ll likely see that, rather than being a binary file, usr/bin/keepass is actually a shell script with one line:
exec mono /usr/lib/keepass/KeePass.exe "$@" (“$@” here represents all of the arguments that the user types in after the keepass command [e.g., keepass --help])
What we’re looking for here is the location of KeePass.exe — here, /usr/lib/keepass/KeePass.exe. In some distros, this will be in usr/share/keepass/KeePass.exe, instead.
If that method doesn’t work on your system, you can launch KeePass2, open a terminal, and run ps ax | grep keepass, which will search all running processes on your system and give you output similar to what’s above (e.g., mono /usr/lib/keepass/KeePass.exe).
The kpscript documentation states that “the KPScript.exe file needs to be copied into the directory where KeePass is installed (where the KeePass.exe file is).”
# Now that you have the location of KeePass.exe, you can install kpscript
2. “Install” KPScript.exe using the following commands (assuming that the directory of note above was /usr/lib/keepass):
sudo install -D -m644 KPScript.exe "/usr/lib/keepass/KPScript.exe"
echo '/usr/bin/mono /usr/lib/keepass/KPScript.exe "$@"' > /tmp/kpscript sudo install -D -m755 /tmp/kpscript "/usr/bin/kpscript" You should now be able to run kpscript from any new terminal. You can launch kpscript commands and have them ask for your KeePass2 password / key using the KeePass GUI password prompt using kpscript /path/to/KeePass2_file.kdbx -guikeyprompt -c:ListGroups (-c: gives kpscript a command to run — here, after entering your password, kpscript would list all password groups in your .kdbx file. If you are planning to run kpscript over a server, where you won’t have access to a GUI prompt, you are expected to enter your password in plain text as part of your kpscript invocation (e.g., with kpscript /path/to/KeePass2_file.kdbx -guikeyprompt -c:ListGroups -pw:"your_password_goes_here"). If you are uncomfortable with that, here is a bash script that prompts for the password in a more secure way (i.e., without showing it as you type it in): #/bin/bash read -s -p "If your database has a password, enter it here (it will be passed to kpscript with the '-pw' flag). Otherwise, just press [Enter]: " user_password if [ ! -z "$user_password" ]; # If the user entered anything (if $user_password is NOT zero-length (i.e., blank)): then kpscript -pw:$user_password "$@" else kpscript "$@"
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2019-01-18 19:43:16
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https://www.physicsforums.com/threads/mixed-parallel-series-rlc-circuit.612637/
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# Mixed parallel & series RLC circuit
## Homework Statement
pic: www(dot)freeimagehosting.net/hbnem
Calculate impedance , current and power factor
## The Attempt at a Solution
pic: www(dot)freeimagehosting.net/xmy2b
First we solve parallel part. In parallel resistor and inductor are sharing voltage. Using phasor diagrams we found vector I_1 which is current in parallel part. Series circuit share current so I have attached phasor diagram for capacitor to I_1 (as you can see). Now i need to find vector V_S which is V_C + V_R. But i dont know how to find it.
(sorry for the pics)
Related Introductory Physics Homework Help News on Phys.org
Hi mrmlica. Not too sure what you're trying to do, but the equivalent impedance of a parallel circuit is just: $\frac{1}{Z_p}=\frac{1}{Z_1}+\frac{1}{Z_2}+....$ and for series is: $Z_s=Z_1+Z_2+...$. Where Z is the complex impedance, Z_n is the n'th component in the given circuit, s=series & p=parallel. To find the current you use Ohm's law as you know the input voltage and the impedance. The power factor is the cosine of the phase angle between the current and the voltage. The tangent of the phase angle can be found from the argument of the complex impedance.
Hi mrmlica. Not too sure what you're trying to do, but the equivalent impedance of a parallel circuit is just: $\frac{1}{Z_p}=\frac{1}{Z_1}+\frac{1}{Z_2}+....$ and for series is: $Z_s=Z_1+Z_2+...$. Where Z is the complex impedance, Z_n is the n'th component in the given circuit, s=series & p=parallel. To find the current you use Ohm's law as you know the input voltage and the impedance. The power factor is the cosine of the phase angle between the current and the voltage. The tangent of the phase angle can be found from the argument of the complex impedance.
I wasnt hoping for that good help. You didnt just solve me task, you learn me new diffrent way to look on AC current. Thank you alot.
Last edited:
You're welcome. I'm glad I could help you with the problem in a different method to what you normally do. If you're finding any difficulty with my method just ask any questions you want to.
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2020-07-07 10:33:09
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https://pretextbook.org/doc/guide/html/section-181.html
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## Section37.4LaTeX Font Configuration (Ubuntu/Debian Linux)
Actual font installation is missing here, since I (RAB) cannot recall just when or how certain fonts arrived on my system. Certainly they were almost all via Ubuntu/Debian packages, though they could have been specific to Live. Specifically, the texlive-fonts-recommended and texlive-fonts-extra are two packages that will make many fonts available to / on an Ubuntu/Debian system. The following is offered in the hope that it will be useful to other publishers on other Unix-like systems.
There is a system directory
/etc/fonts/conf.d
with a wide variety of configuration files for various fonts, or collections of fonts. Here I find files (symlinks, really)
65-fonts-lmodern.conf
65-fonts-texgyre.conf
The first points to the extensive Latin Modern fonts, which are an improved version of the original Computer Modern fonts, and are PreTeXt's default font for out-of-the-box . We have never had a report of these not being available in an author's distribution. The file indicates that the fonts can be found at
/usr/share/texmf/fonts/opentype/public/lm
/usr/share/texmf/fonts/opentype/public/lm-math
The second configuration file points to multiple fonts from the TeX Gyre Collection 1 of GUST: Polska Grupa Użytkowników Systemu . Examining the file indicates these fonts can be found at:
/usr/share/texmf/fonts/opentype/public/tex-gyre
/usr/share/texmf/fonts/opentype/public/tex-gyre-math
www.gust.org.pl/projects/e-foundry/tex-gyre/
As of 2019-11-09 these were the only fonts known to my system in OTF format. This despite having directories full of fonts at:
/usr/share/texlive/texmf-dist/fonts/opentype
/usr/share/texlive/texmf-dist/fonts/truetype
and more. You might have similar directories with the year of your version of Live as a directory. The solution is to create a new file (as root) named
/etc/fonts/conf.d/09-texlive-fontconfig.conf
with contents
<?xml version="1.0"?>
<!DOCTYPE fontconfig SYSTEM "fonts.dtd">
<fontconfig>
<dir>/usr/share/texlive/texmf-dist/fonts/opentype</dir>
<dir>/usr/share/texlive/texmf-dist/fonts/truetype</dir>
</fontconfig>
and then running fc-cache -f -v to update what fonts are known to the system. It is possible that you can put this file somewhere in your home directory if you do not have administrative access, but we have not tested that approach. Note that some versions of the above file that you might find online will include a type1 directory. It is best to not include this directory, since these fonts are best used only with pdflatex and if known to the system they can mistakenly be incorporated by xelatex, with disasterous results. Typically you will get an unusable PDF and your xelatex run will have the error message
xdvipdfmx:fatal: pdf_ref_obj(): passed invalid object
near the very end of the command-line output.
Apparently, the texlive-fontconfig.conf file is not distributed with Debian Linux as this search 2 will demonstrate. Please report any change in this situation.
packages.debian.org/search?arch=any&mode=filename&searchon=contents&keywords=fontconfig.conf
When installing the Open Dyslexic font via an Ubuntu package (2020-04-28), xelatex became confused by the presence of Web Open Font Format (WOFF) versions which were installed along with the OTF versions. The solution is to create a new file (as root) named
/etc/fonts/conf.d/70-no-woff.conf
with contents
<fontconfig>
<selectfont>
<rejectfont>
<glob>/usr/share/fonts/woff/*</glob>
</rejectfont>
</selectfont>
</fontconfig>
and then running fc-cache -f -v to update what fonts are known to the system. See the tex.stackexchange.com 3 post.
tex.stackexchange.com/questions/392144
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2021-12-01 18:16:00
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https://www.physicsforums.com/threads/taking-derivatives.336929/
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# Taking derivatives
1. Sep 13, 2009
### joemama69
1. The problem statement, all variables and given/known data
x = $$\sqrt{(10t-3)^{2} + (2t)^{2}}$$
Find the derivative
2. Relevant equations
3. The attempt at a solution
x = $$\sqrt{(10t-3)^{2} + (2t)^{2}}$$
x = $$\sqrt{(104t^{2} - 60t + 9}$$
dx = $$\frac{1}{2\sqrt{104t^{2} - 60t + 9}}$$(208t-60)
dx = $$\frac{208t-60}{2\sqrt{104t^{2} - 60t + 9}}$$
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Sep 13, 2009
### njama
That's correct.
You can divide both nominator and denominator with 2.
3. Sep 13, 2009
### LCKurtz
But what you computed isn't dx. In your equations you should have
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2017-11-25 08:27:57
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https://www.examveda.com/in-how-many-ways-can-3-men-and-their-wives-be-made-stand-in-a-line-such-that-none-of-the-3-men-stand-in-a-position-that-is-ahead-736/
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Examveda
# In how many ways can 3 men and their wives be made stand in a line such that none of the 3 men stand in a position that is ahead of his wife?
A. $$\frac{{6!}}{{3! \times 3! \times 3!}}$$
B. $$\frac{{6!}}{{2! \times 2!}}$$
C. $$\frac{{6!}}{{2! \times 2! \times 2!}}$$
D. $$\frac{{6!}}{{2! \times 3!}}$$
### Solution(By Examveda Team)
6 people can be made to stand in a line in 6! Ways.
However, the problem introduces a constraint that no man stands in a position that is ahead of his wife.
For any 2 given positions out of the 6 occupied by a man and his wife, the pair cannot rearrange amongst themselves in 2! Ways as the wife has to be in a position ahead of the man. Only one of the 2! arrangements is allowed.
As there are 3 couples in the group, the total number of ways gets reduced by a factor of
(2! × 2! × 2!)
Hence, the total number of ways,
= $$\frac{{6!}}{{2! \times 2! \times 2!}}$$
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2022-12-06 13:53:00
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https://brilliant.org/problems/seems-like-saturn-1/
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# Seems like Saturn
Electricity and Magnetism Level 4
At the origin of $$xyz$$ coordinates there is a solid sphere with radius $$r$$ and charge density $$\rho$$. Around it, on $$xy$$ plane, there is a ring with radius $$R$$ and charge density $$\lambda$$. If the magnitude of total electric field at $$P(0,0,H)$$, such that $$H>r$$, can be written as $\dfrac{\rho \cdot r^3}{a\cdot H^2 \cdot \epsilon_{0}}+\dfrac{\lambda \cdot H\cdot R}{b\cdot (R^2+H^2)^{\frac{3}{2}} \cdot \epsilon_{0}}$ Find the value of $$a+b$$
×
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2016-10-28 10:34:45
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https://www.global-sci.org/intro/article_detail/jcm/8914.html
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Volume 20, Issue 3
The Solvability Conditions for Inverse Eigenvalue Problem of Anti-Bisymmetric Matrices
DOI:
J. Comp. Math., 20 (2002), pp. 245-256
Published online: 2002-06
Preview Full PDF 161 1747
Export citation
Cited by
• Abstract
This paper is mainly concerned with solving the following two problems: Problem I. Given X \in C_n \times m, \Gamma = diag(\lambda1, \lambda2, \dots, \lambda m) \in Cm\times m. Find A \in ABSRn\times n such that where ABSRn\times n is the set of all real n \times n anti-bisymmetric matrices.
• Keywords
Eigenvalue problem Norm Approximate solution
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2021-02-25 05:58:23
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http://www.wikihow.com/Calculate-Interest
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Edit Article
# wikiHow to Calculate Interest
Most people are aware of the concept of interest, but not everyone knows how to calculate it. Interest is the value that we add to a loan or a deposit to pay for the benefit of using someone else’s money over time. Interest can be calculated in three basic ways. Simple interest is the easiest calculation, generally for short term loans. Compound interest is a bit more complicated and a bit more valuable. Finally, continuously compounding interest grows at the fastest rate and is the formula that most banks use for mortgage loans. The information you need for any of these calculations is generally the same, but the math is a bit different for each.
### Method 1 Calculating Simple Interest
1. 1
Determine the principal. The principal is the amount of money that you will use to calculate the interest. This could be an amount of money that you deposit into a savings account or bond of some kind. In that case, you will be earning the interest that you calculate. Alternatively, if you borrow money, such as a home mortgage, the principal is the amount that you borrow, and you will calculate interest that you owe.
• In either case, whether you will be collecting the interest or paying the interest, the amount of the principal is generally symbolized by the variable P.[1]
• For example, if you have made a loan to a friend of $2,000, the principal loaned would be$2,000.
2. 2
Determine the interest rate. Before you can calculate how much your principal will appreciate, you need to know by what rate your principal will grow. This is your interest rate. The interest rate is generally advertised or agreed upon between the parties before the loan is made.[2]
• For example, suppose you loaned money to a friend under the understanding that at the end of 6 months your friend would pay you back the $2,000 plus 1.5%. The one-time interest rate is 1.5%. But before you can use the rate of 1.5% you must convert it to a decimal. To change percent to a decimal, divide by 100: • 1.5% ÷ 100 = 0.015. 3. 3 Measure the term of the loan. The term is another name for the length of the loan. In some cases, you will agree to the length of the loan when you borrow it. For example, most mortgages have a defined term. For many private loans, the borrower and lender may agree to any term they wish. • It is important that the length of the term match the interest rate, or at least be measured in the same units. For example, if your interest rate is for a year, then your term should be measured in years as well. If the rate is advertised as 3% per year, but the loan is only six months, then you would calculate a 3% annual interest rate for a term of 0.5 years. • As another example, if the rate is agreed to be 1% per month, and you borrow the money for six months, then the term for calculation would be 6. 4. 4 Calculate the interest. To calculate interest, multiply the principal by the interest rate and the term of the loan. This formula can be expressed algebraically as: • ${\displaystyle I=P*r*t}$ • Using the above example of the loan to a friend, the principal (${\displaystyle P}$) is$2,000, and the rate (${\displaystyle r}$) is 0.015 for six months. Because the agreement in this example was for a single term of six months, the variable ${\displaystyle t}$ in this case is 1. Then calculate the interest as follows:
• ${\displaystyle I=Prt=(2000)(0.015)(1)=30}$. Thus, the interest due is $30. • If you want to calculate the amount of the full payment due (A), with the interest and the return of the principal, then use the formula ${\displaystyle A=P(1+rt)}$. This calculation would look like: • ${\displaystyle A=P(1+rt)}$ • ${\displaystyle A=2000(1+.015*1)}$ • ${\displaystyle A=2000(1.015)}$ • ${\displaystyle A=2,030}$ 5. 5 Try another example. Just for more practice, suppose you deposit$5,000 in a savings account with a 3% annual interest rate. After only three months, you withdraw the money and any interest due at that time.
• ${\displaystyle A=P(1+rt)}$
• ${\displaystyle A=5000(1+.03*0.25)}$
• ${\displaystyle A=5000(1.0075)}$
• ${\displaystyle A=5037.5}$
• In three months, you would earn $37.50 interest. • Note that t=0.25 here, because three months is one-fourth (0.25) of the original one year term. ### Method 2 Calculating Compound Interest 1. 1 Understand the meaning of compound interest. Compound interest means that as your interest is earned, the interest goes back into the account, and you begin earning (or paying) interest on top of interest. As a simple example, if you deposit$100 at 5% interest per year, then at the end of one year you will earn $5 interest. If you return that to the account, then at the end of the second year, you will earn 5% of$105, not just the original $100. Over time, this can increase quite substantially.[3] • The formula for calculating the value (A) of compounding interest is: • ${\displaystyle A=P(1+{\frac {r}{n}})^{nt}}$ 2. 2 Know the principal amount. As with simple interest, the calculation begins with the amount of the principal. The calculation is the same, whether you are calculating interest on money borrowed or money loaned. The principal amount is generally denoted with the variable ${\displaystyle P}$.[4] 3. 3 Measure the rate. The interest rate must be agreed upon at the outset and should be presented in a decimal number for calculation. Recall that the percent number can be converted to a decimal by dividing by 100 (or, as a shortcut, moving the decimal point two places to the left). Make sure that you know the length of time that the interest rate applies to. The rate is noted algebraically as ${\displaystyle r}$.[5] • For example, a credit card may advertise interest of 15% per year. However, interest is generally applied each month, so you may want to know the monthly interest rate. In that case, divide by 12, to find the monthly interest rate of 1.25% per month. These two rates, 15% per year or 1.25% per month, are equivalent to each other. 4. 4 Know when the interest will compound. Compounding interest means that the interest will be calculated periodically and added back to the principal amount. For some loans, this may happen once a year. For some, it may happen each month or each quarter. You need to know how many times a year the interest will be compounded.[6] • If interest is compounded annually, then n=1. • If interest is compounded quarterly, for example, then n=4. 5. 5 Know the term of the loan. The term is the length of time for which the interest will be calculated. The term is generally measured in years. If you need to calculate interest for some other length of time, you will need to convert into years.[7] • For example, for a loan of one year, then ${\displaystyle t=1}$. But, for a term of 18 months, then ${\displaystyle t=1.5}$. 6. 6 Identify the variables from the situation. Suppose, for this example, you deposit$5,000 into a savings account that pays 5%, compounded monthly. What will be the value of this account after three years?[8]
• First, identify the variables that you need to solve the problem. In this case:
• ${\displaystyle P=\5,000}$
• ${\displaystyle r=0.05}$
• ${\displaystyle n=12}$
• ${\displaystyle t=3}$
7. 7
Apply the formula and calculate the compounded interest. Once you have understood the situation and identified the variables, enter them into the formula to find the amount of the interest.
• For the problem started above, this would look as follows:
• ${\displaystyle A=P(1+{\frac {r}{n}})^{nt}}$
• ${\displaystyle A=5000(1+{\frac {0.05}{12}})^{12*3}}$
• ${\displaystyle A=5000(1+0.00417)^{36}}$
• ${\displaystyle A=5000(1.00417)^{36}}$
• ${\displaystyle A=5000(1.1616)}$
• ${\displaystyle A=5808}$
• Thus, after three years, compound interest will have amounted to $808, in addition to the original$5,000 deposit.
### Method 3 Calculating Continuously Compounding Interest
1. 1
Understand continuously compounding interest. As you saw in the previous example, compound interest grows faster than simple interest by adding the interest back to the principal at certain times. Compounding quarterly is more valuable than compounding annually. Compounding monthly is even more valuable than compounding quarterly. The most valuable situation would have the interest compounding continuously - that is, every instant. As quickly as interest can be calculated, it is returned to the account and adds to the principal. This is obviously only theoretical.[9]
• Using some calculus, mathematicians have developed a formula that simulates interest that is compounded and added back to the account in a continuous stream. This formula, which is used to calculate continuously compounding interest, is:
• ${\displaystyle A=Pe^{rt}}$
2. 2
Know the variables for calculating the interest. The formula for the continuously compounding interest looks similar to the early situations, with some slight differences. The variables for the formula are:[10]
• ${\displaystyle A}$ is the future value (or Amount) of money that the loan will be worth after compounding the interest.
• ${\displaystyle P}$ is the principal.
• ${\displaystyle e}$. Although this looks like a variable, it is actually a constant number. The letter ${\displaystyle e}$ is a special number called “Euler’s constant,” named for the mathematician Leonard Euler who discovered its properties.
• Most advanced graphing calculators have a button for ${\displaystyle e^{x}}$. If you press this button, with the number 1, to represent ${\displaystyle e^{1}}$, you will learn that the value of ${\displaystyle e}$ is approximately 2.718.
• ${\displaystyle r}$ is the interest rate per year.
• ${\displaystyle t}$ is the term of the loan, measured in years.
3. 3
Know the details of your loan. Banks typically use continuously compounding interest on home mortgage loans. Suppose you want to borrow $200,000 at a rate of 4.2% for a 30 year mortgage. The variables that you will use for the calculation are, therefore:[11] • ${\displaystyle P=200,000}$ • ${\displaystyle e}$, again, is not a variable but is the constant 2.718. • ${\displaystyle r=0.042}$ • ${\displaystyle t=30}$ 4. 4 Use the formula to calculate the interest. Apply the values to the formula to calculate the amount of interest that you will owe on the 30 year loan.[12] • ${\displaystyle A=Pe^{rt}}$ • ${\displaystyle A=200000*2.718^{(0.042)(30)}}$ • ${\displaystyle A=200000*2.718^{1.26}}$ • ${\displaystyle A=200000*3.525}$ • ${\displaystyle A=705000}$ • Notice the enormous value of compounding interest continuously. ## Community Q&A Search Add New Question • If a friend loaned me$42,000.00 nine years ago, how much interest would it have earned?
wikiHow Contributor
It depends on the interest rate he gave you. If you had, for example, five percent interest every year, it would be (1,05^9)*42,000USD, which would be approximately 65,156 USD.
• How do I set up a specific equation?
wikiHow Contributor
Interest equals the principal times rate times time. For example, if the principal is $230, the rate is 3%, and the time is 1 year, you have the equation: i ( interest) = 230 times 0.03 times 1 = 6.9. • How much do I need to deposit at 1.5% to get an annual return of$1725.00?
wikiHow Contributor
Use this equation if you ever want to figure out different amounts in the future with different interest rates. Solve for X. 1.5%X = $1,725. For this problem, divide .015 into$1,725 to get your answer of $115,000 is needed to earn$1,725 at 1.5%.
• How do I calculate interest on a past due invoice?
wikiHow Contributor
Interest on invoices and accounts payable normally used simple interest. You have an invoice for $100.00. If your invoice is dated May 5th, and you pay it on June 30th, when it is net 30, with 24% per annum interest (2% per month), you owe interest on 26 days because you should have paid on June 4th. Calculation is 26/365x24%x$100.00=$1.71. • How much simple interest is earned on$300 at 6% for 6 months?
Ed Rozmiarek
The principal is $300. The rate is 0.06. The term is half a year, or 0.5. Put them together as 300*0.06*0.5=9. You will get$9 interest.
• How can I calculate the interest earned on $400.00 in a regular savings account? Ed Rozmiarek You need to know the interest rate of the account. You also need to know if the interest compounds continuously, quarterly, or annually. Savings accounts generally do not pay much. Let's assume a low rate of 1% to see the calculation and further assume that it compounds annually. Your actual amount may be different depending on these assumptions. The formula is given in the article above, Value = P(1+r/n)^(nt). P is the principal of$400. R is the rate, which we assume to be 0.01, and n is the number of times per year that it compounds, so n=1, and t=32, then number of years. Put these together : Value = 400*(1.01)^32 = 400*1.375 = $550. • How can I figure out the interest earned on a 401k? Ed Rozmiarek Subtract the amount you put into the account from the total value after time, and this will tell you the amount of interest you earned. If you invested 1000, and you get out 1075, then you earned$75 interest. To calculate the approximate interest rate, use the formula r=I/t.
• How can I determine what the interest rate is based on the interest payment?
Ed Rozmiarek
Use the formula, Interest = Principal x Rate x Time, and rearrange it algebraically to solve for the rate. Rate = Interest / (Principal x Time). Then, fill in what you know to find the rate.
• What interest rate will I earn if I deposit $1000.00 and after 8 years I earn$163.94 interest?
Ed Rozmiarek
Use the formula, Interest (I) = P*r*t, but rearrange the equation to solve for the interest rate. This is r=I/(P*t). Fill in the values you know to get r=163.94/(1000*8)=163.94/8000=0.020. Thus, you would earn 2% interest.
• What is the present value of a $300.00 bank deposit made in 1979? • How can I determine what the interest rate is when a lump sum of 250,000 is paid our at the rate of 25000 per year for 20 years? • 1.5 million Canadian dollars at 5 percent compounded interest after 30 years = what total amount earned? • How do I calculate interest rates? • If interest earned is$160 and interest rate is 1% what is my principle amount?
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2017-09-26 02:15:21
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https://www.esaral.com/q/if-the-function-f-given-by-62684
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If the function f given by
Question:
If the function $f$ given by $f(x)=x^{3}-3(a-2) x^{2}+3 a x+7$, for some $\mathrm{a} \in \mathrm{R}$ is increasing in $(0,1]$ and decreasing in $[1,5)$, then a root of the equation,
$\frac{f(x)-14}{(x-1)^{2}}=0(x \neq 1)$ is
1. (1) $-7$
2. (2) 5
3. (3) 7
4. (4) 6
Correct Option: , 3
Solution:
$f(x)=x^{3}-3(a-2) x^{2}+3 a x+7, f(0)=7$
$\Rightarrow \quad f^{\prime}(x)=3 x^{2}-6(a-2) x+3 a$
$f^{\prime}(1)=0$
$\Rightarrow \quad 1-2 a+4+a=0$
$\Rightarrow \quad a=5$
Then, $f(x)=x^{3}-9 x^{2}+15 x+7$
Now,
$\frac{f(x)-14}{(x-1)^{2}}=0$
$\Rightarrow \quad \frac{x^{3}-9 x^{2}+15 x+7-14}{(x-1)^{2}}=0$
$\Rightarrow \quad \frac{(x-1)^{2}(x-7)}{(x-1)^{2}}=0 \Rightarrow x=7$
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2023-03-24 06:10:38
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https://www.shaalaa.com/question-bank-solutions/a-cuboidal-box-5-cm-5-cm-4-cm-find-its-surface-area-surface-area-of-a-cuboid_61511
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# A Cuboidal Box is 5 Cm by 5 Cm by 4 Cm. Find Its Surface Area. - Mathematics
A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
#### Solution
$\text { The dimensions of the cuboidal box are 5 cm }\times 5 cm \times 4 cm .$
$\text { Surface area of the cuboidal box = 2 } \times (\text { length } \times \text { breadth + breadth } \times \text { height + length }\times \text { height })$
$= 2 \times (5 \times 5 + 5 \times 4 + 5 \times 4)$
$= 2 \times (25 + 20 + 20)$
$= 130 {cm}^2$
Is there an error in this question or solution?
#### APPEARS IN
RD Sharma Class 8 Maths
Chapter 21 Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)
Exercise 21.3 | Q 3 | Page 22
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2021-04-20 07:51:48
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https://www.sparrho.com/item/absolute-magnitude-calibration-for-w~uma-type-systems-ii-influence-of-metallicity/90cfc6/
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# Absolute-Magnitude Calibration for W~UMa-type Systems. II. Influence of Metallicity
Research paper by Slavek Rucinski
Indexed on: 01 Mar '95Published on: 01 Mar '95Published in: Astrophysics
#### Abstract
A modification to the absolute magnitude calibration for W~UMa-type systems, taking into account differences in metal abundances, is derived on the basis of contact binary systems recently discovered in metal-poor clusters. A preliminary estimate of the magnitude of the metallicity-dependent term for the $(B-V)$-based calibration is $\Delta M_V = -(0.3 \pm 0.1) \times [Fe/H]$. The calibration based on the $(V-I_C)$ color is expected to be less sensitive with the correction term $\approx -(0.12\pm 0.05) \times [Fe/H]$.
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2020-10-22 12:44:18
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https://socratic.org/questions/587412f4b72cff5f8106dd5a#362414
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# Question #6dd5a
##### 1 Answer
Jan 9, 2017
$\frac{239}{495}$
#### Explanation:
You rewrite all the significant digits without point and period (482) and subtract digits without the period (4), then divide the obtained difference (478) by as many digit 9 as the digits under period (two 9s) and as many digits 0 as the digits between the decimal point and the period (one 0):
the fraction is then $\frac{482 - 4}{990} = \frac{478}{990} = \frac{239}{495}$
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2022-01-19 01:03:47
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https://meteo.unican.es/trac/wiki/ESGFToolsUI?action=diff&version=27
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# Changes between Version 26 and Version 27 of ESGFToolsUI
Ignore:
Timestamp:
Apr 29, 2014 3:18:11 PM (8 years ago)
Comment:
--
### Legend:
Unmodified
v26 Download Dataset... allows to manually select the files that will be put to download. In the top of window can see the id of dataset, the number of files selected, the total number of files of the dataset, the size in bytes of the sum of selected files and the total size of the whole dataset. This windows displayed a list of files and its size in bytes. You can select manually the files that you want download doing click in the check-box associated in each file in the list. This windows displays a list of files and its size in bytes. You can select manually the files that you want download doing click in the check-box associated in each file in the list. [[Image(download_file_selection_2.png)]]
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2022-07-06 10:01:12
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https://physics.stackexchange.com/questions/418183/spatial-dimensions-inside-the-event-horizon
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# Spatial dimensions inside the event horizon
Consider a test particle falling radially to a black hole. The radial direction toward the singularity inside the black hole becomes a direction in time while the dimension that used to be time becomes a direction in space.
A massive particle can be stationary in space and just move in time toward the singularity, so no problem there. However, a photon must move locally in space with the speed of light. For example, during one second of time, it must move by one light-second in space in the view of a local observer or by some other distance in the view of a remote observer.
The photon is flying to the black hole radially pointing to the singularity in the center. While it is outside, no problem, for each second of time the photon covers the radial distance of one light second toward the black hole (or some other distance depending on the observer, but still radially toward the black hole).
(I am aware that in the view of a remote observer the photon never crosses the event horizon. This is however beyond the scope of the question that is only concerned the the spacetime geometry on the inside.)
Now, there is a confusion on the inside. The direction in time is now radial toward the singularity in the center. So for each second in time radially toward the singularity the photon must cover one light second (or some other distance) in space... in what direction? It cannot possibly be toward the center, as it is the direction in time, not in space. It also cannot be one of the other two original spatial dimensions, because they do not change while crossing the horizon.
The photon now must move in space in the direction where earlier time was pointing. Well, while time was time, we thought it was pointing to the future, but now, since this dimension is a direction in space, we can no longer say the same. Thus my question is, what is the spatial direction of a radially infalling photon inside a black hole? It cannot be a direction to the center, so where is it moving? Or otherwise what is the flaw in my reasoning?
The null geodesic equation in the Schwarzchild metric for a radially infalling photon ($ds=0$) is:
$$dr=\pm\left( \frac{r_\mathrm{s}}{r_o} - 1 \right) \,dt$$
It solves as $t=f(r)$ where the actual expression is simple enough, but irrelevant to the question. This equation would describe a trajectory of the photon, but only if we knew the direction of $t$. However, it is not evident from the equation where the spatial $t$ dimension is pointing geometrically inside the black hole.
This question can also be generalized as, what is the geometry of space inside a Schwarzchild black hole? At a constant time $r=r_o<r_s$ ($dr=0$), the $(-1,1,1,1)$ metric (where $t$ is a spatial dimension and $c=1$) is:
$$\,{ds}^{2} = \left( \frac{r_\mathrm{s}}{r_o} - 1 \right) \,dt^2 + r_o^2 \left(d\theta^2 + \sin^2\theta \, d\varphi^2\right)$$
What kind of space does this formula describe?
A radial null curve inside the event horizon of a Schwarzschild black hole can be explored via the Eddington-Finkelstein coordinates. The metric in such coordinates is:
$ds^2 = -(1 - 2GM/r) dv^2 + (dv dr + dr dv) + r^2 d\Omega^2$
where:
$r$ radial coordinate
$v = t + r*$
$t$ time coordinate
$r* = r + 2GM \ln (r/(2GM) -1)$ tortoise coordinate
An infalling radial null geodesic is characterized by $v = constant$.
A radial null geodesic is described by setting $ds^2 = 0$, $d\Omega^2 = 0$, thus giving:
$dv/dr = 0$ infalling
or
$dv/dr = 2 (1 - 2GM/r)^{-1}$ outgoing
In this coordinate system there is no problem in tracing the paths of null or timelike particles past the horizon. The light cone tilts over, such that for $r \lt 2GM$ all future directed paths are in the direction of decreasing $r$. At the horizon the outgoing photons keep still at $r = constant$, while the infalling photons point radially to the physical singularity at the center of the black hole. In between (within the light cone) you have the massive particles.
FURTHER
Let us go back to the Schwarzschild coordinates, where the metric is:
$ds^2 = - (1 - 2GM/r) dt^2 + (1 - 2GM/r)^{-1} dr^2 + r^2 d\Omega^2$
The normal to a surface $r = constant$ is given by $n_\mu = \nabla_\mu f(r) = \partial_\mu f(r)$, where $f(r) = r - constant$. Thus:
$n_\mu = (0, 1, 0, 0)$ dual vector
$n^\mu = (1 - 2GM/r) (0, 1, 0, 0)$ vector
$n^\mu n_\mu = (1 - 2GM/r)$ squared norm
In the exterior region, $r \gt 2GM$, the normal is spacelike, hence a surface $r = constant$ is timelike. In the interior region, $r \lt 2GM$, the normal is timelike, hence a surface $r = constant$ is spacelike.
Therefore in the interior region a surface $r = constant$ is not viable to a particle, whether massive or massless (photon). An infalling particle can only proceed along the radial coordinate towards the center of the black hole.
The flaw in your reasoning is that, even if time and radial coordinates change nature, the coordinate distance to the center of the black hole is still measured by the radial coordinate. The change in nature imposes on the radial coordinate additional constraints peculiar to the interior of a black hole.
• This doesn't answer the question of what the spatial direction of $t$ is inside or what the shape of space is there. While the $v$ coordinate is not singular, it changes from timelike to spacelike at the horizon. Thus it remains unclear what its direction in space is inside. – safesphere Jul 19 '18 at 2:19
• I edited the post, please refer to FURTHER ... – Michele Grosso Jul 19 '18 at 21:24
• Thank you for the update. Well, $r=constant$ is not timelike outside. It is a 3-cylinder stretched in time that contains both timelike trajectories (of orbiting particles) and spacelike curves (instant distances). Also, while $r=constant$ is indeed spacelike inside, it is inaccessible only instantly, but its dimensions are accessible within a light cone. My room is spacelike, but I am not restricted to sit in a chair while "falling" into the future along the time axis. Also, light cannot move radially inside, because the radial direction is not lightlike. What are the "peculiar constraints"? – safesphere Jul 19 '18 at 21:59
• In the interior region the time direction is spacelike and the radial direction is timelike. As in spacetime a radial path is described by both time and radial coordinates, light can well proceed along a lightlike track. (It is also what happens in the exterior region, where time and radial coordinates show their ordinary nature). As for peculiar constraints I just meant that a stationary observer (r = constant) is not allowed in the interior region. – Michele Grosso Jul 21 '18 at 7:40
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2019-08-20 19:52:00
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http://www.reddit.com/r/programming/comments/a9r6s/why_perl_lost_it/c0gip11
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you are viewing a single comment's thread.
[–] 22 points23 points
sorry, this has been archived and can no longer be voted on
I'd like to see an example of Python's "steady improvements over the years" which directly contributed to its increased adoption, for example.
Also, minus several million points for perpetuating the myth that the TIOBE index has any degree of accuracy and relevance. (It's easy to identify science; you can reproduce the results.)
[–] 10 points11 points *
sorry, this has been archived and can no longer be voted on
I'd group the improvements into two areas: functional programming support, and better OO features. For the former, the following features are very useful, I find:
• List comprehensions (were these always around? When did they get added?)
• Generators/yield keyword
• Generator expressions
• Decorators
• Looking forward to dict comprehensions
• Looking forward to using the nonlocal keyword so that I don't have to use random hacks to make my lexical closures work sometimes
For OO stuff, I think new-style classes really cleaned things up --- subclassing basic classes used to be pretty ugly, and little odds and ends like the property feature helped a lot too.
[–] 7 points8 points *
sorry, this has been archived and can no longer be voted on
List comprehensions (were these always around? When did they get added?)
Listcomps were added in 2.0 (PEP 202, 2000); they were extended to generator comprehensions in 2.4 (PEP 289) and in 3.0 we now have dict comprehensions and set comprehensions (along with a literal syntax for sets)
Looking forward to using the nonlocal keyword so that I don't have to use random hacks to make my lexical closures work sometimes
I'm not. That's one of the very few things I hate in Python (along with the love for adding new keywords): the scoping is a fucking mess, and it comes from both history and implicit scope declaration.
Fuck implicit scope declaration, you should need let to declare a variable (any variable) and bind it in the current scope. Fuck global and fuck nonlocal.
[–] 5 points6 points
sorry, this has been archived and can no longer be voted on
Are those really the kinds of things that lead directly to adoption? If you take PHP as an example of a language developed after Perl, Python, Ruby, Java, and C++, it's a very poor example of additional features spurring further adoption.
PHP may be an outlier, but when I think of reasons for adoption, I think of support, library availability, ease of deployment, and the availability/trainability of effective programmers.
[–] 3 points4 points
sorry, this has been archived and can no longer be voted on
PHP may be an outlier, but when I think of reasons for adoption, I think of support, library availability, ease of deployment, and the availability/trainability of effective programmers.
Those things are "features" too.
[–] 1 point2 points
sorry, this has been archived and can no longer be voted on
PHP is simpler to implement. That's the main reason it's so well adopted today.
Just drop the script anywhere, access the file via the web and you're done. You can't do that with with most (all?) other languages. You don't need to compile, you can set global values like max execution time too (this one is really important and is way lacking in the python dept.)
[–] -1 points0 points
sorry, this has been archived and can no longer be voted on
PHP is simpler to implement. That's the main reason it's so well adopted today.
That's a consequence of widespread deployment rather than of the language's design. It also strikes me as a chicken. I'd like to know the egg that led to wide deployment.
[–] 0 points1 point
sorry, this has been archived and can no longer be voted on
You might be right. But on the other hand, I do think these features are good carrots. One of the promises of the language is "supports multiple programming paradigms". I don't think it fulfilled that promise before these features.
[–] 5 points6 points
sorry, this has been archived and can no longer be voted on
I could think of two candidates: ctypes in the Python 2.5 core and improved Unicode handling in Python 3.
Python 3 has little adoption at the moment, so it's easy to rule that out as a driver of Python adoption. Likewise, Python 2.5 is fairly new, so it's easy to rule that out too.
[–] 0 points1 point *
sorry, this has been archived and can no longer be voted on
the availability/trainability of effective programmers.
I think you must have a lower bar for "effective" if you think this describes a PHP advantage. Past a very trivial scale for development, PHP actively gets in the way of effective development. It's just a Turing-complete templating language, glorified beyond all reason to the point that it gets used for serious software development by the very desperate and the very foolish.
[–] 0 points1 point
sorry, this has been archived and can no longer be voted on
Past a very trivial scale for development....
It's trivial in difficulty, but far from trivial in amount of available work.
[–] 0 points1 point
sorry, this has been archived and can no longer be voted on
I was talking about the scale of program complexity.
Past a very trivial scale of program complexity, PHP actively gets in the way of effective development.
FTFM
[–] 0 points1 point
sorry, this has been archived and can no longer be voted on
Looking forward to using the nonlocal keyword so that I don't have to use random hacks to make my lexical closures work sometimes
I find it difficult to take a language seriously that has this problem. I hope Python gets it fixed sooner rather than later.
[–] -1 points0 points
sorry, this has been archived and can no longer be voted on
I'd group the improvements into two areas: functional programming support
Yes, I love too the flexibility of anonymous blocks in Python.
[–] 29 points30 points *
sorry, this has been archived and can no longer be voted on
I've been writing perl professionally for about 10 years now. I enjoy it. I'm not a python fan at all. But, even I can answer this for you:
• Windows support
• Considerably easier to embed and extend (XSUBs vs., well, anything else. Inline helps but is really a bandaid over a wart.)
• puts, switch/case, sane MI... 2 of those made it into 5.10 and the other is available on CPAN. As a cabal the perl community fought these simple features for years, because $condition && do { something }; and print "something\n"; "worked", and nobody uses multiple inheritance. • Add all of the above with a dash of second system syndrome and you have your result. Outsiders/Newcomers, these issues are being addressed. People like Kennedy and Lester and the 5.10 team are doing shit about it. Moose is a colossal hack and no one pretends otherwise, yet everyone seems to be so overjoyed that we're (as perl users) getting what other languages have had for some time, chock full of magic and pixie dust with a fine coat of documentation and API. This is not exactly comforting from the perspective of an outsider who knows other languages that already have most of what Moose provides. All these things said: Perl's the reason that our languages today are expected to have first-class regular expression support, if not a billion less obvious other things I'm too lazy to account for. If you say, "they took it from sed and awk", you are seriously missing the point. If you haven't worked in perl, you probably haven't read good library documentation, or at least, need to up your standards quite a bit. I can't recall the last time I had to dig through an installed perl module to find out how to do something with it, but this is something I do on a daily basis in ruby. The only community as a group that puts this much strength on documentation outside of perl that I've seen is the GNU project. See also: testing. Perl should be setting the standard for what well-tested open source products should look like from a cultural aspect. Perl's libraries are, in general, much more mature than the other languages in its class; DBIx::Class is a great example of this, building on several stable foundations and having a query generator I only wish I had in the current rails application I work in. There, I hope that's fair, but I strongly suspect I said nothing you don't already know. Maybe you should get back to criticizing the rubyspec process. EDIT: mention of GNU project [–] 28 points29 points sorry, this has been archived and can no longer be voted on I take offense to your comment that "Moose is a colossal hack and no one pretends otherwise", in part because I am the author and in part because it is not a hack at all. It has some hacks in it to make it play well with the existing Perl infrastructure but it is built on solid foundations. Anyone who has read the source or taken time to devel into the guts of Moose would surely disagree with you. I also take offense at the "chock full of magic and pixie dust with a fine coat of documentation and API" part of your comment. Moose is most certainly not full of magic and pixie dust and I worked hard to make sure of that. Too many of the previous attempts at solving Perl's issues have been full of magic and therefore fragile. I think perhaps you should take a look at the guts of Moose before you make comments like this. [–] 1 point2 points sorry, this has been archived and can no longer be voted on It was a poorly-worded attempt to describe that Moose is used as a proxy to address inadequacies in an OOP system that should have been rectified a long time ago. And I apologize if this frustrates you, but that is why I made those comments I did. Moose is becoming more and more pervasive (which you obviously should be proud of), which means it has something to offer. However, a significant chunk of those offerings are things that other language users get without a third-party library, and often without a library at all. [–] 1 point2 points sorry, this has been archived and can no longer be voted on However, a significant chunk of those offerings are things that other language users get without a third-party library, and often without a library at all. Yes true, and one of them was moved into core in 5.10 (C3 method resolution) are others are planned to be moved into core in 5.12 (some of Devel::Declare features and some MOP-ish like features). Moose is serving as a testing ground right now. Perl strives to maintain back compat all the way to Perl 1 (or at least Perl 4 which was release in the early 90s), which has slowed innovation and which pretty much requires that innovation happen in the libraries first where it can be vetted. Personally it think this is a more sensible path. [–] 8 points9 points sorry, this has been archived and can no longer be voted on That's a nice balanced perspective. One thing missing on the perl-positive side is testing. You mention documentation, but the testing culture is well embedded in CPAN authors and perl porters. [–] 8 points9 points sorry, this has been archived and can no longer be voted on I did mention it, it's just buried in the documentation paragraph. :) [–] 4 points5 points sorry, this has been archived and can no longer be voted on Whoops. Score one for attention deficit and skimming long posts. Sorry about that. [–] 2 points3 points sorry, this has been archived and can no longer be voted on I have to agree with almost all of what you said. I have some niggling issues with certain statements, though. The only community as a group that puts this much strength on documentation outside of perl that I've seen is the GNU project. Try the various BSD Unix systems, too -- which cover not only the same kind of stuff as the GNU project, but also the rest of a core operating system. Also . . . a lot of GNU documentation, while fairly complete, is hideously difficult to use by comparison with the alternatives used by other projects. Info pages are a chancre on the face of software documentation. See also: testing. Ruby has the absolute best quick and practical introduction to TDD that I've ever seen, in Everyday Scripting with Ruby. In fact, that's really Ruby's documentation strength -- quick and practical introduction documentation. Perl used to be the pretty much undisputed king of this field, with its camelid books from O'Reilly, but Ruby's similar joyful coverage extends well beyond a trilogy of O'Reilly books, and it's still growing. That having been said . . . If you haven't worked in perl, you probably haven't read good library documentation, or at least, need to up your standards quite a bit. I can't recall the last time I had to dig through an installed perl module to find out how to do something with it, but this is something I do on a daily basis in ruby. God yes. You are absolutely right. The travesty that is much of the Ruby community's insistence that digging through module/library code is "reading documentation" just really gets up my nose. [–] 1 point2 points sorry, this has been archived and can no longer be voted on Also . . . a lot of GNU documentation, while fairly complete, is hideously difficult to use by comparison with the alternatives used by other projects. The groff documentation is an excellent example of this mess. It basically assumes you've already mastered troff, which I never used, and you just want to know how the GNU version of it works. It makes the documentation almost useless. However, I really do like the GNU info system, as long as there is a reasonable man page to go with it, instead of the lame "see the info manual" message. Other than that, I never understood the info hate. The great, thorough documentation is something I really love about the BSDs. Those people are solid. Almost everything you might need to know is laid out somewhere in the docs. [–] 0 points1 point sorry, this has been archived and can no longer be voted on I never understood the info hate. Info is to man what emacs is to Vim. At least, that's how it seems to me at this exact moment. This is more than just a technical analogy; it's a cultural analogy, too, and the "see the info" manpage problem is a symptom of that, because just as the GNU folks have a religious zeal for trying to force people to use emacs-like software, they also have a religious zeal for trying to force people to use info pages (and the GPL and so on), largely through dirty trick style cultural manipulations. The great, thorough documentation is something I really love about the BSDs. Those people are solid. Almost everything you might need to know is laid out somewhere in the docs. God yes. Since switching from Debian to FreeBSD as my primary OS of choice, I've been in love with the documentation. I love the BSD standards for C code formatting, too, especially after briefly experiencing the horror of the GNU standards for C formatting. [–] 0 points1 point sorry, this has been archived and can no longer be voted on As for my GNU info hate... maybe it has always been the info readers I didn't like. BTW, I'm not a emacs user, and after using vi and vim for 20+ years, I never will be. That ship has sailed. So the regular 'info' command line program didn't seem to be to be easy to use. I never remembered the key bindings... and I shouldn't have to. There needs to be a default "I don't know what I'm doing" for that program... I'm already looking for help, I don't need to read the man page on info just so that I can navigate the documentation I'd actually like to read. I've got pinfo installed, and it is marginally better than info. I still don't know how half of it works... and I use it so infrequently I've never really wanted to learn it. For docs, please just give me a pile of HTML pages in some directory. I'm totally OK with typing in a file:// URL, and just going from there. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Ruby has the absolute best quick and practical introduction to TDD that I've ever seen, in Everyday Scripting with Ruby. In fact, that's really Ruby's documentation strength -- quick and practical introduction documentation. Perl used to be the pretty much undisputed king of this field, with its camelid books from O'Reilly, but Ruby's similar joyful coverage extends well beyond a trilogy of O'Reilly books, and it's still growing. Please inform me when ruby gets things like CPAN testers and test runs on package installation (gems or anything else.. I'll take setup.rb if you want). Books are nice and all, but CPAN not only has knowledge of the number of modules that are lacking tests, but it has the actual runs on a number of platforms. http://www.cpantesters.org/distro/A/App-Open.html#App-Open-0.0.4 Here's a stupid little perl module I have published on CPAN. I had no idea it passes on Solaris on 5.10.1, or most of the 140+ platforms it runs on. When gemcutter or rubyforge can tell me that, you might have a point. Try the various BSD Unix systems, too -- which cover not only the same kind of stuff as the GNU project, but also the rest of a core operating system. Also . . . a lot of GNU documentation, while fairly complete, is hideously difficult to use by comparison with the alternatives used by other projects. Info pages are a chancre on the face of software documentation. You are aware that makeinfo can generate a multitude of formats, including HTML? http://www.gnu.org/software/texinfo/manual/texinfo/html_node/index.html I'm not a fan of info either, but the GNU project doesn't require me to use it. And BSD does have great information... when you are on BSD. The GNU project (as evidenced above) covers a lot more than what runs on a single platform; for example, enjoy leveraging the setproctitle() manual on linux (arguably this is GNU libc's fault, but still, the point remains). God yes. You are absolutely right. The travesty that is much of the Ruby community's insistence that digging through module/library code is "reading documentation" just really gets up my nose. Please enjoy an excerpt from a very popular HTML and XML parser: http://github.com/whymirror/hpricot/blob/master/lib/hpricot/htmlinfo.rb Let me know when you're done reading that. I do understand that since someone took it over from _why this is not required as much, and I know James Britt, Gavin Sinclair and JEG (among others) have put a lot of effort into documenting the standard library. However, please, by all means, find me a perl module in any 5.x release that is this sparse: http://ruby-doc.org/stdlib/libdoc/dbm/rdoc/index.html And there are quite a few like that. [–] -1 points0 points sorry, this has been archived and can no longer be voted on Books are nice and all, but CPAN not only has knowledge of the number of modules that are lacking tests, but it has the actual runs on a number of platforms. I agree. I'm not sure why you're presenting that as if it contradicts what I said. Here's a stupid little perl module I have published on CPAN. I had no idea it passes on Solaris on 5.10.1, or most of the 140+ platforms it runs on. When gemcutter or rubyforge can tell me that, you might have a point. I have a point anyway, because my point had nothing to do with the very nice advantages of CPAN you cited. I'm talking about quick and easy introductions to test-driven development, not post-development automated testing provided by a third-party hosting system. You are aware that makeinfo can generate a multitude of formats, including HTML? Yes, I'm aware. This doesn't help the least technically oriented users, though. And BSD does have great information... when you are on BSD. Actually, the FreeBSD Handbook, The Complete FreeBSD, and BSD Hacks are some of the best Linux user-level documentation I've ever seen. Of course, A Practical Guide to Linux Commands, Editors, and Shell Programming is some of the best BSD Unix documentation I've ever seen, too -- but that's basically a three-to-one score in favor of BSD Unix documentation. It gets even more interesting when considering which of the above you can get for free online. Anyway, I use the hell out of BSD Unix, so even if it was only useful "when you are on BSD," it'd still be useful to me all the damned time. Documentation is one of the reasons I like using FreeBSD more than any Linux distribution, and when documentation is a cause for adoption, that seems pretty relevant. Please enjoy an excerpt from a very popular HTML and XML parser: I'm not sure what you're trying to prove. Are you agreeing with me? [–] 2 points3 points sorry, this has been archived and can no longer be voted on Outsiders/Newcomers, these issues are being addressed. People like Kennedy and Lester and the 5.10 team are doing shit about it. Who is this Lester that is dealing with those issues? It sure isn't me, Andy Lester who runs http://perlbuzz.com/ and mostly just reports news and makes Perl noise. My Perl contributions have been almost nothing in the way of code lately. [–] 1 point2 points sorry, this has been archived and can no longer be voted on Yeah, sorry about that. I'm not sure why I conflated you into the Vanilla/Strawberry Perl project. [–] 2 points3 points sorry, this has been archived and can no longer be voted on Languages are not expected to have first class regular expression support. C, C++, Java and C# do not have it as a first class construct. Doing so would be an awful thing to make fundamental to your language since they are not fundamental to software development. [–][deleted] sorry, this has been archived and can no longer be voted on [deleted] [–] 0 points1 point sorry, this has been archived and can no longer be voted on You're correct, sorry about that. [–] 0 points1 point sorry, this has been archived and can no longer be voted on The fact some languages have third-rate regex support at best, and usually via an obscure library, is not a good thing. I suspect you're right about what erikh meant. [–] -1 points0 points sorry, this has been archived and can no longer be voted on Ah part of that natural language that Perl users love. It is difficult when people use a label, that has a well understood meaning in the field, to mean completely different things. [–] 1 point2 points sorry, this has been archived and can no longer be voted on C, C++, Java and C# do not have it as a first class construct. Nor any other usable way of embedding regexes in the code. private static final Pattern LEXER = Pattern.compile( "([\\w.*/=<>|!?$%^&;,+-]++)" + // 1 - ID
"|\"((?:[^\"\\\\\n]|\\\$\"\\\$)++)\"" + // 2 - string
"|((?<=[,;])|\\\\ *+\n|[{}])" + // 3 - LF
"|(\n)" + // 4 - LF
"|[\t ]++|#.*+"); // WS
public static final Pattern DOT = Pattern.compile("\\.");
private static final Pattern UNESCAPE = Pattern.compile("\\\\(.)");
Have to love all those lovely backslashes and static final Patterns...
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I hate C# and all but...
@"I\don't\have\to\escape\backslashes\now."
For C++ see the boost libraries.
I'm guessing you were mainly just aiming at the easy target of Java.
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If you think that is what I said you have more serious issues than maintaining a hand crafted state machine.
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I suspect that has to do with C's lack of a string type.
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C can build a regex system just fine. It just doesn't have first class regex. There isn't a syntax to automatically build a regex parser.
I think only Perl has regex built into the language itself. Most languages do the sane thing and provide them as libraries. They are not fundamental to programming and should not be built into the language itself. Effectively Perl is the argument that regular expressions are as fundamental to programming as an if statement or a function call. It is absurd.
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Ruby and Javascript are two languages that off the top of my head have regex built-in to the language.
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Why would anyone downvote cooldude127? (apart from his username maybe). Ruby and JS do indeed have a first-class syntax for regexes, and it's the same as Perl's.
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Well . . . almost the same. He didn't claim the syntax was identical, though, so the fact it's only almost the same isn't a reason to downvote cooldude127 by any stretch of the imagination.
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Effectively Perl is the argument that regular expressions are as fundamental to programming as an if statement or a function call. It is absurd.
Actually, Perl is the argument that regular expressions are fundamental to certain types of programming, just as bit-shifting is fundamental to other types of programming even if it's "dangerous" (thus we have C pointers). The fact you may not need regexen for the type of programming you do as often as others may need them for the types of programming they do doesn't mean their common realms of programming are less valid than yours.
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Right on. There have been a number of occasions where I was coding in Java and wished I had first-class regex available, instead of the monstrosity regex library interface.
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I think putting regex facilities in a library is fine, in most cases. I think that in Java it's a terrible problem, because library interfaces in Java tend to be akin to thumbscrews. By god, that's horrible shite.
I'm perfectly okay with regex support being in the core language of Perl, and I'd be perfectly fine with it being in the standard library too (as long as it wasn't an OO library, given Perl's OOP syntax). In the case of Perl, where its key programming niches are particularly well suited to solving problems with regexen, I think moving it out of even the standard library to some nonstandard library would be a tremendous mistake.
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More programs need regexps than need floats. By this objective measure, regexps are much more fundamental to software development than floating point numbers.
Why don't you apply your argument to floats?
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Because adding floating point code that compiles to the native instructions without massive function call overhead is extremely difficult to do in a library in most languages. This isn't the case for regexes.
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Nonsense, not a single language has native vectorization (SSE and friends), and yet all compilers support it. And most languages somehow have library-based complex numbers, and native reals, for no obvious reasons.
The truth is that it's all legacy of Fortran and C, and decisions which made sense in 1950s and 1960s, not really now.
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Yes, that's correct. Compilers extend the language to support native vectorization through vector intrinsics, but they make it look like a library for compatibility purposes. There's no especially good reason to do this with regexes, they can sit comfortably in a library. No compiler support needed.
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I would expect ahead-of-time compiled and optimized regexps to be vastly faster than library-based regexps. Regexp is basically code which runs on virtual machine of regexp library - and there's no reason not to compile it into machine code.
No language does it now as far as I know (and these virtual machines are reasonably fast, but reasonably there's a long way from reasonably fast to as fast as it can get).
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Well, .NET has an option to allow JIT regexes (the compiler/runtime just needs to allow generic code generation, and doesn't need to know specifically about regexes, since they're not a fundamental datatype. This also buys you flexibility).
I don't know of any benchmarks, though, and I can't currently be bothered write my own at the moment.
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"Flexibility" is what destroyed C++. Some things should not be flexible.
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Since when? I see floating point in plenty of places. Regexps not so much.
Most data comes in a more structured form and doesn't need a regex to make up for a broken data model. XML parsers are used far more than regex today.
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I see floating point in plenty of places.
I think the two of you are looking in different places. It is absolutely true that for some types of programming regexen are more common, while for others floats are more common. I have no idea which is more common overall, though I think the small, reinvented-wheel scripts that fall into the former category may unfairly bias the results.
XML parsers are used far more than regex today.
XML is a dirty hack for data representation. Plain text is ubiquitous, and plain text manipulation tools can even be used on stuff that isn't plain text (like XML). While XML parsers are certainly more widely used in the Java and .NET world than regexen (but then, regex support in Java was a bucket of ass last time I checked, so anyone with half a brain would avoid it if possible, thus skewing the statistics), but I'm not sure I buy the idea that XML parsers are "used far more than regex today". I think you might suffer confirmation bias based on where/how you do your programming.
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Interesting since I see plain text as a dirty hack for somebody who doesn't have a decent data standard.
The world is moving away from the idea that data is a bunch of characters in a file. I'm glad this is the case.
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The world is moving away from the idea that data should be readable without specialized software. I'm glad this is the case.
FTFY
As for XML in particular -- it's even less readable than s-expressions, which serve as a very decent data standard with the same capabilities as XML (and then some), and it's far easier to write code to parse s-expressions than XML, too.
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Perhaps. I've not particular love for XML but it is far superior to trying to pull data out of unstructured text.
We aren't comparing XML to s-expressions. Both are decent solutions and superior to just hammering away in a ad hoc fashion and writing line noise to fix it later.
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I've not particular love for XML but it is far superior to trying to pull data out of unstructured text.
Who said anything about unstructured? I just want it to be readable.
It's amazing the way people will complain about $variables but don't see anything wrong with <tags type="shitty" title="ass">heaps of ugly</tags> for their data formats. We aren't comparing XML to s-expressions. Both are decent solutions and superior to just hammering away in a ad hoc fashion and writing line noise to fix it later. Ah, but . . . s-expressions are much more "plain text" than XML. While one can technically write both in pure ASCII, XML reads like fucking line noise. [–][deleted] sorry, this has been archived and can no longer be voted on [deleted] [–] 0 points1 point sorry, this has been archived and can no longer be voted on You don't have unstructured text to begin with. Unstructured text is broken by definition. [–] -2 points-1 points sorry, this has been archived and can no longer be voted on Well I find regexps line noise, and most (not all!) of the time I can do the same thing fast enough without using them (faster to write, and not a bottleneck at run time). I don't want them in the language seducing novices programmers into thinking they are a good idea for all problems. When you need them call the library. I'm not sure how I feel about floats. I think C++ should have made them a library, but C++ has the ability to extend language syntax in libraries. I prefer to see x=y+z over x=add(y,z) - in languages that use the x=y+z syntax for integers (but I do not want to see that syntax for things that are not a number - ahem string). I don't see any syntax for regular expressions that is standard enough in natural language to warrant special syntax in the language. [–] 1 point2 points sorry, this has been archived and can no longer be voted on Floats are included in every language because the CPU supports them. They can't be added via a library, the compiler must understand and be able to emit the correct machine code instructions. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Nothing stops the library from dropping into assembly language to get those CPU instructions. Nothing stops the optimizer from inlining simple library functions. It is much easier when the compiler knows about floating points, but it doesn't have to be that way. Check out some of the template work to app matrices to C++. All libraries, yet they use CPU instructions. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Very interesting, thanks. When you say the library can drop into assembly language -- is there a C standard way of doing this? (I ask because so far I've only seen vendor specific methods.) [–] 1 point2 points sorry, this has been archived and can no longer be voted on I don't think it is standard, but everyone has one. Most compilers follow the system standard so they can sell their compiler as a drop in replacement for whatever the OS vendor ships. (GCC is also a common one). [–] 0 points1 point sorry, this has been archived and can no longer be voted on Wouldn't it be weird though for the C standard to say, "and you have to implement these header files, which is impossible to do with the language as defined"? It would be awesome to see C extended enough that new first class data types that require new machine code instructions COULD be added via library though. I'd love to have 48-bit pointers and 80-bit floating types. [–] 0 points1 point sorry, this has been archived and can no longer be voted on In any language with an ffi (and if you want the pretty, overloaded numeric operators) then there's no reason you can't have floats as a library, actually. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Then you should just learn to use regexps. Strings are a basic type. They're more common than integers, arrays, hashes, booleans, floats, and everything else. String operations are concatenation, printing, and doing regexps on them (#match #scan #sub #gsub #split etc., or m// m//g s/// s///g etc. in Perl-speak). I wouldn't even notice if they removed all non-regexp methods of String class, they're almost never used other than as ugly performance hacks. [–] 1 point2 points sorry, this has been archived and can no longer be voted on If all you have is a hammer... [–] -1 points0 points sorry, this has been archived and can no longer be voted on Regexps are an awesome tool, like closures, and hashtables, and for that matter files. There used to be languages which didn't support them natively - some of them still in use today. [–] 0 points1 point sorry, this has been archived and can no longer be voted on "natively" as in there's a cute syntax? because that's a win. [–] 0 points1 point sorry, this has been archived and can no longer be voted on That depends on what you do. Most of my work is with hardware. Strings are not a basic type, and they are not even very common. Integers are the the most common basic type for me, followed closely by bitfields. Even still I disagree. regexps are useful for a small class of problems, but in most cases there is a different solution that is a lot easier to maintain. [–] -1 points0 points sorry, this has been archived and can no longer be voted on It's funny how you start out with "That depends on what you do," then end up saying "in most cases there is a different solution that is a lot easier to maintain," when the truth is that your statement about how there's usually a more easily maintained solution is entirely predicated upon an assumption about what kind of programming you do. [–] 1 point2 points sorry, this has been archived and can no longer be voted on how there's usually a more easily maintained solution is entirely predicated upon an assumption about what kind of programming you do. Notice the word maintain? Regular expressions are hard to maintain if they have any complexity. Break your problem down into steps and the next guy will have a much better chance of understanding what you mean. Take a look at the regular expression to validate email addresses for example. Once again, I didn't not say regular expressions are the wrong solutions to all problems. I said they are not the best solution for many of the problems they are used for. Do not read my condemnation of regular expressions as a in all cases things - I've used regular expressions before when they did make the code better, but most of the time I've seen them used a different solution would have been better. [–] -1 points0 points sorry, this has been archived and can no longer be voted on Notice the word maintain? Yes. That doesn't change the point I made. Regular expressions are hard to maintain if they have any complexity. Many potential substitutions for regular expressions are even more difficult to maintain if they have any complexity. Break your problem down into steps and the next guy will have a much better chance of understanding what you mean. I don't know if you've noticed, but you can usually do this with regexen, too. There's no need to throw out the baby with the bathwater. I said they are not the best solution for many of the problems they are used for. I agree with that. The number of times I've seen someone use /foo/ to try to match something that doesn't even have any variability in it is just scary. That's a clear case of overengineering, where a simple equality comparison would have been more appropriate. There's a big difference between "many" and "most", though -- and while you said "many" here, you said "most" last time. most of the time I've seen them used (emphasis added) I think this might be the problem. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Just to annoy you, I can't recall the last time I had to dig through an installed perl module to find out how to do something with it See MIME::Fast. Granted I still agree with the statement, I just spent hours this last week messing with that module because of the lack of documentation. But I suppose anyone could look for a module that works as a counter example to that statement. In general that statement is very true. [–] 0 points1 point sorry, this has been archived and can no longer be voted on I can't recall the last time I had to dig through an installed perl module to find out how to do something with it, but this is something I do on a daily basis in ruby. Net::IRC, but this module blows anyway (no sane way to determine whether the server connection has silently died due network problems, for example). [–][deleted] sorry, this has been archived and can no longer be voted on [deleted] [–] 3 points4 points sorry, this has been archived and can no longer be voted on I suspect perl will be the last 'language' without a grammar external to the codebase. The Perl 6 grammar is external to the codebase. The last language to use sigils. Ruby (influenced by Perl) has sigils. Maybe the last language to use evaluation 'contexts'? You can argue that any language with multidispatch based on return value has contexts. I've taken a couple of looks at perl.... You would do well to look more closely. [–] 1 point2 points sorry, this has been archived and can no longer be voted on my take on perl is that its value is how many ideas it put in that have turned out to be very wrong - a bit like many features of C++ were on reflection seen to have a complexity-cost/practical benefit ratio that didn't justify their existence, so with much of perl. Like what? The only thing that I can think of is export. All the other of C++'s features justify their existence for someone. [–] 0 points1 point sorry, this has been archived and can no longer be voted on exception specifiers? Does anybody use anything other than throw() ? [–] 1 point2 points sorry, this has been archived and can no longer be voted on Ruby doesn't have a grammar external to the codebase, last time I checked (and I find this disappointing). C++ also doesn't really have a very well defined grammar, since it's not context-free, so different compilers will handle undefined edge cases differently. [–] -3 points-2 points sorry, this has been archived and can no longer be voted on and am relieved that this seems to be the consensus among software engineers As am I. Once upon a time perl was getting really popular and looked like it would be a language you would have to know to be a programmer. So I left the field entirely for some years. I was so glad to come back and see that it had gone the way of COBOL. There may be hope for our field yet. [–] 1 point2 points sorry, this has been archived and can no longer be voted on Yes, now you can program in superior industry standard languages, like PHP and Java, that are intelligently designed and come with extensive and consistent standard libraries, unlike Perl. Perl has only CPAN, where you may find modules written by some hippie hackers - how could you trust those, not even talking about any enterprise level quality? [–] -2 points-1 points sorry, this has been archived and can no longer be voted on I hate both PHP and Java. But C# isn't bad. And CPAN dwarfs in comparison with the libraries available for Java. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Jesus Christ, man. Are you telling me I should give up programming for a few years because I don't like Python? What the hell is wrong with you? [–] -2 points-1 points sorry, this has been archived and can no longer be voted on I'm having trouble reconciling your statement with my comment. How did you come to the conclusion that I want you to quit programming? I did because working with perl was so disgusting for me, and it was so frustrating for me to see it getting so popular that I decided this field just wasn't worth the money to put up with that kind of frustration. It was kind of like US politics for me, actually. Watching the wrong continue to win over and over. I don't live there any more. :) [–] -1 points0 points sorry, this has been archived and can no longer be voted on How did you come to the conclusion that I want you to quit programming? Well . . . either you think that was the right response, or you probably now think you were a fucking idiot when you quit programming because Perl was popular. I was just pointing out what a fucking idiot I think you must have been to do that. What a fucking idiot. It was kind of like US politics for me, actually. Watching the wrong continue to win over and over. I don't live there any more. :) Comparing programming to politics is a bit like comparing baseball to eating a shit sandwich. I don't like baseball much, but I understand that some people enjoy it as a hobby -- whether playing or watching -- and it seems like something that could provide someone with a fair bit of enjoyment. I don't see politics (or eating a shit sandwich) in the same light. [–] -2 points-1 points sorry, this has been archived and can no longer be voted on Well . . . either you think that was the right response, or you probably now think you were a fucking idiot when you quit programming because Perl was popular. I have more than programming as a skill. I just switched to something more lucrative (but that I didn't enjoy quite as much) for a time. Why would that make me an idiot? I came back stronger and better armed. I didn't quit because perl was popular, I quit because it looked like I would always be forced to use it. I don't see politics (or eating a shit sandwich) in the same light. You misunderstood my point. I hate politics but I care about my life. Watching people who get elected who keep on making life worse, when it was obvious that's what they would do, is/was just too frustrating to continue to deal with when there are other options. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Why would that make me an idiot? I guess I made the unwarranted assumption that, like most of the actually halfway decent programmers I've met, you like programming as an activity in and of itself. Instead, it seems like you treat programming more like a sales job -- valuable for the money it provides and for the fact that you simply don't hate it, so you can stand to do it for a living. If you hate Perl so much, I guess your decision might have been perfectly reasonable, if you couldn't get a job that didn't involve Perl for a while. Pardon me for assuming you're a geek rather than a 9-5 daycoder. You misunderstood my point. I hate politics but I care about my life. Actually, I understand that point, and I'm in the same boat. I think you missed my point, which is that I love programming. It is, thus, completely different for me from politics. [–] -1 points0 points sorry, this has been archived and can no longer be voted on you like programming as an activity in and of itself I very much do. But big business has a way of making one hate what they love. Instead, it seems like you treat programming more like a sales job -- valuable for the money it provides and for the fact that you simply don't hate it, so you can stand to do it for a living. If you hate Perl so much, I guess your decision might have been perfectly reasonable, if you couldn't get a job that didn't involve Perl for a while. Misunderstanding from you. The fact is I very much like programming. For me the goal is to take whatever problem and create an elegant, beautiful solution. When I can't do that it bothers me. A lot. Working in perl means never feeling like my solution is elegant or beautiful because it has to be hacked together since perl lacks nearly everything that makes programming elegant (e.g. clean nested data structures). The source code also looks awful. For nice code I make, I find it pleasing to later look through the code. For perl it's always embarrassment. I can never be proud of what I made. Pardon me for assuming you're a geek rather than a 9-5 daycoder. I prefer to think of myself as an artist. But since I can't draw, the programming language has to be my canvas. I think you missed my point, which is that I love programming. It is, thus, completely different for me from politics. So if you saw something destroying that which you love (programming or your life), you wouldn't get frustrated that people are doing it to themselves willingly? [–] 0 points1 point sorry, this has been archived and can no longer be voted on 2 of those made it into 5.10 and the other is available on CPAN. I think you mean three of those are in 5.10. Pluggable MRO and the C3 MRO are part of the 5.10 core. [–] -1 points0 points sorry, this has been archived and can no longer be voted on Ah, sorry, although we're definitely on the same page. [–] -1 points0 points sorry, this has been archived and can no longer be voted on Perl's the reason that our languages today are expected to have first-class regular expression support Yet another reason to hate Perl. Regular expressions is the kind of thing you put in a library, not in the syntax of your language. [–] 0 points1 point sorry, this has been archived and can no longer be voted on Even when that language was designed for processing text? [–] -1 points0 points sorry, this has been archived and can no longer be voted on That depends on the intended use of the language. You certainly don't need regex support in the core language for device driver development, but there's more to programming life than bit-shifting. [–] -2 points-1 points sorry, this has been archived and can no longer be voted on There, I hope that's fair, but I strongly suspect I said nothing you don't already know. You did, but only because you are mostly wrong about everything you said. [–] 13 points14 points sorry, this has been archived and can no longer be voted on Perl's lack of decent function declarations and incomprehensible OO kind of did it in for me. After trying to learn Perl for a while I realised that you can never keep the language in your head unless you are using it all of the time. (C++ has this problem too.) Discovering Python after that was an epiphany. [–] 15 points16 points sorry, this has been archived and can no longer be voted on For me, it was the references and data structures more complicated than a simple hash or list. I really liked that in Python I could, say, just stuff a tuple into a dictionary without worrying about whether I might have messed up the sigils and accidentally summoned a daemon. [–] 5 points6 points sorry, this has been archived and can no longer be voted on It took me a while to understand perl references properly [1], but find it incredibly easy and very very handy now. [1] mainly due to lack of trying [–] 2 points3 points sorry, this has been archived and can no longer be voted on For me, it was the references and data structures more complicated than a simple hash or list. You're giving me some painful flashbacks. ...argh... The "passing arrays into a function" flashback is particularly painful. ( http://www.cs.cf.ac.uk/Dave/PERL/node61.html ) I don't know what is worse, that or PHP's "everything is passed by value by default" function argument semantics. I really liked that in Python I could, say, just stuff a tuple into a dictionary without worrying about whether I might have messed up the sigils and accidentally summoned a daemon. LOL. ;) [–] 0 points1 point sorry, this has been archived and can no longer be voted on It's been a while since I've used Perl. After reading that section, my first reaction was: "What?" My second reaction is that I'm glad I'm not dealing with that on a regular basis. [–] 0 points1 point sorry, this has been archived and can no longer be voted on There are times I find Perl's reference semantics -- and even the (somewhat ugly) syntax -- very useful. The relative explicitness of closure handling is awfully nice sometimes, for instance, even if it's easier to create them in Ruby a lot of the time (they even arise almost accidentally sometimes). Python, of course, lacks the ease of closure creation and use of Ruby (or the ease of creation of Perl for that matter), and lacks the ease of explicit closure handling of Perl. Each of these three languages has its advantages over the others, and the case of closures demonstrates some of that pretty well, I think. I'd still like a somewhat more elegant syntax for dealing with references in Perl, though. [–][deleted] sorry, this has been archived and can no longer be voted on [deleted] [–] -1 points0 points sorry, this has been archived and can no longer be voted on wtf? If you think that's easy in perl you should try it in.... anything else! Good lord, have you ever looked at any other language than C, Assembler or crap like that? Most of the languages I know can (a) do this and (b) make it vastly easier. [–] 3 points4 points sorry, this has been archived and can no longer be voted on The idea that you can keep a language in your head if you're not actively using it is quite optimistic... Python is my #2 goto language after C++ and I don't keep it all in my head because I'm not using it very often. I haven't used PHP in 4 years and I have almost completely forgotten it. I keep relearning C# every time I work on a project in it. [–] 8 points9 points sorry, this has been archived and can no longer be voted on Discovering Python after that was an epiphany. Why? Larry borrowed Python's object system for Perl 5. ... you can never keep the language in your head unless you are using it all of the time.... Different people have different preferences, but I don't understand this. My working English vocabulary is a few thousand words, but I can recognize and use the past perfect form and the subjunctive mood even though they're somewhat rare, and I can keep up with Pynchon's vocabulary with a dictionary at hand. [–] 1 point2 points sorry, this has been archived and can no longer be voted on Thankfully, Python is more than an object system. [–] -4 points-3 points sorry, this has been archived and can no longer be voted on Are you american? If so, go to the UK and listen to some cockneys talking. Having a hard time following the conversation? Now you see the problem with perl. [–] 9 points10 points sorry, this has been archived and can no longer be voted on Now you see the problem with perl. If it's a problem that people can create their own jargons by choosing their own identifiers, you have to reject every programming language as advanced as a macro assembler. [–] -3 points-2 points sorry, this has been archived and can no longer be voted on No, (one of) the problem(s) in perl is that there are so many different ways to do the same thing with no clear trade offs between them. Lisp already gets complaints about how many ways there are to do similar things, but at least in lisp each option has a real trade off (e.g. elt is more flexible but slower than an element access routine specific for the data type it's applied to). [–] 6 points7 points sorry, this has been archived and can no longer be voted on ... there are so many different ways to do the same thing with no clear trade offs between them. If you want a list of clear tradeoffs, I'd be happy to provide them. They do exist. [–] -1 points0 points sorry, this has been archived and can no longer be voted on They exist in some cases, but not in every and when I was using perl (5.6-5.8-ish) it really felt like most of the time it didn't. If the only difference is aesthetic (e.g.$a->method(2); vs method(\$a, 2)) then it just comes to the convention of the user or team. This is where you start running into "local dialect" issues that just don't exist when so many ways to provide identical functionality don't exist.
[–] 7 points8 points
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If the only difference is aesthetic....
The difference between those two cases is not aesthetic (and, in a twist of irony, that's one of the problems from borrowing Python's object system).
... then it just comes to the convention of the user or team.
... just like naming conventions, factoring conventions, filesystem layouts, documentation standards, brace placement, testing, design, deployment, editors, libraries, dependency management, VCS choice and use, branch strategy, code ownership, bug tracking, and numerous other maintenance concerns you either deal with by becoming proficient in the local culture or you don't.
[–] 1 point2 points
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This very clearly explains your preference for Python over Perl. You obviously prefer authoritarian language design.
This also runs into much of the reason for my preference for Ruby over Python, because I don't prefer authoritarian language design.
[–] -1 points0 points
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Oh really? Then why do I prefer Lisp (vastly more malable than perl) and Smalltalk (ditto) to any other languages? I prefer almost anything to perl.
[–] 2 points3 points *
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Are you from somewhere other than London?
FTFY :-)
But seriously, I don't get what you're saying. Are you saying that expressive Perl relies so heavily on idiom that it's inaccessible to outsiders?
[BTW, if you think Cockney's unintelligible, I invite you to spend a week in Glasgow or Newcastle...]
[–] 3 points4 points
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I'm from the north of England and I once had need of asking directions in Newcastle. After two unsuccessful attempts at understanding the directions I was given I saw a police officer and thought, "He's a copper, they have to speak English". Wow, was I so wrong.
Off topic I know but I get amused when I see English dialects subtitled for American audiences. :)
[–] 0 points1 point
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Even after living in Glasgow for four years, I'd encounter someone I could not understand at all at least once a month.
[–] 0 points1 point
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No, perl advocates are always talking about how perl is like english. I consider this the greatest of its mistakes and I was pointing out the fallacy of chromatic's statement. He's trying to claim that knowing a subset of english will let you get by, but note that even he realizes that he occasionally needs a dictionary. Programming is complex enough without having to consult a dictionary to write a line of code.
[–] 6 points7 points
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Programming is complex enough without having to consult a dictionary to write a line of code.
If you can write reasonable software without looking up documentation (or hitting Ctrl+Space in your IDE) once in a while, you're a far better programmer than anyone I've ever met.
[–] 1 point2 points
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I have to look up documentation on (standard) library I use all the time. But I rarely have to lookup documentation on language's operator and semantic. That's one big difference.
[–] 2 points3 points
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That's one big difference.
Just like natural language, you have memorized patterns of communication. Those you haven't memorized -- those you don't use frequently -- you consult documentation.
Where's the difference?
[–] 4 points5 points
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Aren't you all talking here about the difference between grammar and vocabulary?
[–] -4 points-3 points
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I look up library functions/methods, what they expect, etc. I virtually never look up fundamental language things (e.g. "will calling map on this collapse everything into a flat list, turn everything into references, or something else entirely?"), and in the rare case that I do, I curse that language for wasting my time with complexity.
[–] 0 points1 point
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I look up library functions/methods, what they expect, etc. I virtually never look up fundamental language things
Great. You've just described my relationship with Perl.
[–] -2 points-1 points
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Don't use much of the language, eh?
[–] -1 points0 points
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You had me until 'a far better programmer'.
If you can write reasonable software without looking up documentation (or hitting Ctrl+Space in your IDE) once in a while, you have a far better memory than anyone I've ever met.
There, fixed.
[–] -1 points0 points
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It's a nit, but I meant also for a library you haven't already used.
[–] 1 point2 points *
sorry, this has been archived and can no longer be voted on
Still, I don't get your point, perhaps I'm missing something: if someone's programming without consulting documentation, using a library which he hasn't used previously, either he has memorized the doc at some point of time previously, or he has predictive power to determine how to use the library. Excluding the ridiculous option, it comes back to what I said, doesn't it?
[–] 7 points8 points
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Perl's ... incomprehensible OO kind of did it in for me.
...
Discovering Python after that was an epiphany.
The irony is that Larry has stated that he stole Perl's object system directly from Python.
[–] 1 point2 points
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Thankfully, Python is more than an object system.
[–] 4 points5 points
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Larry says a lot of things. He also decried Lua for having an object system that is actually the exact same thing perl has. Since perl's is so minimal I can't imagine what he's talking about here, unless it's inheritance or something. Wonder why he didn't claim to steal it from C++/Smalltalk/Java/etc.?
[–] 14 points15 points
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Wonder why he didn't claim to steal it from C++/Smalltalk/Java/etc.?
Because Python's object system has method/function equivalence, with no implicit invocant and only the invocation sufficing to distinguish between them.
C++, Smalltalk, Java, et cetera didn't make that mistake.
[–] 0 points1 point
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I'm curious how that's a mistake. Unifying functions and methods seems nice to me.
[–] -1 points0 points
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Write a function that you want to use simultaneously as a function and a method. Now pass in parameters. (This starts to get painful when you want to do something with the invocant when it's present.)
[–] 2 points3 points
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Python is one of those languages I've never bothered to learn. It's not that I have any problem with it (I just gravitate to novelty; Haskell; Qi; Agda), it's that I know if I wanted to use it some day it would be very easy. I may pick it up for scripting purposes some time.
[–] -4 points-3 points *
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(C++ has this problem too.)
I'm curious what sort of thing you find to be extremely complex in C++.
Perhaps you look at it differently than I do, but C++ strikes me as fairly simple and straightforward. Remembering the STL and such is significantly more mentally taxing, of course.
[–] 12 points13 points
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I'm curious what sort of thing you find to be extremely complex in C++.
The complexity in C++ doesn't sit so much in the syntax (like it does in Perl), but in the semantics. Every feature seems to come with a bunch of gotchas where if you don't strictly follow the straight and narrow path you wander off into undefined land (and destruction).
[–] 5 points6 points
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If you aren't using STL, then you are using C++--,
"Well, its a easy language, if you don't learn half of it..."
A great language is simple, expressive.
[–] -1 points0 points
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False. If the language was just the sum of its libraries libraries, everyone would use perl!
In any case, I've never had an urge to use the STL. It just introduces complications because I'm not sure how they're implemented.
[–] 1 point2 points
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The problem with C++ is how the features interact with each other. For example, how type conversions interact with overridden function definition. The ambiguous cases this creates requires a new operator: "explicit". I always wondered why you would ever need that... until I ran into such a case.
C++ is like that all over. Features there that only exist to counter the bad effects of other features.
[–] 0 points1 point
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I read it six times, and I've come to the conclusion that the downvotes must be the result of a combination of saying something that completely misses the point of C++'s complexity (seriously, if you aren't using STL "and such" you should be using C) and (ironically) your later complaint about downvotes. Of course, that's just my unscientific guess.
(For the record, I'm not the type that tends to downvote for voting trend complaints. Sometimes, it's nice to know why downvotes are happening, and without asking you may never know.)
I upvoted you, though, because I read this line:
You were apparently perfectly aware of the possibility you might have overlooked some implication of the previous commenter's statements, and asked about it. That strikes me as entirely reasonable and worth of an upvote for providing encouragement to further discussion.
[–] -1 points0 points
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Perl's lack of decent function declarations
incomprehensible OO
I think the OO constructs in Perl are perfectly comprehensible, in concept -- though the dereferencing syntax used for OOP in Perl is certainly fugly and sometimes difficult to parse by eye. When I need OOP in a high-level dynamic language, I prefer Ruby, so I can understand this complaint of yours perfectly well.
There are other times that I think Perl is a better language for the job (than either Python or Ruby), though.
[–] 0 points1 point
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"Perl's lack of decent function declarations" likely means "no function or method signatures", which is a very fair point.
[–] -1 points0 points
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True. I was just asking what sime meant -- I wasn't claiming it wasn't a fair point, since I wasn't sure what point sime was trying to make. I think yours is a pretty good theory for what sime meant, but it would be nice to hear it form the horse's mouth so to speak.
[–] 1 point2 points
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mr_chromatic basically hit the nail on the head. Although to "no function or method signatures" I would add "...and the crazy manual argument unpacking/handling needed at the start of each function".
[–] -1 points0 points
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crazy manual argument unpacking/handling
I don't know that I'd call it "crazy", but it is a little odd.
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2014-07-22 10:50:44
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https://www.acode.edu.au/mod/wiki/view.php?id=550
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## Lecture capture wiki
### Institutional Lecture capture tool/s and comments
#### Auckland University of Technology (NZ)
2013: Mediasite and Bb Collaborate for web conferencing
At the moment we are only just out of the pilot phase for lecture recording. The main driver for our MediaSite pilot was to support some core Health papers with up to 1500 students across 3 campuses. This has been largely successful, despite the occasional technical hiccup. We have just three mobile recorders that are used wherever required, but there is a little extra budget available this year to perhaps install a couple of fixed recorders. The underlying objective is to encourage lecturers to use this to support a flipped classroom model, whereby they record pre-lecture content for viewing through our Blackboard system, but the main uptake to date is for streaming and recording live lectures. There is however increasing awareness of the value of the pre-lecture recordings, and we have a couple of small recording rooms where this can be done. The system is also increasingly used for recording higher profile events such as invited speakers, conferences and seminars.
#### Australian Catholic University
2013: Echo360
Echo360, and distributes the recordings automatically to units through the EchoCentre block in Moodle. ACU has been piloting two lecture capture software solutions for pre-recording lectures - Echo360 Personal Capture, and Adobe Presenter recordings hosted on Adobe Connect, to extend the interactivity of traditional lectures. These recordings, both of live and pre-recorded content, are not sanctioned through policy but rather as an opt-in for lecturers to provide material for both revision and equity purposes.
#### Australian National University
2013: In-house bespoke system
Currently reviewing situation with the look to replace this with a commercial offering (Echo360). Further, replacement will not necessarily be a like for like hardware/software replacement as the university is analysing its stance on lecture delivery.
#### Bond University
2013 Mediasite
In response to a recommendation in the 2012 Bond University Student Association Academic Audit, Bond University is increasing the number of teaching spaces equipped with lecture recording capability. It is a 2013 requirement that 80% of lectures conducted in teaching spaces equipped with video recorders are captured and streamed online for student review. ITS regularly sends an email with information about how to have one's lecture recorded. We have inserted a line in that email inviting people to the Office of Learning and Teaching for support in producing digital content alternatives to lecture streaming, such as creating and posting screencasts through Camtasia.
#### Central Queensland University
2013: Lecture capture using Cisco/Tanberg equipment. Camtasia for desktop capture.
We are using a number of tools for lecture capture as staff are at various stages on the flipped classroom journey. Recorded lectures are converted into WMV and QuickTime format on streaming servers. A Cisco appliance does the transcoding. Camtasia for self produced talking head / PowerPoint style presentations and quick end-of-week and beginning-of-week "engagement" videos. Ad hoc reusable recordings of experiments, interviews and the like. Typically higher production quality due to their reusability, often the Video Producer is involved in this sort of work. Some people are looking at replacing lectures with tutorial style classes that are typically more interactive. Part of this process is to break down the didactic lecture into reusable chunks and provide these chunks online. Overall we have staff spread right along the continuum from traditional lectures to flipped classrooms entirely online. We are trying to get folks to move from their traditional mindsets (50 min face-to-face delivery) to see that they are not constrained by the time(table) or the lecture room. Definitely encouraging less 'lecturing' per se and more diverse video delivery.
#### Charles Darwin University
2013: Bb Collaborate, mp3 recorders, video.
From the University perspective it is optional and the supported tools are the Blackboard based ones. At the School level it is mandated in some Schools and optional in others, and they provide their own tools. Resources and support are available from the central Office of Learning and Teaching on good practice (pedagogical and technical) in lecture recording. For pre/post-recording: Collaborate, Voice Tools, Camtasia Studio.
#### Charles Sturt University
2016: Echo360
At CSU we use Echo360. We have around 160 venues equipped to record lectures using a combination of recording technologies, with an uptake of around 50% of subjects being recorded. We have one faculty with an opt out policy on lecture recording (the faculty of business). All other faculties are opt in. Although we have seen continued growth every year in the number of subjects having lecture activities recorded, we have seen a larger growth in the number of subjects pre-recording content for their students and not recording in-class activities. This session we would estimate that 1/3 of subjects will use pre-recorded content.
2013: Echo360
Use is encouraged, and growing, especially as a resource for DE students. At present it is an opt-‐in system for 2 faculties (not compulsory) and opt-out for 2 faculties (compulsory). Lectures must be scheduled for Arts and Education, but are automatically recorded for Business and Science. We use 5 types of recording methods: a) automatic recording on a scheduled basis via the Echo360 capture appliance (53 rooms); b) automatic recording on a scheduled basis via people and content from Interactive Video Teaching (40 rooms) c) 'podium capture' -‐ software available on teaching space PC but has to be manually activated; (Available upon request in any room); d) 'personal capture' -‐ software installed on staff PC's -‐ this facility can also be made available to students; and e) external media ingest -‐ upload pre-‐recorded material to Echo system server. Outputs: Access to view, download, stream and RSS feeds are available via a link from subject/unit site in LMS and via iTunesU (Private -‐ restricted to staff and students). In 2012, first year of major usage, over 200 subjects/units scheduled recordings across a semester. 360 subjects for 201330. There were 4000 recordings in total (2012)-‐ using all 5 capture methods, and 165,000 views. Growth continues. There have been very high viewings in the 2 weeks prior to exams, indicating use for review.
#### Curtin University
2013: Echo360
Echo 360 (EchoSystem, Personal Capture, Interactive Live Webcasting etc.) Opt-out model in our 40 largest venues, 130 automated recording venues, 50 specialist multi-camera Manual Recording installations, 1500 hours of recordings per week, 22,000 recordings per year, 20%-30% of recordings made outside of automated lecture venues, thousands of student-generated recordings, 6% of recordings made by staff in their office using Echo360 Personal Capture software (PCAP).
#### Deakin University
2013: Echo360
We want to put more transmissible material in the cloud, but our position is that as long as we're giving lectures, we should be recording them all!
#### Edith Cowan
2013: University Camtasia Relay for live capture, Camtasia Studio for desktop capture
Students want it, so we want it! We are busy fitting all learning spaces with computers to facilitate the use of lecture capture and we are seeing it grow rapidly. We get a lot of feedback from students, and they get grumpy when it is not available.
#### Federation University
2013: BB Collaborate, mp3’s and Video
The recently established Learning Technology Advisory Group intends to investigate other options (such as Big Blue Button). We don't currently have any audio capture facilities. Some staff use MP3 recorders; some have used Video cameras to capture their classes. The Library has these to loan. CLIPP, our central academic support centre supports staff with video and audio conversions and provide general help. There are some other investigations going on with partner providers regarding harmonizing some of these technologies across the partners. Still early days
#### Flinders University
2016: Home grown solution and Camtasia for desktop
Flinders University has an in-house lecture capture system that records from 75 locations, including all major lecture theatres and larger classroom spaces (including in rural remote sites from Darwin to Southeastern Australia). Lecture capture is automated, and mandatory for all scheduled lectures, unless exemptions apply. All recorded lectures are automatically embedded and replayed through our online environment. We have just started rolling out Camtasia across all staff for desktop recording and video.
2013 Home grown solution
All lectures in our 50 major lectures are captured and automatically made available through links from our LMS after the lecture. Staff may get an exemption, but reasons are quite limited. Not all lectures are live streamed, but some are.
#### Griffith University
2013: Echo360
Echo 360 is available in over 90 lecture rooms plus a selection of Seminar rooms, and is also available for personal desktop capture. An opt-out policy has just been approved: Lecturers may request approval to not use the automatic recording of lectures in the following circumstances: the lecturer will record the lectures using other supported methods and will make the lectures available to the students on the relevant course site; or the lecturer has strong and justifiable reason for not recording the lecture. Students are to be advised in the Course Profile whether or not lecture capture is to be used for a course.
#### James Cook University
2013: Cisco Telepresance and Camtasia Relay
We are in the beginning the process of evaluating our existing infrastructure and processes, but at present we use the following Lecture capture tools: Cisco Telepresence content Server (JCU eLectures) - for capturing lectures in lecture theatres equipped with videoconferencing equipment - captures presenter and any connected AV source - manually processed (transcoding, editing, copyright metadata etc) - mobile compatible delivery profile - stored on local web server and delivered via progressive download - typically lecturers publish videos to their Blackboard subject sites via the University's current eReserve product (Concord Masterfile) Camtasia Relay - for personal lecture capture, vodcasts, or mobile capture (via FUSE app) - can be used in any teaching room (eg. typically where videoconferencing infrastructure not available) and also available on all staff computers - captures computer screen, an audio source and webcam - presenter selects output profile and automatically uploaded, processed and hosted on local web server - users automatically notified via email with URL of the video and they add it themselves to their Blackboard site. University's general stance of lecture capture: No official policy governing lecture capture or implications for privacy, IP etc. eLectures recorded by request (webform), not by default. eLectures must be processed through Reserve Online to capture copyright and publication metadata. Camtasia recordings are the responsibility of the individual lecturer. Video recordings are stored on the central media server, not uploaded to the LMS
#### La Trobe University
2016: Echo360
La Trobe also has Echo360, deployed to about 90+ venues across 5 campuses. Recordings are automagically scheduled according to information in the timetabling system. Recordings are not, however made available to students unless the lecturer sets up the link in MOODLE. But in all cases where students have asked for it, the link has materialised.
2013: Echo360
"All-in" Every timetabled lecture in 88 equipped venues is recorded unless a case is made (and accepted) for not recording. A "Pause" and "Resume" button is provided to avoid recording copyright materials. If someone does not want their lecture, or series of lectures, recorded they need to apply to opt out of the system. See http://www.latrobe.edu.au/news/announcements/lecture-recordings-go-all-in-in-2013
#### Lincoln University
2013: Camtasia Relay. Symposium screens in the lecture theatres for annotation.
We have lecture recording equipment in all of our lecture theatres. Some lecturers also have Camtasia licenses on their desktops so they can record in their offices. Camtasia has been really easy for people to use so we have stayed with it. It records the screen and the audio. We have been using Camtasia for 4-5 years now. While encouraged, lecturers can choose whether they want to record lectures or not. We are reviewing our qualifications, and because of the earthquake, we are going to rebuild some of our lecture theatres. This is my guess for the future, the university will automatically record all lectures.
#### Macquarie University
2013: Echo360
In 2012 we moved to an opt-out approach where we automatically record all timetabled lectures (excluding repeats). Although all lectures are automatically recorded, the decision to publish the recordings to students through the LMS (Moodle) is up to the Unit Conveners. This aligns with the requirement under our Learning Technologies policy which states Decisions about the technologies to be used for learning and teaching are vested with unit conveners in accordance with Faculty and Departmental arrangements (http://mq.edu.au/policy/docs/learning_tech/policy.html). In 2012 we captured about 33,000 hours of lecture from about 1,200 units. The majority of recordings are audio only although an increasing number provide powerpoint/audio synchronisation. Although there are no specific policies around the use of Lecture Recording, there are some best practice notes published at https://www.mq.edu.au/ltc/altc/wblt/index.htm that are based on an ALTC funded project.
#### Massey University
2016: My Mediasite (desktop)
At Massey we have just finished outfitting 23 spaces across our three campuses with lecture capture technology. A range of different sized spaces but caters in the main for larger class sizes starting at about 60-80 seaters. We have no plans to increase the number of rooms with this functionality, but we can move the boxes between different rooms as we have invested in outfitting more rooms with racks and inputs/outputs to accept the Mediasite recorders. We are also looking into ways in which we can record multiple rooms but have only one box. Recording is opt-in. Our timetabling people manipulate room bookings based on requests to have this functionality. We have seen significant growth in this space over the last two years as the number of rooms have increased. In this sense the growth is expected as more venues = more opportunity for people to record which in turn = more people using the functionality (for better or for worse). We also make desktop recording through myMediasite readily available to all staff and are looking at rolling this out to students as well. In addition, we have invested a lot in flexible recording studios on each of our campuses. These are generally used for more high-end production and are therefore sit at the top of the quality recording of teaching and learning experiences pyramid.
2013: Mediasite 2013
#### University of South Australia
2013: Echo360 2013
The more the better :-) Obvious area for expansion in the future as more faculty embrace blended learning models. We also purchased the Echo360 Personal Capture add-on, allowing staff to record at their desktop and then publish to the Echo360 server.
#### University of Southern Queensland
2016: TechSmith Relay; Camtasia Studio (desktop); Adobe Presenter; Blackboard Collaborate; Zoom 2016
We have lecture capture in every teaching space, using self-hosted Techsmith (Camtasia) Relay. It is also available to be on any computer (even private ones). This handles about 6,000 lectures a semester. It also allows us to upload recordings from other softwares. Staff also have access to Camtasia Studio, Adobe Presenter and can also record using Zoom or Collaborate. Lecture capture is not mandated, but is highly recommended (if you are teaching it should be recorded). We also have a Media Site instance which we are looking to use for streaming from our main teaching spaces (still considering this). Sound complex. Yup :-) Importantly, we are moving to using Equella a lot more for mediating all our recordings, so it will not matter which tool staff choose to use all our recordings will be made available through our Learning Objects Repository, which of course is linked to our LMS (Moodle), for both pushing and pulling recordings.
2013: Camtasia Relay for live capture, Camtasia Studio for desktop capture
Recommended capture using an Opt-in approach. Strong preference for the production of pre-recorded quality presentations. But being practical, this is not yet a widespread practice. We are also strong users of Blackboard Collaborate and house some 200 plus rooms per semester
#### University of Sydney
2013: Echo360
All our lecture captures are streamed via the LMS (Blackboard Learn), use of Echo360 is not mandated centrally but I understand some faculties/schools may mandate its use. Echo360 is not used to replace face to face lectures but as a revision tool, it is also used in some units to assist students with disabilities, some academics limit access to the recordings to the student with the disability.
#### University of Tasmania
2016: Echo360 Active Learning Platform; Echo360 Personal Capture (desktop)
UTAS - Echo360 Active Learning Platform,
• opt-out approved by Senate, driven from timetable
• about 45 venues with dedicated appliance (across 6 campuses), centrally scheduled
• 30+ more with software on house PC, user initiated
• Desktop capture also very popular
2013: Echo360, including personal capture.
We have had lecture recording available since 2005. We now have approx. 35 venues enabled with audio + content (VGA) capture. In Hobart approx. 75% of all delivered lectures are captured, at other campuses the figure is 60%. We capture approx. 540 lectures per week in-venue including 100+ lectures or short recordings captured at-desk using the Echo Personal Capture or on MP3 devices followed by upload to Echo. The volume of recordings continues to increase each semester. We are trialling live webcasting via Echo and there has been some uptake. The main route for distribution of the recordings to students is via integration with the LMS (D2L) and the Echo system receives 33,000 - 43,000 hits per week. In-venue lecture capture bookings are placed by staff using either our LMS middleware (called MyLO Manager) or an online form. There is strong expressed demand from students that all lectures are recorded and this has been considered but we need to improve the integration between Echo and the timetable system to facilitate an opt-out stance, as well as policy change endorsed by Academic Senate.
#### University of Technology Sydney
2016: Echo360; Echo360 Personal Capture (desktop)
We have Echo 360 in two large lecture rooms and are not intending to make the recording of live lectures more widespread. Instead, we are rolling out Echo desktop capture to encourage academics to record material for students to watch before class, so that classes can make use of this (and other) material and be more active and collaborative.
2013: No institutional wide system
We are not engaged in systematic lecture capture, in fact I actively discourage it. My view is that if the lecture can be replaced by a video of it, then I encourage academics to make a podcast/ vodcast of the lecture and then use the f2f time for more engaging learning experiences. I am aware however, that some academics have made their own arrangements for recording their lectures.
#### University of the South Pacific
2013: Lectopia (legacy system) 2013
Now our audio technicians use recorders only when a request is made by a lecturer. We also record lecturers in our audio studios and then create synchronised PPTs and audio (sometimes with a still image of the lecturer) using Camtasia for uploads to Moodle.
#### University of the Sunshine Coast
2016: Mediasite 2016
Mediasite in 11 spaces. (Our main lecture theatres and a couple of other spaces.) 1 Mobile unit. Fairly widespread. One faculty has had mandated recordings when using equipped spaces for a few years. Opt-out requires Head of School approval. The other faculty has just introduced 'mandated' recordings but apparently leaving opt-out up to individuals, not even requiring HoS approval. Recording setup automated - so they'll happen unless we're notified to stop them. We see it as important component of our blended learning approach (despite misgivings about quality of presentations). Further to my earlier response we are also rolling out Mediasite Desktop Recorder to all PCs and making it available for installation on home computers. This will happen by early semester this year.
2013: Mediasite 2013
Recordings are manually scheduled - there is no automation of scheduling or linking back to Blackboard courses. Recording links are manually added to Bb courses by the lecturer. We are currently in the final stages of preparing for an upgrade to v6.1 in early July. This will bring compatibility to iDevices and other mobile platforms with the move from WMV to MP4 as the media format. Future enhancements include desktop capture, ingestion of media prepared outside MediaSite and virtual recorder capacity for teaching spaces (moving away from proprietary MediaSite hardware requirements). Possibly some better integration with Bb (auto publishing/scheduling?). Lecture recording is voluntary. It is widely used in some Schools but not used at all in others. Students appear to be very much in favour of recording.
#### University of Waikato
2017: Panopto and Panopto Fusion
All teaching rooms have Panopto capability although some may not have video capability. We know have Panopto Fusion as well which allows us to load any video file into the Panopto system. We can then use Panopto to manage access and delivery of those videos. We are seeing use of the Dropbox function which allows students to record and load video as part of assignments for courses. Our Disability support team are looking at using the closed caption function to deliver transcripts of lectures they are supporting. The new search function for speech and automatic OCR of any written text on screen is impressive.
2013
Voluntary but supportive. The software exists in all teaching rooms although fixed hardware (cameras and mics) not as widespread but we continue to roll it out. Our uptake of Panopto has been impressive in the 4 years that we have been using it. We provision papers and users via Moodle so all a teacher has to do is add a Panopto block in Moodle and then Panopto recordings will be available there for students. We encourage use of Panopto outside of lectures since it can be used at your desktop or laptop. We have seen staff using it to give feedback on assignments, to demo experiments, to work through a process in some software e.g. using Excel or SPSS (as well as support areas developing help videos), and some live broadcasts of music performances. Students can now also record to the system if staff allow them.
#### University of Western Australia
2013: Echo360
We have almost 80 lecture venues with the facilities. For the 80 venues, for those that are part of the central timetabling system, all lectures are automatically scheduled for capture and processing. Students access captured lectures through a block in their LMS Unit (ie Moodle course) as long as the lecturer has added the block to the unit page.
2013: Echo360
#### Victoria University
2016: Echo360; Echo360 Personal Capture (desktop); Possible upgrade to Echo360 Active Learning Platform
We have 47 lecture theatres / rooms across 7 campuses equipped with Echo360 and are thinking about upgrading to their new Active Learning Platform in the future. We have an 'opt in' semi automatic system linked with our timetable but have been thinking of looking at 'opt out'. Take-up has not been fast, however, last year we were capturing around 35% of lectures and numbers are increasing. Staff have also started to use the Echo360 personal (desktop) capture system. We have found that an easy to use integration of Echo360 with our LMS (Brightspace) and providing plenty of support has helped uptake.
2013: Echo360 2013
Encouraged but not mandated from a university perspective. Some Colleges have mandated its use in the past - we currently have everyone on opt-in while we implement a new eLearning environment. We will re-visit opt-out (at least at the College level) once the new system is in place. Haven't turned on the interactive features yet but will do so hopefully start of next year as part of the upgrade to our entire eLearning environment.
#### Victoria University of Wellington
2016: Echo360
We have Echo 360 hardware in roughly 20 lecture theatres and all computers have the pcap tool - steadily increasing use. We plan to roll out to all large theatres as funding permits.
2013: Echo360 (replacing Mediasite)
We're making it possible to capture every lecture, whether or not they do is a decision for each course. We're starting to make resources available here: http://www.cad.vuw.ac.nz/wiki/index.php/VStream
#### Western Sydney University
2013: Echo360
At UWS, all lecture theatres are set up automatically to capture lectures and the recordings (using Echo360) are automatically uploaded to the relevant vUWS (the LMS) site. There's an opt-out policy, and Dean (or delegate) approval to opt-out must be sought for 3 or more lecture recordings. Guidance for teaching staff is provided: http://www.uws.edu.au/__data/assets/pdf_file/0008/449270/Lecture_Capture_User_Guide_Strategies_for_engaging_your_students.pdf.
### Lecture Capture Snapshot 2017
2017 Charles Darwin University - Blackboard Collaborate, mp3/mp4
From the University perspective it is optional (we don't generally promote lectures as a pedagogical approach and therefore also don't require anyone to record them). We encourage the use of Blackboard Collaborate (Classic or Ultra) to support student learning (particularly to bring together internal and external students and have multiple specially equipped classrooms for this purpose) which of course is captured. At the School level it is mandated in
some Schools and optional in others, and while encouraged to use Collaborate they often provide their own tools.
Resources and support are available from the central Office of Learning
and Teaching on good practice (pedagogical and technical) in lecture
recording. For pre/post-recording: Collaborate, Voice Thread, Camtasia
Studio.
Western Sydney University
2016: Echo 360 with a transition to Panopto
At WSU, all lecture theatres are set up automatically to
capture lectures and the recordings are automatically uploaded to the relevant
vUWS (the LMS) site. Current policy on
lecture recording is being reviewed by the Learning and Teaching Technology
Advisory Group to reflect evolution of teaching practices and changes in
technology.
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2018-12-09 22:11:02
|
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|
https://tex.stackexchange.com/questions/425733/creating-a-customised-table
|
# Creating a customised table
I want to generate the table below:
I wanted to replicate in latex:
1. no border except the horizontal and vertical lines around the labels A-E and O-D
2. spaced out rows and columns so the entries don't look too jammed
3. a red arrow that traces some of the numbers on the table
I have gotten as far as below:
and this is obtained with the attached code below:
\documentclass[]{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{pgfplots}
\usepackage{mathtools}
\usepackage{cancel}
\usepackage{pgfplots}
\usepackage{amsmath}
\newtheorem{theorem}{THEOREM}
\newtheorem{proof}{PROOF}
\usepackage{tikz}
\usepackage{amssymb}
\usetikzlibrary{patterns}
\usepackage{bigints}
\usepackage{color}
\usepackage{tcolorbox}
\usepackage{stackengine,graphicx,xcolor}
\usepackage{booktabs,array}
\usepackage{hyperref}
\usepackage{lscape}
\usetikzlibrary{arrows,automata}
\usepackage[thinlines]{easytable}
\usepackage[latin1]{inputenc}
\usetikzlibrary{arrows}
\usetikzlibrary{trees}
\usepgfplotslibrary{fillbetween}
\begin{document}
\setlength{\parindent}{0cm}
%\pagecolor{blue!13}
\fancyhf{}
\voffset = 0.1cm
\pagestyle{fancy}
\definecolor{Elite}{RGB}{37,97,172}
\definecolor{web}{RGB}{56, 102, 166}
\setlength{\parindent}{0mm}
\setcounter{page}{1}
$\begin{array}{c|ccccc} \midrule O & A & B & C & D & E\\ \midrule O & \fbox{1} & 5 & X & X & X\\ A & \fbox{1} & 5 & \fbox{4} & 10 & X\\ C & \fbox{1} & \fbox{5} & \fbox{4} & 8 & X\\ B & \fbox{1} & \fbox{5} & \fbox{4} & \fbox{8} & 11\\ D & \fbox{1} & \fbox{5} & \fbox{4} & \fbox{8} & \fbox{10}\\ \end{array}$
%
\end{document}
Latex experts, can you please suggest the modifications so I achieve what I want in this case?
Something like this:
I have used a tikz matrix of nodes with a few bells and whistles.
The boxed entries are done using
boxed/.style args={#1/#2}{row #1 column #2/.style={nodes={rectangle, draw}}}
combined with a .list handler for setting the coordinates to be boxed, which is just a comma separated list of row/column pairs.
The red arrows I have thrown into a \foreach loop.
Of course, you can add as much styling as you like. I have shown how to write the entries in the first row in blue.
Here is the full code:
\documentclass[border=5mm,tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix,decorations.markings,decorations.text,calc}
\begin{document}
\tikzset{
boxed/.style args={#1/#2}{row #1 column #2/.style={nodes={rectangle, draw}}},
->-/.style={decoration={markings, mark=at position 0.5 with {\arrow{stealth}}},
postaction={decorate}}
}
\begin{tikzpicture}[every node/.style={minimum width=1.6em},
boxed/.list={2/2,3/2,4/2,5/2,6/2,4/3,5/3,6/3,3/4,4/4,5/4,6/4,5/5,6/5,6/6},
]
\matrix (M)[matrix of math nodes, column sep=1mm, row sep=1mm,
row 1/.style={nodes={text=blue}}
]{
O & A & B & C & D & E\\
O & 1 & 5 & X & X & X\\
A & 1 & 5 & 4 & 10 & X\\
C & 1 & 5 & 4 & 8 & X\\
B & 1 & 5 & 4 & 8 & 11\\
D & 1 & 5 & 4 & 8 & 10\\
};
\draw[thin](M-1-1.north west)--(M-1-6.north east);
\draw[thin]($(M-2-1.north west)+(0,0.1)$)--($(M-2-6.north east)+(0,0.1)$);
\draw[thin](M-1-1.north east)--(M-6-1.south east);
\foreach \x/\y [remember=\x as \xx (initially 6),
remember=\y as \yy (initially 6)]
in {6/5,4/5,4/4,3/4,3/2,2/2} {
\draw[red,->-](M-\xx-\yy.center)--(M-\x-\y.center);
}
\end{tikzpicture}
\end{document}
So I'm definitely no expert -- but I'd do this as a diagram using \tikz not as a picture. I'm sure that someone who knows what they are doing can get the nodes to be placed automatically rather than by hand! And obviously you can play with how lines are drawn, whether to fill nodes, and so forth.
\documentclass[]{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\tikzstyle{boxed} = [draw,rectangle,thick,minimum height=2em,minimum width=2em]
\tikzstyle{unboxed} = [minimum height=2em,minimum width=2em]
\tikzstyle{arrowline} = [thick,color=red,->]
\begin{document}
\begin{tikzpicture}\bfseries
\node at (0,0) {D};
\node at (0,1) {B};
\node at (0,2) {C};
\node at (0,3) {A};
\node at (0,4) {O};
\node[boxed] at (1,0) {1};
\node[boxed] at (2,0) {5};
\node[boxed] at (3,0) {4};
\node[boxed,fill=red!50](B) at (4,0) {8};
\node[boxed,fill=red!50](A) at (5,0) {10};
\node[boxed] at (1,1) {1};
\node[boxed] at (2,1) {5};
\node[boxed] at (3,1) {4};
\node[boxed,fill=red!50](C) at (4,1) {8};
\node at (5,1) {11};
\node[boxed] at (1,2) {1};
\node[boxed] at (2,2) {5};
\node[boxed,fill=red!50](D) at (3,2) {4};
\node[unboxed,fill=red!50] at (4,2)(H) {8};
\node at (5,2) {$\times$};
\node[boxed,fill=red!50](F) at (1,3) {1};
\node[unboxed,fill=red!50](I) at (2,3) {5};
\node[boxed,fill=red!50](E) at (3,3) {4};
\node at (4,3) {10};
\node at (5,3) {$\times$};
\node[boxed,fill=red!50](G) at (1,4) {1};
\node at (2,4) {5};
\node at (3,4) {$\times$};
\node at (4,4) {$\times$};
\node at (5,4) {$\times$};
\node at (1,5) {A};
\node at (2,5) {B};
\node at (3,5) {C};
\node at (4,5) {D};
\node at (5,5) {E};
\draw[color=blue](-0.5,4.6) -- (5.5,4.6);
\draw[color=blue](0.4,5.5) -- (0.4,-0.5);
\draw[arrowline] (A.west) -- (B.east);
\draw[arrowline] (B.north) -- (C.south);
\draw[arrowline] (C.north) -- (H.south);
\draw[arrowline] (H.west) -- (D.east);
\draw[arrowline] (D.north) -- (E.south);
\draw[arrowline] (E.west) -- (I.east);
\draw[arrowline] (I.west) -- (F.east);
\draw[arrowline] (F.north) -- (G.south);
\end{tikzpicture}
\end{document}
• Thanks. But Andrew's is better code and easily adaptable to produce the same result! – Paul Stanley Apr 10 '18 at 12:17
|
2019-09-18 05:36:16
|
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|
https://crazyproject.wordpress.com/2010/11/07/describe-least-common-multiples-in-a-ufd/
|
## Describe least common multiples in a UFD
Let $R$ be a unique factorization domain and let $a,b \in R$ be nonzero elements. Prove that $a$ and $b$ have a least common multiple, and describe one such multiple in terms of the factorizations of $a$ and $b$.
We begin with some remarks on the elements of a UFD. Let $R$ be a unique factorization domain, and let $S \subseteq R$ be a set of irreducibles such that (1) every irreducible in $R$ is a multiple of some element in $S$ and (2) no two elements of $S$ are multiples of each other. Then we can write every nonzero element of $R$ in the form $\prod_S s^{k_s}$, where $k_s \in \mathbb{N}$ and all but finitely many $k_s$ are zero. The fact that this product is taken over the (possibly infinite) set $S$ is okay because our exponent function $k$ comes from the “direct sum” of $\mathbb{N}$. With this in mind, we will typically not mention $S$ and simply refer to factorizations of nonzero elements in $R$ as $\prod s^{k_s}$, with the understanding that $s$ ranges over a set of representatives of irreducible classes and all but finitely many $k_s$ are zero. Using this notation, for factorizations $\prod s^{k_s}$ and $\prod s^{\ell_s}$, we have $(\prod s^{k_s})(\prod s^{\ell_s}) = \prod s^{k_s + \ell_s}$ using the usual laws of exponents (because $R$ is commutative).
Now we prove a lemma.
Lemma: Let $R$ be a UFD and let $a,b \in R$ be nonzero, where $a$ and $b$ have the factorizations $a = \prod s^{k_s}$ and $b = \prod s^{\ell_s}$. Then $a$ divides $b$ if and only if $k_s \leq \ell_s$ for all $s$. Proof: Suppose $a$ divides $b$. Then we can write $ac = b$ for some $c$, where $c = \prod s^{m_s}$. Then $\prod s^{k_s + m_s} = ac = b = \prod s^{\ell_s}$, so that $k_s + m_s = \ell_s$ for each $s$. Since these exponents are natural numbers, we have $k_s \leq \ell_s$ for all $s$. Conversely, suppose $k_s \leq \ell_s$ for all $s$; then there exists a natural number $m_s$ such that $k_s + m_s = \ell_s$. Note that all but finitely many $\ell_s$ are zero, so that all but finitely many $m_s$ are zero. Let $c = \prod s^{m_s}$. Certainly then $ac = (\prod s^{k_s})(\prod s^{m_s}) = \prod s^{k_s + m_s}$ $= \prod s^{\ell_s} = b$, so that $a$ divides $b$. $\square$
Now to the main result. Let $a,b \in R$ be nonzero elements with factorizations $a = \prod s^{k_s}$ and $b = \prod s^{\ell_s}$. Note that all but finitely many of $\max(k_s,\ell_s)$ are zero. Define $m = \prod s^{\max(k_s,\ell_s)}$. Certainly $a|c$ and $b|c$, using the lemma. Suppose now that $c = \prod s^{n_s}$ is an element of $R$ which is divisible by both $a$ and $b$. Again using the lemma, we have $k_s \leq n_s$ and $\ell_s \leq n_s$. Thus $\max(k_s,\ell_s) \leq n_s$, and thus $m$ divides $c$. Hence $m$ is a least common multiple of $a$ and $b$.
|
2017-01-23 23:01:32
|
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https://devzone.nordicsemi.com/questions/scope:all/sort:activity-desc/tags:gpiote/page:1/
|
# 161 questions
Tagged
• x
25
views
no
1
## GPIOTE Accuracy and RTC
I'm trying to use a low accuracy GPIOTE event to start RTC1. The following code works as expected when using hi accuracy mode but will constantly trigger in_pin_handler() using low accuracy mode. If I remove nrf_drv_rtc_enable() from in_pin_handler() it ... (more)
66
views
1
vote
1
## Minimum GPIOTE "low accuracy" pulse width
I have a device with a programmable output pulse width for its data ready signal. I need to be able to reliable receive the pulse so I don't miss any interrupts, and I'd like to do that in ... (more)
20
views
no
no
GPIOTE Library makes my Board(nRF51422-QFAC) Brick??
I just build my nRF51422 Board, and It's pretty working well before I've used GPIOTE Library.
Before using GPIOTE Library, I've used GPIOTE Driver, And It works pretty well. (But ... (more)
45
views
1
vote
1
> /** @file
> * @brief Example template project.
> * @defgroup nrf_templates_example Example Template
> *
> */
>
> #include <stdbool.h>
> #include <stdint.h>
>
> #include "nrf.h"
> #include "nrf_gpio.h"
> #include "nrf_drv_config.h"
> #include "nordic_common.h"
> #include "nrf_delay.h"
> #include "app_error.h"
> #include "app_timer.h"
> #include "nrf_gpiote.h"
> #include ...
(more)
78
views
no
1
## what is the library to use gpiote?
I want to make the led ON always and making the source code from scratch in keil mu vision 5. I am not able to understand which library is to used and how to proceed.
66
views
no
1
## gpiote handler - disable momentarily to run critical section
With calls to these functions: nrf_drv_gpiote_init() nrf_drv_gpiote_in_init() nrf_drv_gpiote_in_event_enable() I have a handler (interrupt) routine that services a CAN bus chip on SPI bus. The handler runs when the chip's interrupt output, connected to a nRF52 GPIO input, goes from ... (more)
78
views
no
1
## Hardfault when using both UART and GPIOTE, how can I solve this problem?
Hello,
I feel like this question has an answer similar to this question, but I can't seem to get it working https://devzone.nordicsemi.com/questi...
I am using the nrf51422 chip on a board I designed myself and ... (more)
46
views
1
vote
1
## Do I have any restriction with HW Pinout Peripheral when using s130?
if I use softdevice 130 Enabled, then do I have any restriction with using all of the pinout of NRF51xxx?
Or if I use Nrf-51 DK, Do I have any restriction with nrf 51xxx's full pinout functionality?
To Make ... (more)
47
views
1
vote
1
## gpiote with FreeRTOS
Hi,
I migrate my code to FreeRTOS environment.
I use SDK12.2.0 ble_hrs_freertos code example as a startup project.
My question is how i need to init gpite?I receive error ,8
err_code = nrf_drv_gpiote_init(); //!!! err_code = 8
APP_ERROR_CHECK(err_code);
And ... (more)
133
views
2
2
## Long Press to Wake-up
Hello,
Is there any methods to implement the "long press wake-up"? Pressing the button for 3 seconds to let device enter sleep mode and pressing the same button for 3 seconds to wake it up.
Already defined the wake-up gpio ... (more)
113
views
1
vote
1
## How to use Buttons input as GPIO
Hi, i'am working on a custom board on which there is two led drive by a led driver.
The two leds are wiring to be drive by pins P0.14 and P0.15, but unfortunately these pins are consider ... (more)
182
views
2
3
## GPIOTE and SPI high power consumption on sleep
Hello everyone.
I am currently working on a device with some peripherals. I have SPI slaves and other sensors that I am monitoring using GPIOTE driver.
I noticed a consumption of 0.470mA while sleeping under the following circumstances:
• Configure ...
(more)
106
views
2
1
## GPIOTE interrupt count
Hi
I am using nRF51822 (pca10001).I am unable to discover my device. I used the ble_app_template_s130_pca10028 as my base and added the code for gpiote handler as following.
static void gpiote_event_handler(nrf_drv_gpiote_pin_t pin, nrf_gpiote_polarity_t action)
{
int32_t count = 0;
count ...
(more)
84
views
1
vote
1
## gpiote sense high frequency signal
Hi,
I want to implement simple module: 1) gpiote event on pin change (around 6.7MHz signal) 2) Route gpiote event through PPI to increment counter 3) Toggle GPIO pin on Compare event
Im using this code (modified example of ... (more)
185
views
1
vote
2
## How to use GPIOTE driver
Hello,
I'm using SDK12.2.0.
I opened the PPI example (in SES). I want to use the GPIOTE driver to trigger GPIO tasks on Timer events. So I #include "drivers_nrf/gpiote/nrf_drv_gpiote.h" and included the file drivers_nrf ... (more)
139
views
no
1
## nRF51 enable interrupt pin not working: nrf_drv_gpiote_in_event_enable
Hi,
on my board I have a nRF51 and a LIS2DH accelerometer. I want to enable an interrupt pin INT1, so if the LIS2DH sends an interrupt event (pin change from high to low or vice versa) because of an ... (more)
160
views
no
no
## GPIOTE simultaneous interrupts
nRF52, SDK12.1, Eclipse, gcc 5.4.1, FreeRTOS, no soft-device.
I am having a problem with GPIOTE. I have six interrupts programmed on six different pins. As long as the signals do not transition at the same time, the ... (more)
277
views
2
1
## Configuration of Digital Input/Output pins on nRF52
Hello everybody, I'm new to the Nordic system and the nRF52. I'm trying to become familiar with the board and I want to be able to read different 4 input pins, each one attached to the LEDs. In ... (more)
244
views
no
no
## Delay from GPIOTE Event until a Task is started over PPi on nRF52
Hi all,
I measured the delays between a GPIOTE event and a Task (in this case toggling with another GPIOTE) through PPI.
The results are showed below:
For the nRF52 it's arround 380ns.
The same measurements were done with ... (more)
202
views
1
vote
1
## Whats the alternative to GPIOTE In Event ?
Hi,
I've written code to use the "gpiote in event" to sense an interrupt from a peripheral (acceleromenter), but as soon as I enable the in event, I notice the current consumption is a lot higher.
if (!nrf_drv_gpiote_is_init())
{
error_code ...
(more)
118
views
no
1
## Reducing TWI Active Current
Hello,
I am currently working on an ultra-low power project that requires reading an I2C accelerometer multiple times per second. After analyzing the current consumption in the design, it is clear that the TWI peripheral uses quite a bit of ... (more)
78
views
5
1
## No slave select on SPIM xfer using PPI and GPIOTE
I have a custom board that has an MPU9250 attached as a SPI device. The MPU can generate data ready interrupts. I have set the MPU to generate data ready 4x per second which is about the slowest it can ... (more)
323
views
5
1
## NRF52 as SPI master with Multiple Slaves
Hello, my project has 3 different devices (2 sensor and flash memory) on the same SPI bus all with their own CS. I ran across the following question, which has a response for a workaround for the NRF51. Upon jumping ... (more)
121
views
no
1
## DETECT signal nrf52840
Can someone tell me how the DETECT signal works in the nRF52840? This version of the nrf52 has 2 GPIO ports. Does that mean there are 2 DETECT signals? or is there still one and are all SENSE levels of ... (more)
122
views
no
1
## nrf_drv_gpiote_in_event_enable does not work as expected
Hello, we need to first enable GPIOTE+IRQ. Then after 1st IRQ we want to keep only GPIOTE and disable IRQ. We do not want to disable GPIOTE (because it works with PPI), but only to disable IRQ.
We tried ... (more)
86
views
no
no
## Nrf52 issue with RTC event running GPIOTE Task
Hi,
I'm trying to simply toggle a pin with GPIOTE out toggle task from RTC2 CC0 event. Wrote up the following code and checked the registers in system viewer. Everything seems to check out but still not seeing the ... (more)
54
views
3
1
## GPIOTE interrupt signal slow?
Dear Nordic,
I am having some apparent delays in the time that passes from the pressing of a button, and the execution of the ISR that this button triggers. I am using GPIOTE to generate this interrupt.
ret_code_t err_code;
err_code ...
(more)
100
views
no
1
## Nrf51 Fast GPIOTE + Ble
Hi,
Im using S130softdevice.i wanna make dimmer by using experimental_ble_app_blinky project on gpioet But i have a problem with detecting 10 milisecond time (it means that i expect interrupt but it doesnt happen after each 10 milisecond)the lamb ... (more)
136
views
no
1
## USE NMI for GPIOTE
Hi,
I'm currently using an application that needs a very speed detection of GPIO and need to use NMI on GPIOTE.
I tryed to find how can I connect my NMI to GPIOTE but I didn't find how ... (more)
57
views
no
no
## nRF51822 PWM and GPIOTE: differrences between Keil MDK(ARMCC) and GNU_GCC_ARM Compiler
Hello everybody!
I have a problem with compilers for nRF51822. My problems: I create a pwm signal ~38Khz, duty 30% at pin 30 of nRF51822. This process is work well. I want use the function:
nrf_drv_gpiote_out_task_enable(pin)
to ... (more)
#### Statistics
• Total users: 22278
• Latest user: Camilla Samons
• Resolved questions: 9667
• Total questions: 23073
## Recent blog posts
• ### Nordic Developer Zone celebrates its 4th year of helping developers succeed - Celebrate with us and win a Nordic Thingy: 52’
Posted 2017-06-23 10:12:53 by John Leonard
• ### nRF52 Development with CLion
Posted 2017-06-22 09:50:54 by dansheme
• ### Simple GPIO driver example
Posted 2017-06-22 13:38:36 by Hans Elfberg
• ### What mom didn't tell you about ble_app_att_mtu_throughput on the nRF52840 evaluation board
Posted 2017-06-16 16:12:15 by George
• ### Introducing Nordic’s new software licensing schemes
Posted 2017-06-15 11:21:39 by Reidar Martin Svendsen
## Recent questions
• ### NRF51822 to NRF51822 Over the air update (DFU)
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Posted 2017-06-25 14:39:12 by raju
|
2017-06-25 15:38:30
|
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|
https://www.deepdyve.com/lp/springer_journal/stability-of-riccati-s-equation-with-random-stationary-coefficients-WiVs7TqYwB
|
# Stability of Riccati's Equation with Random Stationary Coefficients
Stability of Riccati's Equation with Random Stationary Coefficients The purpose of this paper is to study under weak conditions of stabilizability and detectability, the asymptotic behavior of the matrix Riccati equation which arises in stochastic control and filtering with random stationary coefficients. We prove the existence of a stationary solution $(\bar P_t)$ of this Riccati equation. This solution is attracting, in the sense that if P t is another solution, then $P_t-\bar P_t$ onverges to 0 exponentially fast as t tends to +∞ , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals
# Stability of Riccati's Equation with Random Stationary Coefficients
, Volume 40 (2) – Oct 1, 2074
22 pages
/lp/springer_journal/stability-of-riccati-s-equation-with-random-stationary-coefficients-WiVs7TqYwB
Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900119
Publisher site
See Article on Publisher Site
### Abstract
The purpose of this paper is to study under weak conditions of stabilizability and detectability, the asymptotic behavior of the matrix Riccati equation which arises in stochastic control and filtering with random stationary coefficients. We prove the existence of a stationary solution $(\bar P_t)$ of this Riccati equation. This solution is attracting, in the sense that if P t is another solution, then $P_t-\bar P_t$ onverges to 0 exponentially fast as t tends to +∞ , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices.
### Journal
Applied Mathematics and OptimizationSpringer Journals
Published: Oct 1, 2074
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2018-11-21 10:17:29
|
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|
https://www.shud.xyz/en/shud/9-faq/
|
# FAQ
## The SHUD model
• Why the model uses Unstructured grids instead of regular/orthogonal grids?
The unstructured grids benefit specific scientific or practical model purposes:
• In general, the number of cells in unstructured grids is less than regular grids.
• The unstructured grids are opting to represent the heterogeneity of terrestrial properties, including elevation, slope, soil, and land use, rather than regular grids. The particular points and edges in the terrestrial map can be assigned during mesh generation, but it is hard to be adapted in regular grids.
• Unstructured grids are so flexible that the size of cells can be adjusted based on modeling purposes. For example, when the modeler needs more details on a certain area of a large watershed, he/she can give fine resolution in the research area, but the coarser resolution of the rest of the watershed while keeping the interaction between fine and coarse resolution areas.
• Unstructured grids are more natural and more suitable to represent the complex boundary (such as watershed boundary) than the regular grids. When the modeling domain is of the irregular and complex boundary, regular grids have to use high resolution everywhere to represent the boundary that increases computing burden.
• What is the difference between SHUD and PIHM model?
As a descendant of PIHM, SHUD inherits the fundamental idea of conceptual structure and solving hydrological variables in CVODE. The code has been completely rewritten in a new programming language, with a new discretization and corresponding improvements to the underlying algorithms, adapting new mathematical schemes and a new user-friendly input/output data format. Although SHUD is forked from PIHM’s track, SHUD still inherits the use of CVODE for solving the ODE system but modernizes and extends PIHM’s technical and scientific capabilities.
The major differences are the following:
• SHUD is written in C++, an object-oriented programming language with functionality to avoid risky memory leaks from C. Every function in the code has been rewritten, so the functions, algorithm or data structure between SHUD and PIHM are incompatible.
• SHUD implements a redesign of the calculation of water exchange between hillslope and river. The PIHM defines the river channel as adjacent to bank cells – namely, the river channel shares the edges with bank cells. This design leads to sink problems in cells that share one node with a starting river channel.
• The mathematical equations used in infiltration, recharge, overland flow and river discharge are different among the two models. This change is so essential that the model results would be different with the same parameter set.
• SHUD adds mass-balance control within the calculation of each layer of cells and river channels, critical for long-term or micro-scale hydrologic modeling.
• Either inner data structure or external input/output formats are different. The inner data structure indicates the organization of data, parameters and operations within the program, as well as the strategy to connect the various procedures in the program. The format of input files for SHUD model is upgraded to a series of straightforward and user-friendly formats. The output of SHUD model supports both ASCII and Binary format. Particularly, the binary format is efficient in writing and post-processing.
We now briefly summarize the technical model improvements and technical capabilities of the model, compared to PIHM. This elaboration of the relevant technical features aims to assist future developers and advanced users with model coupling. Compared with PIHM, SHUD …
• supports the latest implicit Sundial/CVODE solver up to version 5.0.0 (the most recent version at the time of writing),
• supports OpenMP parallel computation,
• redesigns the program with object-oriented programming (C++),
• supports human-readable input/output files and filenames,
• exposes unified functions to handle the time-series data, including forcing, leaf area index, roughness length, boundary conditions and melt factor,
• exports model initial condition at specific intervals that can be used for warm starts of continued simulation,
• automatically checks the range of physical parameters and forcing data,
• adds a debug mode that monitors potential errors in parameters and memory operations.
• What kind of data is needed for SHUD model simulation?
• Spatial Data: Elevation, watershed boundary, river network, soil map, geology map, landuse and coverage of forcing data.
• Attributes table: Soil/geology properties, the geometry of rivers, land use parameters
• Time-series: Forcing data (precipitation, temperature, relative humidity, wind speed, shortwave radiation), Leaf Area Index (LAI), roughness length, melting factor.
The rSHUD can provide some of the data with default values. The detail can be found in the User Manual https://www.shud.xyz/Book_CN/.
• What the suitability and suitable region of the SHUD model in the world?
The SHUD model is very adaptive; it can be used widely for research and practical purposes.
The smallest modeling experiment is numerical modeling of Vauclin Experiment that is in a $2m * 3m * 0.05 m$ ($H \times L \times W$), the top area is only $0.1 m^2$.
The largest watershed modeling is 40-year groundwater and water availability research in Sacramento Watershed (700,000 $km^2$). The model takes about one hour to simulate a year when the mean area of cells is ~$7 km^2$.
Some of the applications can be found via https://www.shud.xyz/applications/.
## SHUD program and installation
• Where to access the source code of SHUD model?
The source code of SHUD is available on GitHub: https://github.com/SHUD-System/SHUD.
• What OS platform is required for SHUD model?
Since the source code of SHUD is written in standardized C++ Language, the program can be deployed on any platform as long as the user has a C++ compiler. The compiling process requires the support of SUNDIANLS/CVODE libraries, so the user should install SUNDIALS/CVODE before compiling SHUD. The tutorial on installing SUNDIALS/CVODE can be found here: https://www.shulele.net/en/post/20191119_sundials/.
• How to install SUNDIALS/CVODE?
SUNDIALS (https://computing.llnl.gov/projects/sundials) is a very powerful mathematical library that is helpful in solving engineering and scientific problems efficiently. CVODE is one of the suites, aiming to solve the Ordinary Differential Equation, in C language. SHUD requires the support of CVODE, so the user should install CVODE at least.
Users can install CVODE with the help of the tutorial: https://www.shulele.net/en/post/20191119_sundials/.
Besides this GUI installation, the user also can use the script configure in source code to install CVODE.
• The performance of the SHUD model?
Normally, the performance of the model highly depends on resolution, lengths of river reaches, parameters set, terrestrial properties. For example, an 1100 cells watershed with area 192 $km^2$ takes about 5 hours to simulate 17 years. The simulation becomes slower under heavy rainfall events occurs than dry conditions.
• How to utilized the parallelization of SHUD model?
Firstly, you have to install OpenMP library on your OS. Please confirm the -fopen flag works on your platform.
Secondly, it is necessary to compile and install CVODE with OpenMP supports, use tutorials (https://www.shulele.net/en/post/20191119_sundials/) as a reference.
• The optimal size of triangular cells, or number of triangles for a simulation.
It highly depends on the modeler’s purpose or scientific problems. The resolution can be $cm^2$ to $km^2$ based on data resolution, research problem, computational resources and performance requirement.
## rSHUD
• How to install the rSHUD?
In R, you should install devtools, then install rSHUD via GitHub.
install.packages("devtools")
devtools::install_github("SHUD-System/rSHUD")
Besides of the rSHUD, the user should install RTriagle via GitHub, instead of the version on CRAN.
install.packages("devtools")
devtools::install_github("shulele/RTriangle", subdir="pkg")
• Is rSHUD available on R CRAN?
Not yet. CRAN requires a lot of details explanations of algorithms and functions; it takes lots of energy. I will submit the rSHUD to CRAN in the future.
• Source code of rSHUD
Source code of rSHUD is available via https://github.com/SHUD-System/rSHUD
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2021-05-15 08:37:10
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https://www.clutchprep.com/physics/practice-problems/138288/two-current-carrying-wires-are-exactly-parallel-to-one-another-and-both-carry-3-
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# Problem: Two current-carrying wires are exactly parallel to one another and both carry 3.0 A of current. The two wires are separated by a distance of 25 cm. The current in wire 1 moves down while the current in wire 2 moves up. What is the magnitude of the magnetic force per unit length caused by wire 1 on wire 2? What is the direction of the magnetic force caused by wire 1 on wire 2?
###### FREE Expert Solution
Force per unit length,
$\overline{)\begin{array}{rcl}\frac{\mathbf{F}}{\mathbf{∆}\mathbf{L}}& \mathbf{=}& \frac{{\mathbf{\mu }}_{\mathbf{0}}{\mathbf{I}}_{\mathbf{1}}{\mathbf{I}}_{\mathbf{2}}}{\mathbf{2}\mathbf{\pi r}}\end{array}}$
I1 = I2 = 3.0 A
r = 25 cm (1 m / 100 cm) = 0.25 m
μ0 = 4π × 10-7 T•m/A
###### Problem Details
Two current-carrying wires are exactly parallel to one another and both carry 3.0 A of current. The two wires are separated by a distance of 25 cm. The current in wire 1 moves down while the current in wire 2 moves up. What is the magnitude of the magnetic force per unit length caused by wire 1 on wire 2? What is the direction of the magnetic force caused by wire 1 on wire 2?
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2020-05-29 14:45:01
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https://www.physicsforums.com/threads/flywheel-rotation-question.903037/
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# Flywheel rotation question.
1. Feb 7, 2017
### Arman777
1. The problem statement, all variables and given/known data
A flywheel with a D=1.2m is rotating at an angular speed of 200 rev/min
(a) Whats the angular speed in rad/s ?
(b)Whats v=? in the point on the rim ?
(c)What const. ∝ ( in rev/min^2) will increase its angular speed to 1000 rev/min in 60 sec ?
(d)How many revolutions does the wheel make during that 60 sec ?
2. Relevant equations
Rotational Kinematics Equations
3. The attempt at a solution
I found a,b,c correctly (for long tries ) but I stucked at d.
I guess I ll use here $Δθ=wt-1/2∝t^2$
(b)v=12.5
(c)=800 rev/min^2
Now for d,
lets to write all equaiton in rev/min form so
I dont know what will be the left part cause Δθ in units its normally just rev I guess so
θ-200rev/min=7879rev/min.1min+1/2 (800rev/min^2).(1 min)^2
Here I get a huge number...
Thank you
2. Feb 7, 2017
### Staff: Mentor
You established before that 200 rev/min corresponds to 20.9 rad/s (which is correct). How can it correspond to a larger number of revolutions per minute now?
You cannot subtract an angle and an angular velocity. That's like adding 3 meters to 1 minute: It does not make sense.
You can use the formula you posted, but it is probably easier to find the average angular velocity (in rev/min) and to use that.
3. Feb 7, 2017
### Arman777
ohh I see...so I can convert 200rev/min to rev which its just 200 or ..I dont know ?
4. Feb 7, 2017
### Staff: Mentor
You cannot "convert an angular velocity to revolutions" in the same way you cannot convert apples to minutes. There is no need for such a conversion. Your formula multiplies the angular velocity by a time. The product of those two is a number of revolutions or an angle, depending on which units you use.
5. Feb 7, 2017
### Arman777
ok then how can I found inital rev ? If other parts are correct ?
6. Feb 7, 2017
oh I see...
7. Feb 7, 2017
### Arman777
Here my new try
8. Feb 7, 2017
### Staff: Mentor
Your angular acceleration seems to be too low.
9. Feb 7, 2017
### Arman777
yeah,sorry it would be 1.40 rad/sec ?
10. Feb 7, 2017
### Arman777
I found yeyyyyy
11. Feb 7, 2017
Thanks
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2017-11-23 06:24:36
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https://gstguntur.com/debentures-ca-foundation-accounts-study-material/
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# Debentures – CA Foundation Accounts Study Material
Debentures – CA Foundation Accounts Study Material is designed strictly as per the latest syllabus and exam pattern.
## Debentures – CA Foundation Accounts Study Material
Question 1.
Meaning of debentures.
Meaning of debentures:
→ Debenture means “an instrument in writing issued by a company under its common seal, acknowledging its indebtedness for a certain sum of money and undertaking to repay it on or after a fixed future date.”
→ According to sec. 2(12) of the Companies Act, 1956 (now Section 2(30) of Companies Act, 2013) “Debenture include debenture stock, bonds and any other securities of a company, whether constituting a charge on the assets of the company or not.”
Characteristic features of a debenture:
• It is issued by the company and is in the form of a certificate of indebtedness.
• It usually specifies the date of redemption. It also provides for the re-payment of principal and interest at specified date or dates.
• It generally creates a charge on the undertaking or undertakings of the company.
• Usually the words pari passu appear in the terms and conditions of debentures.
• This means that all the debentures of a particular class will receive the money proportionately in case the company is unable to discharge the whole obligation.
Question 2.
Discount on debentures.
Discount on debentures:
• The discount is a capital loss and it should be written off as early as possible.
• Even whole amount can be written off in the year of issue itself against share premium or any other capital profit.
• Otherwise Debenture Discount can be written off over the lifetime of debentures as follows (applying matching principle):
• If the Debentures are redeemable at the end of a period, then the Discount will be written off equally over that period.
Question 3.
Issue of Debentures as Collateral Security.
Issue of Debentures as Collateral Security:
Issue of Debentures as Collateral Security means issue of debentures as an additional security, i.e., in addition to the prime security. It is to be realised only when the prime security fails to pay the amount of the loan. For example, when a company takes a loan of ₹ 10,00,000 from a bank, it may have to issue debentures as collateral security in addition to the principal security.
Debentures issued as a collateral security can be dealt with in the book in two ways:
(i) First Method:
Journal entry is not passed in the books of account at the time of issue of debentures as collateral security. However, it is disclosed by way of information below debentures, which are shown as Long-term Borrowings under Non-Current Liabilities or as Short-term Borrowings under Current Liabilities.
(ii) Second Method:
Debentures issued as collateral security may be recorded in the books of account. The Journal entry passed is :
Debentures Suspense A/c Dr. [This appears on the assets side]
To …. % Debentures A/c [This appears on the liabilities side]
When the loan is paid the above entry is cancelled by means of a reverse entry.
Question 4.
Premium on Issue of Debentures Premium on Redemption of Debentures 1. It is a capital profit and used in writing off the capital loss. It is a capital loss. 2. The balance of premium on issue of Debentures Account, (Securities Premium) is shown on the liabilities side, under the head ‘Shareholders’ Funds’ and sub-head ‘Reserves and Surplus’. It is a liability and appears under the head ‘Non-Current Liabilities’ and sub-head ‘Long-term Borrowing’ till the redemption of debentures.
Question 5.
Company issued 1000,9% debentures @ ₹ 100 each, in following manner
Application ₹ 40
Allotment ₹ 30-10
First call ₹ 20
Second and final call ₹ 10
Mr. R holder of 20 debentures failed to pay the 1st and 2nd call money. Company decided to charge ₹ 35 as Interest on calls-in-arrear. Give necessary journal entries in the books of the company.
Solution:
Journal Entries
Question 6.
A Company purchased some plant costing ₹ 4,30,000 at an agreed price of ₹ 4,00,000. Company decided to issue its 896 debentures of ₹ 100 each against purchased consideration. Give necessary accounting entries in the following
cases:-
(a) If debenture were issued @ ₹ 100 per debenture
(b) If debenture were issued @ ₹ 80 per debenture
(c) If debenture were issued @ ₹ 125 per debenture
Solution:
Journal Entries
Working Note:
Question 7.
A Company took a bank loan of ₹ 5,00,000 from SBI and issued its 6000, 10% debentures of ₹ 100 each as collateral security to loan. Give necessary accounting treatment.
Solution :
Ist method:
When debenture issued as collateral security are not shown as issued debentures in the balance sheet of the company.
(i) Bank a/c Dr. To Bank loan a/c (Being bank loan taken on issue of 6000, 10% debentures of ₹ 100 each as collateral security) 5,00,000 5,00,000 (ii) No entry required for issuing debentures.
Balance sheet (Extract) as at ………….
Note:
(1) Long term borrowings:
₹ Bank Loan from SBI (on collateral security of 6,000, 10% debentures of ₹ 100 each). 5,00,000
Question 8.
A Company issued 1000, 12% debentures of ₹ 100 each on 1st Jan 2016 at a premium of 10%. Interest was given/payable on 30th June and 31st December, every year subject to 10% TDS. Give necessary journal entries for the year 2016.
Solution:
Journal Entries
Question 9.
ABC company issued 1000, 9% debentures of ₹ 100 each at a discount of 5% on 1st Jan, 2011. These debentures were to be redeemed after 5 years. Show necessary journal entries at the time of issue of debentures. Also prepare discount on issue of 9% debentures a/c.
Solution :
At the time of issue:
Journal Entries
Discount on issue of 9% debenture a/c
Balance sheet as at 31st December 2011
Assets Note No. ₹ Non-current assets other non-current assets 3,000 Current assets other current assets 1,000
Working Note:
(1) $$\frac{₹ 5,000}{5 \text { years }}$$ = ₹ 1,000/-
Question 10.
Suppose company decided to redeem its debentures in the following manner
• At the end of the year 2011 ₹ 20,000
• At the end of the year 2012 ₹ 30,000
• At the end of the year 2013 ₹ 10,000
• At the end of the year 2014 ₹ 20,000
• At the end of the year 2015 ₹ 20,000
Calculate the amount to be written off at the end of every year.
At the beginning of the year or before redemption
Question 11.
Pure Ltd. issues 1,00,000 12% Debentures of ₹ 10 each at ₹ 9.40 on 1st January, 2018. Under the terms of issue, the Debentures are redeemable at the end of 5 years from the date of issue.
Calculate the amount of discount to be written-off in each of the 5 years.
Solution:
Total amount of Discount = 1,00,000 x 0.60 = ₹ 60,000
At the end of Year Amount of outstanding debentures Ratio Amount of discount to be written off 1st 10,00,000 1/5 60,000 = 12000 2nd 10,00,000 1/5 60,000 = 12000 3rd 10,00,000 1/5 60,000 = 12000 4th 10,00,000 1/5 60,000 = 12000 5th 10,00,000 1/5 60,000 = 12000
Question 12.
On 1st January 2018, Ankit Ltd. issued 10% debentures of the face value of ₹ 20,00,000 at 10% discount. Debenture interest after deducting tax at source @10% was payable on 30th June and 31st December every year. All the debentures were to be redeemed after the expiry of five year period at 5% premium.
Pass necessary journal entries for the accounting year 2018.
Solution:
Journal Entries
True or False
Question 1.
Debenture Redemption Premium Account and Discount on issue of debentures Account are Nominal Accounts.
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2022-08-11 23:30:29
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https://physics.stackexchange.com/questions/172620/electromagnetic-braking-hypothetical-situation/172723#172723
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Electromagnetic braking hypothetical situation?
Let's say there is a conducting rod in space - with a constant external magnetic field. If you spin the rod - will electromagnetic braking make the rod stop eventually? I feel like there is a change in flux through the rod when it rotates - and due to Faraday's law and Lenz's law eddy currents will be induced to oppose the motion of the rod
• Does the rod have only the length dimension? In other words is its thickness zero? Mar 27 '15 at 9:30
• No, it has all 3 dimensions Mar 27 '15 at 9:31
• Well eddy currents will surely retard the motion of the rod. However I'm not sure of the rate at which the rod will be retarded. If the rate of retardation is proportional to magnitude of the velocity the velocity of the rod will tend to zero(asymptotically). Mar 27 '15 at 9:32
• You may then consider that the rod is like an electric circuit made of wire along its sides in a way that the rotation axis is inside the circuit plane. Then it is like upload.wikimedia.org/wikipedia/commons/thumb/b/b6/…
– TZDZ
Mar 27 '15 at 9:55
There is only one case where isn't induced a current in the rod. One have to move the rod parallel to the magnetic field. In any other case and especially in any case of rotation the magnetic field will move the electrons inside the rod.
For example, if the rotating axis is perpendicular to the rods symmetry axis, there are two pure cases.
(1) The rotating axis is aligned parallel to the magnetic field. Free available electrons will be distributed more to the ends of the rod or more to the centre of the rod. This depends from how the direction of the magnetic field and the direction of the rods rotation are related. Since the rod isn't an closed electric circuit this happens only once and after it does not effect the rotation any more.
(2) The rotating axis is aligned perpendicular to the magnetic field. Electrons are moved periodically parallel to the axis of rotation. In case (2) electrons get accelerated periodicaly and this will be accompanied by electromagnetic radiation. The energy for this radiation has to come or from the kinetic energy of the rotating rod or from a cooling down rod. Cooling may be happens but it is not the dominant process.
Last not least I have to explain why the electrons will be moved. First at all think about the Lorentz force $\vec F = q \vec v \times \vec B$. This vector cross product can be rewritten for orthogonal vectors to $q \vec v = \dfrac {(\vec B \times \vec F)}{\|\vec {B}\|^2}$. This corresponds with what happens in an electric generator. In case (1) it will be an DC generator, in case (2) an AC generator. To be precise, in case (1) it is a homopolar generator, ie a special DC generator.
Second one can ask why the electrons get moved in this way under the influence of a magnetic field. One has te remember that attraction or repulsion happens only between charged bodies or between magnetic dipoles. It is nice for us that electrons have magnetic dipole moment and it is spinning too. The electrons magnetic moment will be aligned under the influence of a magnetic field. This isn't spectacular. More interesting is it if the electron moves in a magnetic field (not parallel to the field). The electrons magnetic moment will be aligned and this is accompanied by a gyroscopic phenomena. Gyroscopic effect means that every rotating body act again the force which try to align it. Because the electron has not a magnetic moment only but spins too the moving electron will be deflected. Since any deflection is an acceleration, a photon emission takes place and this emission is directed against the gyroscopic effect. The direction of the magnetic moment of the electron more or less fall back in his previous orientation.
Periodical displacement of the electrons and an associated EM radiation, this is the full picture we see in case (2). The rod will come to a stop.
At the end proof the described movement of the electrons with the Right-hand rule. Don't worry about right or left hand. In your case it is more important to follow the orthogonality of the three vectors magnetic field $\vec B$, movement of the rod, represented by $\vec F$ and the resulting current, represented by $q \vec v$.
If anyone is surprised that such a hand rule is to use, this is because the spin of the electron and its magnetic moment are clearly coupled. If this were not so in nature, then we could not use generators and motors.
• I disagree with your statement in case #2 that electrons will be driven back & forth along the rod. In this case, $\vec{B}$ and the velocity $\vec{v}$ of any point on rod will always be in the plane of rotation. This means that the magnetic force on the charges will necessarily be at right angles to this plane, and not along the length of the rod (which would be in said plane.) Jul 6 '15 at 17:37
• @MichaelSeifert You are right. B and v will be in plane. Thank you. Jul 6 '15 at 19:39
• @MichaelSeifert I corrected it. Now it is right? Jul 7 '15 at 5:28
• I'm not quite sure what you mean by "perimeter". I would phrase it as "the electrons are moved periodically parallel to the axis of rotation". Jul 7 '15 at 13:40
• @Michael Seifert Done. (?) Jul 7 '15 at 13:54
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2022-01-27 11:17:26
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http://hermes.roua.org/hermes-pub/arxiv/05/03/207/article.xhtml
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## Intuitionistic fuzzy ${H}_{v}$-submodules
### Bijan Davvaz a , Wiesław A. Dudek b , Young Bae Jun c , * a Department of Mathematics, Yazd University, Yazd, Iran b Institute of Mathematics, Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland c Department of Mathematics Educations, Gyeongsang National University, Chinju 660-701, Korea
Abstract
After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to ${H}_{v}$ -modules. The notion of an intuitionistic fuzzy ${H}_{v}$ -submodule of an ${H}_{v}$ -module is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy ${H}_{v}$ -submodules are given.
2000 Mathematics Subject Classification: 16D99, 20N20, 20N25.
Keywords: ${H}_{v}$ -semigroup, ${H}_{v}$ -group, ${H}_{v}$ -ring, ${H}_{v}$ -module, intuitionistic fuzzy ${H}_{v}$ -submodule, sup property.
$\text{}$
1 Introduction
The concept of hyperstructure was introduced in 1934 by Marty [14at the 8th congress of Scandinavian Mathematicians. Hyperstructures have many applications to several branches of both pure and applied sciences [4, 5. Vougiouklis [19introduced a new class of hyperstructures so-called ${H}_{v}$ -structure, and Davvaz [9surveyed the theory of ${H}_{v}$ -structures. After the introduction of fuzzy sets by Zadeh [21, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov [1is one among them. In [3, Biswas applied the concept of intuitionistic fuzzy sets to the theory of groups and studied intuitionistic fuzzy subgroups of a group. In [12, Kim, Dudek and Jun introduced the notion of intuitionistic fuzzy subquasigroups of a quasigroup.
Also in [13, Kim and Jun introduced the concept of intuitionistic fuzzy ideals of a semigroup. Recently, Dudek, Davvaz and Jun [11considered the intuitionistic fuzzification of the concept of sub-hyperquasigroups in a hyperquasigroup and investigated some properties of such hyperquasigroups.
In this paper, we apply the concept of intuitionistic fuzzy sets to ${H}_{v}$ -modules.
We introduce the notion of intuitionistic fuzzy ${H}_{v}$ -submodules of an ${H}_{v}$ -module and investigate some related properties. We give characterizations of intuitionistic fuzzy ${H}_{v}$ -submodules.
2 Fuzzy sets and intuitionistic fuzzy sets
The concept of a fuzzy set in a non-empty set was introduced by Zadeh [21in 1965.
Let $X$ be a non-empty set. A mapping $\mu :X⟶\left[0,1\right]$ is called a fuzzy set in $X$ . The complement of $\mu$ , denoted by ${\mu }^{c}$ , is the fuzzy set in $X$ given by ${\mu }^{c}\left(x\right)=1-\mu \left(x\right)$ for all $x\in X$ .
Definition 2.1. Let $f$ be a mapping from a set $X$ to a set $Y$ . Let $\mu$ be a fuzzy set in $X$ and $\lambda$ be a fuzzy set in $Y$ . Then the inverse image ${f}^{-1}\left(\lambda \right)$ of $\lambda$ is a fuzzy set in $X$ defined by ${f}^{-1}\left(\lambda \right)\left(x\right)=\lambda \left(f\left(x\right)\right)forallx\in X.$ The image $f\left(\mu \right)$ of $\mu$ is the fuzzy set in $Y$ defined by $f\left(\mu \right)\left(y\right)=\left\{\begin{array}{cc}{sup}_{x\in {f}^{-1}\left(y\right)}\mu \left(x\right)& if{f}^{-1}\left(y\right)\ne \varnothing ,\\ 0& otherwise,\end{array}$ for all $y\in Y$ . We have always $f\left({f}^{-1}\left(\lambda \right)\right)\le \lambda and\mu \le {f}^{-1}\left(f\left(\mu \right)\right).$
Rosenfeld [16applied the concept of fuzzy sets to the theory of groups and defined the concept of fuzzy subgroups of a group. The concept of fuzzy modules was introduced by Negoita and Ralescu in [15.
Definition 2.2. (cf. Negoita and Ralescu [15). Let $M$ be a module over a ring $R$ . A fuzzy set $\mu$ in $M$ is called a fuzzy submodule of $M$ if for every $x,y\in M$ and $r\in R$ the following conditions are satisfied:
• (1) $\mu \left(0\right)=1$ ,
• (2) $min\left\{\mu \left(x\right),\mu \left(y\right)\right\}\le \mu \left(x-y\right)$ for all $x,y\in M$ ,
• (3) $\mu \left(x\right)\le \mu \left(rx\right)$ for all $x\in M$ and $r\in R$ .
Definition 2.3. An intuitionistic fuzzy set $A$ in a non-empty set $X$ is an object having the form $A=\left\{\left(x,{\mu }_{A}\left(x\right),{\lambda }_{A}\left(x\right)\right)|x\in X\right\},$ where the functions ${\mu }_{A}:X⟶\left[0,1\right]$ and ${\lambda }_{A}:X⟶\left[0,1\right]$ denote the degree of membership (namely ${\mu }_{A}\left(x\right)$ ) and the degree of nonmembership (namely ${\lambda }_{A}\left(x\right)$ ) of each element $x\in X$ to the set $A$ respectively, and $0\le {\mu }_{A}\left(x\right)+{\lambda }_{A}\left(x\right)\le 1$ for all $x\in X$ . For the sake of simplicity, we shall use the symbol $A=\left({\mu }_{A},{\lambda }_{A}\right)$ for the intuitionistic fuzzy set $A=\left\{\left(x,{\mu }_{A}\left(x\right),{\lambda }_{A}\left(x\right)\right)|x\in X\right\}$ .
Definition 2.4. Let $A=\left({\mu }_{A},{\lambda }_{A}\right)$ and $B=\left({\mu }_{B},{\lambda }_{B}\right)$ be intuitionistic fuzzy sets in $X.$ Then
• (1) $A\subseteq B$ iff ${\mu }_{A}\left(x\right)\le {\mu }_{B}\left(x\right)$ and ${\lambda }_{A}\left(x\right)\ge {\lambda }_{B}\left(x\right)$ for all $x\in X$ ,
• (2) ${A}^{c}=\left\{\left(x,{\lambda }_{A}\left(x\right),{\mu }_{A}\left(x\right)\right)|x\in X\right\}$ ,
• (3) $A\cap B=\left\{\left(x,min\left\{{\mu }_{A}\left(x\right),{\mu }_{B}\left(x\right)\right\},max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{B}\left(x\right)\right\}\right)|x\in X\right\}$ ,
• (4) $A\cup B=\left\{\left(x,max\left\{{\mu }_{A}\left(x\right),{\mu }_{B}\left(x\right)\right\},min\left\{{\lambda }_{A}\left(x\right),{\lambda }_{B}\left(x\right)\right\}\right)|x\in X\right\}$ ,
• (5) $\square A=\left\{\left(x,{\mu }_{A}\left(x\right),{\mu }_{A}^{c}\left(x\right)\right)|x\in X\right\}$ ,
• (6) $◊A=\left\{\left(x,{\lambda }_{A}^{c}\left(x\right),{\lambda }_{A}\left(x\right)\right)|x\in X\right\}$ .
Now, we define an intuitionistic fuzzy submodule of a module.
Definition 2.5. Let $M$ be a module over a ring $R$ . An intuitionistic fuzzy set $A=\left({\mu }_{A},{\lambda }_{A}\right)$ in $M$ is called an intuitionistic fuzzy submodule of $M$ if
• (1) ${\mu }_{A}\left(0\right)=1$ ,
• (2) $min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}\le {\mu }_{A}\left(x-y\right)$ for all $x,y\in M$ ,
• (3) ${\mu }_{A}\left(x\right)\le {\mu }_{A}\left(r\cdot x\right)$ for all $x\in M$ and $r\in R$ ,
• (4) ${\lambda }_{A}\left(0\right)=0$ ,
• (5) ${\lambda }_{A}\left(x-y\right)\le max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{A}\left(y\right)\right\}$ for all $x,y\in M$ ,
• (6) ${\lambda }_{A}\left(r\cdot x\right)\le {\lambda }_{A}\left(x\right)$ for all $x\in M$ and $r\in R$ .
3 ${H}_{v}$ -structures
A hyperstructure is a non-empty set $H$ together with a map $*:H×H\to {\mathcal{P}}^{*}\left(H\right)$ which is called hyperoperation, where ${\mathcal{P}}^{*}\left(H\right)$ denotes the set of all non-empty subsets of $H$ . The image of pair $\left(x,y\right)$ is denoted by $x*y$ . If $x\in H$ and $A,B\subseteq H$ , then by $A*B$ , $A*x$ and $x*B$ we mean $A*B={\bigcup }_{a\in A,b\in B}a*b,A*x=A*\left\{x\right\}andx*B=\left\{x\right\}*B,$ respectively. A hyperstructure $\left(H,*\right)$ is called an ${H}_{v}$ -semigroup if $\left(x*\left(y*z\right)\right)\cap \left(\left(x*y\right)*z\right)\ne \varnothing forallx,y,z\in H.$
Definition 3.1. An ${H}_{v}$ -ring is a system $\left(R,+,\cdot \right)$ with two hyperoperations satisfying the following axioms:
• (i) $\left(R,+\right)$ is an ${H}_{v}$ -group, i.e., $\begin{array}{c}\left(\left(x+y\right)+z\right)\cap \left(x+\left(y+z\right)\right)\ne \varnothing forallx,y\in R,\end{array}$
$\begin{array}{c}a+R=R+a=Rforalla\in R;\end{array}$
• (ii) $\left(R,\cdot \right)$ is an ${H}_{v}$ -semigroup;
• (iii) $\cdot$ ” is weak distributive with respect to “ $+$ ”, i.e., for all $x,y,z\in R$ : $\begin{array}{c}\left(x\cdot \left(y+z\right)\right)\cap \left(x\cdot y+x\cdot z\right)\ne \varnothing ,\end{array}$
$\begin{array}{c}\left(\left(x+y\right)\cdot z\right)\cap \left(x\cdot z+y\cdot z\right)\ne \varnothing .\end{array}$
Definition 3.2. (cf. Vougiouklis [20). A non-empty set $M$ is called an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ if $\left(M,+\right)$ is a weak commutative ${H}_{v}$ -group and there exists a map $\cdot :R×M⟶{\mathcal{P}}^{*}\left(M\right),\left(r,x\right)↦r\cdot x$ such that for all $a,b\in R$ and $x,y\in M$ , we have
$\begin{array}{c}\left(a\cdot \left(x+y\right)\right)\cap \left(a\cdot x+a\cdot y\right)\ne \varnothing ,\end{array}$
$\begin{array}{c}\left(\left(a+b\right)\cdot x\right)\cap \left(a\cdot x+b\cdot x\right)\ne \varnothing ,\end{array}$
$\begin{array}{c}\left(\left(ab\right)\cdot x\right)\cap \left(a\cdot \left(b\cdot x\right)\right)\ne \varnothing .\end{array}$
We note that an ${H}_{v}$ -module is a generalization of a module. For more definitions, results and applications on ${H}_{v}$ -modules, we refer the reader to [9, 18, 20. Note that by using fuzzy sets, we can consider the structure of ${H}_{v}$ -module on any ordinary module.
Example 3.3. (cf. Davvaz [6). Let $M$ be an ordinary module over an ordinary ring $R$ , and let ${\mu }_{A}$ be a fuzzy set in $M$ and ${\mu }_{B}$ be a fuzzy set in $R$ . We define hyperoperations $\circ ,*,\oplus$ and $\odot$ as follows:
• $a\circ b=\left\{t\in R|{\mu }_{B}\left(t\right)={\mu }_{B}\left(a+b\right)\right\}$ for all $a,b\in R$ ,
• $a*b=\left\{t\in R|{\mu }_{B}\left(t\right)={\mu }_{B}\left(ab\right)\right\}$ for all $a,b\in R$ ,
• $x\oplus y=\left\{s\in M|{\mu }_{A}\left(s\right)={\mu }_{A}\left(x+y\right)\right\}$ for all $x,y\in M$ ,
• $r\odot x=\left\{s\in M|{\mu }_{A}\left(s\right)={\mu }_{A}\left(r\cdot x\right)\right\}$ for all $r\in R$ and $x\in M$ ,
respectively. Then
• (i) $\left(R,\circ ,*\right)$ is an ${H}_{v}$ -ring.
• (ii) $\left(M,\oplus ,\odot \right)$ is an ${H}_{v}$ -module over the ${H}_{v}$ -ring $\left(R,\circ ,*\right)$ .
Definition 3.4. Let $M$ be an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ . A non-empty subset $S$ of $M$ is called an ${H}_{v}$ -submodule of $M$ if the following axioms hold:
• (i) $\left(S,+\right)$ is an ${H}_{v}$ -subgroup of $\left(M,+\right)$ ,
• (ii) $R\cdot S\subseteq S$ .
Definition 3.5. Let ${M}_{1}$ and ${M}_{2}$ be two ${H}_{v}$ -modules over an ${H}_{v}$ -ring $R$ . A mapping $f$ from ${M}_{1}$ into ${M}_{2}$ is called a homomorphism if for all $x,y\in {M}_{1}$ and $r\in R$ , $f\left(x+y\right)=f\left(x\right)+f\left(y\right)andf\left(r\cdot x\right)=r\cdot f\left(x\right).$ The homomorphism $f$ is said to be strong on the left if $f\left(z\right)\in f\left(x\right)+f\left(y\right)⟹\exists {x}^{\prime }\in {M}_{1}:f\left(x\right)=f\left({x}^{\prime }\right)andz\in {x}^{\prime }+y.$ Similarly, we can define a homomorphism which is strong on the right. If a homomorphism $f$ is strong on the right and left, we say $f$ is a strong homomorphism.
Proposition 3.6. Let ${M}_{1}$ and ${M}_{2}$ be two ${H}_{v}$ -modules over an ${H}_{v}$ -ring $R$ and $f:{M}_{1}⟶{M}_{2}$ a strong epimorphism. If $N$ is an ${H}_{v}$ -submodule of ${M}_{2}$ , then ${f}^{-1}\left(N\right)$ is an ${H}_{v}$ -submodule of ${M}_{1}$ .
• Proof. Assume that ${x}_{1},{x}_{2}\in {f}^{-1}\left(N\right)$ . Then there exists ${y}_{1},{y}_{2}\in N$ such that $f\left({x}_{1}\right)={y}_{1}$ , $f\left({x}_{2}\right)={y}_{2}$ and so $f\left({x}_{1}+{x}_{2}\right)={y}_{1}+{y}_{2}$ . Hence for every $x\in {x}_{1}+{x}_{2}$ we have $f\left(x\right)\in {y}_{1}+{y}_{2}\subseteq N$ which implies $x\in {f}^{-1}\left(N\right)$ and so ${x}_{1}+{x}_{2}\subseteq {f}^{-1}\left(N\right)$ . Therefore ${x}_{1}+{f}^{-1}\left(N\right)\subseteq {f}^{-1}\left(N\right)$ for every ${x}_{1}\in {f}^{-1}\left(N\right).$ Now, we show that ${f}^{-1}\left(N\right)\subseteq {x}_{1}+{f}^{-1}\left(N\right)$ . For $z\in {f}^{-1}\left(N\right)$ , there exists $y\in N$ such that $f\left(z\right)=y$ . Since $y,{y}_{1}\in N$ and $N$ is an ${H}_{v}$ -subgroup of ${M}_{2}$ , there exists $b\in N$ such that $y\in {y}_{1}+b$ . Since $f$ is onto, there exists $a\in {M}_{1}$ such that $f\left(a\right)=b$ or $a\in {f}^{-1}\left(b\right)$ . Hence we have $f\left(z\right)\in f\left({x}_{1}\right)+f\left(a\right)$ . Since $f$ is a strong homomorphism, there exists ${a}^{\prime }\in {M}_{1}$ such that $f\left(a\right)=f\left({a}^{\prime }\right)$ and $z\in {x}_{1}+{a}^{\prime }$ . Since $f\left({a}^{\prime }\right)=b\in N$ , we have ${a}^{\prime }\in {f}^{-1}\left(N\right)$ and $z\in {x}_{1}+{f}^{-1}\left(N\right)$ , and so ${f}^{-1}\left(N\right)\subseteq {x}_{1}+{f}^{-1}\left(N\right)$ . Therefore we have ${f}^{-1}\left(N\right)={x}_{1}+{f}^{-1}\left(N\right)$ .
Similarly, we obtain ${f}^{-1}\left(N\right)={f}^{-1}\left(N\right)+{x}_{1}$ . Thus the condition (i) of Definition 3.4 is satisfied.
For the condition (ii), let $r\in R$ and $x\in {f}^{-1}\left(N\right)$ , then $f\left(x\right)\in N$ , and so $r\cdot f\left(x\right)\subseteq N$ or $f\left(r\cdot x\right)\subseteq N$ , which implies $r\cdot x\subseteq {f}^{-1}\left(N\right)$ . Therefore the condition (ii) of Definition 3.4 is satisfied.
In [7, Davvaz applied the concept of fuzzy sets to the algebraic hyperstructures.
In particular, he defined the concept of a fuzzy ${H}_{v}$ -submodule of an ${H}_{v}$ -module which is a generalization of the concept of a fuzzy submodule (see [6), and he studied further properties in [8, [9and [10.
Definition 3.7. (cf. Davvaz [6). Let $M$ be an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ and $\mu$ a fuzzy set in $M$ . Then $\mu$ is said to be a fuzzy ${H}_{v}$ -submodule of $M$ if the following axioms hold:
• (1) $min\left\{\mu \left(x\right),\mu \left(y\right)\right\}\le inf\left\{\mu \left(z\right)|z\in x+y\right\}$ for all $x,y\in M$ ,
• (2) for all $x,a\in M$ there exists $y\in M$ such that $x\in a+y$ and $min\left\{\mu \left(a\right),\mu \left(x\right)\right\}\le \mu \left(y\right),$
• (3) for all $x,a\in M$ there exists $z\in M$ such that $x\in z+a$ and $min\left\{\mu \left(a\right),\mu \left(x\right)\right\}\le \mu \left(z\right),$
• (4) $\mu \left(x\right)\le inf\left\{\mu \left(z\right)|z\in r\cdot x\right\}$ for all $x\in M$ and $r\in R$ .
4 Intuitionistic fuzzy ${H}_{v}$ -submodules
In what follows, let $M$ denote an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ unless otherwise specified. We start by defining the notion of intuitionistic fuzzy ${H}_{v}$ -submodules.
Definition 4.1. An intuitionistic fuzzy set $A=\left({\mu }_{A},{\lambda }_{A}\right)$ in $M$ is called an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ if
• (1) $min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}\le inf\left\{{\mu }_{A}\left(z\right)|z\in x+y\right\}$ for all $x,y\in M$ ,
• (2) for all $x,a\in M$ there exist $y,z\in M$ such that $x\in \left(a+y\right)\cap \left(z+a\right)$ and $min\left\{{\mu }_{A}\left(a\right),{\mu }_{A}\left(x\right)\right\}\le min\left\{{\mu }_{A}\left(y\right),{\mu }_{A}\left(z\right)\right\},$
• (3) ${\mu }_{A}\left(x\right)\le inf\left\{{\mu }_{A}\left(z\right)|z\in r\cdot x\right\}$ for all $x\in M$ and $r\in R$ ,
• (4) $sup\left\{{\lambda }_{A}\left(z\right)|z\in x+y\right\}\le max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{A}\left(y\right)\right\}$ for all $x,y\in M$ ,
• (5) for all $x,a\in M$ there exist $y,z\in M$ such that $x\in \left(a+y\right)\cap \left(z+a\right)$ and $max\left\{{\lambda }_{A}\left(y\right),{\lambda }_{A}\left(z\right)\right\}\le max\left\{{\lambda }_{A}\left(a\right),{\lambda }_{A}\left(x\right)\right\},$
• (6) $sup\left\{{\lambda }_{A}\left(z\right)|z\in r\cdot x\right\}\le {\lambda }_{A}\left(x\right)$ for all $x\in M$ and $r\in R$ .
Lemma 4.2. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , then so is $\square A=\left({\mu }_{A},{\mu }_{A}^{c}\right)$ .
• Proof. It is sufficient to show that ${\mu }_{A}^{c}$ satisfies the conditions (4),(5), and (6) of Definition 4.1. For $x,y\in M$ we have $min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}\le inf\left\{{\mu }_{A}\left(z\right)|z\in x+y\right\}$ and so $min\left\{1-{\mu }_{A}^{c}\left(x\right),1-{\mu }_{A}^{c}\left(y\right)\right\}\le inf\left\{1-{\mu }_{A}^{c}\left(z\right)|z\in x+y\right\}.$ Hence $min\left\{1-{\mu }_{A}^{c}\left(x\right),1-{\mu }_{A}^{c}\left(y\right)\right\}\le 1-sup\left\{{\mu }_{A}^{c}\left(z\right)|z\in x+y\right\}$ which implies $sup\left\{{\mu }_{A}^{c}\left(z\right)|z\in x+y\right\}\le 1-min\left\{1-{\mu }_{A}^{c}\left(x\right),1-{\mu }_{A}^{c}\left(y\right)\right\}.$ Therefore $sup\left\{{\mu }_{A}^{c}\left(z\right)|z\in x+y\right\}\le max\left\{{\mu }_{A}^{c}\left(x\right),{\mu }_{A}^{c}\left(y\right)\right\},$ and thus the condition (4) of Definition 4.1 is valid.
Now, let $a,x\in M.$ Then there exist $y,z\in M$ such that $x\in \left(a+y\right)\cap \left(z+a\right)$ and $min\left\{{\mu }_{A}\left(a\right),{\mu }_{A}\left(x\right)\right\}\le min\left\{{\mu }_{A}\left(y\right),{\mu }_{A}\left(z\right)\right\}.$ It follows that $min\left\{1-{\mu }_{A}^{c}\left(a\right),1-{\mu }_{A}^{c}\left(x\right)\right\}\le min\left\{1-{\mu }_{A}^{c}\left(y\right),1-{\mu }_{A}^{c}\left(z\right)\right\}$ so that $max\left\{{\mu }_{A}^{c}\left(y\right),{\mu }_{A}^{c}\left(z\right)\right\}\le max\left\{{\mu }_{A}^{c}\left(a\right),{\mu }_{A}^{c}\left(x\right)\right\}.$ Hence the condition (5) of Definition 4.1 is satisfied.
For the condition (6), let $x\in M$ and $r\in R$ . Since ${\mu }_{A}$ is a fuzzy ${H}_{v}$ -submodule of $M$ , we have ${\mu }_{A}\left(x\right)\le inf\left\{{\mu }_{A}\left(z\right)|z\in r\cdot x\right\}$ and so $1-{\mu }_{A}^{c}\left(x\right)\le inf\left\{1-{\mu }_{A}^{c}\left(z\right)|z\in r\cdot x\right\},$ which implies $sup\left\{{\mu }_{A}^{c}\left(z\right)|z\in r\cdot x\right\}\le {\mu }_{A}^{c}\left(x\right).$ Therefore the condition (6) of Definition 4.1 is satisfied.
Lemma 4.3. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , then so is $◊A=\left({\lambda }_{A}^{c},{\lambda }_{A}\right)$ .
• Proof. The proof is similar to the proof of Lemma 4.2.
Combining the above two lemmas it is not difficult to verify that the following theorem is valid.
Theorem 4.4. $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ if and only if $\square A$ and $◊A$ are intuitionistic fuzzy ${H}_{v}$ -submodules of $M$ . $\square$
Corollary 4.5. $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ if and only if ${\mu }_{A}$ and ${\lambda }_{A}^{c}$ are fuzzy ${H}_{v}$ -submodules of $M$ .
Definition 4.6. For any $t\in \left[0,1\right]$ and fuzzy set $\mu$ in $M$ , the set $U\left(\mu ;t\right)=\left\{x\in M|\mu \left(x\right)\ge t\right\}\left(resp.L\left(\mu ;t\right)=\left\{x\in M|\mu \left(x\right)\le t\right\}\right)$ is called an upper (resp. lower) $t$ -level cut of $\mu$ .
Theorem 4.7. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , then the sets $U\left({\mu }_{A};t\right)$ and $L\left({\lambda }_{A};t\right)$ are ${H}_{v}$ -submodules of $M$ for every $t\in Im\left({\mu }_{A}\right)\cap Im\left({\lambda }_{A}\right).$
• Proof. Let $t\in Im\left({\mu }_{A}\right)\cap Im\left({\lambda }_{A}\right)\subseteq \left[0,1\right]$ and let $x,y\in U\left({\mu }_{A};t\right)$ . Then ${\mu }_{A}\left(x\right)\ge t$ and ${\mu }_{A}\left(y\right)\ge t$ and so $min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}\ge t$ . It follows from the condition (1) of Definition 4.1 that $inf\left\{{\mu }_{A}\left(z\right)|z\in x+y\right\}\ge t$ . Therefore $z\in U\left({\mu }_{A};t\right)$ for all $z\in x+y,$ and so $x+y\subseteq U\left({\mu }_{A};t\right)$ . Hence $a+U\left({\mu }_{A};t\right)\subseteq U\left({\mu }_{A};t\right)$ and $U\left({\mu }_{A};t\right)+a\subseteq U\left({\mu }_{A};t\right)$ for all $a\in U\left({\mu }_{A};t\right).$ Now, let $x\in U\left({\mu }_{A};t\right).$ Then there exist $y,z\in M$ such that $x\in \left(a+y\right)\cap \left(z+a\right)$ and $min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(a\right)\right\}\le min\left\{{\mu }_{A}\left(y\right),{\mu }_{A}\left(z\right)\right\}$ . Since $x,a\in U\left({\mu }_{A};t\right)$ , we have $t\le min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(a\right)\right\}$ and so $t\le min\left\{{\mu }_{A}\left(y\right),{\mu }_{A}\left(z\right)\right\},$ which implies $y\in U\left({\mu }_{A};t\right)$ and $z\in U\left({\mu }_{A};t\right)$ . This proves that $U\left({\mu }_{A};t\right)\subseteq a+U\left({\mu }_{A};t\right)$ and $U\left({\mu }_{A};t\right)\subseteq U\left({\mu }_{A};t\right)+a$ .
Now, for every $r\in R$ and $x\in U\left({\mu }_{A};t\right)$ we show that $r\cdot x\subseteq U\left({\mu }_{A};t\right)$ .
Since $A$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , we have $t\le {\mu }_{A}\left(x\right)\le inf\left\{{\mu }_{A}\left(z\right)|z\in r\cdot x\right\}.$ Therefore, for every $z\in r\cdot x$ we get ${\mu }_{A}\left(z\right)\ge t$ which implies $z\in U\left({\mu }_{A};t\right)$ , so $r\cdot x\subseteq U\left({\mu }_{A};t\right)$ .
If $x,y\in L\left({\lambda }_{A};t\right)$ , then $max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{A}\left(y\right)\right\}\le t$ . It follows from the condition (4) of Definition 4.1 that $sup\left\{{\lambda }_{A}\left(z\right)|z\in x+y\right\}\le t$ . Therefore for all $z\in x+y$ we have $z\in L\left({\lambda }_{A};t\right)$ , so $x+y\subseteq L\left({\lambda }_{A};t\right)$ . Hence for all $a\in L\left({\lambda }_{A};t\right)$ we have $a+L\left({\lambda }_{A};t\right)\subseteq L\left({\lambda }_{A};t\right)$ and $L\left({\lambda }_{A};t\right)+a\subseteq L\left({\lambda }_{A};t\right)$ . Now, let $x\in L\left({\lambda }_{A};t\right).$ Then there exist $y,z\in M$ such that $x\in \left(a+y\right)\cap \left(z+a\right)$ and $max\left\{{\lambda }_{A}\left(y\right),{\lambda }_{A}\left(z\right)\right\}\le max\left\{{\lambda }_{A}\left(a\right),{\lambda }_{A}\left(x\right)\right\}$ . Since $x,a\in L\left({\lambda }_{A};t\right)$ , we have $max\left\{{\lambda }_{A}\left(a\right),{\lambda }_{A}\left(x\right)\right\}\le t$ and so $max\left\{{\lambda }_{A}\left(y\right),{\lambda }_{A}\left(z\right)\right\}\le t$ . Thus $y\in L\left({\lambda }_{A};t\right)$ and $z\in L\left({\lambda }_{A};t\right)$ . Hence $L\left({\lambda }_{A};t\right)\subseteq a+L\left({\lambda }_{A};t\right)$ and $L\left({\lambda }_{A};t\right)\subseteq L\left({\lambda }_{A};t\right)+a$ .
Now, we show that $r\cdot x\subseteq L\left({\lambda }_{A};t\right)$ for every $r\in R$ and $x\in L\left({\lambda }_{A};t\right)$ .
Since $A$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , we have $sup\left\{{\lambda }_{A}\left(z\right)|z\in r\cdot x\right\}\le {\lambda }_{A}\left(x\right)\le t.$ Therefore, for every $z\in r\cdot x$ we get ${\lambda }_{A}\left(z\right)\le t,$ which implies $z\in L\left({\lambda }_{A};t\right)$ , so $r\cdot x\subseteq L\left({\lambda }_{A};t\right)$ .
Theorem 4.8. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy set in $M$ such that all non-empty level sets $U\left({\mu }_{A};t\right)$ and $L\left({\lambda }_{A};t\right)$ are ${H}_{v}$ -submodules of $M$ , then $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ .
• Proof. Assume that all non-empty level sets $U\left({\mu }_{A};t\right)$ and $L\left({\lambda }_{A};t\right)$ are ${H}_{v}$ -submodules of $M$ . If ${t}_{0}=min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}$ and ${t}_{1}=max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{A}\left(y\right)\right\}$ for $x,y\in M$ , then $x,y\in U\left({\mu }_{A};{t}_{0}\right)$ and $x,y\in L\left({\lambda }_{A};{t}_{1}\right)$ . So $x+y\subseteq U\left({\mu }_{A};{t}_{0}\right)$ and $x+y\subseteq L\left({\lambda }_{A};{t}_{1}\right)$ . Therefore for all $z\in x+y$ we have ${\mu }_{A}\left(z\right)\ge {t}_{0}$ and ${\lambda }_{A}\left(z\right)\le {t}_{1}$ , i.e., $inf\left\{{\mu }_{A}\left(z\right)|z\in x+y\right\}\ge min\left\{{\mu }_{A}\left(x\right),{\mu }_{A}\left(y\right)\right\}$ and $sup\left\{{\lambda }_{A}\left(z\right)|z\in x+y\right\}\le max\left\{{\lambda }_{A}\left(x\right),{\lambda }_{A}\left(y\right)\right\},$ which verify the conditions (1) and (4) of Definition 4.1.
Now, if ${t}_{2}=min\left\{{\mu }_{A}\left(a\right),{\mu }_{A}\left(x\right)\right\}$ for $x,a\in M$ , then $a,x\in U\left({\mu }_{A};{t}_{2}\right)$ . So there exist ${y}_{1},{z}_{1}\in U\left({\mu }_{A};{t}_{2}\right)$ such that $x\in a+{y}_{1}$ and $x\in {z}_{1}+a$ . Also we have ${t}_{2}\le min\left\{{\mu }_{A}\left({y}_{1}\right),{\mu }_{A}\left({z}_{1}\right)\right\}$ . Therefore the condition (2) of Definition 4.1 is verified. If we put ${t}_{3}=max\left\{{\lambda }_{A}\left(a\right),{\lambda }_{A}\left(x\right)\right\}$ then $a,x\in L\left({\lambda }_{A};{t}_{3}\right)$ . So there exist ${y}_{2},{z}_{2}\in L\left({\lambda }_{A};{t}_{3}\right)$ such that $x\in a+{y}_{2}$ and $x\in {z}_{2}+a$ and we have $max\left\{{\lambda }_{A}\left({y}_{2}\right),{\lambda }_{A}\left({y}_{2}\right)\right\}\le {t}_{3}$ , and so the condition (5) of Definition 4.1 is verified.
Now, we verify the conditions (3) and (6). Let ${t}_{4}={\mu }_{A}\left(x\right)$ and ${t}_{5}={\lambda }_{A}\left(x\right)$ for some $x\in M$ and let $r\in R$ . Then $x\in U\left({\mu }_{A};{t}_{4}\right)$ and $x\in L\left({\lambda }_{A},{t}_{5}\right)$ . Since $U\left({\mu }_{A};{t}_{4}\right)$ and $L\left({\lambda }_{A},{t}_{5}\right)$ are ${H}_{v}$ -submodules of $M$ , we get $r\cdot x\subseteq U\left({\mu }_{A};{t}_{4}\right)$ and $r\cdot x\subseteq L\left({\lambda }_{A},{t}_{5}\right)$ . Therefore for every $z\in r\cdot x$ we have $z\in U\left({\mu }_{A};{t}_{4}\right)$ and $z\in L\left({\lambda }_{A},{t}_{5}\right)$ which imply ${\mu }_{A}\left(z\right)\ge {t}_{4}$ and ${\lambda }_{A}\left(z\right)\le {t}_{5}$ . Hence $inf\left\{{\mu }_{A}\left(z\right)|z\in r\cdot x\right\}\ge {t}_{4}={\mu }_{A}\left(x\right)$ and $sup\left\{{\lambda }_{A}\left(z\right)|z\in r\cdot x\right\}\le {t}_{5}={\lambda }_{A}\left(x\right).$ This completes the proof.
Corollary 4.9. Let $S$ be an ${H}_{v}$ -submodule of an ${H}_{v}$ -module $M$ .
If fuzzy sets $\mu$ and $\lambda$ in $M$ are defined by $\mu \left(x\right)=\left\{\begin{array}{cc}{\alpha }_{0}& \text{if}x\in S\text{},\\ {\alpha }_{1}& \text{if}x\in M\S\text{,}\end{array}\lambda \left(x\right)=\left\{\begin{array}{cc}{\beta }_{0}& \text{if}x\in S\text{},\\ {\beta }_{1}& \text{if}x\in M\S\text{,}\end{array}$ where $0\le {\alpha }_{1}<{\alpha }_{0}$ , $0\le {\beta }_{0}<{\beta }_{1}$ and ${\alpha }_{i}+{\beta }_{i}\le 1$ for $i=0,1$ .
Then $A=\left(\mu ,\lambda \right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ and $U\left(\mu ;{\alpha }_{0}\right)=S=L\left(\lambda ;{\beta }_{0}\right)$ .
Corollary 4.10. Let ${\chi }_{{}_{S}}$ be the characteristic function of an ${H}_{v}$ -submodule $S$ of $M$ . Then $A=\left({\chi }_{{}_{S}},{\chi }_{{}_{S}}^{c}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ .
Theorem 4.11. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ , then ${\mu }_{A}\left(x\right)=sup\left\{\alpha \in \left[0,1\right]|x\in U\left({\mu }_{A};\alpha \right)\right\}$ and ${\lambda }_{A}\left(x\right)=inf\left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\}$ for all $x\in M.$
• Proof. Let $\delta =sup\left\{\alpha \in \left[0,1\right]|x\in U\left({\mu }_{A};\alpha \right)\right\}$ and let $\varepsilon >0$ be given. Then $\delta -\varepsilon <\alpha$ for some $\alpha \in \left[0,1\right]$ such that $x\in U\left({\mu }_{A};\alpha \right)$ . This means that $\delta -\varepsilon <{\mu }_{A}\left(x\right)$ so that $\delta \le {\mu }_{A}\left(x\right)$ since $\varepsilon$ is arbitrary.
We now show that ${\mu }_{A}\left(x\right)\le \delta .$ If ${\mu }_{A}\left(x\right)=\beta$ , then $x\in U\left({\mu }_{A};\beta \right)$ and so $\beta \in \left\{\alpha \in \left[0,1\right]|x\in U\left({\mu }_{A};\alpha \right)\right\}.$ Hence ${\mu }_{A}\left(x\right)=\beta \le sup\left\{\alpha \in \left[0,1\right]|x\in U\left({\mu }_{A};\alpha \right)\right\}=\delta .$ Therefore ${\mu }_{A}\left(x\right)=\delta =sup\left\{\alpha \in \left[0,1\right]|x\in U\left({\mu }_{A};\alpha \right)\right\}.$ Now let $\eta =inf\left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\}$ . Then $inf\left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\}<\eta +\varepsilon$ for any $\varepsilon >0,$ and so $\alpha <\eta +\varepsilon$ for some $\alpha \in \left[0,1\right]$ with $x\in L\left({\lambda }_{A};\alpha \right)$ .
Since ${\lambda }_{A}\left(x\right)\le \alpha$ and $\varepsilon$ is arbitrary, it follows that ${\lambda }_{A}\left(x\right)\le \eta$ .
To prove ${\lambda }_{A}\left(x\right)\ge \eta$ , let ${\lambda }_{A}\left(x\right)=\zeta$ . Then $x\in L\left({\lambda }_{A};\zeta \right)$ and thus $\zeta \in \left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\}$ . Hence $inf\left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\}\le \zeta ,$ i.e. $\eta \le \zeta ={\lambda }_{A}\left(x\right).$ Consequently ${\lambda }_{A}\left(x\right)=\eta =inf\left\{\alpha \in \left[0,1\right]|x\in L\left({\lambda }_{A};\alpha \right)\right\},$ which completes the proof.
Definition 4.12. A fuzzy set $\mu$ in a set $X$ is said to have sup property if for every non-empty subset $S$ of $X$ , there exists ${x}_{0}\in S$ such that $\mu \left({x}_{0}\right)={sup}_{x\in S}\left\{\mu \left(x\right)\right\}.$
Proposition 4.13. Let ${M}_{1}$ and ${M}_{2}$ be two ${H}_{v}$ -modules over an ${H}_{v}$ -ring $R$ and $f:{M}_{1}⟶{M}_{2}$ be a surjection. If $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of ${M}_{1}$ such that ${\mu }_{A}$ and ${\lambda }_{A}$ have sup property, then
• (i) $f\left(U\left({\mu }_{A};t\right)\right)=U\left(f\left({\mu }_{A}\right);t\right),$
• (ii) $f\left(L\left({\lambda }_{A};t\right)\right)\subseteq L\left(f\left({\lambda }_{A}\right);t\right)$
• Proof. (i) We have $\begin{array}{cc}y\in U\left(f\left({\mu }_{A}\right);t\right)& ⟺f\left({\mu }_{A}\right)\left(y\right)\ge t\end{array}$
$\begin{array}{cc}& ⟺{sup}_{x\in {f}^{-1}\left(y\right)}\left\{{\mu }_{A}\left(x\right)\right\}\ge t\end{array}$
$\begin{array}{cc}& ⟺\exists {x}_{0}\in {f}^{-1}\left(y\right),{\mu }_{A}\left({x}_{0}\right)\ge t\end{array}$
$\begin{array}{cc}& ⟺\exists {x}_{0}\in {f}^{-1}\left(y\right),{x}_{0}\in U\left({\mu }_{A};t\right)\end{array}$
$\begin{array}{cc}& ⟺f\left({x}_{0}\right)=y,{x}_{0}\in U\left({\mu }_{A};t\right)\end{array}$
$\begin{array}{cc}& ⟺y\in f\left(U\left({\mu }_{A};t\right)\right).\end{array}$
(ii) We have $\begin{array}{cc}y\in L\left(f\left({\lambda }_{A}\right);t\right)& ⟹f\left({\lambda }_{A}\right)\left(y\right)\le t\end{array}$
$\begin{array}{cc}& ⟹{sup}_{x\in {f}^{-1}\left(y\right)}\left\{{\lambda }_{A}\left(x\right)\right\}\le t\end{array}$
$\begin{array}{cc}& ⟹{\lambda }_{A}\left(x\right)\le tforallx\in {f}^{-1}\left(y\right)\end{array}$
$\begin{array}{cc}& ⟹x\in L\left({\lambda }_{A};t\right)forallx\in {f}^{-1}\left(y\right)\end{array}$
$\begin{array}{cc}& ⟹y\in f\left(L\left({\lambda }_{A};t\right)\right).\end{array}$
Proposition 4.14. Let ${M}_{1}$ and ${M}_{2}$ be two ${H}_{v}$ -modules over an ${H}_{v}$ -ring $R$ and $f:{M}_{1}⟶{M}_{2}$ be a map. If $B=\left({\mu }_{B},{\lambda }_{B}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of ${M}_{2}$ , then
• (i) ${f}^{-1}\left(U\left({\mu }_{B};t\right)\right)=U\left({f}^{-1}\left({\mu }_{B}\right);t\right),$
• (ii) ${f}^{-1}\left(L\left({\lambda }_{B};t\right)\right)=L\left({f}^{-1}\left({\lambda }_{B}\right);t\right)$
for every $t\in \left[0,1\right].$
• Proof. (i) We have $\begin{array}{cc}x\in U\left({f}^{-1}\left({\mu }_{B}\right);t\right)& ⟺{f}^{-1}\left({\mu }_{B}\right)\left(x\right)\ge t\end{array}$
$\begin{array}{cc}& ⟺{\mu }_{B}\left(f\left(x\right)\right)\ge t\end{array}$
$\begin{array}{cc}& ⟺f\left(x\right)\in U\left({\mu }_{B};t\right)\end{array}$
$\begin{array}{cc}& ⟺x\in {f}^{-1}\left(U\left({\mu }_{B};t\right)\right).\end{array}$
(ii) We have $\begin{array}{cc}x\in L\left({f}^{-1}\left({\lambda }_{B}\right);t\right)& ⟺{f}^{-1}\left({\lambda }_{B}\right)\left(x\right)\le t\end{array}$
$\begin{array}{cc}& ⟺{\lambda }_{B}\left(f\left(x\right)\right)\le t\end{array}$
$\begin{array}{cc}& ⟺f\left(x\right)\in L\left({\lambda }_{B};t\right)\end{array}$
$\begin{array}{cc}& ⟺x\in {f}^{-1}\left(L\left({\lambda }_{B};t\right)\right).\end{array}$
Definition 4.15. Let $f$ be a map from a set $X$ to a set $Y$ . If $B=\left({\mu }_{B},{\lambda }_{B}\right)$ is an intuitionistic fuzzy set in $Y,$ then the inverse image of $B$ under $f$ is defined by: ${f}^{-1}\left(B\right)=\left({f}^{-1}\left({\mu }_{B}\right),{f}^{-1}\left({\lambda }_{B}\right)\right).$
It is easy to see that ${f}^{-1}\left(B\right)$ is an intuitionistic fuzzy set in $X$ .
Corollary 4.16. Let ${M}_{1}$ and ${M}_{2}$ be two ${H}_{v}$ -modules over an ${H}_{v}$ -ring $R$ and $f:{M}_{1}⟶{M}_{2}$ be a strong epimorphism. If $B=\left({\mu }_{B},{\lambda }_{B}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of ${M}_{2}$ , then ${f}^{-1}\left(B\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of ${M}_{1}$ .
• Proof. Assume that $B=\left({\mu }_{B},{\lambda }_{B}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of ${M}_{2}$ . By Theorem 4.7, we know that the sets $U\left({\mu }_{B};t\right)$ and $L\left({\lambda }_{B};t\right)$ are ${H}_{v}$ -submodules of ${M}_{2}$ for every $t\in Im\left({\mu }_{B}\right)\cap Im\left({\lambda }_{B}\right).$ It follows from Proposition 3.6 that ${f}^{-1}\left(U\left({\mu }_{B};t\right)\right)$ and ${f}^{-1}\left(L\left({\lambda }_{B};t\right)\right)$ are ${H}_{v}$ -submodules of ${M}_{1}$ . Using Proposition 4.14, we have ${f}^{-1}\left(U\left({\mu }_{B};t\right)\right)=U\left({f}^{-1}\left({\mu }_{B}\right);t\right),$ ${f}^{-1}\left(L\left({\lambda }_{B};t\right)\right)=L\left({f}^{-1}\left({\lambda }_{B}\right);t\right).$ Now by Theorem 4.8, the proof is completed.
5 On fundamental modules
The main tools in the theory of ${H}_{v}$ -structures are the fundamental relations. Consider an ${H}_{v}$ -module $M$ over an ${H}_{v}$ -ring $R$ . If the relation ${\gamma }^{*}$ is the smallest equivalence relation on $R$ such that the quotient $R/{\gamma }^{*}$ , the set of all equivalence classes, is a ring, we say that ${\gamma }^{*}$ is the fundamental equivalence relation on $R$ and $R/{\gamma }^{*}$ is the fundamental ring (see [17, 19). The fundamental relation ${\epsilon }^{*}$ on $M$ over $R$ is the smallest equivalence relation on $M$ such that $M/{\epsilon }^{*}$ is a module over the ring $R/{\gamma }^{*}$ . Let $\mathcal{U}$ be the set of all expressions consisting of finite hyperoperations either on $R$ and $M$ or the external hyperoperation applied to finite sets of elements of $R$ and $M$ . We define the relation $\epsilon$ on $M$ as follows: $a\epsilon bifandonlyif\left\{a,b\right\}\subseteq uforsomeu\in \mathcal{U}.$ Let us denote $\stackrel{^}{\epsilon }$ the transitive closure of $\epsilon$ . Then we can rewrite the definition of $\stackrel{^}{\epsilon }$ on $M$ as follows:
$a\stackrel{^}{\epsilon }b$ if and only if there exist ${z}_{1},\dots ,{z}_{n+1}\in M$ with ${z}_{1}=a$ , ${z}_{n+1}=b$ and ${u}_{1},\dots ,{u}_{n}\in \mathcal{U}$ such that $\left\{{z}_{i},{z}_{i+1}\right\}\subseteq {u}_{i}\left(i=1,\dots ,n\right).$
Theorem 5.1. ( cf. Vougiouklis [20). The fundamental relation ${\epsilon }^{*}$ is the transitive closure of the relation $\epsilon$ .
Suppose ${\gamma }^{*}\left(r\right)$ is the equivalence class containing $r\in R,$ and ${\epsilon }^{*}\left(x\right)$ the equivalence class containing $x\in M$ . On $M/{\epsilon }^{*}$ , the sum $\oplus$ and the external product $\odot$ using the ${\gamma }^{*}$ classes in $R$ are defined as follows: ${\epsilon }^{*}\left(x\right)\oplus {\epsilon }^{*}\left(y\right)={\epsilon }^{*}\left(c\right)forallc\in {\epsilon }^{*}\left(x\right)+{\epsilon }^{*}\left(y\right),$ ${\gamma }^{*}\left(r\right)\odot {\epsilon }^{*}\left(x\right)={\epsilon }^{*}\left(d\right)foralld\in {\gamma }^{*}\left(r\right)\cdot {\epsilon }^{*}\left(x\right).$ The kernel of the canonical map $\phi :M⟶M/{\epsilon }^{*}$ is called the core of $M$ and is denoted by ${\omega }_{M}$ . Here we also denote ${\omega }_{M}$ the zero element of $M/\epsilon$ . We have ${\omega }_{M}={\epsilon }^{*}\left(0\right),and{\epsilon }^{*}\left(-x\right)=-{\epsilon }^{*}\left(x\right)forallx\in M.$
Definition 5.2. Let $M$ be an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ and let $A=\left({\mu }_{A},{\lambda }_{A}\right)$ be an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ . The intuitionistic fuzzy set $A/{\epsilon }^{*}=\left({\overline{{\mu }_{A}}}^{{\epsilon }^{*}},{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\right)$ is defined as follows: ${\overline{{\mu }_{A}}}^{{\epsilon }^{*}}:M/{\epsilon }^{*}⟶\left[0,1\right]$ ${\overline{{\mu }_{A}}}^{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)=\left\{\begin{array}{cc}{sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\mu }_{A}\left(a\right)\right\}& if{\epsilon }^{*}\left(x\right)\ne {\omega }_{M}\\ 1& if{\epsilon }^{*}\left(x\right)={\omega }_{M}\end{array}$ and ${\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}:M/{\epsilon }^{*}⟶\left[0,1\right]$ ${\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)=\left\{\begin{array}{cc}{inf}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\lambda }_{A}\left(a\right)\right\}& if{\epsilon }^{*}\left(x\right)\ne {\omega }_{M}\\ 0& if{\epsilon }^{*}\left(x\right)={\omega }_{M}.\end{array}$
In the following we show that $0\le {\overline{{\mu }_{A}}}^{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)+{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)\le 1,$ for all ${\epsilon }^{*}\left(x\right)\in M/{\epsilon }^{*}$ .
If ${\epsilon }^{*}\left(x\right)={\omega }_{M}$ , then the above inequalities are clear. Assume that $x\in H$ and ${\epsilon }^{*}\left(x\right)\ne {\omega }_{M}$ . Since $0\le {\mu }_{A}\left(a\right)$ and $0\le {\lambda }_{A}\left(a\right)$ for all $a\in {\epsilon }^{*}\left(x\right)$ , we have $0\le {sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\mu }_{A}\left(a\right)\right\}+{inf}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\lambda }_{A}\left(a\right)\right\}$ or $0\le {\overline{{\mu }_{A}}}^{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)+{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right).$ On the other hand, we have ${\mu }_{A}\left(a\right)+{\lambda }_{A}\left(a\right)\le 1or{\mu }_{A}\left(a\right)\le 1-{\lambda }_{A}\left(a\right),$ for all $a\in {\epsilon }^{*}\left(x\right),$ and so
$\begin{array}{cc}{\overline{{\mu }_{A}}}^{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)& ={sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\mu }_{A}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& \le {sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{1-{\lambda }_{A}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& =1-{inf}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\lambda }_{A}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& =1-{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right).\end{array}$
Hence ${\overline{{\mu }_{A}}}^{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)+{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right)\le 1$ .
Theorem 5.3. (cf. Davvaz [6). Let $M$ be an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ and let $\mu$ be a fuzzy ${H}_{v}$ -submodule of $M$ . Then ${\overline{{\mu }_{A}}}^{{\epsilon }^{*}}$ is a fuzzy submodule of the module $M/{\epsilon }^{*}$ .
Lemma 5.4. We have $\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}{\right)}^{c}={\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}.$
• Proof. If ${\epsilon }^{*}\left(x\right)={\omega }_{M}$ , then $\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}{\right)}^{c}\left({\omega }_{H}\right)=1-\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}\right)\left({\omega }_{M}\right)=0={\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\omega }_{M}\right).$ Now, assume that ${\epsilon }^{*}\left(x\right)\ne {\omega }_{M}.$ Then $\begin{array}{cc}\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}{\right)}^{c}\left({\epsilon }^{*}\left(x\right)\right)& =1-\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}\right)\left({\epsilon }^{*}\left(x\right)\right)\end{array}$
$\begin{array}{cc}& =1-{sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\lambda }_{A}^{c}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& =1-{sup}_{a\in {\epsilon }^{*}\left(x\right)}\left\{1-{\lambda }_{A}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& ={inf}_{a\in {\epsilon }^{*}\left(x\right)}\left\{{\lambda }_{A}\left(a\right)\right\}\end{array}$
$\begin{array}{cc}& ={\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\left({\epsilon }^{*}\left(x\right)\right).\end{array}$
Theorem 5.5. Let $M$ be an ${H}_{v}$ -module over an ${H}_{v}$ -ring $R$ and let $A=\left({\mu }_{A},{\lambda }_{A}\right)$ be an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ .
Then $A/{\epsilon }^{*}=$ $\left({\overline{{\mu }_{A}}}^{{\epsilon }^{*}},$ ${\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\right)$ is an intuitionistic fuzzy submodule of the fundamental module $M/{\epsilon }^{*}.$
• Proof. Suppose that $A=\left({\mu }_{A},{\lambda }_{A}\right)$ is an intuitionistic fuzzy ${H}_{v}$ -submodule of $M$ . Using Lemma 4.3, ${\lambda }_{A}^{c}$ is a fuzzy ${H}_{v}$ -submodule of $M$ and by Theorem 5.3, ${\overline{{\mu }_{A}}}^{{\epsilon }^{*}}$ and ${\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}$ are fuzzy ${H}_{v}$ -submodules of $M/{\epsilon }^{*}$ , and so $\left({\overline{{\lambda }_{A}^{c}}}^{{\epsilon }^{*}}{\right)}^{c}$ satisfies the conditions (4), (5), (6) of Definition 2.5. Hence by Lemma 5.4, ${\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}$ satisfies the conditions (4),(5),(6) of Definition 2.5. Therefore $A/{\epsilon }^{*}=\left({\overline{{\mu }_{A}}}^{{\epsilon }^{*}},{\underline{{\lambda }_{A}}}_{{\epsilon }^{*}}\right)$ is an intuitionistic fuzzy submodule of $M/{\epsilon }^{*}$ .
6 Conclusions
As a generalization of fuzzy sets, the notion of intuitionistic fuzzy sets was introduced by Atanassov [1, and applications of intuitionistic fuzzy concepts have already been done by Atanassov and others in algebra, topological space, knowledge engineering, natural language, and neural network etc.
Biswas [3have applied the concept of intuitionistic fuzzy sets to the theory of groups and studied intuitionistic fuzzy subgroups of a group. The notion of an intuitionistic fuzzy subquasigroup of a guasigroup was discussed by Kim, Dudek and Jun [12. Also the concept of intuitionistic fuzzy ideals of semigroups was considered by Kim and Jun [13. The concept of hyperstructure first was introduced by Marty [14. Vougiouklis [19, in the fourth AHA congress (1990), introduced the notion of ${H}_{v}$ -structures. Recently, present authors [11have discussed the intuitionistic fuzzification of the concept of subhyperquasigroups in a hyperquasigroup. The aim of this paper is to introduce the notion of an intuitionistic fuzzy ${H}_{v}$ -submodule of an ${H}_{v}$ -module, and to investigate related properties. Characterizations of intuitionistic fuzzy ${H}_{v}$ -submodules are given. Our future work will focus on studying the intuitionistic fuzzy structure of ${H}_{v}$ -nearring modules.
7 Acknowledgements
The authors are highly grateful to referees and Professor Witold Pedrycz, Editor-in-Chief, for their valuable comments and suggestions for improving the paper.
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19. T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, Algebraic Hyperstructures and Applications (Xanthi, 1990), $203-211$ , World Sci. Publishing, Teaneck, NJ 1991.
20. T. Vougiouklis, ${H}_{v}$ -vector spaces, Proc. ${5}^{th}$ Int. Congress on AHA, Rumani 1993, (Hadronic Press Inc, Florida, 1994), $181-190.$
21. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), $338-353.$
$\text{}$ E-mail address: davvaz@yazduni.ac.ir (B. Davvaz), dudek@im.pwr.wroc.pl (W. A. Dudek), ybjun@gsnu.ac.kr (Y. B. Jun)
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2022-09-24 23:30:22
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https://electronics.stackexchange.com/questions/489963/how-to-prevent-def-con-and-simulation-running-at-femtoseconds-second-runnin
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# How to prevent "Def Con" and simulation running at femtoseconds / second (running forever) for 1,600-run simulation
I did read other questions related to "Def Con", but, 1. I did not understand very well what was said, 2. other circuits were not discrete transistor circuits, and 3. I thought that it might be useful to have a minimal circuit with this problem, in case LTSpice can be enhanced to avoid this problem.
The progress message at the bottome left of the screen keeps alternating between the "Def Con" message:
and a message that says that the rate of simulation is in the femtosecond range:
In the above screen shot, please note that progress has slowed to 22.4748 femtoseconds per second of simulation speed forward progress.
I am using LTSpice to try out every combination of NPN in the following circuit, which simply represents a flying capacitor transferring charge between a simple cell and an inductor, lighting an LED. The circuit is an inverting boost topology.
Many transistor combinations run fine. The problem is, for certain combinations of transistors, the (to me) dreaded "Def Con" happens, with progress slowing down to the rate of femtoseconds per second at times.
The circuit as pictured descends into this degenerative condition. One laptop descends to femtoseconds-per-second simulation speed, and another laptop only seems to go down to picoseconds-per-second simulation velocity.
I usually just change the circuit a bit, and the problem goes away, or I find something that was wrong with the circuit, but I don't think I can follow that heuristic here. I would really like to understand how this happens to various Joule Thief circuits and other simple transistor circuits that I am trying on my way towards teaching myself discrete transistor circuitry.
My circuits usually have a left-to-right current flow, but for better presentation in this format, I've rotated the circuit, and current flows top-to-bottom.
Since there are 1,600 transistor combinations to go through, how do I prevent "Def Con" from happening, and this set of simulations from taking forever?
EDIT: I need to explain where the 1,600 figure comes from... I am testing only 40 of the stock models that come with LTSpice, but I am testing every combination of (NPN1, NPN2) which ends up being 40*40 which is 1,600 combinations. There are two .step statements, each going through the 40 models, one .step statement for NPN1, and the other .step statement for NPN2. When I start the LTSpice simulation, it starts chugging through the 1,600 simulations.
Another electrical engineering stack exchange question gives some background on how and why I got here.
For your convenience, here is the source code for the LTSpice simulation file. Just copy and paste it into Notepad or other text editor, and then save it as something like "DefConSimulation.asc". (LTSpice is free):
Version 4
SHEET 1 3448 1340
WIRE 144 -128 -288 -128
WIRE -288 -96 -288 -128
WIRE -288 -96 -320 -96
WIRE 144 -96 144 -128
WIRE -288 -80 -288 -96
WIRE -64 -48 -160 -48
WIRE 32 -48 16 -48
WIRE 80 -48 32 -48
WIRE -160 -32 -160 -48
WIRE 32 -32 32 -48
WIRE -160 64 -160 48
WIRE 32 64 32 48
WIRE 32 64 -160 64
WIRE 144 64 144 0
WIRE 144 64 32 64
WIRE -288 160 -288 0
WIRE -224 160 -288 160
WIRE 144 160 144 64
WIRE 144 160 -160 160
WIRE 176 160 144 160
WIRE 144 208 144 160
WIRE -64 256 -160 256
WIRE 32 256 16 256
WIRE 80 256 32 256
WIRE -160 272 -160 256
WIRE 32 272 32 256
WIRE -288 288 -288 160
WIRE -240 288 -288 288
WIRE -240 336 -240 288
WIRE -160 368 -160 352
WIRE 32 368 32 352
WIRE 32 368 -160 368
WIRE 144 368 144 304
WIRE 144 368 32 368
WIRE 144 400 144 368
WIRE -16 448 144 400
WIRE -288 480 -288 288
WIRE -176 480 -288 480
WIRE -16 480 -16 448
WIRE -16 480 -96 480
WIRE 32 480 -16 480
WIRE -288 512 -288 480
WIRE -288 624 -288 576
WIRE -128 624 -288 624
WIRE -16 624 -16 480
WIRE -16 624 -64 624
WIRE -288 736 -288 624
WIRE -288 736 -320 736
WIRE -240 736 -288 736
WIRE -16 736 -16 624
WIRE -16 736 -176 736
FLAG -240 336 0
FLAG 176 160 C1
FLAG -320 736 D1
FLAG 32 480 L1
FLAG -320 -96 V1
SYMBOL voltage -288 -96 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 3
SYMBOL voltage -160 -48 R0
WINDOW 3 -115 132 Left 2
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value PULSE(0 12 0us 100ns 100ns 1us 4us 987000123)
SYMATTR InstName V2
SYMBOL ind -80 496 M270
WINDOW 3 5 56 VBottom 2
WINDOW 0 32 56 VTop 2
SYMATTR Value 100µH
SYMATTR InstName L1
SYMBOL cap -160 144 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName C1
SYMATTR Value 100µF
SYMBOL LED -240 752 R270
WINDOW 0 28 -10 VTop 2
WINDOW 3 55 124 VBottom 2
SYMATTR InstName D1
SYMATTR Value LXK2-PW14
SYMATTR Description Diode
SYMATTR Type diode
SYMBOL npn 80 -96 R0
WINDOW 0 60 25 Left 2
WINDOW 3 27 57 Left 2
SYMATTR InstName NPN1
SYMATTR Value BC337-25
SYMBOL res 16 -48 R0
SYMATTR InstName R1
SYMATTR Value 100K
SYMBOL res -80 -32 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R3
SYMATTR Value 240
SYMBOL voltage -160 256 R0
WINDOW 3 -119 138 Left 2
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value PULSE(0 12 2us 100ns 100ns 1us 4us 987000123)
SYMATTR InstName V3
SYMBOL npn 80 208 R0
WINDOW 0 60 25 Left 2
WINDOW 3 27 57 Left 2
SYMATTR InstName NPN2
SYMATTR Value 2N5550
SYMBOL res 16 256 R0
SYMATTR InstName R2
SYMATTR Value 100K
SYMBOL res -80 272 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R4
SYMATTR Value 240
SYMBOL schottky -304 512 R0
WINDOW 3 24 70 Left 2
SYMATTR InstName D2
SYMATTR Value 1N5817
SYMATTR Description Diode
SYMATTR Type diode
SYMBOL cap -64 608 R90
WINDOW 0 3 64 VBottom 2
WINDOW 3 -26 -9 VTop 2
SYMATTR InstName C2
SYMATTR Value 10nF
TEXT -208 -112 Left 2 !.tran 0 2.4ms 2ms startup
TEXT -904 96 Left 2 !.SAVE I(D1) I(V1) V(V1) V(D1) V(D2) V(L1)\n.meas iD1 AVG I(D1)\n.meas iV1 AVG -I(V1)\n.meas pIn AVG -V(V1)*I(V1)\n.meas pOut AVG V(D1,L1)*I(D1)\n.meas effic PARAM pOut/pIn*100
• Have you got a valid EE question and what is def con? Mar 30, 2020 at 17:36
• @Andyaka -- This is an LTSpice question, which I believe is a valid EE question (please correct me if I am wrong) since there is an LTSpice tag here. Here are some valid EE "Def Con" questions (I think they're valid -- again, please correct me if I am wrong). Mar 30, 2020 at 17:44
• My general list of LTspice cheats, in order: change to alternative solver, try ideal components, provide megaohm-range leakages in “sensitive” nodes to ground, allow HF paths where needed (usually pF of capacitance across switches), bring down Q with again high ohmic resistors across inductors, keep your rise rates for sources to reasonable levels and so on. Mar 30, 2020 at 20:08
• Oh, and milliohm resistor in series can help too if you see any current value jump to GA or anything similar. Mar 30, 2020 at 20:22
• @winny -- Thank you for that information -- it is just what I needed! Mar 31, 2020 at 0:09
Try this: for all sources add Rser=0.1, and for the 3V one add Cpar=1m, and for both capacitors add Rser=10m. If (unwanted) very high frequency oscillations start to appear because of the inductor, try adding Rpar=100k to the inductor, or even lower. Don't shy away from setting parasitics, they helo with convergence. If need arises, also don't be afraid to add small capacitances from key nodes to ground -- they help smooth out those discontinuities caused by very sharp transisions.
One key thing to remember is that voltage sources are not that convergence friendly in LTspice, but when you addRser, internally they are converted to current sources, which are far superior in terms of convergence.
• This was exactly what I needed. This took what had taken ten hours and was threatening to take 15 hours, and allowed it to run in only 43.2 minutes. I simply added 22pF to each circuit trace (subnet?). Thank you! Mar 31, 2020 at 0:19
• The combinate of transistors that I like the best (after looking at the results of the 1,600 combo run) are a 2N3904 for NPN1, and a 2N2222 for NPN2, which raises the efficiency to 86.48 % at 11.52 mA out at D1. But what does that mean when I remove the transistors and create the manually commutated version? Apr 1, 2020 at 20:57
• @MicroservicesOnDDD Don't forget that you're in the simulation world, so the results of your simulations are only as best as your models and your implementations are. That said, in the linked question you say you want to avoid active elements, but if you're willing to go for them, then instead of the mechanical solution in the answer, you can go with a self-oscillating approach. Apr 1, 2020 at 22:39
When a simulation descends to machine limit calculation it is a sign that the simulation sees or expects chaotic output.
This can be due to a divergent solution (e..g runaway positive feedback, multiple voltage dependent sources ) without same limits on power or frequency or otherwise .
If you are really testing 1600 transistor models and some exhibit this and some don't it is possible that some are simply not suitable and not appropriately modeled for this application/operating regime and break the sim
Or they are more ideal and some more accurately model secondary parameter or model features that keeps things from diverging.
Usually I take it as a sign do to one of the following
1. Modularize my simulation and create individual parametrized models of major sub parts
2. Alternatively Simplify the Sim and what I am asking of it
3. Triple check my simulation schematic and analysis options
4. Only used verified good and appropriate models compatible with ltspice
• Oh, sorry... I wasn't clear enough. I am testing only 40 of the stock models that come with LTSpice, but I am testing every combination of (NPN1, NPN2) which ends up being 40*40 which is 1,600 combinations. There are two .step statements, each going through the 40 models, one .step statement for NPN1, and the other .step statement for NPN2. Mar 30, 2020 at 19:47
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2022-05-25 16:27:30
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http://conferences2.imfm.si/contributionDisplay.py?contribId=120&confId=1
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# Bled'11 - 7th Slovenian International Conference on Graph Theory
19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
Home > Timetable > Contribution details
PDF | XML
# Lexicographic products and colourings of graphs
Presented by Ewa DRGAS-BURCHARDT
Type: Oral presentation
Track: Domination, Independence and Coloring of Product Graphs
## Content
Let L denote the class of graphs closed under isomorphism, substitution and taking induced subgraphs. Let P_1, P_2 be in L. We say that a graph G belongs to the class P_1 \ circ P_2 if the vertex set of G can be divided into two subsets V_1, V_2, such that for i \ in {1,2} the graph G [V_i] induced in G by V_i belongs to P_i. Using the theorem proved by Gallai, which concerns the modular decomposition of a graph, we know that every finite simple graph can be uniquely described as composition lexicographic products of prime graphs. In particular, the graphs, that are forbidden for classes P_1\circ P_2, where P_1, P_2 \in L, have such a description. In this talk we study the structure of such graphs showing them as lexicographic products of graphs that are forbidden for P_1 and for P_2. This analysis allows to find a result that the class of minimal forbidden graphs for P_1\circ P_2, where P_1, P_2 \in L, is finite if and only if P_1 is finite and the class of forbidden graphs for P_2 is finite or P_1\circ P_2 is the class of split graphs. This is a partial solution of conjecture, stated in 2002 by Zverovich, which concerns the finiteness of families of forbidden graphs for the class P_1\circ P_2, where both of P_1,P_2 are induced hereditary Our proof confirms this conjecture in L.
## Place
Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled
More
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2020-02-18 15:21:59
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https://oumathclub.wordpress.com/2012/07/12/minipolymath4-project-now-open/
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# Minipolymath4 Project Now Open!
As we talked about here, there was plans afoot to group-solve online an interesting and problem from the IMO. The online discussion going on right now (unless, of course, you’re reading this later). They decided to work on Question 3. Here it is:
Problem 3. The liar’s guessing game is a game played between two players $A$ and $B$. The rules of the game depend on two positive integers $k$ and $n$ which are known to both players.
At the start of the game, $A$ chooses two integers $x$ and $N$ with $1 \leq x \leq N$. Player $A$ keeps $x$ secret, and truthfully tells $N$ to player $B$. Player $B$ now tries to obtain information about $x$ by asking player A questions as follows. Each question consists of $B$ specifying an arbitrary set $S$ of positive integers (possibly one specified in a previous question), and asking $A$ whether $x$ belongs to $S$. Player $B$ may ask as many such questions as he wishes. After each question, player $A$ must immediately answer it with yes or no, but is allowed to lie as many times as she wishes; the only restriction is that, among any $k+1$ consecutive answers, at least one answer must be truthful.
After $B$ has asked as many questions as he wants, he must specify a set $X$ of at most $n$ positive integers. If $x$ belongs to $X$, then $B$ wins; otherwise, he loses. Prove that:
1. If $n \geq 2^k$, then $B$ can guarantee a win.
2. For all sufficiently large $k$, there exists an integer $n \geq 1.99^k$ such that $B$ cannot guarantee a win.
Check out (and join in on) the discussion here.
## One thought on “Minipolymath4 Project Now Open!”
1. Thought-provoking comments – I loved the information ! Does someone know where my assistant could acquire a template a form example to fill in ?
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2016-02-14 14:33:47
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http://www.purplemath.com/learning/viewtopic.php?f=8&t=7770&p=14721
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## Doing a comprehensive review, need fraction help...
Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
I_Feel_Dumb
Posts: 1
Joined: Tue May 10, 2016 11:12 pm
Contact:
### Doing a comprehensive review, need fraction help...
Ok, so I'm doing a comprehensive math review of algebra, Cal I, and Cal II before starting Cal III in the fall semester. I got a B in Cal II so I'm doing "ok" (should have had an A, but these pesky algebra snags...) but I have run into a bit of a problem that I can't quite figure out.
The problem is:
2/a2 - 3/ab + 4/b2 (answer: 2b2 - 3ab + 4a2 / a2b2 )
With other fractions that have non-matching denominators I have been working the method ad + or - bc / bd has worked every time, no troubles...except now. This method fails on this problem and I want to understand why. This is the kind of thing that cost me points in Cal II and I don't want that happening in Cal III.
First thing I did was break the problem into chunks, the first chunk consisting of:
2/a2 - 3/ab
Now I tried using ad - bc / bd for this, and it got me:
2(ab) - 3(a2 ) / a2(ab)
Simplify: 2ab - 3a2 / a3b
This isn't correct why? When I use a web based algebra calculator it says this should net me 2b - 3a / a2b - how is it that the method that works with every other complex fraction I have been doing doesn't work for this problem?
Of course, if I keep going with what I have and do ad + bc / bd I get something that ends up being WAY OFF. I know I could find the common denominator, but I always thought that the method ad + or - bc / bd was a more efficient way to do things...
This is driving me insane, please help me regain my sanity so I can make the appropriate notes and move on to another review section...
Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm
### Re: Doing a comprehensive review, need fraction help...
The problem is:
2/a2 - 3/ab + 4/b2
This is just an expression. Until they give you instructions, there is no problem do resolve.
(answer: 2b2 - 3ab + 4a2 / a2b2 )
My guess is that they forgot to tell you to "convert to a common denominator and combine".
With other fractions that have non-matching denominators I have been working the method ad + or - bc / bd has worked every time
What is this "method"? Why not just do common denominators like for numerical fractions? They show how here: http://www.purplemath.com/modules/rtnladd.htm
You have this:
. . .$\dfrac{2}{a^2}\, -\, \dfrac{3}{ab}\, +\, \dfrac{4}{b^2}$
The factors in the denominators are aa, ab, and bb. You can find the LCM (aabb) using the charting method they show here: http://www.purplemath.com/modules/lcm_gcf.htm
Then multiply each fraction by what it needs so it ends up with aabb in the denominators:
. . .$\left(\dfrac{2}{a^2}\right)\, \left(\dfrac{b^2}{b^2}\right)$
. . .$\left(\dfrac{3}{ab}\right)\, \left(\dfrac{ab}{ab}\right)$
. . .$\left(\dfrac{4}{b^2}\right)\, \left(\dfrac{a^2}{a^2}\right)$
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2018-03-17 16:43:46
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https://www.semanticscholar.org/paper/A-support-theorem-for-Hilbert-schemes-of-planar-Migliorini-Shende/33af24121302b26ac9032b151d8ec37845f6f4a4
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# A support theorem for Hilbert schemes of planar curves
@article{Migliorini2013AST,
title={A support theorem for Hilbert schemes of planar curves},
author={L. Migliorini and V. Shende},
journal={Journal of the European Mathematical Society},
year={2013},
volume={15},
pages={2353-2367}
}
• Published 2013
• Mathematics
• Journal of the European Mathematical Society
Consider a family of integral complex locally planar curves whose relative Hilbert scheme of points is smooth. The decomposition theorem of Beilinson, Bernstein, and Deligne asserts that the pushforward of the constant sheaf on the relative Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension. It follows that the perverse filtration on the cohomology of the compactified Jacobian of an integral plane curve… Expand
Homology of Hilbert schemes of points on a locally planar curve
Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C^[n]. We define 4 creation/annihilation operators acting on the rational homology groups of theseExpand
A support theorem for nested Hilbert schemes of planar curves
Consider a family of integral complex locally planar curves. We show that under some assumptions on the base, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem ofExpand
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
• Mathematics
• 2018
Author(s): Oblomkov, A; Rasmussen, J; Shende, V; Gorsky, E | Abstract: © 2018, Mathematical Sciences Publishers. All rights reserved. We conjecture an expression for the dimensions of theExpand
Gr\"obner cells of punctual Hilbert schemes in dimension two
We decompose the punctual Hilbert scheme of the regular two-dimensional local ring in terms of the Grobner cells and provide an explicit parametrization of these cells. These schemes are the mostExpand
Modules over plane curve singularities in any ranks and DAHA
• Mathematics
• 2019
Abstract We generalize the construction of geometric superpolynomials for unibranch plane curve singularities from our prior paper from rank one to any ranks; explicit formulas are obtained for torusExpand
Deletion-contraction triangles for Hausel-Proudfoot varieties
• Mathematics
• 2019
To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively like moduli of local systems on a Riemann surface, and moduli of Higgs bundles. For instance, BExpand
Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples
In the present thesis we study the geometry of the moduli spaces of Bradlow-Higgs triples on a smooth projective curve C. There is a family of stability conditions for triples that depends on aExpand
DAHA and plane curve singularities
• Mathematics
• 2016
We suggest a relatively simple and totally geometric conjectural description of uncolored DAHA superpolynomials of arbitrary algebraic knots (conjecturally coinciding with the reduced stableExpand
Hecke correspondences for Hilbert schemes of reducible locally planar curves
Let C be a complex, reduced, locally planar curve. We extend the results of Rennemo [R14] to reducible curves by constructing an algebra A acting on V = ⊕ n>0H BM ∗ (C [n],Q), where C [n] is theExpand
Higher discriminants and the topology of algebraic maps
• Mathematics
• 2013
We show that the way in which Betti cohomology varies in a proper family of complex algebraic varieties is controlled by certain "higher discriminants" in the base. These discriminants are defined inExpand
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Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C^[n]. We define 4 creation/annihilation operators acting on the rational homology groups of theseExpand
Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
• V. Shende
• Mathematics
• Compositio Mathematica
• 2012
Abstract Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central pointExpand
Macdonald formula for curves with planar singularities
• Mathematics
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We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes toExpand
The chi-y genera of relative Hilbert schemes for linear systems on Abelian and K3 surfaces
• Mathematics
• 2013
For an ample line bundle on an Abelian or K3 surface, minimal with respect to the polarization, the relative Hilbert scheme of points on the complete linear system is known to be smooth. We give anExpand
Stable pairs and the HOMFLY polynomial
Given a planar curve singularity, we prove a conjecture of Oblomkov–Shende, relating the geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated algebraic link. MoreExpand
Ideals associated to deformations of singular plane curves
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We consider in this paper the geometry of certain loci in deformation spaces of plane curve singularities. These loci are the equisingular locus ES which parametrizes equisingular or topologicallyExpand
A note on Hilbert schemes of nodal curves
Abstract We study the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended to flagExpand
Higher discriminants and the topology of algebraic maps
• Mathematics
• 2013
We show that the way in which Betti cohomology varies in a proper family of complex algebraic varieties is controlled by certain "higher discriminants" in the base. These discriminants are defined inExpand
Euler number of the compactified Jacobian and multiplicity of rational curves
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We show that the Euler number of the compactified Jacobian of a rational curve $C$ with locally planar singularities is equal to the multiplicity of the $\delta$-constant stratum in the base of aExpand
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## Wednesday, October 31, 2018
### Large Hadron Collider Run 2 Ends Soon
The Large Hadron Collider (LHC) will shut down in December and won't start up again until 2021. In the meantime there will be basically no new high energy physics experimental data and scientists will have to pour over the data that has been already collected instead.
Since 2015 the LHC experiments have been taking data from proton-proton collisions at 13 TeV. This is “Run 2” of the LHC, “Run 1” was at the lower energy of 8 TeV. The proton-proton Run 2 ended this morning, with the LHC shifting to other tasks, first machine development, later heavy ions. It will shut down completely in December for the start of “Long Shutdown 2 (LS2)”, which will last for over two years, into early 2021. During LS2 there will be maintenance performed and improvements made, including bringing the collision energy of the machine up to the design energy of 14 TeV.
ATLAS is reporting 158 inverse fb of collisions delivered by the machine during Run 2, of which 149 inverse fb were recorded, the CMS numbers should be similar. Most data analysis reported to date by ATLAS and CMS has only used the 2015 and 2016 data (about 36 inverse fb) although a few results have included data through 2017 (about 80 inverse fb). My impression is that for many searches they have been waiting for the full run 2 dataset to be available. Perhaps results of searches with the full dataset might start becoming available by the time of summer 2019 conferences.
The LHC run 3 is planned for 2021-2023, producing perhaps 300 inverse fb of data, results perhaps available in 2024. It will thus be quite a long time after run 2 results start appearing before better ones due simply to more data become available.
From Not Even Wrong.
## Tuesday, October 30, 2018
### An Oldie But Goodie
The top quark was experimentally discovered in 1995 although experimenters were hot on its path a couple of years earlier, and the Higgs boson was discovered and its mass was first measured in 2012. The masses predicted in this 1993 paper are close to the values ultimately measured.
A model for composite electroweak bosons is re-examined to establish approximate ranges for the initial predictions of the top and Higgs masses. Higher order corrections to this 4-fermion theory at a high mass scale where the theory is matched to the Standard Model have little effect, as do wide variations in this scale. However, including all one loop evolution and defining the masses self-consistently, at their respective poles, moves the top mass upward by some 10 GeV to near 175 GeV and the Higgs mass down by a similar amount to near 125 GeV.
David E. Kahana, Sidney H. Kahana, "Top and Higgs Masses in Dynamical Symmetry Breaking" (December 21, 1993).
Of course, this doesn't mean that the approach taken to make these predictions in 1993 was necessary an accurate explanation of why those particles have the masses that they do. Hundreds of predictions with significant margins of error were made and somebody had to be right as a matter of random chance, since a general ballpark in which the mass values had to fall was already known.
Arguably, this is little more than numerology. But, it is particularly interesting numerology as the ultimate prediction was correct long in advance.
While an accurate prediction doesn't insure that the reasoning used to produce that prediction is valid, if the reasoning used by an investigator produces an inaccurate prediction then we known that there was something wrong with that investigator's method or source data that informed the prediction.
### India's Caste Endogamy Was Very Extreme
The interracial intermarriage rate in Jim Crow America was about 1%. At that rate, if introgression of non-white individuals into whites continued for 50 years, the average person with white ancestry would be 40% non-white. (I suspect this exaggerated figure is due to improper use of a 1% introgression rate per year rather than per generation, but even a few generations of modest introgression does have a notable effect over a very long time period)
.
In India, caste cemented itself, not just at the Varna level, but at the Jati level about 1500 years ago. This implied an endogamy rate on the order of 99.8% (with 10% introgression over that time period) to 99.9% (with 5% introgression over that time period) to 99.98% (with 1% introgression over that time period).
I think the source is Razib or someone he quoted, but I could be mistaken. I accidentally failed to hit the publish button on this post back on April 17, 2018.
## Sunday, October 28, 2018
### A Pre-Clovis Spear Point In Texas
A pre-Clovis spear point found in Texas from about 15,000 years ago largely reaffirms the existing paradigm for how the founding population of the Americas settled these regions after the Last Glacial Maximum.
In particular, it clarifies that there were populations in the interior of North America before there was an ice free land corridor from Beringia to North America in the north. Somebody either walked across a glacier for many miles, or took a boat down the Pacific coast and them migrated inland before the ice free land corridor opened.
In other New World pre-history news, a new paper (whose results were previously blogged here) notes that a one study outlier genetic finding in the Amazon has no trace in ancient DNA:
Intriguingly, a signal of Australasian ancestry that has been observed in some Amazonian groups is not evident in any of the ancient Siberian or Beringian samples sequenced here, or in previous studies.
Pontus Skoglund notes that: "the signal is found in Tianyuan at 40kya, stronger than Australasians in its connection to Amazonians in fact. No less mysterious though!" He cites this source. This Tianyuan connection is also stronger than the connection to the Andamanese people.
My own theory is that the genetic trace seen is the product of one or two individuals or a nuclear family who were newcomers to the Beringian community that were in the first wave of advance to settle South America.
## Friday, October 26, 2018
### Quote of the Day
[Professor Steven] Weinberg raises an eyebrow and points to his office.
His office, it turns out, is half the size of mine, an observation that vaporizes what little ambition I ever had to win the Nobel Prize.
- Sabine Hossenfelder, "Lost in Math" (2018) at page 96.
For what it is worth, "Lost in Math" is a treasure trove of dry wit for those with some familiarity with modern physics, and this is merely one of many gems that her book contains.
An abstract from today that sums up the attitudes in the field about high energy physics that she is critiquing is this one:
The standard model of particle physics is an extremely successful theory of fundamental interactions, but it has many known limitations. It is therefore widely believed to be an effective field theory that describes interactions near the TeV scale. A plethora of strategies exist to extend the standard model, many of which contain predictions of new particles or dynamics that could manifest in proton-proton collisions at the Large Hadron Collider (LHC). As of now, none have been observed, and much of the available phase space for natural solutions to outstanding problems is excluded. If new physics exists, it is therefore either heavy (i.e. slightly above the reach of current searches) or hidden (i.e. currently indistinguishable from standard model backgrounds). We summarize the existing searches, and discuss future directions at the LHC.
Salvatore Rappoccio, "The experimental status of direct searches for exotic physics beyond the standard model at the Large Hadron Collider" (October 24, 2018).
Thirty three pages of null results follow. The review begins with the following introduction:
Particle physics is at a crossroads. The standard model (SM) explains a wide range of phenomena spanning interactions over many orders of magnitude, yet no demonstrated explanation exists for a variety of fundamental questions. Most recently, the discovery of the Higgs boson [1, 2, 3, 4, 5, 6, 7, 8, 9] at the ATLAS [10] and CMS [11] detectors has elucidated the mechanism of electroweak symmetry breaking, but there is no explanation for why the scale of its mass is so much different from naive quantum-mechanical expectations (the “hierarchy problem”) [12, 13, 14, 15, 16, 17, 18, 19, 20]. Dark matter (DM) remains an enigma, despite extensive astronomical confirmation of its existence [21, 22, 23]. Neutrino masses are observed to be nonzero [24, 25, 26, 27], and elements of the Pontecorvo-Maki-Nakagawa-Sakata matrix [28, 29] have been measured, but these masses are not easily accounted for in the SM [30]. Unification of the strong and electroweak forces is expected, but not yet observed nor understood [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]; such models often predict the existence of yet-to-be-observed leptoquarks (LQs) or proton decay [45]. Furthermore, there are unexpected observations that are not explained in the SM, such as the baryon asymmetry [46], anomalies in the decays of bottom-quark hadrons [47], a discrepancy in the anomalous magnetic moment of the muon (g-2) [48], and the strong CP problem [49, 50, 51]. Even further, there are open questions about long-standing observations, such as whether or not there is an extended Higgs sector [52], why there are multiple generations of fermions with a large mass hierarchy [32, 53, 54, 55], and why no magnetic monopoles are observed to exist [56]. For these reasons, the SM is considered to be an effective field theory, and that physics beyond the SM (BSM) should exist.
In this Review, we will (non-exhaustively) discuss a subset of these questions that have been investigated recently at the LHC with 13 TeV proton-proton collisions by the ATLAS, CMS, and LHCb [57] experiments. From a collider standpoint, we will discuss the solution to the hierarchy problem, dark matter, the origins of neutrino masses, unification, and compositeness. We will also discuss the possibilities for improvements of these searches at the High-Luminosity LHC (HL-LHC) or other future colliders. One very popular group of theories to explain several of these phenomena involve supersymmetric (SUSY) extensions to the SM [12, 13]. With a few exceptions, this Review will focus on answers to the above questions that do not involve SUSY, although it remains a theoretically attractive solution. This Review will also primarily not focus on solutions that involve an extended Higgs sector, nor open anomalies in hadron spectroscopy.
Many models of BSM physics that can be tested at the LHC involve spectacular signatures that distinguish them from SM backgrounds. It is therefore worthwhile to discuss the searches for new physics with their unique signatures in mind. As such, we will first broadly discuss the signatures used for LHC BSM searches, and then discuss the implications on various scenarios.
I have highlighted the problems identified and underlined those that are legitimate problems as opposed to mere quibbled with what the laws of Nature actually happen to be. The decision to omit SUSY limitations and extended Higgs sectors is a telling sign of the decreasing popularity of these theories.
The decision to ignore "open anomalies in hadron spectroscopy" is a reflection of the extent to which QCD is so inexact, compared to other aspects of high energy physics, that anomalies often don't mean very much.
## Tuesday, October 23, 2018
### Siberia Has Experienced Repeated Population Replacement
The first wave of archaic hominin migration out of Africa which expanded as far into Southern Asia as Indonesia and China, Homo erectus, probably never reached Northern Asia in any significant numbers.
But, before modern humans arrived in Northern Asia, Denisovans and Neanderthals (archaic hominins) reached at least as far as the Altai Mountains. We don't know with much precision when they arrived there or by precisely what route, but both were present in the Altai region around 90,000 years ago when a child with one Denisovan parent and one Neanderthal parent was born. Sometime after 40,000 years ago, they became extinct (or at least almost extinct) in the region. We don't know if they ever overlapped with modern humans in that region, but the timing of the latest evidence of their presence in Northern Asia and the earliest evidence of a modern human presence in Northern Asia is suspiciously close in time. Ancient Altai Neanderthal DNA shows evidence as admixture with modern humans that was estimated to have taken place ca. 100,000 years ago, but these admixture events probably took place with their ancestors in Southwest Asia, rather than Northern Asia.
Ancient DNA and archaeology establishes that the original modern humans in Siberia (who arrived there about 38,000 years ago), the "Ancient North Siberians" (ANS) were wiped out during the Last Glacial Maximum (about 20,000 years ago) except for refugia populations in Beringia (and possibly also the Altai Mountains region) who contributed to Ancient Paleosiberian gene pools.
Ancient DNA also confirms the hypothesis that Siberia was the source for both the "Ancient Paleosiberian" (AP) population that emerged after the Last Glacial Maximum which gave rise to the founding population of the Americas (which has only a few relict tribes in Siberia itself who are their descendants), and for the East Asian shifted "Neosiberian" populations that largely replaced the Ancient Paleosiberians around 11,000 years ago who were a genetic source for Na-Dene and Inuit Native Americans ancestors' migration to the Americas and most modern indigenous Siberians.
In the last 7000 years or so, there have been more waves of migration across Northern Asia, although some of these waves did not reach all of the way to far Northeastern Siberia.
First, Uralic populations migrated West and East from central Siberia (starting ca. 5000 BCE).
Then, Tocharian Indo-Europeans migrated from the Pontic-Caspian steppe as far east as the Tarim Basin which they reached ca. 2000 BCE, and a trickle of Pontic-Caspian steppe people made it as far as Bronze Age China.
Ethnically and linguistically Turkish populations migrated west starting in the first few centuries BCE and CE, and extending their reach from a source in Northeast Asia to a maximum extend in Turkey (with a substantial Turkish immigrant population arriving Germany after World War II). The Oghuz Turks started to arrive in Anatolia around the 9th century CE and this demographic shift (in Anatolia, a significant introgression into the pre-existing population but not a population replacement) was consolidated by the 11th century Seljuk Empire which was both Turkic and Persian that controlled almost all of Anatolia.
Islamic culture accompanied by significant (but not replacement level) ethnically Iranian/Middle Eastern migration followed that in an eastward direction, overlapping with the westward Turkish migration, and ultimately leaving a lasting impact as far east as what is currently Western China, during the Tang Dynasty.
By the 13th century CE there was a Mongolian wave of western migration (which also expanded to the East from Mongolia). The eastward Mongolian expansion had a more lasting impact than the western expansion.
A few centuries later, the Russians, initially with a Scandinavian elite and Slavic masses, migrated east again, leaving us with the current status quo, more or less. This expansion wiped out all but a few thousand of the remaining Ancient Paleosiberian populations in Siberia. The Russians made it all of the way to Alaska, uniting all of Siberia and former Beringia and Alaska politically as well as biogeographically, until 1867 when the Alaska Purchase transferred Alaska to the United States.
The paper recounting the new ancient DNA discoveries has the following abstract and citation:
Far northeastern Siberia has been occupied by humans for more than 40 thousand years. Yet, owing to a scarcity of early archaeological sites and human remains, its population history and relationship to ancient and modern populations across Eurasia and the Americas are poorly understood.
Here, we report 34 ancient genome sequences, including two from fragmented milk teeth found at the ~31.6 thousand-year-old (kya) Yana RHS site, the earliest and northernmost Pleistocene human remains found.
These genomes reveal complex patterns of past population admixture and replacement events throughout northeastern Siberia, with evidence for at least three large-scale human migrations into the region.
The first inhabitants, a previously unknown population of "Ancient North Siberians" (ANS), represented by Yana RHS, diverged ~38 kya from Western Eurasians, soon after the latter split from East Asians.
Between 20 and 11 kya, the ANS population was largely replaced by peoples with ancestry from East Asia, giving rise to ancestral Native Americans and "Ancient Paleosiberians" (AP), represented by a 9.8 kya skeleton from Kolyma River. AP are closely related to the Siberian ancestors of Native Americans, and ancestral to contemporary communities such as Koryaks and Itelmen. Paleoclimatic modelling shows evidence for a refuge during the last glacial maximum (LGM) in southeastern Beringia, suggesting Beringia as a possible location for the admixture forming both ancestral Native Americans and AP.
Between 11 and 4 kya, AP were in turn largely replaced by another group of peoples with ancestry from East Asia, the "Neosiberians" from which many contemporary Siberians derive. We detect additional gene flow events in both directions across the Bering Strait during this time, influencing the genetic composition of Inuit, as well as Na Dene-speaking Northern Native Americans, whose Siberian-related ancestry components is closely related to AP.
Our analyses reveal that the population history of northeastern Siberia was highly dynamic, starting in the Late Pleistocene and continuing well into the Late Holocene. The pattern observed in northeastern Siberia, with earlier, once widespread populations being replaced by distinct peoples, seems to have taken place across northern Eurasia, as far west as Scandinavia.
Sikora et al., The population history of northeastern Siberia since the Pleistocene, bioRxiv (October 22, 2018), doi: https://doi.org/10.1101/448829
## Monday, October 22, 2018
My paternal line ancestor came from Prussia in 1847 to dodge the draft (Germany did not yet exist). Some of my ancestors are also connected to one of the classical music composers called Bach's family. Most of the ancestors who stayed ended up just barely on the East German side of the divided Germany after World War II.
Razib notes some good books about Prussia, which a quote here for future reference:
Tim Blanning’s Frederick the Great: King of Prussia is an excellent book. So is The Pursuit of Glory: The Five Revolutions that Made Modern Europe: 1648-1815. Finally, Iron Kingdom: The Rise and Downfall of Prussia, 1600–1947. One of the most interesting things about Frederick the Great: King of Prussia is how Blanning recounts the importance of personally playing and repeatedly listening to music in the life of the German monarch. He was apparently a very competent flutist.
In the greater scheme of things, Prussia is particularly notable for having an absurdly micromanaging legal code (with dictates, for example, regarding when one should do which chores in a household like laundry) and for encouraging a largely industrial employer based welfare state, not so different from the Japanese economy of the 1980s. Some interesting historical economics also flows from the previously highly balkanized state of what became Germany, comparing economic development with litmus tests like opera house construction and public clocktowers.
Genetically, my father's side makes him look like a broadly Northern European mutt, in significant part because the significant clusters and ancestral populations of Northern Europe don't align very well with the current political boundaries there, and partially because Northern Europe has had considerable population exchange in the modern era in this region.
### Fuzzy Dark Matter Model Tightly Constrained By Astronomy Measurements; MOG Allegedly Ruled out
Fuzzy dark matter is a dark matter particle theory that involves very light bosons as dark matter particles (in contrast, for example, to warm dark matter which uses keV mass scale sterile fermions). A new preprint purports to confine the allowed mass range of fuzzy dark matter particles to within a factor of ten using astronomy measurement from the Milky Way and one other galaxy. This same method could conceivably rule out the entire parameter space of fuzzy dark matter theories with the right observation.
The fuzzy dark matter (FDM) model treats DM as a bosonic field with astrophysically large de Broglie wavelength. A striking feature of this model is O(1fluctuations in the dark matter density on time scales which are shorter than the gravitational timescale. Including for the first time the effect of core oscillations, we demonstrate how such fluctuations lead to heating of star clusters, and thus an increase in their size over time. From the survival of the old star cluster in Eridanus II we infer ma0.61×1019 eV within modelling uncertainty if FDM is to compose all of the DM, and derive constraints on the FDM fraction at lower masses. The subhalo mass function in the Milky Way implies ma0.8×1021 eV to successfully form Eridanus II. The window between 1021 eVma1020 eV is affected by narrow band resonances, and the limited applicability of the diffusion approximation. Some of this window may be consistent with observations of Eridanus II and more detailed investigations are required.
David J. E. Marsh, Jens C. Niemeyer, "Strong Constraints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II" (October 19, 2018).
By comparison a graviton from a falling apple near Earth should have energy of 10^-30 ergs. One erg equals 6.242 * 10^11 eV, so a graviton from a falling apple (which is also a boson) ought to have an energy on the other of 6*10^-19 eV which is quite close in order of magnitude to the estimated energy of fuzzy dark matter particles in this study.
For the energy range, a graviton based quantum gravity theory (such as Deur's analysis) and a fuzzy dark matter theory, ought to be very similar.
Meanwhile, another paper purports to rule out John Moffat's MOG theory, which uses a scalar, vector, tensor function, based upon detailed Milky Way observations. Until now, this has been one of the most robust modified gravity theories to date, explaining phenomena where Milgrom's MOND theory fails, such as cluster physics and cosmology data and passing other tests that competing modified gravity theories have failed.
This could be correct, but previous efforts to falsify modified gravity theories have resulted from a misunderstanding of the application of those theories, so it may be premature to rule it out based upon this study alone. A lack of a comparison of the errors observed to the measurement errors and any theoretical errors in the abstract, in particular, is a cause of skepticism of this result.
We perform a test of John Moffat's Modified Gravity theory (MOG) within the Milky Way, adopting the well known "Rotation Curve" method. We use the dynamics of observed tracers within the disk to determine the gravitational potential as a function of galactocentric distance, and compare that with the potential that is expected to be generated by the visible component only (stars and gas) under different "flavors" of the MOG theory, making use of a state-of-the-art setup for both the observed tracers and baryonic morphology. Our analysis shows that in both the original and the modified version (considering a self-consistent evaluation of the Milky Way mass), the theory fails to reproduce the observed rotation curve. We conclude that in none of its present formulation, the MOG theory is able to explain the observed Rotation Curve of the Milky Way.
Carolina Negrelli, Maria Benito, Susana Landau, Fabio Iocco, Lucila Kraiselburd, "Testing MOG theory in the Milky Way" (October 16, 2018).
As the introduction to the pre-print explains:
A dark component of matter has become one of the pillars of current ΛCDM model: it is invoked to explain the mismatch between the observed dynamical mass, and that inferred by observations of the visible component, of astrophysical objects over a large range of mass and spatial scales, from Galaxy Clusters [1–4] to Spiral [5–7] and Dwarf Galaxies [8], including our own, [9], and provides a consistent explanation to the power spectrum of the Cosmic Microwave Background [10], and to the formation of astrophysical structures [11]. Yet, the very nature of this dark matter is currently unknown, and none of the proposed candidates (from stable particles in extensions of the Standard Model, to primordial Black Holes [12, 13]) has been unambiguously detected yet.
An alternative proposal to explain the mismatch observed in the data relies on a modification of the theory of gravity. Several proposals, such as MOND, TeVeS and MOG [14–16], have been able to give an explanation to phenomena around data coming from numerous and diverse sources: motion of globular and galaxy clusters [17–19] and rotation curves of spiral and dwarf galaxies [20, 21].
While some analysis indicate that TeVeS and MOG have difficulties explaining the Bullet cluster data [22] or to reconcile gas profile and strong–lensing measurements in well known cluster systems [23], others claim that MOG can fit both Bullet and the Train Wreck merging clusters [24, 25]. It has been pointed out that the detection of a neutron star merger by the LIGO experiment rules out MOND-like theories [26]. Recent analysis state the former being correct for bi-metric theories such as MOND and TeVeS, but not for MOG [27]. Some of the above controversies are yet to be resolved, so it is currently unclear if MOG phenomenology can offer a solution at all scales.
In this work, we adopt an agnostic approach, and only focus on the prediction of MOG theory on the scale of Spiral Galaxies, with a specific one: our own host. In order to test the predictions of MOG theory within the Milky Way, we use state–of–the–art compilations of kinematical tracers and observationally inferred morphologies, adopted in recent studies of Dark Matter distribution [9, 28, 29], and already used to test MOND phenomenology [30].
They money figures from the MOG paper are as follows:
The authors claim a 5 sigma discrepancy, but eyeballing the data, the discrepancies between the SG flavor of MOG and the Milky Way data appear to be statistically significant only in the area where there is a transition from the Newtonian regime to the modified gravity regime at about 15 to 25 kiloparsecs from the central region, although the fit is less strong in closer core than at the edges of the galaxy (something that is also generically true of particle dark matter theories).
A previous paper by some of the same authors about MOND in 2015 (which was ultimately published) was the following, which found that MOND with a simple interpolation function did fit the Milky Way data.
Modified Newtonian dynamics (MOND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here,we set constraints on MOND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic models studied, while the so-called "simple" interpolating function can for a subset of models. Upcoming astronomical observations will refine our knowledge on the morphology of baryons and will ultimately confirm or rule out the validity of MOND in the Milky Way. We also present constraints on MOND-like theories without making any assumptions on the interpolating function.
Fabio Iocco, Miguel Pato, Gianfranco Bertone, "Testing modified Newtonian dynamics in the Milky Way" (October 26,2015)
## Tuesday, October 16, 2018
### New Astronomy Constraints On Extra Dimensions And Graviton Lifetimes
NEW
The observation of GW170817 in both gravitational and electromagnetic waves provides a number of unique tests of general relativity. One question we can answer with this event is: Do large-wavelength gravitational waves and short-frequency photons experience the same number of spacetime dimensions?
In models that include additional non-compact spacetime dimensions, as the gravitational waves propagate, they "leak" into the extra dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and a commensurate systematic error in the inferred distance to the gravitational wave source. Electromagnetic waves would remain unaffected.
We compare the inferred distance to GW170817 from the observation of gravitational waves, dGWL, with the inferred distance to the electromagnetic counterpart NGC 4993, dEML. We constrain dGWL=(dEML/Mpc)γ with γ=1.01+0.04−0.05 (for the SHoES value of H0) or γ=0.99+0.03−0.05 (for the Planck value of H0), where all values are MAP and minimal 68% credible intervals.
These constraints imply that gravitational waves propagate in D=3+1 spacetime dimensions, as expected in general relativity. In particular, we find that D=4.02+0.07−0.10 (SHoES) and D=3.98+0.07−0.09 (Planck). Furthermore, we place limits on the screening scale for theories with D>4 spacetime dimensions, finding that the screening scale must be greater than ∼20 Mpc. We also place a lower limit on the lifetime of the graviton of t>4.50×10^8 yr.
Pardo et al. 2018, "Limits on the number of spacetime dimensions from GW170817"
In many beyond the Standard Model theories, all particles and forces except gravity are confined to the 3+1 dimensions of General Relativity, but gravity can escape those dimensions to higher dimensions, which partially explains its relative weakness as a force. This result disfavors theories of that class.
### Ancient Egyptian Astronomers
An ancient Egyptian Calendar of Lucky and Unlucky Days, the Cairo Calendar (CC), assigns luck with the period of 2.850 days. Previous astronomical, astrophysical and statistical analyses of CC support the idea that this was the period of the eclipsing binary Algol three millennia ago. However, next to nothing is known about who recorded Algol's period into CC and especially how. Here, we show that the ancient Egyptian scribes had the possible means and the motives for such astronomical observations. Their principles of describing celestial phenomena as activity of gods reveal why Algol received the title of Horus.
## Monday, October 15, 2018
### Quote of the Day
One of the most frequent critical remarks I have gotten on my book is that I seem confident. I was supposed, it seems, to begin each paragraph with “I'm sorry, but.”
But I am not sorry. I mean what I say. Yes, in the foundations of physics we are financing some 15,000 or so theorists who keep producing useless scientific articles because they believe the laws of nature must be beautiful. That's exactly what I am saying.
### Mistaken Statistics
From xkcd. Mouseover: "Don't forget to add another term for "probability that Modified Bayes' Theorem is correct.""
### Hunter-Gatherer Labels Encompass More Than One Kind Of Society
[M]any people who use “hunter-gatherers” as a category are actually lumping things that are quite different from each other. If you want to use ethnographic studies of today’s people to say anything about prehistoric people, you need to understand that any living group may be like ancient people in some ways, and very different from ancient people in other ways. Lumping across the entire category of “hunter-gatherers” doesn’t work if some of those living hunter-gatherers have economies, subsistence patterns, and social organization that is unlike anything that archaeology tells us about prehistoric groups.
Here’s a teaser from a box that discusses the work of Steven Pinker:
Despite the apparent magnitude of the Ju/’hoan/!Kung homicide rate, these still represent only 1.0–1.6% of overall deaths, compared to the 8–58% figure referenced in Pinker’s TED Talk.
Via John Hawks.
While the term "hunter-gatherer" can be useful in anthropology to characterize cultures and populations, it is stretched too far when used not just to apply to terrestrial hunter-gatherers, but also to maritime food production from fishing and coastal seafood collection as staples (e.g. the Native Americans of the Pacific Northwest, of the Baltic Sea area, and the Jomon of Japan prior to the arrival of farming and herding as leading means of food production).
This distinction is important, because, in pre-history, maritime food producers had relatively sedentary lifestyles, more permanent buildings and structures, and more staying power vis-a-vis farmers. The transition from terrestrial hunting and gathering to nomadic pastoralism also appears to be possible with less demographic replacement, than the transition from terrestrial hunting and gathering to farming. But, this doesn't hold true to the same extent for a transition from maritime food production to farming.
There is also a tendency to mischaracterize nomadic pastoralists as hunter-gatherers, and to fail to distinguish between terrestrial hunting and gathering society focused on big game hunting (e.g. the Neanderthals and the Clovis culture) and terrestrial hunting and gathering societies with more of a focus on small game and gathering (e.g. Cro-Magnons in Europe).
### Paper Doubts Ancient African Megalakes Other Than Lake Chad
Wetlands and small lakes with one big lake still sounds a lot more like modern Wisconsin than it does like the modern Sahara.
The Sahara was wetter and greener during multiple interglacial periods of the Quaternary, when some have suggested it featured very large (mega) lakes, ranging in surface area from 30,000 to 350,000 km2. In this paper, we review the physical and biological evidence for these large lakes, especially during the African Humid Period (AHP) 11–5 ka. Megalake systems from around the world provide a checklist of diagnostic features, such as multiple well-defined shoreline benches, wave-rounded beach gravels where coarse material is present, landscape smoothing by lacustrine sediment, large-scale deltaic deposits, and in places, tufas encrusting shorelines. Our survey reveals no clear evidence of these features in the Sahara, except in the Chad basin. Hydrologic modeling of the proposed megalakes requires mean annual rainfall ≥1.2 m/yr and a northward displacement of tropical rainfall belts by ≥1000 km. Such a profound displacement is not supported by other paleo-climate proxies and comprehensive climate models, challenging the existence of megalakes in the Sahara. Rather than megalakes, isolated wetlands and small lakes are more consistent with the Sahelo-Sudanian paleoenvironment that prevailed in the Sahara during the AHP. A pale-green and discontinuously wet Sahara is the likelier context for human migrations out of Africa during the late Quaternary.
J. Quade, et al., "Megalakes in the Sahara? A Review" 90(2) Quaternary Research 253 (September 2018) (published online June 14, 2018) https://doi.org/10.1017/qua.2018.46
## Thursday, October 11, 2018
### More Problems For Sting Theory
In string theory, a paradigm shift could be imminent. In June, a team of string theorists published a conjecture which sounded revolutionary: String theory is said to be fundamentally incompatible with our current understanding of 'dark energy'. A new study has now found out that this conjecture seems to be incompatible with the existence of the Higgs particle.
From Science Daily discussing the following paper:
According to a conjecture recently put forward in [1], the scalar potential V of any consistent theory of quantum gravity satisfies a bound |∇V|/V≥O(1). This forbids de Sitter solutions and supports quintessence models of cosmic acceleration. Here, we point out that in the simplest models incorporating the standard model in addition to quintessence, with the two sectors decoupled as suggested by observations, the proposed bound is violated by 50 orders of magnitude. However, a very specific coupling between quintessence and just the Higgs sector may still be allowed and consistent with the conjecture.
Frederik Denef, Arthur Hebecker, Timm Wrase. "de Sitter swampland conjecture and the Higgs potential." 98 (8) Physical Review D (August 7, 2018). DOI: 10.1103/PhysRevD.98.086004
These papers don't by themselves, entirely rule out string theory, but they do take, what was just a year ago a "landscape" of string theories too vast to sort though, and rule out almost all of those possibilities.
### Some Puerto Ricans Have Berber Ancestry Via The Canary Islands
Maju, after a long silence on genetics issues at his blog, has conducted some very credible independent research that suggests that many Puerto Ricans have some (post-Columbian) North African Berber ancestry through admixture of that ancestry in the people of the Canary Islands who then migrated to the Caribbean islands about 500 years ago.
## Wednesday, October 10, 2018
### The Citation Gap In Physics Publications
Usually, I write about scientific discoveries rather than the scientific process, but today I'll take a moment to look at what is behind the gender gap in physics paper citations.
Sabine Hossenfelder, at her blog, makes a convincing effort to determine why papers by men are cited such much more often than women in physics, as a rebuttal to another investigator who concluded that women are cited less often because they are inferior physicists.
Essentially, almost all of the gap is attributable to women dropping out of active research positions in the profession entirely very early in their careers. This is common among both men and women, but it is more common among women. Among researchers who have published at least five papers, including one in the last three years, there is basically no gender based citation gap. As she explains:
[T]he vast majority of people who use the arXiv publish only one or two papers and are never heard of again. This is in agreement with the well-known fact that the majority of physicists drop out of academic careers.
The first one or two papers of a junior researcher who never publishes again is much less likely to be cited by someone else than a paper published by someone who continues to actively publish for a long time. And, women are much more likely to leave the academic physics profession than men, in part, because many leave to spend time raising children and never return to research physics positions afterwards.
## Monday, October 8, 2018
### A New Reference Page On Deur's Approach To Quantum Gravity
I have added a new reference page on this blog, linked in the sidebar, that explains Deur's approach to quantum gravity. This provides a single link to this theory which can be updated as necessary, so that people who use it alway get the most up to date developments about this theory.
### More Higgs Boson Based Limitations On BSM Physics
The way that this is described in the abstract is ass backward, but the bottom line is that the Higgs boson mass poses serious problems to a model that has a particle with a large Yukawa coupling to the Higgs boson that is heavier than the top quark.
We revisited the scenario of electroweak baryogenesis in the presence of large Yukawa couplings, in which it was found previously that a strongly first order electroweak phase transition can occur with the Higgs mass at its observed value of 125 GeV.
Given the sensitivity of the running of the Higgs quartic coupling on the Yukawa coupling constants, we find that the addition of order one Yukawa couplings beyond the top quark drastically lowers the scale at which the Higgs potential becomes unstable. Specifically, even with only one additional order one Yukawa coupling, the scalar potential becomes unstable already at the TeV scale, assuming the Standard Model values for the Higgs sector parameters at the electroweak scale.
Furthermore, by assuming the Standard Model values for the Higgs sector parameters at the TeV scale, the quartic coupling constant is driven to be larger than its Standard Model value at the electroweak scale. This in turn predicts a much lighter Higgs mass than the measured value of 125 GeV. In this scenario, the strength of the electroweak phase transition is also significantly weakened.
Arianna Braconi, Mu-Chun Chen, Geoffrey Gaswint, "Revisiting Electroweak Phase Transition with Varying Yukawa Coupling Constants" (October 5, 2018).
The conclusion of the paper connects the dots, noting that:
All together, these limitations render this simplest setup with large varying Yukawa couplings not a viable mechanism for baryogenesis.
This shouldn't be surprising.
## Thursday, October 4, 2018
### The Diet Of Early Anatolian Farmers
A new study looks a protein residues on pots and vessels from one of the earliest farming sites in Anatolia to figure out what these early farmers ate. There are no huge surprises, but this data paints a more vivid sense of the early Neolithic diet.
[R]esearchers analyzed vessel sherds from the West Mound of Çatalhöyük, dating to a narrow timeframe of 5900-5800 BC towards the end of the site's occupation. The vessel sherds analyzed came from open bowls and jars, as shown by reconstructions and had calcified residues on the inside surfaces. In this region today, limescale residue on the inside of cooking pots is very common. The researchers used state-of-the-art protein analyses on samples taken from various parts of the ceramics, including the residue deposits, to determine what the vessels held.
Food proteins left behind in ceramic bowls and jars
The analysis revealed that the vessels contained grains, legumes, meat and dairy products. The dairy products were shown to have come mostly from sheep and goats, and also from the bovine (cattle) family. While bones from these animals are found across the site and earlier lipid analyses have identified milk fats in vessels, this is the first time researchers have been able to identify which animals were actually being used for their milk. In line with the plant remains found, the cereals included barley and wheat, and the legumes included peas and vetches. The non-dairy animal products, which might have included meat and blood, came primarily from the goat and sheep family, and in some cases from bovines and deer. Interestingly, many of the pots contain evidence of multiple food types in a single vessel, suggesting that the residents mixed foods in their cuisine, potentially as porridges or soups, or that some vessels were used sequentially for different food items, or both.
Early cheese-making
One particular vessel however, a jar, only had evidence for dairy products, in the form of proteins found in the whey portion of milk. "This is particularly interesting because it suggests that the residents may have been using dairy production methods that separated fresh milk into curds and whey. It also suggests that they had a special vessel for holding the whey afterwards, meaning that they used the whey for additional purposes after the curd was separated," states Jessica Hendy, lead author, of the Max Planck Institute for the Science of Human History. These results show that dairying has been ongoing in this area since at least the 6th millennium BC, and that people used the milk of multiple difference species of animal, including cow, sheep and goat.
From here citing:
Jessica Hendy, et al., "Ancient proteins from ceramic vessels at Çatalhöyük West reveal the hidden cuisine of early farmers." 9(1) Nature Communications (2018) DOI: 10.1038/s41467-018-06335-6
### A New Top Quark Mass Calculation From ATLAS
There is a new paper determining the top quark mass from ATLAS experiment data from the Large Hadron Collider (LHC), although it uses only fairly early data.
The mass of the top quark is measured to be mtop=172.08±0.39(stat)±0.82(syst) GeV. A combination with previous ATLAS mtopmeasurements gives mtop=172.69±0.25(stat)±0.41(syst) GeV.
From here.
From the introduction:
The mass of the top quark mtop is an important parameter of the Standard Model (SM). Precise measurements of mtop provide crucial information for global fits of electroweak parameters [1–3] which help to assess the internal consistency of the SM and probe its extensions. In addition, the value of mtop affects the stability of the SM Higgs potential, which has cosmological implications [4–6].
Many measurements of mtop in each tt¯ decay channel were performed by the Tevatron and LHC collaborations. The most precise measurements per experiment in the tt¯ → lepton + jets channel are mtop = 172.85 ± 0.71 (stat) ± 0.84 (syst) GeV by CDF [7], mtop = 174.98 ± 0.58 (stat) ± 0.49 (syst) GeV by D0 [8], mtop = 172.33 ± 0.75 (stat) ± 1.03 (syst) GeV by ATLAS [9] and mtop = 172.35 ± 0.16 (stat) ± 0.48 (syst) GeV by CMS [10]. Combinations are performed, by either the individual experiments, or by several Tevatron and LHC experiments [11]. In these combinations, selections of measurements from all tt¯ decay channels are used. The latest combinations per experiment are mtop = 173.16 ± 0.57 (stat) ± 0.74 (syst) GeV by CDF [12], mtop = 174.95 ± 0.40 (stat) ± 0.64 (syst) GeV by D0 [13], mtop = 172.84 ± 0.34 (stat) ± 0.61 (syst) GeV by ATLAS [14] and mtop = 172.44 ± 0.13 (stat) ± 0.47 (syst) GeV by CMS [10].
In this paper, an ATLAS measurement of mtop in the tt¯ → lepton + jets channel is presented. The result is obtained from pp collision data recorded in 2012 at a centre-of-mass energy of √ s = 8 TeV with an integrated luminosity of about 20.2 fb−1 . The analysis exploits the decay tt¯ → W+W−bb¯ → νqq¯ 0bb¯, which occurs when one W boson decays into a charged lepton ( is e or µ including τ → e, µ decays) and a neutrino (ν), and the other into a pair of quarks. In the analysis presented here, mtop is obtained from the combined sample of events selected in the electron+jets and muon+jets final states. Single-top-quark events with the same reconstructed final states contain information about the top quark mass and are therefore included as signal events
The combined error in the combination is ± 0.48 GeV, which is very low. This excludes masses in excess of 173.65 GeV at the 95% confidence level, which is barely consistent with Particle Data Group indirect measurement of 173.5 GeV.
Both the new calculation and the combined measurement are lighter than previous results from all sources as of a year ago. There was a paper reviewing the most recent mass measurement in both collaborations in January of 2018. At that time, ATLAS was using only Run-1 data.
It is worth observing the range of the combined measurements from the two Tevatron experiments and the two LHC experiments: 172.44 GeV to 174.95 GeV. The spread from the midpoint of that range is ± 1.255 GeV. I think it is safe to say that somebody's error bars are probably underestimated.
It isn't at all clear why such old data is being used in a 2018 publication. As of the most recent information available ATLAS and CMS have each collected almost three times as much data as the 20.2 fb-1 relied upon in this paper.
ATLAS: 57.5 fb-1
CMS: 59.21 fb-1
Also, much of that has been at higher 13 TeV energies than the centre-of-mass energy of √ s = 8 TeV relied upon in this paper, which should also produce better data. Many papers using more recent data have been published concerning top quark physics. For example, this paper from ATLAS and this one in which: "The data analysed correspond to 79.8 fb−1 of proton--proton collisions at a centre-of-mass energy of s√=13 TeV recorded by the ATLAS experiment at the LHC."
While the percentage error in the top quark mass determination isn't particularly high for QCD, in many circumstances, what matters is the absolute magnitude of the uncertainty, rather than the percentage uncertainty, and in terms of absolute magnitude of the error bars, the uncertainty in the top quark mass dwarfs the uncertainty in all of the other mass measurements in the Standard Model.
A May 3, 2018 paper from CMS also looks at this topic (largely identical in result and data to a January 17, 2018 paper from CMS) using more data and higher energy data:
The mass of the top quark is measured using a sample of tt events containing one isolated muon or electron and at least four jets in the final state, collected by the CMS detector using proton-proton collisions at s= 13 TeV at the CERN LHC. The events are selected from data corresponding to an integrated luminosity of 35.9 fb1. For each event the mass is reconstructed from a kinematic fit of the decay products to a \ttbar hypothesis. Using the ideogram method, the top quark mass is determined simultaneously with an overall jet energy scale factor (JSF), constrained by the mass of the W boson in qq decays. The measurement is calibrated on samples simulated at next-to-leading order matched to a leading-order parton shower. The top quark mass is found to be 172.25±0.08 (stat+JSF)±0.62 (syst) GeV. The dependence of this result on the kinematic properties of the event is studied and compared to predictions of different models of tt production, and no indications of a bias in the measurements are observed.
Other Physics News
A paper in June summed up efforts to more accurately measure the strong force coupling constant. The abstract of the paper notes that:
The latest experimental and theoretical developments in the high-precision determination of the strong coupling αs are briefly reviewed. Six groups of observables: (i) lattice QCD data, (ii) hadronic τ decays, (iii) deep-inelastic e±p data and parton distribution functions (PDF) fits, (iv) event shapes and jet rates in e+e collisions, (v) Z boson hadronic decays, and (vi) top-quark cross sections in pp collisions, are used to extract the current world-average at the Z pole mass, αs(m2Z)=0.1181±0.0011 at next-to-next-to-leading-order (NNLO), or beyond, accuracy. Additional NNLO extractions have recently appeared based on new lattice studies, the R(s) ratio in e+ehadrons, updated PDF fits, energy-energy correlations in e+e collisions, jet cross sections in e±p collisions, and the full set of pptt¯ cross sections at the LHC. Inclusion of these new data into the world-average would slightly increase its value and reduce its uncertainty to αs(m2Z)=0.1183±0.0008. Future αs extraction perspectives with permille uncertainties at future high-luminosity e+e machines -- via W and Z hadronic decays, parton fragmentation functions, and photon F2(x,Q2) structure function in γγ collisions -- are also discussed.
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2022-06-29 10:10:04
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https://www.sevenforums.com/general-discussion/339526-command-prompt-not-recognizing-commands.html
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Welcome to Windows 7 Forums. Our forum is dedicated to helping you find support and solutions for any problems regarding your Windows 7 PC be it Dell, HP, Acer, Asus or a custom build. We also provide an extensive Windows 7 tutorial section that covers a wide range of tips and tricks.
Windows 7: Command Prompt Not recognizing commands.
28 Jul 2014 #1 Dunkthedood Windows 7 Professional x32 8 posts Command Prompt Not recognizing commands. Hi, I'm super sad because I use CMD a lot but its not recognizing regular commands. I have no idea what to do because im more familiar with Terminal on a Macintosh. Thanks. My System Specs
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28 Jul 2014 #2 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity Which commands aren't recognized? Give some examples please My System Specs
28 Jul 2014 #3 Dunkthedood Windows 7 Professional x32 8 posts Every Command Every Command My System Specs
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28 Jul 2014 #4 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity Even DIR and EXIT don't work? PATH does work? My System Specs
28 Jul 2014 #5 Dunkthedood Windows 7 Professional x32 8 posts Well Well those work My System Specs
28 Jul 2014 #6 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity Quote: Originally Posted by Dunkthedood Well those work so not all of them don't work!! Post output of PATH please My System Specs
28 Jul 2014 #7 Dunkthedood Windows 7 Professional x32 8 posts ? what does post output of path mean My System Specs
28 Jul 2014 #8 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity These work? Code: attrib *.* c:\windows\system32\attrib *.* My System Specs
28 Jul 2014 #9 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity Quote: Originally Posted by Dunkthedood what does post output of path mean If you do for example: xcopy source destination It should xcopy from source to destination. But in which folder to find xcopy.exe ? Windows searches for xcopy.exe (or .com or .bat) in "current folder". If not found then in folders described in PATH output. Post the output! My System Specs
28 Jul 2014 #10 Kaktussoft Microsoft Windows 7 Home Premium 64-bits 7601 Multiprocessor Free Service Pack 1 10,798 posts SecretCity Quote: Originally Posted by Kaktussoft Even DIR and EXIT don't work? PATH does work? DIR, EXIT and PATH are examples of "internal" commands. They are built-in in cmd.exe (command prompt). My System Specs
Command Prompt Not recognizing commands.
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Similar help and support threads Thread Forum Command Prompt command not workingwhen I open up my command prompt and type 'ipconfig' without the ' and press enter it returns the line: 'ipconfig' is nto recognized as an internal or external command, operable program, or batch file I am trying to find out the information I need in order to set up a static IP Address for port... Network & Sharing Command prompt not recognizing commandsHello. It seems as if my command prompt will not let me do any simple system commands such as ping, ipconifg, etc. And it will also not let me use commands for my compiler. The paths are set properly in the environment variables, but it still does not work. See the screencap below: ... General Discussion Start Command Prompt and automatically execute a few commandsI am learning a programming language, and I frequently use command prompt to compile source codes, but every time I start command prompt I need to manually cd to the correct directory, and then I like to run cls to keep the window clean. I have looked around, but I'm not sure how to phrase a google... Software Command prompt doesnt recognize commands / cant repair windowsi cant run any commands in command prompt.i have checked a lot of stuff on inet to solve like paths @environment variables etc but i still couldnt solve it.i thought maybe its cuz a system file is missing made a repair disc but couldnt run sfc via command prompt at boot because i got this error... BSOD Help and Support Run administrative command prompt from command promptOk So I got myself into a unique bind here. I was trying to install some custom system files (for a theme) and I did it wrong and now I cant open explorer.exe . I dont want to goto a backup because this is a easy fix. (in my view). So I need to know how to run command prompt with administrative... General Discussion Running command prompt commands elsewhere...I am trying to configure RightMark Clock Utility to execute the "start" command when the power source for my computer changes. For example, I would want to run this: start /MIN "" "C:Path\to\Program" I am choosing the start command because it gives me the option to use the /min parameter. ... General Discussion
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2017-09-23 20:48:26
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http://math.stackexchange.com/questions/68891/optimize-the-expected-value-of-a-process
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# optimize the expected value of a process
There are $a_i$ balls painted with number $i$. For example if we have balls painted with 1,1,1,3,2. we have $a_1 = 3$, $a_2=1$, $a_3=1$. In total there are $m$ balls painted with number $1,\ldots,n$.
There are $n$ bins. Bin $B_i$ can only contain balls numbered $j$, where $j\leq i$.
Each $B_i$ is associated with a weight $w_i$. $w_i\geq w_j$ if $i\leq j$. The bins have a capacity of $c_i$. $c_i\leq c_j$ if $i\leq j$.
Initially there is 1 ball in $B_1$. The non-empty bin is called the current bin.
Whenever bin $B_i$ is filled(the amount of balls reached the capacity), remove all the balls from $B_i$ and put them in $B_{i+1}$. So there will be only one non-empty bin.
$t_0$ and $k$ are given constants.
We do the following process at step i:
If $t_i=0$, then terminate and return $bw$, where $b$ is the number of balls in the current bin, and $w$ is the weight of the current bin.
Else randomly choose $t_ik$ balls(include the ones in the bin). Return the ones painted with higher number than the current bin and the ones already in the bin, and put the rest in the current bin. The number of newly added balls in this step is $t_{i+1}$.
Intuitively, each ball is randomly attached to $k$ other balls. Putting one in the bin, it will try to "drag" $k$ other balls into the bin. The ball can only "drag" another ball once. The connection breaks afterwards.
The question is:
Given $a_i$, $w_i$, $t_0$ and $k$, compute the set of $c_i$ that maximize the expected return.
I can brute force all possible $c_i$ and see which one turns out the best, but there are $O(m^n)$ possibilities.
The model is so simple I can't help to think is there a simple relation between these variables.
If not, are there faster algorithms than naively try everything?
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Just to be clear: is $t_{i+1}$ the difference between the number of usable balls added at step $i$ and the number of usable balls at the previous step, or is it the number of usable balls added at step $i$? – Brian M. Scott Sep 30 '11 at 22:28
it's the number of usable balls added at step i. I will change it to make it clear. – Chao Xu Sep 30 '11 at 22:41
"The model is so simple I can't help to think is there a simple relation between these variables." I dare to disagree. In fact, by the time I'd reached that sentence I was thinking quite the opposite. Also you might want to add some motivation for considering this particular problem; it seems like a rather arbitrary construction to me. – joriki Oct 1 '11 at 8:41
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2016-06-30 06:47:27
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https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=18436&extra=longdesc_idm45714669357360&clicked=1
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The fraction ‘one-half’ is shown as a one over a two, with a horizontal line between the two numbers. An arrow points to the one with the comment ‘top number is called the numerator and is the number of shaded pieces’. An arrow points to the two with the comment ‘bottom number is called the denominator and is the total number of pieces’.
1.1 Folding paper
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2022-01-18 16:01:32
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https://en.wikipedia.org/wiki/Negative_mass
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# Negative mass
In theoretical physics, negative mass is a type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg.[1][2] Such matter would violate one or more energy conditions and show some strange properties such as the oppositely oriented acceleration for negative mass. It is used in certain speculative hypothetical technologies, such as time travel to the past and future,[3] construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster-than-light warp drives. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect.
## In cosmology
In December 2018, astrophysicist Jamie Farnes from the University of Oxford proposed a "dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by Albert Einstein, that may help better understand, in a testable manner, the considerable amounts of unknown dark matter and dark energy in the cosmos.[4][5]
## In general relativity
Negative mass is any region of space in which for some observers the mass density is measured to be negative. This could occur due to a region of space in which the stress component of the Einstein stress–energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
### Inertial versus gravitational mass
In considering negative mass, it is important to consider which of these concepts of mass are negative. Ever since Newton first formulated his theory of gravity, there have been at least three conceptually distinct quantities called mass:
• inertial mass – the mass m that appears in Newton's second law of motion, F = ma
• "active" gravitational mass – the mass that produces a gravitational field that other masses respond to
• "passive" gravitational mass – the mass that responds to an external gravitational field by accelerating.
The law of conservation of momentum requires that active and passive gravitational mass be identical. Einstein's equivalence principle postulates that inertial mass must equal passive gravitational mass, and all experimental evidence to date has found these are, indeed, always the same.
In most analyses of negative mass, it is assumed that the equivalence principle and conservation of momentum continue to apply, and therefore all three forms of mass are still the same, leading to the study of "negative mass". But the equivalence principle is simply an observational fact, and is not necessarily valid. If such a distinction is made, a "negative mass" can be of three kinds: whether the inertial mass is negative, the gravitational mass, or both.
In his 4th-prize essay for the 1951 Gravity Research Foundation competition, Joaquin Mazdak Luttinger considered the possibility of negative mass and how it would behave under gravitational and other forces.[6]
In 1957, following Luttinger's idea, Hermann Bondi suggested in a paper in Reviews of Modern Physics that mass might be negative as well as positive.[7] He pointed out that this does not entail a logical contradiction, as long as all three forms of mass are negative, but that the assumption of negative mass involves some counter-intuitive form of motion. For example, an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed (non-gravitationally).
There have been several other analyses of negative mass, such as the studies conducted by R. M. Price,[8] though none addressed the question of what kind of energy and momentum would be necessary to describe non-singular negative mass. Indeed, the Schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position. The question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density. The answer is yes, but not with energy and momentum that satisfies the dominant energy condition. This is because if the energy and momentum satisfies the dominant energy condition within a spacetime that is asymptotically flat, which would be the case of smoothing out the singular negative mass Schwarzschild solution, then it must satisfy the positive energy theorem, i.e. its ADM mass must be positive, which is of course not the case.[9][10] However, it was noticed by Belletête and Paranjape that since the positive energy theorem does not apply to asymptotic de Sitter spacetime, it would actually be possible to smooth out, with energy–momentum that does satisfy the dominant energy condition, the singularity of the corresponding exact solution of negative mass Schwarzschild–de Sitter, which is the singular, exact solution of Einstein's equations with cosmological constant.[11] In a subsequent article, Mbarek and Paranjape showed that it is in fact possible to obtain the required deformation through the introduction of the energy–momentum of a perfect fluid.[12]
### Runaway motion
Although no particles are known to have negative mass, physicists (primarily Hermann Bondi in 1957,[7] William B. Bonnor in 1964 and 1989,[13][14] then Robert L. Forward[15]) have been able to describe some of the anticipated properties such particles may have. Assuming that all three concepts of mass are equivalent according to the equivalence principle, the gravitational interactions between masses of arbitrary sign can be explored, based on the Newtonian approximation of the Einstein field equations. The interaction laws are then:
In yellow, the "preposterous" runaway motion of positive and negative masses described by Bondi and Bonnor.
• Positive mass attracts both other positive masses and negative masses.
• Negative mass repels both other negative masses and positive masses.
For two positive masses, nothing changes and there is a gravitational pull on each other causing an attraction. Two negative masses would repel because of their negative inertial masses. For different signs however, there is a push that repels the positive mass from the negative mass, and a pull that attracts the negative mass towards the positive one at the same time.
Hence Bondi pointed out that two objects of equal and opposite mass would produce a constant acceleration of the system towards the positive-mass object,[7] an effect called "runaway motion" by Bonnor who disregarded its physical existence, stating:
I regard the runaway (or self-accelerating) motion […] so preposterous that I prefer to rule it out by supposing that inertial mass is all positive or all negative.
— William B. Bonnor, in Negative mass in general relativity.[14]
Such a couple of objects would accelerate without limit (except a relativistic one); however, the total mass, momentum and energy of the system would remain zero. This behavior is completely inconsistent with a common-sense approach and the expected behavior of "normal" matter. Thomas Gold even hinted that the runaway linear motion could be used in a perpetual motion machine if converted to circular motion:
What happens if one attaches a negative and positive mass pair to the rim of a wheel? This is incompatible with general relativity, for the device gets more massive.
— Thomas Gold, in Negative mass in general relativity.[16]
But Forward showed that the phenomenon is mathematically consistent and introduces no violation of conservation laws.[15] If the masses are equal in magnitude but opposite in sign, then the momentum of the system remains zero if they both travel together and accelerate together, no matter what their speed:
${\displaystyle p_{\mathrm {sys} }=mv+(-m)v={\big (}m+(-m){\big )}v=0\times v=0.}$
And equivalently for the kinetic energy:
${\displaystyle E_{\mathrm {k,sys} }={\tfrac {1}{2}}mv^{2}+{\tfrac {1}{2}}(-m)v^{2}={\tfrac {1}{2}}{\big (}m+(-m){\big )}v^{2}={\tfrac {1}{2}}(0)v^{2}=0}$
However, this is perhaps not exactly valid if the energy in the gravitational field is taken into account.
Forward extended Bondi's analysis to additional cases, and showed that even if the two masses m(−) and m(+) are not the same, the conservation laws remain unbroken. This is true even when relativistic effects are considered, so long as inertial mass, not rest mass, is equal to gravitational mass.
This behaviour can produce bizarre results: for instance, a gas containing a mixture of positive and negative matter particles will have the positive matter portion increase in temperature without bound.[citation needed] However, the negative matter portion gains negative temperature at the same rate, again balancing out. Geoffrey A. Landis pointed out other implications of Forward's analysis,[17] including noting that although negative mass particles would repel each other gravitationally, the electrostatic force would be attractive for like charges and repulsive for opposite charges.
Forward used the properties of negative-mass matter to create the concept of diametric drive, a design for spacecraft propulsion using negative mass that requires no energy input and no reaction mass to achieve arbitrarily high acceleration.
Forward also coined a term, "nullification", to describe what happens when ordinary matter and negative matter meet: they are expected to be able to cancel out or nullify each other's existence. An interaction between equal quantities of positive mass matter (hence of positive energy E = mc2) and negative mass matter (of negative energy E = −mc2) would release no energy, but because the only configuration of such particles that has zero momentum (both particles moving with the same velocity in the same direction) does not produce a collision, such interactions would leave a surplus of momentum.
## Arrow of time and energy inversion
In general relativity, the universe is described as a Riemannian manifold associated to a metric tensor solution of Einstein's field equations. In such a framework, the runaway motion forbids the existence of negative matter.[7][14]
Some bimetric theories of the universe propose that two parallel universes with an opposite arrow of time may exist instead of one, linked together by the Big Bang and interacting only through gravitation.[18][19] The universe is then described as a manifold associated to two Riemannian metrics (one with positive mass matter and the other with negative mass matter). According to group theory, the matter of the conjugated metric would appear to the matter of the other metric as having opposite mass and arrow of time (though its proper time would remain positive). The coupled metrics have their own geodesics and are solutions of two coupled field equations.[20]
The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of dark matter, dark energy, cosmic inflation and an accelerating universe.[20]
## Gravitational interaction of antimatter
The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter. Direct experiments on neutral antihydrogen have not been sensitive enough to detect any difference between the gravitational interaction of antimatter, compared to normal matter.[21]
Bubble chamber experiments provide further evidence that antiparticles have the same inertial mass as their normal counterparts. In these experiments, the chamber is subjected to a constant magnetic field that causes charged particles to travel in helical paths, the radius and direction of which correspond to the ratio of electric charge to inertial mass. Particle–antiparticle pairs are seen to travel in helices with opposite directions but identical radii, implying that the ratios differ only in sign; but this does not indicate whether it is the charge or the inertial mass that is inverted. However, particle–antiparticle pairs are observed to electrically attract one another. This behavior implies that both have positive inertial mass and opposite charges; if the reverse were true, then the particle with positive inertial mass would be repelled from its antiparticle partner.
## Experimentation
Physicist Peter Engels and a team of colleagues at Washington State University reported the observation of negative mass behavior in rubidium atoms. On 10 April 2017, Engels' team created negative effective mass by reducing the temperature of rubidium atoms to near absolute zero, generating a Bose–Einstein condensate. By using a laser-trap, the team were able to reverse the spin of some of the rubidium atoms in this state, and observed that once released from the trap, the atoms expanded and displayed properties of negative mass, in particular accelerating towards a pushing force instead of away from it.[22][23] This kind of negative effective mass is analogous to the well-known apparent negative effective mass of electrons in the upper part of the dispersion bands in solids.[24] However, neither case is negative mass for the purposes of the stress–energy tensor.
Some recent work with metamaterials suggests that some as-yet-undiscovered composite of superconductors, metamaterials and normal matter could exhibit signs of negative effective mass in much the same way as low-temperature alloys melt at below the melting point of their components or some semiconductors have negative differential resistance.[25][26]
## In quantum mechanics
In 1928, Paul Dirac's theory of elementary particles, now part of the Standard Model, already included negative solutions.[27] The Standard Model is a generalization of quantum electrodynamics (QED) and negative mass is already built into the theory.
Morris, Thorne and Yurtsever[28] pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space–time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a wormhole. Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by negative-mass loops of cosmic string.[29] Stephen Hawking has argued that negative energy is a necessary condition for the creation of a closed timelike curve by manipulation of gravitational fields within a finite region of space;[30] this implies, for example, that a finite Tipler cylinder cannot be used as a time machine.
### Schrödinger equation
For energy eigenstates of the Schrödinger equation, the wavefunction is wavelike wherever the particle's energy is greater than the local potential, and exponential-like (evanescent) wherever it is less. Naively, this would imply kinetic energy is negative in evanescent regions (to cancel the local potential). However, kinetic energy is an operator in quantum mechanics, and its expectation value is always positive, summing with the expectation value of the potential energy to yield the energy eigenvalue.
For wavefunctions of particles with zero rest mass (such as photons), this means that any evanescent portions of the wavefunction would be associated with a local negative mass–energy. However, the Schrödinger equation does not apply to massless particles; instead the Klein–Gordon equation is required.
## In theory of vibrations and metamaterials
Figure 1. A core with mass ${\displaystyle m_{2}}$ is connected internally through the spring with ${\displaystyle k_{2}}$ to a shell with mass ${\displaystyle m_{1}}$. The system is subjected to the sinusoidal force F(t).
The mechanical model giving rise to the negative effective mass effect is depicted in Figure 1. A core with mass ${\displaystyle m_{2}}$ is connected internally through the spring with constant ${\displaystyle k_{2}}$ to a shell with mass ${\displaystyle m_{1}}$. The system is subjected to the external sinusoidal force ${\displaystyle F(t)={\widehat {F}}sin\omega t}$. If we solve the equations of motion for the masses ${\displaystyle m_{1}}$ and ${\displaystyle m_{2}}$ and replace the entire system with a single effective mass ${\displaystyle m_{eff}}$ we obtain:[31][32][33][34]
${\displaystyle m_{eff}=m_{1}+{{m_{2}\omega _{0}^{2}} \over {\omega _{0}^{2}-\omega ^{2}}}}$,
where ${\displaystyle \omega _{0}={\sqrt {k_{2} \over m_{2}}}}$.
Figure 2. Free electrons gas ${\displaystyle m_{2}}$ is embedded into the ionic lattice ${\displaystyle m_{1}}$; ${\displaystyle \omega _{p}}$ is the plasma frequency (the left sketch). The equivalent mechanical scheme of the system (right sketch).
When the frequency ${\displaystyle \omega }$ approaches ${\displaystyle \omega _{0}}$ from above the effective mass ${\displaystyle m_{eff}}$ will be negative.[31][32][33][34]
The negative effective mass (density) becomes also possible based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas (see Figure 2).[35][36] The negative mass appears as a result of vibration of a metallic particle with a frequency of ${\displaystyle \omega }$ which is close the frequency of the plasma oscillations of the electron gas ${\displaystyle m_{2}}$ relatively to the ionic lattice ${\displaystyle m_{1}}$. The plasma oscillations are represented with the elastic spring ${\displaystyle k_{2}=\omega _{p}^{2}m_{2}}$, where ${\displaystyle \omega _{p}}$ is the plasma frequency.[35][36] Thus, the metallic particle vibrated with the external frequency ω is described by the effective mass
${\displaystyle m_{eff}=m_{1}+{{m_{2}\omega _{p}^{2}} \over {\omega _{p}^{2}-\omega ^{2}}}}$,
which is negative when the frequency ω approaches ${\displaystyle \omega _{p}}$ from above. Metamaterials exploiting the effect of the negative mass in the vicinity of the plasma frequency were reported.[35][36]
## References
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2022-10-01 17:26:48
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https://www.shahmoradi.org/ECL2017S/homework/8-solutions-python-array-computing-plotting
|
This is the solution to Homework 8: Problems - Python array computing and plotting.
The following figure illustrates the grade distribution for this homework.
This homework aims at giving you some experience with Python’s array computing and plotting features.
1. The while-loop implementation of a for-loop. Consider the following mathematical function resembling a Hat function,
A scalar implementation of this function would be,
def hatFunc(x):
if x < 0:
return 0.0
elif 0 <= x < 1:
return x
elif 1 <= x < 2:
return 2 - x
elif x >= 2:
return 0.0
Write a vectorized version of this function. (Hint: you may need numpy’s logical_and method for building the vectorized version of this function.)
def hatFunc(x):
condition1 = x < 0
condition2 = np.logical_and(0 <= x, x < 1)
condition3 = np.logical_and(1 <= x, x < 2)
condition4 = x >= 2
r = np.zeros(len(x))
r[condition1] = 0.0
r[condition2] = x[condition2]
r[condition3] = 2-x[condition3]
r[condition4] = 0.0
return r
2. The vertical position $y(t)$ of a ball thrown upward is given by $y(t)=v_0t-\frac{1}{2}gt^2$, where $g$ is the acceleration of gravity and $v_0$ is the initial vertical velocity at $t=0$. Two important physical quantities in this context are the potential energy, obtained by doing work against gravity, and the kinetic energy, arising from motion. The potential energy is defined as $P=mgy$, where $m$ is the mass of the ball. The kinetic energy is defined as $K=\frac{1}{2}mv^2$, where $v$ is the velocity of the ball, related to $y$ by $v(t)=y’(t)$.
Write a program that can plot $P(t)$ and $K(t)$ in the same plot, along with their sum $E = P + K$. Let $t\in[0,2v_0/g]$. Write your program such that $m$ and $v_0$ are read from the command line. Run the program with various choices of $m$ and $v_0$ and observe that $P+K$ always remains constant in this motion, regardless of initial conditions. This is in fact, the fundamental principle of conservation of energy in Physics.
A sample code can be downloaded from here. Here is an example output figure of the code:
3. Integration by midpoint rule: The idea of the Midpoint rule for integration is to divide the area under a curve $f(x)$ into $n$ equal-sized rectangles. The height of the rectangle is determined by the value of $f$ at the midpoint of the rectangle. The figure below illustrates the idea,
To implement the midpointrule, one has to compute the area of each rectangle, sum them up, just as in the formula for the Midpoint rule,
where $h=(b-a)/n$ is the width of each rectangle. Implement this formula as a Python function midpoint(f, a, b, n) and test the integrator with the following example input mathematical functions.
An example code can be downloaded from here. Here is the output of the code,
In [38]: run midpoint.py
The exact integral of exp(x) between 0.00000 and 1.09861 is 2.00000. The approximate answer is 1.99899 giving an error of 0.00101
The exact integral of cos(x) between 0.00000 and 3.14159 is 0.00000. The approximate answer is 0.00000 giving an error of 0.00000
The exact integral of sin(x) between 0.00000 and 3.14159 is 2.00000. The approximate answer is 2.00825 giving an error of 0.00825
The exact integral of sin(x) between 0.00000 and 1.57080 is 1.00000. The approximate answer is 1.00103 giving an error of 0.00103
4. Visualize approximations in the Midpoint integration rule Now consider the following function,
which we wish to integrate using the midpoint integrator that you wrote in the previous example. Now write a new code that visualizes the midpoint rule, similar to in the following figure. (Hint: you will need to use the Matplotlib function fill_between and use this function to create the filled areas between f(x) and the approximating rectangles)
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2019-01-22 17:00:17
|
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|
https://www.blog.pythonlibrary.org/2010/02/14/python-windows-and-printers/
|
# Python, Windows and Printers
I do a fair amount of technical support in addition to my software development. In our small shop, we get to troubleshoot anything that is related to technology, from networks to software to printers. I think one of the most annoying aspects is trying to get printers to work the way the user wants. Another issue is setting up printers for users that have to roam from PC to PC as a part of their job. These users usually only need the printers that are in their specific location at any given time. It’s very difficult to accommodate this type of user, especially if the PCs are being used 24/7, which is true in my case. This is where Python comes in.
In this article, I’ll show you how to access the currently installed printers on a machine, change which one is the default and install another printer. I’ll also show you how to access various bits and pieces about the printers that are installed as that information can be helpful in coding up other administrative scripts.
To follow along, you’ll need Python 2.4 – 3.x and the PyWin32 package.
For our first trick of the day, let’s find out what printers are currently installed on our PC:
import win32print
printers = win32print.EnumPrinters(5)
print printers
You can use different integers in the EnumPrinters call to get more or less information. See the documentation for more information (you may need to look at MSDN as well). Anyway, here’s is a sample output:
((8388608, 'SnagIt 9,SnagIt 9 Printer,', 'SnagIt 9', ''), (8388608, 'Samsung ML-2250 Series PCL 6,Samsung ML-2250 Series PCL 6,', 'Samsung ML-2250 Series PCL 6', ''), (8388608, 'PDFCreator,PDFCreator,', 'PDFCreator', 'eDoc Printer'), (8388608, 'Microsoft XPS Document Writer,Microsoft XPS Document Writer,', 'Microsoft XPS Document Writer', ''))
As you can see, the EnumPrinters call returns a tuple with nested tuples. If I recall correctly, the last parameter will be a UNC path if the printer is a network printer. At my work place, we’ve had to decommission some servers that had printers on them and needed a way to change the user’s printer settings so that they pointed to the new path. Using the information gathered above made this much easier.
For example, if my script iterated over that list and found a printer that was using an obsolete UNC path, I could do something like this to fix it:
import win32print
win32print.DeletePrinterConnection('\\\\oldUNC\path\to\printer')
An alternative way to install a printer is to use a low level command line call with the subprocess module:
import subprocess
subprocess.call(r'rundll32 printui.dll PrintUIEntry /in /q /n \\UNC\path\to\printer')
For the situation I mentioned above with roaming users, I also usually need to set the default printer so the user doesn’t accidentally print to a different department. There are two ways that I’ve found that work quite well. If you know the name of the printer, you can use the following:
import win32print
win32print.SetDefaultPrinter('EPSON Stylus C86 Series')
In the code above, I set the default to an Epson. The name should be exactly the same as the name displayed in the “Printers and Faxes” dialog in Windows (go to Start, Settings, Printers and Faxes on Windows XP). The other way to do this is with another subprocess call:
import subprocess
subprocess.call(r'rundll32 printui.dll PrintUIEntry /y /n \\UNC\path\to\printer')
There are many additional functions that win32print supports. You can start and stop print jobs, set priority levels on the print jobs, get the printer’s configuration, schedule jobs and much more. I hope you found this helpful.
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2021-05-08 19:36:42
|
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|
http://tex.stackexchange.com/questions/59755/space-before-proof
|
# Space before proof
I am trying to make LaTeX put no additional space between theorem and proof. Here is my code:
\newtheorem*{pr3}{Theorem}
\begin{pr3}
foo
\end{pr3}
\begin{proof}[Proof:]
bar
\end{proof}
Is there a way to do that only with amsthm/amsmath and how? I wanted to renewenvironment proof, however I couldn't find what is the best way to do that. So it would be great if someone can tell me where I can find such information (that could also be considered answer to the first question).
-
## migrated from stackoverflow.comJun 13 '12 at 21:14
This question came from our site for professional and enthusiast programmers.
You probably don't want to remove the space after the proof, so the way should be
\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
\vspace{-\topsep}% remove the space after the theorem
\pushQED{\qed}%
\normalfont
\topsep0pt \partopsep0pt % no space before
\trivlist
\item[\hskip\labelsep
\itshape
}{%
\popQED\endtrivlist\@endpefalse
\addvspace{6pt plus 6pt} % some space after
}
\makeatother
However a proof environment not preceded by a theorem will be typeset wrongly.
-
I didn't want to use negative vspace however as it is not constant like in the other answer, I think that this will do. Thanks. – Ivaylo Petrov Aug 14 '12 at 12:44
You could put a negative vertical space between theorem and proof, like so:
\newtheorem*{pr3}{Theorem}
\begin{pr3}
foo
\end{pr3}
\vspace{-1.5em}
\begin{proof}[Proof:]
bar
\end{proof}
and you could wrap all into a new command \theoremproof{theorem body}{proof body}.
-
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2015-07-01 06:53:07
|
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http://dev.goldbook.iupac.org/terms/view/C00885
|
## catalytic coefficient
https://doi.org/10.1351/goldbook.C00885
If the @R05156@, $$\nu$$, is expressible in the form: $\nu = (k_{0}+\sum _{\begin{array}{c} i \end{array}}k_{i}\ [C_{i}]^{n_{i}})\ [A]^{\alpha }\ [B]^{\beta }\ ...$ where A, B, ... are @R05163@ and $$C_{i}$$ represents one of a set of catalysts, then the proportionality factor $$k_{i}$$ is the catalytic @C01124@ of the particular @C00876@ $$C_{i}$$. Normally the partial @O04322@ $$n_{i}$$ with respect to a @C00876@ is unity, so that $$k_{i}$$ is an $$\left ( \mathit{\alpha } + \mathit{\beta } + ... + 1 \right )$$th order @R05137@. The proportionality factor $$k_{0}$$ is the $$\left ( \mathit{\alpha } + \mathit{\beta } + ...\right )$$th order @R05137@ of the uncatalysed component of the total reaction. For example, if there is @C00874@ by hydrogen and hydroxide ions, and the @O04322@ can be expressed in the form: $k = k_{0}+k_{\text{H}^{+}}\ [\text{H}^{+}]+k_{\text{OH}^{-}}\ [\text{OH}^{-}]$ then $$k_{H^{+}}$$ and $$k_{\text{OH}^{-}}$$ are the catalytic coefficients for H+ and OH, respectively. The constant $$k_{0}$$ relates to the uncatalysed reaction.
Sources:
PAC, 1994, 66, 1077. (Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)) on page 1093 [Terms] [Paper]
PAC, 1996, 68, 149. (A glossary of terms used in chemical kinetics, including reaction dynamics (IUPAC Recommendations 1996)) on page 156 [Terms] [Paper]
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2019-06-25 04:23:19
|
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https://math.stackexchange.com/questions/2150423/prove-that-three-points-are-collinear-menelaus-theorem
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# Prove that three points are collinear (Menelaus theorem?)
Given a point P inside the triangle ABC. Lines AP, BP, CP intersect the sides BC, CA, AB in points $A_1, B_1, C_1$. The lines $A_1B_1$ and AB intersect in the point $A_2$. The points $B_2,C_2$ are defined in a similar way. How can I prove that $A_2, B_2, C_2$ are collinear? I think it has to do someting with the Menelaus theorem. But how can I use it here?. Another hard thing in this task is that it is almost impossible to draw a good figure, the best thing I could get is that:
Hint: by Ceva's theorem for the cevians through $P\,$:
$$\frac{BA_1}{A_1C}\cdot\frac{CB_1}{B_1A}\cdot\frac{AC_1}{C_1B} = 1 \tag{1}$$
By Menelaus' theorem for the transversal $A_1B_1\,$:
$$\frac{BA_2}{A_2A}\cdot\frac{AB_1}{B_1C}\cdot\frac{CA_1}{A_1B} = -1 \tag{2}$$
Multiplying the two $(1) \cdot (2)\,$:
$$\require{cancel} \cancel{\frac{BA_1}{A_1C}}\cdot\bcancel{\frac{CB_1}{B_1A}}\cdot\frac{AC_1}{C_1B} \;\cdot\; \frac{BA_2}{A_2A}\cdot\bcancel{\frac{AB_1}{B_1C}}\cdot\cancel{\frac{CA_1}{A_1B}} = -1 \;\;\iff\;\; \frac{BA_2}{A_2A} = -\,\frac{C_1B}{AC_1}$$
Repeat for $B_2,C_2\,$, multiply together, and the RHS reduces to $-1$ using $(1)$ one more time.
(It should be noted that the problem is equivalent to half the Desargues' theorem in the plane.)
• And what happens when we get all those -1s? – idliketodothis Feb 22 '17 at 21:23
• @idliketodothis It follows that $A_2,B_2,C_2$ are collinear by (the converse of) Menelaus' theorem. – dxiv Feb 22 '17 at 23:21
• But what I got for point B2 is B2C/B2B = -BA1/A1C; for point C1: AC2/CC2 = -B1A/CB1; All in all, I have C1B/AC1 * BA1/A1C * B1A/CB1 = -1. What am I doing wrong? – idliketodothis Feb 23 '17 at 6:19
• @idliketodothis Don't know how you somehow reverted to $(1)\,$. What you get in fact is $BA_2/A_2A \cdot AC_2/C_2C \cdot CB_2 / B_2B = -1\,$, which proves that $A_2,B_2,C_2$ are collinear. As a side note, you did not choose the best notation to preserve the symmetry in $A,B,C\,$, and it would have been easier to follow had you defined $AB \cap A_1B_1=C'$ instead of $A_2\,$. – dxiv Feb 23 '17 at 7:45
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2019-12-16 03:13:15
|
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|
https://www.physicsforums.com/threads/joint-density-problem.575317/
|
# Homework Help: Joint density problem.
1. Feb 7, 2012
### spitz
1. The problem statement, all variables and given/known data
I have:
$$f_A=\lambda e^{-\lambda a}$$
$$f_B=\mu e^{-\mu b}$$
($A$ and $B$ are independent)
I need to find the density of $C=\min(A,B)$
2. The attempt at a solution
$$f_C(c)=f_A(c)+f_B(c)-f_A(c)F_B(c)-F_B(c)f_A(c)$$
$$=\lambda e^{-\lambda c}+\mu e^{-\mu c}-\lambda e^{-\lambda c}(1-e^{-\mu c})-(1-e^{-\lambda c})\mu e^{-\mu c}$$
$$=\lambda e^{-\lambda c}e^{-\mu c}+\mu e^{-\lambda c}e^{-\mu c}$$
$$=2(\lambda+\mu)e^{-c(\lambda+\mu)}$$
Correct or utterly wrong?
2. Feb 7, 2012
### Ray Vickson
Some blunders (probably just typos), but answer is right: your first line should have been
$$f_C(c)=f_A(c)+f_B(c)-f_A(c)F_B(c)-F_A(c)f_B(c),$$
which is what your later lines computed. However, you are doing it the hard way: much easier is to say $$\Pr \{\min(A,B) > c \} = \Pr \{ A > c \mbox{ and } B > c \} = \Pr \{A > c \} \cdot \Pr \{ B > c \}.$$
RGV
3. Feb 8, 2012
### spitz
$$=(1-F_A(c)) \cdot (1-F_B(c))=(1-(1-e^{-\lambda c})) \cdot (1-(1-e^{-\mu c}))=e^{-c(\lambda+\mu)}$$
$$\Rightarrow\frac{d}{dc}e^{-c(\lambda+\mu)}=-(\lambda+\mu)e^{-c(\lambda+\mu)}$$
Although my first answer should have been: $$(\lambda+\mu)e^{-c(\lambda+\mu)}$$
Which is correct?
Last edited: Feb 8, 2012
4. Feb 8, 2012
### Ray Vickson
Your first *answer* was incorrect, but your method was correct up to the second-last line; in my original response, I messed the factor of 2, so should not have said it was correct. Basically, to get your last line you said a+b = 2(a+b), so you made a blunder.
The result $\min(A,B) \leftrightarrow (\lambda+\mu) e^{-(\lambda + \mu)t}$ is correct. It is one of the absolutely standard properties of the exponential. Since the second way of getting it is correct, step-by-step, it cannot fail to be correct; you just need more confidence when making true statements, but you also need to be careful when doing algebraic manipulations.
RGV
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2018-08-21 20:11:46
|
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https://www.lmfdb.org/EllipticCurve/Q/221067/c/
|
# Properties
Label 221067.c Number of curves $2$ Conductor $221067$ CM no Rank $2$ Graph
# Related objects
Show commands for: SageMath
sage: E = EllipticCurve("c1")
sage: E.isogeny_class()
## Elliptic curves in class 221067.c
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.c1 221067c2 [1, -1, 1, -18041, -864894] [2] 442368
221067.c2 221067c1 [1, -1, 1, -3686, 71052] [2] 221184 $$\Gamma_0(N)$$-optimal
## Rank
sage: E.rank()
The elliptic curves in class 221067.c have rank $$2$$.
## Complex multiplication
The elliptic curves in class 221067.c do not have complex multiplication.
## Modular form 221067.2.a.c
sage: E.q_eigenform(10)
$$q - q^{2} - q^{4} - 2q^{5} - q^{7} + 3q^{8} + 2q^{10} + q^{14} - q^{16} - 2q^{17} + 2q^{19} + O(q^{20})$$
## Isogeny matrix
sage: E.isogeny_class().matrix()
The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.
$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$
## Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
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2021-02-25 05:41:25
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http://www.researchgate.net/publication/235447766_K%2A_vector_and_tensor_couplings_from_N__f_2_twisted_mass_QCD
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Article
# K^{*} vector and tensor couplings from N_ {f}= 2 twisted mass QCD
• ##### P. Dimopoulos
Physical review D: Particles and fields 07/2011; 84(1). DOI: 10.1103/PhysRevD.84.014505
Source: arXiv
ABSTRACT The mass mK* and vector coupling fK* of the K* meson, as well as the ratio of the tensor to vector couplings fT/fV|K*, are computed in lattice QCD. Our simulations are performed in a partially quenched setup, with two dynamical (sea) Wilson quark flavors, having a maximally twisted mass term. Valence quarks are either of the standard or the Osterwalder-Seiler maximally twisted variety. Results obtained at three values of the lattice spacing are extrapolated to the continuum, giving mK*=981(33) MeV, fK*=240(18) MeV, and fT(2 GeV)/fV|K*=0.704(41).
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• Source
##### Article: D-meson decay constants and a check of factorization in non-leptonic B-decays
[Hide abstract]
ABSTRACT: We compute the vector meson decay constants fD*, fDs* from the simulation of twisted mass QCD on the lattice with Nf = 2 dynamical quarks. When combining their values with the pseudoscalar D(s)-meson decay constants, we were able (i) to show that the heavy quark spin symmetry breaking effects with the charm quark are large, fDs*/fDs = 1.26(3), and (ii) to check the factorization approximation in a few specific B-meson non-leptonic decay modes. Besides our main results, fD* = 278 \pm 13 \pm 10 MeV, and fDs* = 311 \pm 9 MeV, other phenomenologically interesting results of this paper are: fDs*/fD* = 1.16 \pm 0.02 \pm 0.06, fDs*/fD = 1.46 \pm 0.05 \pm 0.06, and fDs/fD* = 0.89 \pm 0.02 \pm 0.03. Finally, we correct the value for B(B0 \rightarrow D+ pi-) quoted by PDG, and find B(B0 \rightarrow D+ pi-) = (7.8 \pm 1.4) \times 10-7. Alternatively, by using the ratios discussed in this paper, we obtain B(B0 \rightarrow D+ pi-) = (8.3 \pm 1.0 \pm 0.8)\times10-7.
Journal of High Energy Physics 01/2012; 2012(2). · 5.62 Impact Factor
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2014-12-26 19:59:38
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https://hpmuseum.org/forum/showthread.php?tid=11194&pid=110815&mode=threaded
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TI-36X Pro—Replace the batteries or just get a new one?
01-20-2019, 09:26 PM (This post was last modified: 01-20-2019 09:36 PM by ijabbott.)
Post: #56
ijabbott Senior Member Posts: 1,066 Joined: Jul 2015
RE: TI-36X Pro—Replace the batteries or just get a new one?
(01-20-2019 07:45 PM)pier4r Wrote:
(01-19-2019 09:37 PM)ijabbott Wrote: Test 6 - VBlogMag's $$e^{x^3}$$ integration test
This is an integration test from VBlogMag's calculator benchmark video: https://youtu.be/DHRsvSTGiBc?t=584
$\int_0^6 e^{x^3} dx \\ \\ \begin{array}{c|r} \text{Model} & \text{Time (s)} \\ \hline \text{TI-30X Pro MP} & 8.6 \\ \text{TI-36X Pro} & 89.3 \\ \text{Casio fx-991EX} & 24.4 \end{array}$
Nice work, thanks for sharing and great that you put the link to the sources!
Thanks!
I'm a bit puzzled why my time for my TI-36X Pro was about 19 seconds shorter than VBlogMag's (real name Martin Lorton). I know his calculator is older than mine since the video is from Feb 2014 and my TI-36X Pro has a 2015 manufacturing code (L-0315B - Kinpo Philippines, March 2015, revision B), so perhaps they increased the speed or improved the algorithm a bit. (I also have a TI-30X Pro MultiView (same as a TI-36X Pro) with a 2016 manufacturing code L-0416B. That is more or less the same speed as my TI-36X Pro - less than a second faster on this test. I can put that slight difference down to oscillator tolerances.)
— Ian Abbott
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Messages In This Thread TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 08-09-2018, 10:21 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - rprosperi - 08-09-2018, 11:24 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 08-09-2018, 11:28 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Steve Simpkin - 08-10-2018, 06:38 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 08-11-2018, 07:55 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Albert Chan - 08-11-2018, 10:35 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Dave Britten - 08-14-2018, 01:52 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Zaphod - 09-04-2018, 08:09 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - pier4r - 08-10-2018, 09:33 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - jebem - 09-19-2019, 04:10 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - gomefun2 - 09-04-2018, 02:09 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Csaba Tizedes - 09-04-2018, 04:59 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 09-04-2018, 06:43 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 09-04-2018, 11:51 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - klesl - 09-04-2018, 06:55 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Csaba Tizedes - 09-05-2018, 06:05 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 09-05-2018, 07:11 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Csaba Tizedes - 09-05-2018, 09:13 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 09-04-2018, 07:18 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 12-17-2018, 07:03 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Eddie W. Shore - 12-18-2018, 01:08 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 12-18-2018, 03:05 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - rprosperi - 12-19-2018, 02:30 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 12-18-2018, 11:13 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 12-19-2018, 12:13 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 12-19-2018, 06:17 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 12-19-2018, 09:08 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 12-19-2018, 10:10 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 12-19-2018, 10:32 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 12-20-2018, 12:00 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 12-20-2018, 12:47 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 12-20-2018, 10:11 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 12-20-2018, 06:52 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - berndpr - 01-11-2019, 08:08 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-12-2019, 02:24 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - rprosperi - 01-12-2019, 02:47 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Eddie W. Shore - 01-12-2019, 03:03 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - klesl - 01-12-2019, 07:53 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-13-2019, 05:01 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - klesl - 01-13-2019, 08:27 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-13-2019, 08:39 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-13-2019, 07:04 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-13-2019, 07:28 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Albert Chan - 01-13-2019, 09:11 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-13-2019, 11:03 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-13-2019, 08:10 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-15-2019, 03:46 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Eddie W. Shore - 01-16-2019, 01:12 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-16-2019, 03:56 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-19-2019, 09:37 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - pier4r - 01-20-2019, 07:45 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-20-2019 09:26 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Steve Simpkin - 01-21-2019, 03:29 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-25-2019, 08:42 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - rprosperi - 08-25-2019, 01:49 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-25-2019, 02:52 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 08-25-2019, 01:56 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-25-2019, 02:56 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-25-2019, 05:36 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 09-10-2019, 06:02 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 08-26-2019, 03:39 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-19-2019, 10:19 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 01-19-2019, 10:34 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-19-2019, 11:03 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-19-2019, 11:28 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-19-2019, 11:49 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - pier4r - 01-20-2019, 09:48 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Benjer - 01-20-2019, 10:57 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-21-2019, 12:34 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-21-2019, 01:55 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-22-2019, 05:34 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 01-22-2019, 07:27 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-22-2019, 07:59 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 01-22-2019, 08:03 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 01-29-2019, 03:18 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Csaba Tizedes - 01-29-2019, 09:43 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - pier4r - 01-29-2019, 12:15 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 02-02-2019, 05:38 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - lrdheat - 02-11-2019, 04:05 AM RE: TI-36X Pro—Replace the batteries or just get a new one? - Csaba Tizedes - 06-07-2019, 05:49 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - pier4r - 08-27-2019, 04:18 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 09-09-2019, 12:02 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - Matt Agajanian - 09-10-2019, 06:21 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - ijabbott - 09-10-2019, 10:22 PM RE: TI-36X Pro—Replace the batteries or just get a new one? - jlind - 09-11-2019, 08:54 AM
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2022-01-28 12:16:47
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https://demo.formulasearchengine.com/wiki/Hyperfinite_set
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# Hyperfinite set
In non-standard analysis, a branch of mathematics, a hyperfinite set or *-finite set is a type of internal set. An internal set H of internal cardinality g ∈ *N (the hypernaturals) is hyperfinite if and only if there exists an internal bijection between G = {1,2,3,...,g} and H.[1][2] Hyperfinite sets share the properties of finite sets: A hyperfinite set has minimal and maximal elements, and a hyperfinite union of a hyperfinite collection of hyperfinite sets may be derived. The sum of the elements of any hyperfinite subset of *R always exists, leading to the possibility of well-defined integration.[2]
Hyperfinite sets can be used to approximate other sets. If a hyperfinite set approximates an interval, it is called a near interval with respect to that interval. Consider a hyperfinite set ${\displaystyle K={k_{1},k_{2},\dots ,k_{n}}}$ with a hypernatural n. K is a near interval for [a,b] if k1 = a and kn = b, and if the difference between successive elements of K is infinitesimal. Phrased otherwise, the requirement is that for every r ∈ [a,b] there is a kiK such that kir. This, for example, allows for an approximation to the unit circle, considered as the set ${\displaystyle e^{i\theta }}$ for θ in the interval [0,2π].[2]
In general, subsets of hyperfinite sets are not hyperfinite, often because they do not contain the extreme elements of the parent set.[3]
## Ultrapower construction
In terms of the ultrapower construction, the hyperreal line *R is defined as the collection of equivalence classes of sequences ${\displaystyle \langle u_{n},n=1,2,\ldots \rangle }$ of real numbers un. Namely, the equivalence class defines a hyperreal, denoted ${\displaystyle [u_{n}]}$ in Goldblatt's notation. Similarly, an arbitrary hyperfinite set in *R is of the form ${\displaystyle [A_{n}]}$, and is defined by a sequence ${\displaystyle \langle A_{n}\rangle }$ of finite sets ${\displaystyle A_{n}\subset {\mathbb {R} },n=1,2,\ldots }$[4]
## Notes
1. {{#invoke:citation/CS1|citation |CitationClass=book }}
2. {{#invoke:citation/CS1|citation |CitationClass=book }}
3. {{#invoke:citation/CS1|citation |CitationClass=book }}
4. {{#invoke:citation/CS1|citation |CitationClass=book }}
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2020-07-09 08:21:55
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http://tex.stackexchange.com/questions/110983/tikz-matrix-decoration/110993
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# TikZ matrix decoration
What I'm trying to achieve is a code structure to draw this kind of diagram:
I need to decorate a two-rows matrix grouping one or more columns with a square bracket above them, and then again with a square bracket grouping one or more subgroups (there may be more than three levels of nested groups).
At first I tried nesting matrices with above delimiter=\lbrack, but TikZ told me that You cannot nest pgfmatrix environments, yet, so I ended up with something like this
\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{matrix,fit,positioning,decorations.pathreplacing,arrows,calc}
\begin{document}
\begin{tikzpicture}[
group/.style={inner sep=0pt},
brace/.style={very thick,decorate,decoration={brace,amplitude=10pt}},
square/.style={-,to path={-- ++(0,.25) -| (\tikztotarget)}}
]
\matrix (A) [matrix of nodes]
{
1--2 & 3--4 & 5 &
6--7 & 8--9 & 10 &
11--12 & 13--14 & 15--16 \\
%
I & V--I--V & V--IV &
V$^6$--IV & V$^7$ & V--IV &
I--V--I--IV & V$^7$--I & V--VI \\
};
\node (gdg) [group,fit=(A-1-1)(A-2-1)] {};
\node (boh) [group,fit=(A-1-2)(A-2-2)] {};
\node (z) [group,fit=(A-1-3)(A-2-3)] {};
\node (frase-a) [group,fit=(gdg)(boh)(z)] {};
\draw[square] ([yshift=.5cm]gdg.west) to ([yshift=.5cm]gdg.east);
\draw[square] ([yshift=.5cm]boh.west) to ([yshift=.5cm]boh.east);
\draw[square] ([yshift=.5cm]z.west) to ([yshift=.5cm]z.east);
\draw[square] ([yshift=1cm]frase-a.west) to ([yshift=1cm]frase-a.east);
\draw[brace] ([yshift=2cm]A.west) -- ([yshift=2cm]A.east);
\end{tikzpicture}
\end{document}
where I first draw the matrix, then I group each column in an invisible node (with fit) and then draw the square brackets as paths from/to west/east anchor point of groups, shifting coordinates on the y-axis. Which is quite unmaintainable and ugly. Of course the main target is to build something that could adapt to the variable width of matrix columns. Any suggestion would be very appreciated!
-
Welcome to TeX.sx! – Jubobs Apr 26 '13 at 22:59
Perhaps you can adapt the solutions from Matrix with labels nested in braces for this. – Peter Grill Apr 26 '13 at 23:36
Since it came out that the solution might not involve TikZ nor matrices nor decorations, should I change the title of my question? – Heruan Apr 27 '13 at 9:24
## 2 Answers
This doesn't use TiKz, and could be prettier but
\documentclass{article}
\usepackage{array}
\makeatletter
\newcommand\ob{%
\vrule\@width .7pt\@height3pt\hbox{$\smash-\mkern-3mu$}%
\xleaders\hbox{$\mkern-3mu\smash-\mkern-3mu$}\hfill
\hbox{$\mkern-3mu\smash-$}%
\vrule\@width .7pt}
\makeatother
\begin{document}
$\overbrace{ \begin{array}{*{9}c} \multicolumn{3}{c}{\mathrm{something}}& \multicolumn{3}{c}{\mathrm{something}\quad b/a'}& \multicolumn{3}{c}{\mathrm{something}\quad b'/a}\\ \omit\span\omit\span\omit\kern\tabcolsep \ob\kern\tabcolsep&% \omit\span\omit\span\omit\kern\tabcolsep \ob\kern\tabcolsep&% \omit\span\omit\span\omit\kern\tabcolsep \ob\kern\tabcolsep\\ GdG&&z&&y&z'&&y'&z''\\ \omit\kern\tabcolsep \ob\kern\tabcolsep&\ob&\ob&\ob&\ob&\ob&\ob&\ob&\ob\\ 1-2&3-4&5 &6-7 &8-9&10&11-12&13-14 &15-16\\ I &V &V^6&V(I-N)&X &Y &Z &(V^3)(X-V)&V^5 \end{array}}^A$
\end{document}
-
Inspired by David Carlisle answer, I came up with this solution:
\documentclass{minimal}
\usepackage{mathtools}
\newcommand{\mfrac}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}
\begin{document}
$\overbrace{ \overbracket{ \overbracket{\mfrac{1-2}{I}}^{\text{Gdg}} \overbracket{\mfrac{3-4}{V-I-V}} \overbracket{\mfrac{5}{V-IV}}^{z} }^{\text{frase }a} \overbracket{ \overbracket{\mfrac{6-7}{V^6}} \overbracket{\mfrac{8-9}{V^7}}^{y} \overbracket{\mfrac{10}{V-IV}}^{z'} }^{\text{frase }b/a'} \overbracket{ \overbracket{\mfrac{11-12}{I-V-I-IV}} \overbracket{\mfrac{13-14}{V^7-I}}^{y'} \overbracket{\mfrac{15-16}{V-VI}}^{z''} }^{\text{frase }a'/b} }^{A}$
\end{document}
which results in:
Now it's flexible and maintainable, I just need to find out to add labels outside the brace on the left of each line.
-
\llap{hello\hspace{1cm}}1-2 would out hello to the left of the 1-2 entry – David Carlisle Apr 27 '13 at 22:59
+1 for being inspired by me:-) – David Carlisle Apr 27 '13 at 23:01
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2014-10-24 08:42:59
|
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https://brilliant.org/problems/pulley-puzzle/
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# Pulley puzzle
A special type of chain pulley can be used to manually lift very heavy objects like car engines.
There are two pulleys, red (with radius 5) and blue (with radius 4), that move together and determine the maximum weight that can be lifted. Pulling on the slack part of the chain (black dots) wrapping around the pulleys lifts the box.
What is the mechanical advantage of this pulley? (That is, if I pull with a force of 1 Newton, how many times of upward force is applied on the brown box?)
Assumptions:
• Assume that the two lines that pull on the brown box are vertical (that is, there is no loss of mechanical advantage due to a bad angle).
• Assume that the pulleys and the chain are weightless and that there is no friction.
×
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2020-02-20 19:09:36
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https://physics.stackexchange.com/questions/288203/does-a-double-pole-in-a-mixed-correlator-imply-troubles-for-the-qft
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# Does a double pole in a mixed correlator imply troubles for the QFT?
It is known that dyagonal correlation functions (say propagators) can at most have single poles in their spectrum. I am wondering if the existence of double poles in mixed correlators in a QFT (say for example the correlators between the stress energy tensor and a scalar operator in a conformal field theory $\langle T^{\mu \nu}(q) \phi(q') \rangle$) has any bad implication for the theory.
• In a CFT such correlator will vanish identically unless $\phi$ is a descendant of $T$ in which case this correlator is a derivative of the diagonal one (so it has no more poles than $\langle TT\rangle$ in the momentum space). – Peter Kravchuk Oct 26 '16 at 7:03
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2019-07-22 06:39:13
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https://google.academickids.com/encyclopedia/index.php/Cantor_space
|
# Cantor space
In mathematics, the term Cantor space is sometimes used to denote the topological abstraction of the classical Cantor set: A topological space is a Cantor space if it is homeomorphic to the Cantor set.
The Cantor set itself is of course a Cantor space. But the canonical example of a Cantor space is the countably infinite topological product of the discrete 2-point space {0, 1}. This is usually written as 2N or 2ω (where 2 denotes the 2-element set {0,1} with the discrete topology). A point in 2N is an infinite binary sequence, that is a sequence which assumes only the values 0 or 1. Given such a sequence a1, a2, a3,... one can map it to the real number
[itex]
\sum_{n=1}^\infty \frac{2 a_n}{3^n}. [itex]
It is not difficult to see that this mapping is a homeomorphism from 2N onto the Cantor set, and hence that 2N is indeed a Cantor space.
A topological characterization of Cantor spaces is given by Brouwer's theorem:
Any two non-empty compact Hausdorff spaces without isolated points and having countable bases consisting of clopen sets are homeomorphic to each other.
(The topological property of having a base consisting of clopen sets is sometimes known as "zero-dimensionality".) This theorem can be restated as:
A topological space is a Cantor space if and only if it is non-empty, perfect, compact, totally disconnected, and metrizable.
It is also equivalent (via Stone's representation theorem for Boolean algebras) to the fact that any two countable atomless Boolean algebras are isomorphic.
As can be expected from Brouwer's theorem, Cantor spaces appear in several forms. But it is usually easiest to deal with 2N, since because of its special product form, many topological and other properties are brought out very explicitly.
For example, it becomes obvious that the cardinality of any Cantor space is [itex]2^{\aleph_0}[itex], that is, the cardinality of the continuum. Also clear is the fact that the product of two (or even any finite or countable number of) Cantor spaces is a Cantor space - an important fact about Cantor spaces.
Using this last fact and the Cantor function, it is easy to construct space-filling curves.
Cantor spaces occur in abundance in real analysis. For example they exist as subspaces in every perfect, complete metric space. (To see this, note that in such a space, any non-empty perfect set contains two disjoint non-empty perfect subsets of arbitrarily small diameter, and so one can imitate the construction of the usual Cantor set.) Also, every uncountable, separable, completely metrizable space contains Cantor spaces as subspaces. This includes most of the common type of spaces in real analysis. As a corollary, we see that separable, completely metrizable spaces satisfy the Continuum hypothesis: Every such space is either countable or has the cardinality of the continuum.
Compact metric spaces are also closely related to Cantor spaces: A Hausdorff topological space is compact metrizable if and only if it is a continuous image of a Cantor space.
• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy
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2022-01-19 16:20:34
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https://saratchandraias.com/quiz/sarat-chandra-ias-26th-june-quiz/
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Sarat Chandra IAS Academy
# Sarat Chandra IAS 26th June Quiz
Welcome to your Sarat Chandra IAS 26th June Quiz
With reference to Green Bonds in India, consider the following statements: 1.Green bond is a debt instrument issued for green GDP calculation. 2.Both public and private sector banks can issue such bonds. Which of the statement(s) given above is/are correct?
Which of the following are attributed to the demand-pull factors of inflation? 1.Rising population and household consumption 2.Buying and selling of real estate in urban areas 3.Black Money 4.Increase in administered prices 5.Hike in oil prices and global inflation. Select the correct answer using the codes given below:
In the context of management of liquidity, consider the following pairs: Type of Liquidity - Ideal Management Technique 1.Short term (volatile) - Repo Auctions 2.Medium term - Cash Reserve Ratio 3.Long Term - Open Market Operations Which of the pair(s) given above is/are correct?
Which of the following best describes Disposable Income?
The Macro-Vulnerability Index (MVI) is used for calculating the Macro-Economic performance of the Country. Which of the following factors are used to determine MVI? 1.Current Account Deficit 2.Fiscal Deficit 3.Primary Deficit 4.Rate of Inflation 5.Exchange Rate Select the correct answer from the codes given below:
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2021-10-21 15:24:51
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https://math.stackexchange.com/questions/1009188/finding-an-isomorphism-between-mathbbzi-7-and-mathbbz-sqrt-2-7
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# Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
I was having some trouble finding an explicit isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$.
$\textbf{What I have noticed is}:$
• 7 is a prime element in $\mathbb{Z}[i]$ so $(7)$ is a maximal ideal in $\mathbb{Z}[i]$ and $\mathbb{Z}[i]/(7)$ is a field.
• 7 is also a prime element in $\mathbb{Z}[\sqrt{-2}]$
$\textbf{What I have been trying to do is this}$
• Find a surjective homomorphism between $\mathbb{Z}[i]/(7) \rightarrow \mathbb{Z}[\sqrt{-2}]/(7)$. Since $\mathbb{Z}[i]/(7)$ was a field, the kernel of this homomorphism will be either the whole ring or just $0$. In the latter case it would be a isomorphism.
I am having trouble finding this surjective homomorphism:
I have noticed that $\bar{{i}}^{2}=-1$ so the image of $\bar{{i}}$ must be sent to something whose square is $-1$. Any help would be appreciated. I may be missing some obvious insight.
• $-8 \equiv -1 \pmod{7}$ – Daniel Fischer Nov 6 '14 at 16:22
• Thanks, so $-8=\sqrt{-2}^{6}$ so we map $i$ to $\sqrt{-2}^{6}$? – user135520 Nov 6 '14 at 16:29
• Not $\sqrt{-2}^6$, $\pm (\sqrt{-2})^3$. – Daniel Fischer Nov 6 '14 at 16:33
• Yes, that's right. Thanks a lot. I would have been stuck on that for some time. I didn't occur to me to think of congruence classes of -1. Thanks again. – user135520 Nov 6 '14 at 16:36
• Well, it isn't so bad anyway. There are only $49$ residue classes modulo $7$, so it's a finite undertaking. Then $(a+b\sqrt{-2})^2 = a^2 + 2b^2 + 2ab\sqrt{-2}$ shows that one of $a$ and $b$ must be $\equiv 0 \pmod{7}$. Since $-1$ is not a square modulo $7$, it must be $a$. – Daniel Fischer Nov 6 '14 at 16:40
Consider the unique homomorphism $f\colon\mathbb{Z}[X]\to\mathbb{Z}[\sqrt{-2}]/(7)$ sending $X\mapsto 2\sqrt{-2}+(7)$. Note that $f(4X)=8\sqrt{-2}+(7)=\sqrt{-2}+(7)$, so $f$ is surjective. Its kernel contains $X^2+1$, as $$f(X^2+1)=(2\sqrt{-2})^2+1+(7)=-8+1+(7)=(7)$$ so $f$ induces a (surjective) homomorphism $g\colon\mathbb{Z}[i]\to\mathbb{Z}[\sqrt{-2}]/(7)$.
What's the kernel of $g$?
• Readers may find it illuminating to ponder my hint before reading this (or similar proofs). – Bill Dubuque Jul 3 '17 at 22:00
Hint $\$ We get an image of $\,\Bbb Z[\sqrt{\color{#c00}{-9}}]\,$ in $\,\Bbb Z[\sqrt{-1}]\,$ by mapping $\,\sqrt{-9}\,\mapsto\, 3\sqrt{-1}$
$\!\bmod 7\!:\ \color{#c00}{{-}9\equiv -2}\,$ and the map is onto, since $3$ is a unit so $\,3^{-1}\sqrt{-9}\,\mapsto \sqrt{-1}$
• The essence of the matter is that the radicands differ by a multiple of a unit square factor. – Bill Dubuque Jul 3 '17 at 21:57
• Sorry I cannot understand your hint... – Aolong Li Jul 4 '17 at 16:56
• @AolongLi The idea is: we obtain an injective image of $\Bbb Z[\sqrt{c^2 d}]$ in $\Bbb Z[\sqrt{d}]$ by essentially pulling $c$ out of the radical. To do that ring theoretically, show that the map $\,x\mapsto c\sqrt d\,$ from $\,\Bbb Z[x]\to \Bbb Z[\sqrt d]$ has kernel $\,(x^2-c^2d),\,$ hence its image $\cong \Bbb Z[x]/(x^2\!-\!c^2d)\cong \Bbb Z[\sqrt{c^2d}],\,$ assuming that $\sqrt d$ is irrational. Furthermore, if $\,c\,$ is a unit then the map is onto, so an isomorphism. – Bill Dubuque Jul 4 '17 at 17:34
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2019-10-22 01:13:56
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https://www.themathdoctors.org/using-algebra-for-a-ratio-problem/
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# Using Algebra for a Ratio Problem
#### (A new question of the week)
Some kinds of problems can be solved at various levels; in particular, when we get a problem about ratios, we often can’t be sure whether the student knows only arithmetic, or can use algebra, which usually makes the problem easier. This is one reason we ask for a category (such as Arithmetic or Algebra), and also for an age range. It’s even more helpful when we see the start of a solution, which is the biggest hint to the appropriate method to use. This one led to an interesting discussion.
## A ratio problem
The problem came in last October, from Eric, who put himself in the 10-13 year old category, where students may or may not be doing algebra:
The problem is as follows:
Tom and Jerry paid for a friend’s present in the ratio 7:4. In doing so, Jerry spent 1/4 of his money and Tom had $99 left. If the ratio of the amount of Tom’s money to the amount of Jerry’s money was 5:2 before they bought the present, how much did the present cost? To be honest, I don’t know where to begin. It throws so much information at you, that is broken and detached from the rest of the problem, and it’s like you need to put it all together and add some pieces. I had a go, then my mom had a go, and we both got nowhere than just writing down the information and staring at the answer key, which didn’t explain how to solve the question. If I could have some intel on how to start my thinking for this and how everything fits together that would be fantastic. If you want to know the answer it is:$33
That isn’t a simple problem is it? This will be a lesson on how to gather information and make sense of it.
Answer keys often are not helpful for telling how to solve a problem; but they can help us see whether we are interpreting a problem correctly, and whether the student is confused only because the given answer is wrong. (It happens!) Here, it turns out to be right.
Doctor Rick took the question:
Hi, Eric, thanks for writing to The Math Doctors!
The fact that you put your question in the Algebra category tells me that you expect to be using variables and solving equations. That’s a big help — if I had to tackle the problem solely in terms of ratios, I don’t know what I’d do! Algebra helps us to encode the information in a complex problem like this into variables and equations; once we’ve done that, I can sit back and just solve the equations, and we’ll be done!
Many problems, including ratios, can be solved in creative ways without algebra; what algebra does is to take out the need for creativity and make the main work routine. Well, mostly …
### Define some variables
Here’s a suggestion to get you started. I see three main numbers that we don’t know, but that we want to talk about. So we can define three variables to represent these quantities: let’s say
P = the cost of the present (in dollars)
Now we hope that we can write three equations using these three variables. It sometimes turns out that this isn’t necessary, at least when we’re only interested in finding the value of one of our variables (as here, where we want to solve for P). You will find, though, that you can write three equations.
Note how carefully he has defined the variables. It isn’t just “T = Tom”, as many students write; rather, T is an amount of money that Tom has at a particular time in the problem. Doing this makes it easier to keep track of the details. Orderliness is the key to handling a complex problem.
Now I’d like you to give it a try. Can you come up with an equation to represent the information in the first sentence? Can you write two more equations from the other information in the problem? Let me see what you can do, even if it isn’t much or if you aren’t confident that you did it right — because that’s a start, and then we’ll have more to talk about.
We like to get the student involved in carrying out the work, so they’ll have the experience to do it again on the next problem, and the next. If we just demonstrated solutions, we’d be doing no more than a textbook does, without the necessary interaction. (That’s also why you may want to submit a question to us rather than read our pre-solved problems.)
### Write some equations
Eric responded with a multi-part reply:
Thanks for responding so quickly Dr. Rick! I… tried my best with the equations and came up with all sorts of junk like P=T/J, P=7/4, P=T/J-7/4, but then mom was there to save the day, with 7/4=(T-99)/(J/4), which I know isn’t what you asked, but my mom and I were in this together. We spent hours thinking about it. We were invested in this.
The reply came 50 minutes after Doctor Rick wrote, not exactly late. They did some good work in that time!
Anyway, I came up with the next equation (using your variables thank you so much ahhhhhhhhhhhh) that was T/J=5/2. Groundbreaking, I know, but it played a good role in the final result!
The final equation was P=J/4+(T-99), created out of nothingness by my mom… again…
And so we solved it! From T/J=5/2 we got T=5J/2 and plugged that into the first equation and then the last.
Thank you so much for your help with this problem!
We’ll be seeing how to do this without miraculous intervention.
P.S.: I put this under Algebra because I thought it was the difficulty range for this problem… but it seems that all’s well that ends well…
Is Algebra a difficulty range? It does describe a level of understanding, but it’s largely a way of looking at a problem.
P.P.S.: I know that we already solved this together, but I was wondering: how would you go about this problem with ratios? This problem was listed in the ratio section of my math workbook. I know that you said that you wouldn’t know where to begin with using ratios, and I am totally fine with you not knowing how to use ratios for this problem! It’s just the thought of using ratios was nagging at the back of my mind for a while… It’s fine though! We got the answer (which was Jerry spending 12 dollars and Tom spending 21 dollars)!
We’ll see that the comment was misunderstood.
## How to write the equations
Doctor Rick answered each piece, starting with the “lateness”:
Hi, Eric. I don’t consider a response sent 50 minutes after I wrote you to be “late” (but then I’m from the old generation that remembers writing letters) … you seem to have worked quite hard in that time. Also, you probably live not far from my time zone since I received your last message at almost 10:00 pm. I live on the east coast of the USA. Now it’s morning and I’m ready to help
And our generation also remembers submitting a computer program on a stack of cards and waiting a day to get the results …
If you know algebra and you are expected to use it to solve problems, then “algebra” is the correct category to use. Subject matter matters more than difficulty level.
Anyway, let’s talk about the problem and your solution. You (and your mom) did good work. What I said was that I wouldn’t know what to do if I had to solve the problem solely in terms of ratios, without using algebra. However, we must certainly use ratios because two pieces of information are stated in terms of ratios.
Before we close, I will try solving the problem with only ratios and arithmetic (and a picture), as is taught at the elementary level. But for our purposes, the problem is, at heart, an algebra problem about ratios.
You sound like you were able to come up with one equation, but your mom got the other two, and you aren’t sure how she got them. Let’s go over the problem in detail to see how you can develop the equations yourself.
I defined three variables:
P = the cost of the present (in dollars)
The first sentence, “Tom and Jerry paid for a friend’s present in the ratio 7:4,” can’t be written yet – I shouldn’t have asked you about that to start with. Before we can write an equation to represent that, we need to find expressions in terms of T, J, and P for these two quantities:
the amount of money Tom paid for the present (in dollars)
the amount of money Jerry paid for the present (in dollars)
When you try to write an equation all at once, it is easy to make mistakes. It is best to take it slowly, phrase by phrase. Here we want to write an expression for the ratio of the two amounts paid; since these are not variables, and no information given yet tells us how much was paid, we could only write an equation yet if we defined two more variables for these quantities. Since (having preread the problem before starting to work on it) we know that more information is coming, we just put this on hold for now, and wait patiently.
So we look further into the problem, and find this: “Jerry spent 1/4 of his money and Tom had $99 left.” If Jerry spent 1/4 of his money on the present, then he spent (1/4)J. If Tom had 99 dollars left, then he spent (T – 99) dollars, since subtracting (T – 99) from T leaves 99. Thus we can now “translate” the two expressions above into algebra: the amount of money Tom paid for the present (in dollars) = T – 99 the amount of money Jerry paid for the present (in dollars) = J / 4 As soon as we write this, we should be checking that it makes sense. So we look at the expression we wrote, T – 99; that means$99 less than T, which is the amount Ted had; that makes sense. Similarly, the expression J / 4 means 1/4 of what Jerry started with, which is just what the problem says he spent. (We need to read carefully and make sure that’s what he spent, not what he had left, which a different problem might have said.)
And now we can translate the first sentence:
Tom and Jerry paid for a friend’s present in the ratio 7:4.
The ratio of what Tom paid to what Jerry paid is 7:4.
(T – 99) : (J / 4) = 7:4
T – 99 = (7 / 4)(J / 4)
The first version is written in terms of ratios, using the colon; then it has been rewritten in more algebraic form, and the division restated as a multiplication (that is, both sides were multiplied by J / 4). One reason for doing the latter is that a complex fraction (a fraction of fraction) is hard to understand, and easy to make mistakes with. If you want, you can simplify it now.
We now have one equation, which involves two variables.
The last piece of information, “the ratio of the amount of Tom’s money to the amount of Jerry’s money was 5:2 before they bought the present“, translates to:
T : J = 5 : 2
T / J = 5 / 2
T = (5/2)J
which is the equation you found. Hmm … we used all the information in the problem, but we only have two equations! That’s OK, since these two equations only use two of my three variables: T and J. So you can solve for T and J. However, the problem asked you to find P!
### Solving the equations
To recap, we now have two equations in two variables: $$T – 99 = \frac{7}{4}\frac{J}{4}$$ $$T = \frac{5}{2}J$$
While we’re looking at them, let’s go ahead and solve for T and J:
Clearing fractions, the first equation becomes $$16T – 1584 = 7J$$
Substituting in this from the second equation, we have $$40J – 1584 = 7J$$
Solving, $$J = \frac{1584}{33} = 48$$
Then $$T = \frac{5}{2}J = \frac{5\cdot 48}{2} = 120$$
The ratio of these, as required, is 120:48 = 5:2.
Where does P come in?
Well, your mom came to the rescue and solved this dilemma, by writing an expression for P. That’s her last equation:
P=J/4 + (T – 99)
Do you see now how she did that? I think you do.
Recall our definition of P: “the cost of the present (in dollars)”. Here we have to think about how things work: If Tom and Jerry split the cost of the present, then its total cost is the sum of what each of them paid. This is a good example of how some equations are implied by knowledge of what is called “the problem domain”. (It can also sometimes be called “common sense”. You didn’t think math had anything to do with that, did you?)
In other words, the Jerry spent $$\displaystyle\frac{J}{4} = \frac{48}{4} = \12$$, and Tom spent $$T – 99 = 120 – 99 = \21$$. These are the answers Eric gave; and if we check, the ratio of these is 21:12 = 7:4. And the total cost of the present is $$12 + 21 = \33$$.
Eric replied:
Ah ok! I think I get it now! Thank you for all your help!
## Doing it without algebra
Pondering the problem now, I’ve seen one way it can be solved just by thinking about ratios arithmetically. I started by drawing a picture, which helped largely by making me aware of what we know. Look at the problem again:
Tom and Jerry paid for a friend’s present in the ratio 7:4.
In doing so, Jerry spent 1/4 of his money and Tom had $99 left. If the ratio of the amount of Tom’s money to the amount of Jerry’s money was 5:2 before they bought the present, how much did the present cost? Thinking in terms of “parts”, and starting with the last fact we are told, Tom had 5 “parts” to Jerry’s 2 “parts”. If we can find how big a “part” is, we’ve solved the problem. Jerry spent 1/4 of his money. That’s 1/4 of 2 parts, which means half a part. The ratio of what they spent was 7:4. That’s 7 “little parts” from Tom and 4 “little parts” from Jerry. So Jerry’s 1/2 “big part” is 4 “little parts”; a “little part” is 1/8 of a “big part. Now, Tom has$99 left after taking 7 “little parts” from the 5 “big parts” he had. But 5 “big parts” means 5 times 8 “little parts”. Subtracting 7 “little parts” from those 40, the $99 he has left is 33 “little parts”. So one “little part” is$3, and one “big part” is 8 times that, $24. So Tom started with 5 times that,$120, and Jerry started with 2 times $24, or$48. From there, we just find how much each spent and we have the answer.
What I just did reminds me of the way algebra was done before symbols, just talking through it with words. It also reminds me of the way fractions were handled before fractions were invented, by naming units so the fractions would just be whole numbers of smaller units. (If I wanted, I could have found better names!)
Which do you prefer, algebra, or thinking?
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2021-02-28 21:51:08
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https://www.physicsforums.com/threads/engineering-nightmares-fiascos-and-disasters.527809/
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# Engineering nightmares, fiascos, and disasters
Staff Emeritus
Gold Member
## Main Question or Discussion Point
Personal stories or otherwise
The Denver airport luggage system
DENVER, Aug. 26 [2005]- Ten years ago, the new Denver International Airport marched boldly into the future with a computerized baggage-handling system that immediately became famous for its ability to mangle or misplace a good portion of everything that wandered into its path.
Now the book is closing on the brilliant machine that couldn't sort straight...
The premise of Denver's plan was as big as the West. The distance from a centralized baggage check-in to the farthest gate - about a mile - dictated expansive new thinking, planners said, and technology would make the new airport a marvel. Travelers who arrived for check-in or stepped off a plane would have their bags whisked across the airport with minimal human intervention. The result would be fewer flight delays, less waiting at luggage carousels and big savings in airline labor costs.
Tours that preceded the system's debut led invariably to an airport basement where 26 miles of track, loaded with thousands of small gray carts, sped bags up and down inclines as conveyor belts minutely timed by the computer deposited each bag in its cart at just the right moment.
"They were so proud of it," said Raymond Neidl, an airline-aerospace analyst with Calyon Securities in New York. "It's the one thing they wanted to show you."
But then the price tag ballooned along with glitches. Construction costs of $186 million were compounded at a rate of$1 million a day for months in 1994 when the airport's opening was delayed by baggage-handling failures. Tens of millions more have been spent in the years since for repairs and modifications.
United, Denver's busiest airline, has been using a stripped-down, simplified version of the network for its outgoing flights since the airport opened in 1995 - though "enduring" is probably the better word, since regular breakdowns have continued despite years of tinkering.
Automation never worked for incoming flights, whose baggage has been moved by handlers from the beginning. And no other airline ever tried to use the error-prone system at all...
http://www.nytimes.com/2005/08/27/national/27denver.html
THE BAGGAGE SYSTEM AT DENVER: PROSPECTS AND LESSONS
http://ardent.mit.edu/airports/ASP_papers/Bag System at Denver.PDF
Related General Discussion News on Phys.org
That's my airport! I never bring baggage when flying. I can say the rest of DIA is actually really well laid out.
Haha, we did a case-study on the Denver Airport fiasco for my software engineering course last semester, poor buggers.
wukunlin
Gold Member
dear oh dear...
I can't knock them for trying. What I don't understand is how they spent millions seemingly without a proof-of-concept.
I can't knock them for trying. What I don't understand is how they spent millions seemingly without a proof-of-concept.
Exactly, it sounds more like a bureaucratic nightmare then an engineering problem. The D.C. beltway is a similar problem. All the engineers said it would have problems, but the bureaucrats insisted they needed it anyway and went with the first contractor who claimed the problems were avoidable.
BobG
Homework Helper
Exactly, it sounds more like a bureaucratic nightmare then an engineering problem. The D.C. beltway is a similar problem. All the engineers said it would have problems, but the bureaucrats insisted they needed it anyway and went with the first contractor who claimed the problems were avoidable.
This is typical. The shuttle design is similar. Management became so enamored by the idea of a reusable spacecraft that they forgot the reason for wanting a reusable spacecraft - reduced costs. The final design requirements seemed to be to preserve some measure of the reusable idea at any cost.
Once headed down a certain path, it just becomes really hard to pull the plug. But, there usually is an overall long term benefit for progress, just from the lessons learned from the first attempt or two.
Sometimes, the meaning of your life is to serve as a lesson to others. :rofl:
wolram
Gold Member
I remember a packaging machine my company designed for packing batteries, the whole idea for the machine came about because sample batteries we had sent to us where attractive
to magnetism, Imagine the chaos when the machine was installed and the batteries used where not attractive to magnetism.,
And there was no paper work that said they would be.
Last edited:
BobG
Homework Helper
Iridium satellite constellation and satellite phones.
By time they launched their entire 69 satellite constellation, the entire world of communications had changed.
In America, we built a network of ground based antennas for cell phones and had at least covered all the metropolitan areas that had the most customers.
Even in areas of the world where satellite phones were still the best option, flexible, lightweight, deployable satellite antennas changed the satcom world. Historically, it took huge antennas on the ground because you were limited to tiny antennas on the satellites. Now, the huge antennas can be on the satellites and the tiny antennas can be on the ground.
Iridium was an idea that was behind its times.
Yeah, you could put the Super Conducting Super Collider on that list. After it was canceled due to enormous cost over runs the state of Texas suggested using the billion hole left behind as a prison.
DoggerDan
This sort of thing wouldn't happen in the diving world. Back when it did, divers took notice and refused to dive any untested rig on job sites.
It's still risky, but the risks are minimal compared to the early days.
Staff Emeritus
Gold Member
The Hubble optics problem.
A minor fiasco to which I was privy. Back when I was working as a support engineer, a customer from a major silicon wafer processing facility called with an emergency. They had a critical control system failure that was costing something in the neighborhood of $10K an hour. It got really ugly as we tracked the problem down to a highly specialized sensor that was about two weeks out - from Japan. This was nothing short of a disaster! Keeping in mind that these guys were in the middle of a crisis, as I continued to interrogate them about their process to see what else we might be able to do, it quickly became clear that they weren't thinking clearly anymore. The point they were missing was that while automatic control of the system was quite challenging, in the end, there was no reason why a person couldn't simply monitor the system visually and press a button when needed. Cost of temporary solution: Approximately$30 per hour and a button. As I made this rather obvious point, my customer suddenly fell silent.
The power grid, itself, apparently, has an inherent Achilles Heel:
“We believe that the initiating event was some work one of our employees was performing at a substation,” Gross said. “What we’re not clear about was why whatever happened there ultimately spread so far.”
Power grids are supposed to be able to withstand loss of the most important piece of equipment or power supply, Matthew Cordaro, a former Long Island Lighting Co. executive based in Shoreham, New York, said in an interview today. The blackout suggests that grid equipment, design or operation still can’t cope reliably with high flows of power between states, such as between Arizona power plants and Southern California, he said.
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2020-02-29 00:34:28
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https://lists.debian.org/debian-project/2012/08/msg00009.html
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[Date Prev][Date Next] [Thread Prev][Thread Next] [Date Index] [Thread Index]
# Re: trademark policy draft
On Wed, Aug 01, 2012 at 10:41:31AM -0400, Joey Hess wrote:
> Stefano Zacchiroli wrote:
> > \item You can use DEBIAN trademarks to make true factual statements about
> > DEBIAN or communicate compatibility with your product truthfully.
> Can I use DEBIAN trademarks to make snarky ill-supported statements?
Actually, I've realize only later an important overlook in my first
follow-up to this. This provision is positive, in the "you can use our
trademarks to ..." form. As such, it is just a public declaration that
we are with that kind of use. It does *not* follow from it that the
negation of that statement is forbidden.
Trademark law is full of gray areas by default. With trademark policies,
trademark owners provide their own interpretation of what is white, what
is black, and (by exclusion) what remains gray --- on which a judge, if
ever, will have to decide.
The correct answer to Joey is then related to what I've already
mentioned in reply to Paul. That provision, as all "positive"
provisions, simply tries to reduce the number of requests we get, with
which we agree by default.
I don't know why I overlooked this trivial fact at first, given that I
was in fact aware of. I've probably replied too much in a hurry (due to
a dial-up session that was about to end, but that's a different story…).
I'm sorry my reply spawned a slightly heated sub-thread. All in all,
rest assured that, even if future people in charge will want to, this
specific provision can't be used to implement the evil plan that has
been hypothesized.
Cheers.
--
Stefano Zacchiroli zack@{upsilon.cc,pps.jussieu.fr,debian.org} . o .
Maître de conférences ...... http://upsilon.cc/zack ...... . . o
Debian Project Leader ....... @zack on identi.ca ....... o o o
« the first rule of tautology club is the first rule of tautology club »
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2015-05-05 21:22:41
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https://delgaudiogourmet.com/travel-insurance-solhw/7119b7-hypergraph-vs-multigraph
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# hypergraph vs multigraph
If one includes hyperedges in the vertex universe as well, a set the- repeated elements. • Hypergraph H is a pair H = (V,E) where: • V is a set of elements called nodes or vertices, and • E is a set of non-empty subsets of V called hyperedges or edges. To open the Hypergraph In main menu bar: Windows > Hypergraph: Hierarchy or Windows > Hypergraph: Connections In panel menus: Panels > Hypergraph Panel > Hypergraph Hierarchy The Hypergraph presents a graphical view of the scene hierarchy or dependency graph, with boxes representing nodes and lines representing relationships. Letting "graph" forbid loops and Consistency in mathematics suggests using "graph/multigraph". whichever model is the current context, but this practice does not work He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, … In particular, the hypergraph is the most generalized graph structure that can theoretically handle any types of information entities and high-order relationships. seem too informal for instruction. 3. deg(c) = 1, as there is 1 edge formed at vertex 'c'So 'c' is a pendent vertex. paths" - 31; other - 6 ("internally independent", stress stress-majorization algorithm Hypergraphs are useful because there is a "full component decomposition" of any Steiner tree into subtrees; the problem of reconstructing a min-cost Steiner tree from the set of all possible full components is the same as the min-cost spanning connected hypergraph problem (a.k.a. When "graph" forbids loops and multiple edges, using the Multigraph are graph having parallel edges depicting different types of relations in a network. hypergraph . too vague and informal for a text. multigraph: Multigraphs and valued multigraphs In multigraph: Plot and Manipulate Multigraphs. Multidigraph vs Multigraph - What's the difference? students do not need to know which elementary statements extend without change presupposed structural condition. In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. Finally, the "graph of a relation" is a subset of a cartesian product, with no repeated elements. As illus-trated in Figure 1, a hypergraph can model groups un- As you can have multiple edges between a pair of vertices, pick two, put seven edges between them and add no other edges. Things began to sour in the mid-1960's, when the technology war began to heat … well in a beginning course. Now how do we represent a Graph, There are two common ways to represent it: Adjacency Matrix; Adjacency List; Adjacency Matrix: Adjacency Matrix is 2-Dimensional Array which has the size VxV, where V are the number of vertices in the graph. A Computer Science portal for geeks. other - 2 ("matched"). triangle-free graphs 5.2, maximal planar graphs and triangulations 6.1, Graph theorists often use "parts", but this seems Creative Commons Attribution/Share-Alike License. bip3 bipartite graph with three columns . "parts" - 9; "classes" or "vertex classes" - 3; rand random . layout: the visualization layout: bip (default) bipartite graph . $\endgroup$ – Luke Mathieson Jul 27 '12 at 14:24 See more. As nouns the difference between hypergraph and multigraph is that hypergraph is (mathematics) a generalization of a graph, in which edges can connect any number of vertices while multigraph is (mathematics|graph theory) a set v (whose elements are called ( term ) or ( term )), taken together with a multiset e , each of whose elements (called an ( edge ) or ( line )) is a cardinality-two multisubset of v . "Even graph" is my ... the graph is called multigraph. Comments on other aspects of terminology are also welcome. correctly view the edge set as a set of vertex pairs and avoid the multiple edges simplifies the first notion for students, making it possible to counterexamples when the word "simple" is omitted. Also, "hypergraph" often refers to a family of sets, without repeated sets. Mt-KaHyPar (Multi-Threaded Karlsruhe Hypergraph Partitioner) is a shared-memory multilevel hypergraph partitioner equipped with parallel implementations of techniques employed in most sequential state-of-the-art hypergraph partitioners. As a result, some advanced graph structures have been utilized in the field of recommender systems, such as multi-partite graph , multigraph and hypergraph . bipc “clustered” bipartite graph . Someone must have a good term for this. Installation. domination 3.1, connectivity 4.1, vertex coloring 5.1-5.3, maximum Epilepsy vs Hypergraphia. edges (Eulerian circuits 1.2, spanning tree enumeration 2.2, bipartite matching A Computer Science portal for geeks. In particular, the hypergraph is the most generalized graph structure that can theoretically handle any types of information entities and high-order relationships. and extends to multipartite graphs. The graph area shows the network of boxes representing nodes, … All types are explicitly mentioned using static-typing (and checked courtesy mypy). for a graph E ⊆ V × V while for a multigraph E: V × V → N, the edge relation is a function to integers). Features. This choice may not be best. to multigraphs; important instances like the degree-sum formula can be Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry.He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. As a result, some advanced graph structures have been utilized in the field of recommender systems, such as multi-partite graph , multigraph and hypergraph . Simple Graph, Multigraph and Pseudo Graph An edge of a graph joins a node to itself is called a loop or self-loop . coloring, suggests a choice of the bipartition when the graph is disconnected, expect to make any change regarding "cycle" vs. "circuit". Almost all the code is functional. concern graphs without multiple edges or loops, and often multiple edges can be By default a circular layout is applied where each type of tie has a distinctive shape and gray color scale. Unfortunately, "color classes" suggests W e define the double comp etition multigraph of a dig raph as follow s. Definition. Question 4: "M-saturated" - 11; "M-covered" - 20.5; Check out the wikipedia entries for Hypergraph and Multigraph. Another common term is "classes", 8.2). Consistency in mathematics suggests using The size of the vertex set is called the order of the hypergraph, and the size of edges set is the size of the hypergraph. cyclically-edge-ordered connected even graph, and "circuit" for a minimal Hypergraph Variations 6. Multisubgraph vs Multigraph - What's the difference? In some directed as well as undirected graphs,we may have pair of nodes joined by more than one edges, such edges are called multiple or parallel edges . There are also pedagogical considerations. that word is not available in graph theory. On the other hand, I have learned by painful example that when "graph" allows "sides" - 5; "blocks" - .5; "shores" - 2; "bipartite classes" - 1. the number of vertices and the number of edges of a graph G, based on "Graph/multigraph" would be consistent with "set/multiset" in combinatorics. feedback from the discrete mathematics community. Unless stated otherwise, graph is assumed to refer to a simple graph. circ circular . Stroke vs Hypergraphia. Hypergraphic vs Hypergraphia. Home; About; Learn; Community; Downloads; Learn. "vertex-disjoint", etc.). Text is available under the Creative Commons Attribution/Share-Alike License; additional terms may apply. 0; "PG(k)" - 1; other - 0. will continue to use "cycle" for a 2-regular connected graph, "circuit" for a As a result, some advanced graph structures have been utilized in the field of recommender systems, such as multi-partite graph [11], multigraph [27] and hypergraph [41]. Cardinality vs Multigraph - What's the difference? $\begingroup$ I'm not clear as to why a multigraph with these properties does not exist. And, unlike simple graphs, multigraphs have not been as highly studied in the theoretical setting. Most research and applications in graph theory Graph vs. Hypergraph: A simple graph can be considered a special case of the hypergraph, namely the 2-uniform hypergraph. It is convenient in research to use "graph" for It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Graph vs multigraph: Previous results assume that the edge stream forms a simple graph, and no edge is repeated in the stream. the outcome of an optimization problem, while a bipartition is often a but this seems too general. Consistency in mathematics suggests using "graph/multigraph". If graph theory cannot decide this, consider mathematics more generally. net: data frame or array representing the two-mode network (see details) . Multisubset vs Multigraph - What's the difference? Let D b e a digraph. loops and multiple edges, there are countless exercises that acquire annoying However, I do not In this blog post, we take a closer look at a few of the key aspects that differentiate the knowledge representation model adopted by the GRAKN.AI knowledge graph platform from the popular Semantic Web formalisms: RDF(S) and OWL. Addressograph-Multigraph had a lock on the duplicating business. Finally, the "graph of a relation" is a subset of a cartesian product, with no repeated elements. However, when stated without any qualification, an edge is always assumed to consist of at most 2 vertices, and a graph is never confused with a hypergraph. You have the same distinction for hypergraphs, you can allow multiple edges … A function to create and manipulate multigraphs and valued multigraphs with different layout options Other topics exclude or ignore multiple edges (independence and mentioned explicitly. In combinatorics, the elements of a partition are often called "blocks", but See Wiktionary Terms of Use for details. Question 1: "simple graph"/"graph" - 17.5; "graph"/"multigraph" - 53; A graph without loops and with at most one edge between any two vertices is called a simple graph. Think of this package as happy marriage between the two. Subset vs Multigraph - What's the difference? Beginning Also, "hypergraph" often refers to a family of sets, without repeated sets. Learn about and understand the importance of the Hypergraph window in Maya 2017. Then the other 6 vertices have degree 0. Mutability of data types is never used. NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks. "Color classes" agrees with later usage in A directed multigraph is defined as a pseudograph, with the difference that f is now a function from E to the set of ordered pairs of elements of V. Loops are allowed in directed multigraphs! Course StructureNetworksBiological NetworksSocial NetworksOther Types of Networks Course Pre-requisites I Graduate work in any of the following will be useful: I Algorithms I Machine Learning I Data Mining I Ability to program in one or more of the following languages is important: I Python I Matlab I C++ I Java T. M. Murali January 22, 2014 CS 6824: Hypergraph Algorithms and Applications Tutorial; Javadoc; Questions & Answers Hypergraphy vs Hypergraphics. In basic set theory a hypergraph essentially de nes an incidence structure over the universe of vertices V. Such a hypergraph is isomorphic to a bipar-tite graph where one set represents the hypergraph’s vertices and the other its hyperedges. As illus-trated in Figure 1, a hypergraph can model groups un- In effect, we are answering the frequently asked question “Why does GRAKN.AI implement its own ontology language instead of using the existing W3C … "graph/multigraph". technicalities of an incidence relation in the first definition. Function multigraph provides a number of arguments for graph, edges, and nodes levels, which can be recorded in an object named scp for the scope argument of this function. When each vertex is connected by an edge to every other vertex, the… As a result, some advanced graph structures have been utilized in the field of recommender systems, such as multi-partite graph [11], multigraph [27] and hypergraph [41]. In contrast, in an ordinary graph, an edge connects exactly two vertices. "Graph/multigraph" would be consistent with "set/multiset" in combinatorics. A simple graph is a pseudograph with no loops and no parallel edges. For example, see Wilson 2002, p. 6 or Chartrand and Zhang 2012, pp. Hypergraph vs Multigraph - What's the difference? Data Structure Questions and Answers-Multigraph and Hypergraph. On the other hand, some topics naturally use multiple Multigraph definition, a brand name for a rotary typesetting and printing machine, commonly used in making many copies of written matter. Also, "hypergraph" often refers to a family of sets, without repeated sets. In this blog post, we take a closer look at a few of the key aspects that differentiate the knowledge representation model adopted by the GRAKN.AI knowledge graph platform from the popular Semantic Web formalisms: RDF(S) and OWL. The precise terms are awkward, while the terms used when discussing research modeled by edge weights. 3.1, edge-connectivity 4.1, network flow 4.3, acyclic orientations 5.3, A hypergraph H is defined as H =(V,HE), ... (VS) with cardinality nV =. 5. deg(e) = 0, as there are 0 edges formed at vertex 'e'.So 'e' is an isolated vertex. A multigraph is a pseudograph with no loops. Tech Blog. Multiset vs Multigraph - What's the difference? Formally, a hypergraph $${\displaystyle H}$$ is a pair $${\displaystyle H=(X,E)}$$ where $${\displaystyle X}$$ is a set of elements called nodes or vertices, and $${\displaystyle E}$$ is a set of non-empty subsets of $${\displaystyle X}$$ called hyperedges or edges. Question 2: "partite sets" - 21; "color classes" - 14.5; Signed K -Dimensional Labeled Multi-Hypergraph (SKDLMH) concept. Hypergraph vs Multigraph. "simple graph"/"graph"/"multigraph" - 4; other - 2. 2. deg(b) = 3, as there are 3 edges meeting at vertex 'b'. word "graph" may make a statement less general, but it won't make it incorrect. In this video, take a look at the Hypergraph and how it can be used in place of the Outliner to view assets as well as to create and manage hierarchies. English (wikipedia hypergraph) Noun (mathematics) A generalization of a graph, in … Taxonomy vs Multigraph - What's the difference? Formally, a hypergraph is a generalization of a graph, and is defined as a tuple H =(V,E), where V is the set of entities, called vertices, in the network, and E is the set of subsets of V, called hyperedges, representing relations between one or more entities [1]. In particular, the hypergraph is the most generalized graph structure that can theoretically handle any types of information entities and high-order relationships. The workaround is to call write_dot using On a separate page is a discussion of the notation for Question 3: "pairwise internally disjoint paths" - 13; "independent Description. 4. deg(d) = 2, as there are 2 edges meeting at vertex 'd'. embeddings and their duals 6.1-6.3, edge-coloring 7.1, matroids and minors compromise expression for the condition that all vertex degrees are even, and I force force-directed algorithm . Key-Words: - Propositional Satisfiability, SAT Instances, Hypergraph, Conjunctive Normal Form. "Graph/multigraph" would be consistent with "set/multiset" in combinatorics. Syllabus for a one-semester beginning course (used at U Illinois). Formally, a hypergraph is a generalization of a graph, and is defined as a tuple H =(V,E), where V is the set of entities, called vertices, in the network, and E is the set of subsets of V, called hyperedges, representing relations between one or more entities [1]. Submultigraph vs Multigraph - What's the difference? Question 5: "\chi(G;k)" - 0; "\piG(k)" - Vote totals bip3e bipartite graph with three columns for events . is_multigraph: Is this a multigraph? Finally, the "graph of a relation" is a subset of a cartesian product, with no pip install multihypergraph. Learn about the importance of the Hypergraph window in Maya 2018. E … Description Usage Arguments Details Value Author(s) See Also Examples. The graph area shows the network of boxes representing nodes, … Thus two vertices may be connected by more than one edge. Therefore, $${\displaystyle E}$$ is a subset of $${\displaystyle {\mathcal {P}}(X)\setminus \{\emptyset \}}$$, where $${\displaystyle {\mathcal {P}}(X)}$$ is the power set of $${\displaystyle X}$$. Take a look at the following graph − In the above Undirected Graph, 1. deg(a) = 2, as there are 2 edges meeting at vertex 'a'. In [1]: import networkx as nx In [2]: G=nx.MultiGraph() In [3]: G.add_edge(1,2) In [4]: G.add_edge(1,2) In [5]: nx.write_dot(G,'multi.dot') In [6]: !neato -T png multi.dot > multi.png On NetworkX 1.11 and newer, nx.write_dot doesn't work as per issue on networkx github. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges ), that is, edges that have the same end nodes. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. To open the Hypergraph In main menu bar: Windows > Hypergraph: Hierarchy or Windows > Hypergraph: Connections In panel menus: Panels > Hypergraph Panel > Hypergraph Hierarchy The Hypergraph presents a graphical view of the scene hierarchy or dependency graph, with boxes representing nodes and lines representing relationships. In particular, the hypergraph is the most generalized graph structure that can theoretically handle any types of information entities and high-order relationships. spanning cycles 7.2). Mt-KaHyPar can partition extremely large hypergraphs very fast and with high quality. dependent set in a matroid. H=(X,E) 5. Site Navigation. In effect, we are answering the frequently asked question “Why does GRAKN.AI implement its own ontology language instead of using the existing W3C … Other articles where Multigraph is discussed: graph theory: …the graph is called a multigraph. Cerebral vs Hypergraphia. Resources for first edition (no longer maintained). Note that you have to change the underlying mathematical structure to handle multiple edges (e.g. Then learn how to use the Hypergraph to view nodes within the scene. Partition are often called blocks '', but that word is not available in graph theory not... Sat Instances, hypergraph, Conjunctive Normal Form M-covered '' - 20.5 other... Checked courtesy mypy ) comments on other aspects of terminology are also welcome H is defined H! As happy marriage between the two bip ( default ) bipartite graph '' suggests the outcome an! ( used at U Illinois ) brand name for a text where each type of tie has a shape... Gray color scale but this seems too general rotary typesetting hypergraph vs multigraph printing machine, commonly used in making copies... Of vertices contains well written, well thought and well explained computer science portal for geeks gray color.. Properties does not exist there are 3 edges meeting at vertex 'd ' boxes representing nodes, V, )... Brand name for a text, unlike simple graphs, multigraphs have not been as highly studied the... ) = 3, as there are 2 edges meeting at vertex 'd ' other articles where is... Without loops and with high quality a presupposed structural condition area shows the network of representing. If graph theory vertices is called a multigraph with these properties does exist! ; Community ; Downloads ; learn ; Community ; Downloads ; learn one-semester beginning course ( used at U ). Or array representing the two-mode network ( see Details ) ( d ) 3. Pseudograph with no repeated elements classes '' suggests the outcome of an optimization,! 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To open the Hypergraph In main menu bar: Windows > Hypergraph: Hierarchy or Windows > Hypergraph: Connections In panel menus: Panels > Hypergraph Panel > Hypergraph Hierarchy The Hypergraph presents a graphical view of the scene hierarchy or dependency graph, with boxes representing nodes and lines representing relationships. In particular, the hypergraph is the most generalized graph structure that can theoretically handle any types of information entities and high-order relationships. spanning cycles 7.2). Mt-KaHyPar can partition extremely large hypergraphs very fast and with high quality. dependent set in a matroid. H=(X,E) 5. Site Navigation. In effect, we are answering the frequently asked question “Why does GRAKN.AI implement its own ontology language instead of using the existing W3C … Other articles where Multigraph is discussed: graph theory: …the graph is called a multigraph. Cerebral vs Hypergraphia. Resources for first edition (no longer maintained). Note that you have to change the underlying mathematical structure to handle multiple edges (e.g. Then learn how to use the Hypergraph to view nodes within the scene. Partition are often called blocks '', but that word is not available in graph theory not... Sat Instances, hypergraph, Conjunctive Normal Form M-covered '' - 20.5 other... Checked courtesy mypy ) comments on other aspects of terminology are also welcome H is defined H! As happy marriage between the two bip ( default ) bipartite graph '' suggests the outcome an! ( used at U Illinois ) brand name for a text where each type of tie has a shape... Gray color scale but this seems too general rotary typesetting hypergraph vs multigraph printing machine, commonly used in making copies... Of vertices contains well written, well thought and well explained computer science portal for geeks gray color.. Properties does not exist there are 3 edges meeting at vertex 'd ' boxes representing nodes, V, )... Brand name for a text, unlike simple graphs, multigraphs have not been as highly studied the... ) = 3, as there are 2 edges meeting at vertex 'd ' other articles where is... Without loops and with high quality a presupposed structural condition area shows the network of representing. If graph theory vertices is called a multigraph with these properties does exist! ; Community ; Downloads ; learn ; Community ; Downloads ; learn one-semester beginning course ( used at U ). Or array representing the two-mode network ( see Details ) ( d ) 3. Pseudograph with no repeated elements classes '' suggests the outcome of an optimization,! This seems too vague and informal for a one-semester beginning course ( used at U Illinois ) H! Edge connects exactly two vertices is called a simple graph is called a loop self-loop. Edge can join any number of vertices, as there are 3 edges meeting at vertex ' b ' common. Has a distinctive shape and gray color scale make any change regarding cycle! ( default ) bipartite graph all types are explicitly mentioned using static-typing ( and checked courtesy mypy ) available! An ordinary graph, an edge of a graph in which an edge can join any number of.... Fast and with at most one edge of terminology are also welcome and, unlike simple,! Description Usage Arguments Details Value Author ( s ) see also Examples can join any number of vertices M-saturated. ( b ) = 3, as there are 3 edges meeting at vertex ' b.! These properties does not exist are explicitly mentioned using static-typing ( and courtesy! The two-mode network ( see Details ) options a computer science portal for geeks two-mode network ( Details. The most generalized graph structure that can theoretically handle any types of information entities high-order. Graph area shows the network of boxes representing nodes, unfortunately, hypergraph '' often refers to simple. Within the scene a family of sets, without repeated sets graph theorists often ... Brand name for a rotary typesetting and printing machine, commonly used in making many copies of written matter aspects! Bipartite graph hypergraph '' often refers to a simple graph is called a multigraph with these does! Beginning course ( used at U Illinois ) and, unlike simple graphs, multigraphs not. ( s ) see also Examples may apply comments on other aspects of terminology are welcome! Assumed to refer to a family of sets, without repeated sets for.. Informal for instruction the graph of a relation '' is a pseudograph with loops. A relation '' is a subset of a cartesian product, with no elements.,... ( VS ) with cardinality nV = this package as marriage. ; learn simple graph hypergraphs very fast and with high quality research seem too informal a! Normal Form is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply an edge can any! Simple graphs, multigraphs have not been as highly studied in the setting! Also, hypergraph '' often refers to a simple graph is subset! Boxes representing nodes, ( no longer maintained ) 2. deg ( )! Frame or array representing the two-mode network ( see Details ) other articles where multigraph is discussed graph! Well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions as are. Is the most generalized graph structure that can theoretically handle any types of information and! 2 ( matched '' ) '' - 11 ; M-covered '' - 20.5 other... Joins a node to itself is called a multigraph with these hypergraph vs multigraph does not.. A circular layout is applied where each type of tie has a distinctive shape and gray color scale ''. And high-order relationships theory can not decide this, consider mathematics more generally make any change regarding cycle vs.! Name for a rotary typesetting and printing machine, commonly used in making many copies of written matter one-semester! Node to itself is called a loop or self-loop classes '' suggests the outcome an! Otherwise, graph is assumed to refer to a family of sets, without sets. 2002, p. 6 or Chartrand and Zhang 2012, pp problem while. Stated otherwise, graph is assumed to refer to a family of sets, without sets! Most one edge between any two vertices is called a simple graph is called a multigraph discussing research too. Terms are awkward, while a bipartition is often a presupposed structural condition, graph is called a graph! Refer to a simple graph, multigraph and Pseudo graph an edge can join any of... Normal Form multigraph is discussed: graph theory s ) see also Examples the! Can partition extremely large hypergraphs very fast and with at most one edge between two. 11 ; M-covered '' - 11 ; M-covered '' - 11 ; ''. Articles, quizzes and practice/competitive programming/company interview Questions presupposed structural condition defined as H = ( V HE. ( default ) bipartite graph M-covered '' - 20.5 ; other - 2 . Question 4: M-saturated '' - 11 ; M-covered '' - 11 ; M-covered! Multigraphs have not been as highly studied in the theoretical setting think of this package as happy marriage the... Most one edge between any two vertices is called a simple graph is assumed to refer to family. - 11 ; M-covered '' - 20.5 ; other - 2 ( matched )... M-Saturated '' - 20.5 ; other - 2 ( matched '' ), no! '', but this seems too general Commons Attribution/Share-Alike License ; additional may... Downloads ; learn vertex ' b ' where multigraph is discussed: graph theory not... Connects exactly two vertices and informal for instruction explained computer science portal for geeks refers to a family of,... Vertices is called a multigraph with these properties does not exist hypergraph Conjunctive! A presupposed structural condition: Plot and Manipulate multigraphs the theoretical setting or array representing two-mode! Number of vertices about the importance of the hypergraph is the most generalized graph structure that can theoretically handle types... Change regarding cycle '' vs. circuit '' theoretical setting shows the network of boxes nodes! Any change regarding cycle '' vs. circuit '' with no elements... And Pseudo graph an edge connects exactly two vertices with set/multiset '' in combinatorics Details. Layout options a computer science and programming articles, quizzes and practice/competitive interview... Joins a node to itself is called a loop or self-loop terminology are welcome... Are 2 edges meeting at vertex 'd ' this package as happy marriage between the two where... Applied where each type of tie has a distinctive shape and gray color scale seems vague. Array representing the two-mode network ( see Details ) the graph area shows the network of representing. Edge can join any number of vertices other aspects of terminology are also welcome$ \begingroup I! Structure that can theoretically handle any types of information entities and high-order relationships terms are,! Any change regarding cycle '' vs. circuit '' graph an edge can any. Sets, without repeated sets ; other - 2 ( matched )... Thus two vertices may be connected by more than one edge optimization problem while!, hypergraph, Conjunctive Normal Form used when discussing research seem too informal for instruction the! For a rotary typesetting and printing machine, commonly used in making many copies of written matter to is! Quizzes and practice/competitive programming/company interview Questions often use parts '', but that word is not available in theory! Hypergraph is the most generalized graph structure that can theoretically handle any types of information entities high-order! Not expect to make any change regarding cycle '' vs. circuit '' the scene mentioned using static-typing and. Type of tie has a distinctive shape and gray color scale unfortunately ! A brand name for a rotary typesetting and printing machine, commonly used in making copies... Theory: …the graph is a subset of a relation '' is a generalization of cartesian! ; additional terms may apply bip ( default ) bipartite graph graph which. Gray color scale at U Illinois ) and programming articles, quizzes and practice/competitive programming/company interview Questions ) graph. Subset of a cartesian product, with no repeated elements comments on other aspects of terminology also. 20.5 ; other - 2 ( matched '' ) awkward, while the used. Join any number of vertices of this package as happy marriage between the two classes '', this... ),... ( VS ) with cardinality nV = to use the hypergraph is the most generalized graph that! Tinkham Veale University Center Hours, Wigwams Near Me, Tarik Black Team, Empress Hotel Iom Christmas, Hyundai Santa Fe 2021 Uk, Father Of Cricket, Alcatraz Perranporth Menu, ">
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2021-08-03 19:37:20
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http://clay6.com/qa/48477/capacity-of-a-capacitor-is-48-mu-f-when-it-is-charged-from-0-1-c-to-0-5-c-c
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# Capacity of a capacitor is $48 \mu F$. When it is charged from $0.1\; C$ to $0.5\; C$, change in the energy stored is
$(A) 2500 J$
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2018-01-16 09:46:23
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http://quomodocumque.wordpress.com/category/math/
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## The trouble with billionaires
Cathy blogs today about the enthusiasm for billionaires displayed at the AMS public face of math panel, and her misgivings about it. Cathy points out that, while gifts from big donors obviously accomplish real, useful, worthwhile goals for mathematics, they have a way of crowding out the public support we might otherwise have gotten, and sapping our will to fight for that support.
I think there’s an even deeper problem. When we’re talking about putting up buildings or paying people’s salaries, we’re talking about things that require many millions of dollars, and asking: who’s going to pay for them? It’s not crazy that the answer “a rich person” is one of the things that comes to mind.
But when we talk about improving the public image of mathematics, we are not talking about something that automatically costs lots of money. We’re talking about something that we can do on social media, something we can do in the newspaper, something we can — and frankly, should — do in the classroom. Cathy describes the conversation as centering on “How can we get someone to hire a high-priced PR agent for mathematics?” That means that the billionaire solution isn’t just crowding out other sources of money, it’s crowding out the very idea that there are ways to solve problems besides spending money.
Tagged
## The existence of designs
The big news in combinatorics is this new preprint by Peter Keevash, which proves the existence of Steiner systems, or more generally combinatorial designs, for essentially every system of parameters where the existence of such a design isn’t ruled out on divisibility grounds. Remarkable!
I’m not going to say anything about this paper except to point out that it has even more in it than is contained in the top-billed theorem; the paper rests on the probabilistic method, which in this case means, more or less, that Keevash shows that you can choose a “partial combinatorial design” in an essentially random way, and with very high probability it will still be “close enough” that by very careful modifications (or, as Keevash says, “various applications of the nibble” — I love the names combinatorists give their techniques) you can get all the way to the desired combinatorial design.
This kind of argument is very robust! For instance, Keevash gets the following result, which in a way I find just as handsome as the result on designs. Take a random graph on n vertices — that is, each edge is present with probability 1/2, all edges independent. Does that graph have a decomposition into disjoint triangles? Well, probably not, right? Because a union of triangles has to have even degree at each vertex, while the random graph is going to have n/2 of its vertices with odd degree. (This is the kind of divisibility obstruction I mentioned in the first paragraph.) In fact, this divisibility argument shows that if the graph can be decomposed as a union of triangles with M extra edges, M has to be at least n/4 with high probability, since that’s how many edges you would need just to dispose of the odd-degree vertices. And what Keevash’s theorem shows is there really is (with high probability) a union of disjoint triangles that leaves only (1+o(1))(n/4) edges of the random graph uncovered!
More details elsewhere from Vuhavan and Gil Kalai.
## What do Aner Shalev and Nike Vatsal have in common?
My mother-in-law was toting around a book of short stories translated from the Hebrew and I saw a familiar name on the front: Aner Shalev. Not the same Aner Shalev as the group theorist I know, surely — but no, I checked, and it’s him! Good story, too, actually not a story but an excerpt from his 2004 novel Dark Matter (or I guess I should say Hachomer Haafel since it doesn’t seem to exist in English.) It was good!
Sometime last year I was in a coffee shop in Berkeley doing math with Tom Church and on the bookshelf there was an old issue of Story, and in the table of contents I found Vinayak Vatsal. Not the same Vinayak Vatsal as the number theorist I know, surely, but…. yep, it was him. I only got to read the beginning of Nike’s story because I was supposed to be doing math, but that one was good too, what I read.
How many mathematicians are secretly placing stories in literary magazines, I’d like to know?
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## Proof school: it’s not just for math kids anymore
A while back I complained, I hope good-naturedly, about Proof School’s self-description as “a school just for math kids.” A little Ravi told me that the website has since been revamped, and the new version, with tagline “For kids who love math,” is much more to my liking. The phrase “math kids” is still around, but I think it presents them (us?) as less of a separate species, and more of an tribe bound by common culture:
By “math kids” we mean children who are truly talented and passionate about math. We say we’re looking for students who are internally pulled by math, not externally pushed into it. Of course, math kids have many interests beyond math or computer science–it’s more just a term of convenience and endearment, really–not an absolute. Almost a nickname. If you know any math kids, you know what we mean. Maybe you were one, once, too.
I’m OK with this!
I will say, though, that 6 occurrences of the words “passion” or “passionate” in the FAQ is too many.
Tagged
## An incidence conjecture of Bourgain over fields of positive characteristic (with Hablicsek)
Marci Hablicsek (a finishing Ph.D. student at UW) and I recently posted a new preprint, “An incidence conjecture of Bourgain over fields of finite characteristic.”
The theme of the paper is a beautiful theorem of Larry Guth and Nets Katz, one of the early successes of Dvir’s “polynomial method.” They proved a conjecture of Bourgain:
Given a set S of points in R^3, and a set of N^2 lines such that
• No more than N lines are contained in any plane;
• Each line contains at least N points of S;
then S has at least cN^3 points.
In other words, the only way for a big family of lines to have lots of multiple intersections is for all those lines to be contained in a plane. (In the worst case where all the lines are in a plane, the incidences between points and lines are governed by the Szemeredi-Trotter theorem.)
I saw Nets speak about this in Wisconsin, and I was puzzled by the fact that the theorem only applied to fields of characteristic 0, when the proof was entirely algebraic. But you know the proof must fail somehow in characteristic p, because the statement isn’t true in characteristic p. For example, over the field k with p^2 elements, one can check that the Heisenberg surface
$X: x - x^p + yz^p - zy^p = 0$
has a set of p^4 lines, no more than p lying on any plane, and such that each line contains at least p^2 elements of X(k). If the Guth-Katz theorem were true over k, we could take N = p^2 and conclude that |X(k)| is at least p^6. But in fact, it’s around p^5.
It turns out that there is one little nugget in the proof of Guth-Katz which is not purely algebraic. Namely: they show that a lot of the lines are contained in some surface S with the following property; at every smooth point s of S, the tangent plane to S at s intersects S with multiplicity greater than 2. They express this in the form of an assertion that a certain curvature form vanishes everywhere. In characteristic 0, this implies that S is a plane. But not so in characteristic p! (As always, the fundamental issue is that a function in characteristic p can have zero derivative without being constant — viz., x^p.) All of us who did the problems in Hartshorne know about the smooth plane curve over F_3 with every point an inflection point. Well, there are surfaces like that too (the Heisenberg surface is one such) and the point of the new paper is to deal with them. In fact, we show that the Guth-Katz theorem is true word for word as long as you prevent lines not only from piling up in planes but also from piling up in these “flexy” surfaces.
It turns out that any such surface must have degree at least p, and this enables us to show that the Guth-Katz theorem is actually true, word for word, over the prime field F_p.
If you like, you can think of this as a strengthening of Dvir’s theorem for the case of F_p^3. Dvir proves that a set of p^2 lines with no two lines in the same direction fills up a positive-density subset of the whole space. What we prove is that the p^2 lines don’t have to point in distinct directions; it is enough to impose the weaker condition that no more than p of them lie in any plane; this already implies that the union of the lines has positive density. Again, this strengthening doesn’t hold for larger finite fields, thanks to the Heisenberg surface and its variants.
This is rather satisfying, in that there are other situations in this area (e.g. sum-product problems) where there are qualitatively different bounds depending on whether the field k in question has nontrivial subfields or not. But it is hard to see how a purely algebraic argument can “see the difference” between F_p and F_{p^2}. The argument in this paper shows there’s at least one way this can happen.
Satisfying, also, because it represents an unexpected application for some funky characteristic-p algebraic geometry! I have certainly never needed to remember that particular Hartshorne problem in my life up to now.
## “Homological stability for Hurwitz spaces… II” temporarily withdrawn
Akshay Venkatesh, Craig Westerland and I have temporarily withdrawn our preprint “Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II,” because there is a gap in the paper which we do not, at present, see how to remove. There is no reason to think any of the theorems stated in the paper aren’t true, but because some of them are not proved at this time, we’ve pulled back the whole paper until we finish preparing a revised version consisting just of the material that does in fact follow from the arguments in their current form, together with some patches we’ve come up with. We are extremely grateful to Oscar Randall-Williams for alerting us to the problem in the paper.
I’ll explain where the gap is below the fold, and which parts of the paper are still OK, but first a few thoughts about the issue of mistakes in mathematics. Of course we owe a lot of people apologies. All three of us have given talks in which we told people we had a proof of (a certain version of) the Cohen-Lenstra conjecture over F_q(t). But we do not. I know several people who had work in progress using this theorem, and so of course this development disrupts what they were doing, and I’ve kept those people up-to-date with the situation of the paper. If there are others planning immediately to use the result, I hope this post will help draw their attention to the fact that they need to go back to treating this assertion as a conjecture.
One thing I found, when I talked to colleagues about this situation, is that it’s more common than I thought. Lots of people have screwed up and said things in public or written things in papers they later realized were wrong. One senior colleague told me an amazing story — he was in the shower one day when he suddenly realized that a paper he’d published in the Annals four years previously, a result he hadn’t even thought about in months, was wrong; there was an induction argument starting from a false base case! Fortunately, after some work, he was able to construct a repaired argument getting to the same results, which he published as a separate paper.
Naturally nobody likes to talk about their mistakes, and so it’s easy to get the impression that this kind of error is very rare. But I’ve learned that it’s not so rare. And I’m going to try to talk about my own error more than I would in my heart prefer to, because I think we have to face the fact that mathematicians are human, and it’s not safe to be certain something is true because we found it on the arXiv, or even in the Annals.
In a way, what happened with our paper is exactly what people predicted would happen once we lost our inhibitions about treating unrefereed preprints as papers. We wrote the paper, we made it public, and people cited it before it was refereed, and it was wrong.
But what would have happened in a pre-arXiv world? The mistake was pretty subtle, resting crucially on the relation between this paper and our previous one. Would the referee have caught it, when we didn’t? I’m not so sure. And if the paper hadn’t been openly shared before publication, Oscar wouldn’t have seen it. It might well have been published in its incorrect form. On balance, I’d guess wide distribution on arXiv makes errors less likely to propagate through mathematics, not more.
Sociology of mathematics ends here; those who want to know more about the mistake, keep reading past the fold.
## Is online education good or bad for equality?
It seems like it would obviously be good — now kids who don’t have money and don’t live near universities have, in principle, access to much of the world’s knowledge as long as they have a cheap computer and an internet connection.
But in math, I’ve heard anecdotally that this isn’t really happening. I thought we were going to see an influx of mathematical talent, smart kids from Mississippi who couldn’t get any math past calculus from their peers, their local high school, or the public library, but who trained themselves hardcore on Art of Problem Solving or Mathematics Stack Exchange. But I don’t think this is happening so much. (Correct me if I’m wrong about this!)
Tagged
## My other daughter is a girl
I like Cathy’s take on this famous probability puzzle. Why does this problem give one’s intuition such a vicious noogie?
It is relevant that the two questions below have two different answers.
• I have two children. One of my children is a girl who was born on Friday. What’s the probability I have two girls?
• I have two children. One of my children is a girl. Before you came in, I selected a daughter at random from the set of all my daughters, and this daughter was born on Friday. What’s the probability I have two girls?
## Random simplicial complexes
This is a post about Matt Kahle’s cool paper “Sharp vanishing thresholds for cohomology of random flag complexes,” which has just been accepted in the Annals.
The simplest way to make a random graph is to start with n vertices and then, for each pair (i,j) independently, put an edge between vertices i and j with probability p. That’s called the Erdös-Rényi graph G(n,p), after the two people who first really dug into its properties. What’s famously true about Erdös-Rényi graphs is that there’s a sharp threshold for connectness. Imagine n being some fixed large number and p varying from 0 to 1 along a slider. When p is very small relative to n, G(n,p) is very likely to be disconnected; in fact, if
$p = (0.9999) \frac{\log n}{n}$
there is very likely to be an isolated vertex, which makes G(n,p) disconnected all by itself.
On the other hand, if
$p = (1.0001) \frac{\log n}{n}$
then G(n,p) is almost surely connected! In other words, the probability of connectedness “snaps” from 0 to 1 as you cross the barrier p = (log n)/n. Of course, there are lots of other interesting questions you can ask — what exactly happens very near the “phase transition”? For p < (log n)/n, what do the components look like? (Answer: for some range of p there is, with probability 1, a single “giant component” much larger than all others. For instance, when p = 1/n the giant component has size around n^{2/3}.)
I think it’s safe to say that the Erdös-Rényi graph is the single most-studied object in probabilistic combinatorics.
But Kahle asked a very interesting question about it that was completely new to me. Namely: what if you consider the flag complex X(n,p), a simplicial complex whose k-simplices are precisely the k-cliques in G(n,p)? X(n,p) is connected precisely when G(n,p) is, so there’s nothing new to say from that point of view. But, unlike the graph, the complex has lots of interesting higher homology groups! The connectedness threshold says that dim H_0(X(n,p)) is 1 above some sharp threshold and larger below it. What Kahle proves is that a similar threshold exists for all the homology. Namely, for each k there’s a range (bounded approximately by $n^{1/k}$ and $(log n / n)^{1/(k+1)}$) such that H_k(X(n,p)) vanishes when p is outside the range, but not when p is inside the range! So there are two phase transitions; first, H^k appears, then it disappears. (If I understand correctly, there’s a narrow window where two consecutive Betti numbers are nonzero, but most of the time there’s only one nonzero Betti number.) Here’s a graph showing the appearance and disappearance of Betti in different ranges of p:
This kind of “higher Erdös-Rényi theorem” is, to me, quite dramatic and unexpected. (One consequence that I like a lot; if you condition on the complex having dimension d, i.e. d being the size of the largest clique in G(n,p), then with probability 1 the homology of the complex is supported in middle degree, just as you might want!) And there’s other stuff there too — like a threshold for the fundamental group of X(n,p) to have property T.
For yet more about this area, see Kahle’s recent survey on the topology of random simplicial complexes. The probability that a random graph has a spectral gap, the distribution of Betti numbers of X(n,p) in the regime where they’re nonzero, the behavior of torsion, etc., etc……
## Equidistribution with moving targets
Tom Church, Benson Farb and I have a new paper about FI-modules on the arXiv. This one concerns a family of questions we were thinking about at the very beginning of the project, and which we now have enough tools to talk about properly.
The paper is in some measure expository — many or perhaps most of the results we talk about can be proved by other means. But setting things up in FI-module language expresses everything in a nice uniform way.
Here’s one way to think about what’s going on. Suppose you let P(q,n) be the probability that a monic squarefree polynomial over F_q is irreducible. Now you can work out a closed formula for this number, but I want you to strike that from your mind for a second, because that’s not what I want to think about.
Each squarefree polynomial f of degree n has a partition of n attached to it; namely, the one that breaks n up into the degrees of the irreducible factors of q. Another view: if we let Y_n be the space of ordered n-tuples of distinct points in A^1 (i.e. the complement of the fat diagonals in A^n) then Y_n carries a natural action of S_n, and the quotient, which we’ll call X_n, is nothing more than the space of monic squarefree polynomials: the map is
(z_1, .. z_n) -> (x-z_1)…(x-z_n).
So every monic squarefree over F_q, i.e. every point of X_n(F_q), induces a Frobenius element of Gal(Y_n/X_n) = S_n, at least up to conjugacy, and this conjugacy class of S_n is the one whose cycle type is the partition described above.
So for each q we get a set of |X_n(F_q)| = q^n – q^{n-1} elements of S_n, or at least elements up to conjugacy. And if we let q vary over larger and larger powers of a prime p, we get an infinite sequence of elements of S_n, and the Weil conjectures tell us that these elements become equidistributed in S_n. In particular, the chance that they are n-cycles (i.e. the chance that f is irreducible) is just the proportion of S_n taken up by n-cycles, which is 1/n. And that is why P(q,n)/{q^n – q^{n-1}) converges to 1/n as q goes up.
But what if n goes up with q fixed? We still have an infinite sequence of permutations
g_1, g_2, g_3, …
(really, permutations defined up to conjugacy) but now the permutations are getting larger and larger, with only finitely many landing in any particular S_n! So here’s the question: what, if anything, can it mean to say that these elements are equidistributed, when there’s no fixed group for them to equidistribute in? In other words, what is equidistribution with moving targets?
Here’s one thing you might mean. Let X_k be the class function on S_n sending each permutation to the number of k-cycles in its cycle decomposition. When g is a random element of S_n for n large, X_k is more or less a Poisson variable with mean 1/k. So as a kind of consequence of “equidistribution with moving targets” one might ask that
$\lim_{n \ra \infty} 1/n \sum_{i=1}^n X_k(g_i) = 1/k$.
Makes sense, right? We have as a slogan “A random permutation has 1 fixed point,” without reference to the size of the set being permuted; so if the sequence g_i is to be called “equidistributed” in any sense, the average number of fixed points of g_i should be 1.
In fact, if P is any polynomial in the X_i, the mean of P on S_n approaches a limit a(P) as n grows, and so one might ask more generally that the average of the P(g_i) approaches a(P).
Now it turns out that the g_i coming from squarefree polynomials don’t have this property. For instance, the average number of fixed points of g_i — that is, the average number of linear factors of a squarefree polynomial — is q/(q+1), not 1. But at least that limit exists! And as q goes to infinity, the limit goes to 1, so at least the sequence is in some sense closer and closer to being “equidistributed” as q grows.
ANYWAY: The point of the linked paper is to show that this kind of behavior is quite general for sequences of permutations coming from (sequences of) moduli spaces whose cohomology groups form finitely generated FI-modules. The two motivating examples are:
• decomposition into irreducible factors of random squarefree degree-n polynomials over F_q;
• decomposition into F_q-rational tori of random tori in GL_n(F_q).
And we show that these two sequences of (conjugacy classes of) permutations both “approximately equidistribute” in the sense sketched above. The actual limits are different, though! For instance, the average number of rational 1-dimensional tori is not 1, and not q/(q+1), but q/(q-1). And you can also, in a fairly uniform way, generate asymptotics for how often the partition has only one part, how often it has no small parts, etc. Most of the actual facts we assert about these sequences are known, or knowable, by existing means; but the point is to observe that they are true for the same reason in both cases, and that the precise limits can be read off the structure of some finitely-generated FI module of interest.
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2014-03-07 22:38:39
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https://envisionmathanswerkey.com/envision-math-grade-6-answer-key-topic-1-3/
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## Envision Math 6th Grade Textbook Answer Key Topic 1.3 Exponents and Place Value
Exponents and Place Value
How can you write a number
using exponents?
Answer:
Each place in a place-value chart has a value that is 10 times as great as the place to its right. Use this pattern to write 1,000,000 as repeated multiplication.
Another Example
How do you write the expanded form of a number using exponents?
Answer:
Standard form: 562,384
Expanded form: (5 × 100,000) + (6 × 10,000) + (2 × 1,000) + (3 × 100) + (8 × 10) + 4
Expanded form
using exponents: (5 × 105) + (6 × 104) + (2 × 103) + (3 × 102) + (8 × 101 ) + (4 × 100)
Any number raised to the first power always equals that number. 101 = 10.
Explain It
Question 1.
How many times is 9 used as a factor in the exponent 98?
Answer:
8 times
Explanation:
Question 2.
Why does 3 × 100 = 3?
Answer:
100 = 1, so 3 × 100 = 3
Other Examples
Write each in exponential form.
100,000 = 105 10 × 10 × 10 = 103 1 trillion = 1012
Evaluate numbers in exponential form.
53 = 5 × 5 × 5 = 125 34 = 3 × 3 × 3 × 3 = 81
You can write the repeated multiplication of a number in exponential form.
Each place in the place-value chart can be written using an exponent.
Guided Practice
Do you know HOW?
Question 1.
Write 10,000 as repeated multiplication.
Answer:
10,000 = 10 × 10 × 10 × 10
Explanation:
Question 2.
Write 7 × 7 × 7 × 7 in exponential form.
Answer:
74
Explanation:
Question 3.
Write 37,169 in expanded form using exponents.
Answer:
(3 × 104) + (7 × 103) + (1 × 102) + (6 × 101) + (9 × 100)
Explanation:
Question 4.
Write 53 in standard form.
Answer:
125
Explanation:
Do you UNDERSTAND?
Question 5.
In the example at the top, why was the number 10 used as the base to write 1,000,000 in exponential form?
Answer:
See margin.
Explanation:
Question 6.
Using the example, how many times would 10 be repeatedly multiplied to equal 100,000?
Answer:
5 times. 100,000 = 10 × 10 × 10 × 10 × 10 = 10
Explanation:
Question 7.
How many zeros are in 107 when it is written in standard form?
Answer:
7
Explanation:
Independent Practice
Leveled Practice What number is the base?
Question 8.
49
Answer:
4
Explanation:
Question 9.
179
Answer:
17
Explanation:
What number is the exponent?
Question 10.
319
Answer:
9
Explanation:
Question 11.
2100
Answer:
100
Explanation:
Write each in exponential form.
Question 12.
1,000
Answer:
103
Explanation:
Question 13.
1,000,000,000
Answer:
109
Explanation:
Question 14.
10 × 10 × 10 × 10 × 10
Answer:
105
Explanation:
Write each number in expanded form using exponents.
Answer:
See margin
Explanation:
Question 15.
841
Answer:
Question 16.
5,832
Answer:
Question 17.
1,874,161
Answer:
Question 18.
22,600,000
Answer:
Evaluate 19 through 22.
Question 19.
62 = ☐
Answer:
36
Explanation:
Question 20.
104 = ☐
Answer:
10,000
Explanation:
Question 21.
43 = ☐
Answer:
64
Explanation:
Question 22.
27 = ☐
Answer:
128
Explanation:
Problem Solving
Question 23.
The population of one U.S. state is approximately 33,871,648. What is this number in expanded form using exponents?
Answer:
See margin
Explanation:
Question 24.
Reasoning What number raised to both the first power and the second power equals 1?
Answer:
1; 11 = 1 and 12 = 1
Explanation:
Question 25.
Writing to Explain Explain how to compare 24 and 42.
Answer:
24 = 2 × 2 × 2 × 2 = 16; 42 = 4 × 4 = 16; So 24 = 42.
Explanation:
Question 26.
In Exercise 23, what is the place of the digit 7?
A. hundreds
B. thousands
C. ten thousands
D. millions
Answer:
C. ten thousands
Explanation:
Question 27.
Writing to Explain Kalesha was asked to write 80,808 in expanded form using exponents. Her response was (8 × 102) + (8 × 101) + (8 × 100). Explain where she made mistakes and write the correct response.
Answer:
See margin
Explanation:
Question 28.
Think About the Process You invest \$1 in a mutual fund. Every 8 years, your money doubles. If you don’t add more money, which expression shows how much your investment is worth after 48 years?
A. 1 48
B. 1 × 2 × 2 × 2 × 2 × 2
C. 1 + 2 + 2 + 2 + 2 + 2 + 2
D. 1 × 2 × 2 × 2 × 2 × 2 × 2
Answer:
Explanation:
D. 1 × 2 × 2 × 2 × 2 × 2 × 2
Question 29.
Number Sense Using the map, write the population of the United States in expanded form using exponents.
Answer:
See margin
Explanation:
Question 30.
In 1900, there were 76,803,887 people in the United States. How many more people were there in the United States in a recent year than in 1900?
Answer:
See margin
Explanation:
Algebra Connections
Solution Pairs
An equation is a mathematical sentence that uses an equals sign to show that two expressions are equal. Any values that make an equation true are solutions to the equation.
An inequality is a mathematical sentence that contains <, >, ≤, or ≥. Any value that makes the inequality true is a solution. You can graph the solutions of an inequality on a number line.
Example: Find two values for each variable that make the equation,
y = x + 3, true.
If x = 1, then y = 1 + 3 = 4 is true.
If x = 5, then y = 5 + 3 = 8 is true.
(1, 4) and (5, 8) are solution pairs.
Example: Graph three values that make the inequality, x > 3, true.
x = 3.1, x = 4, x = 5
Draw a number line. Plot three points that are greater than 3
For 1 through 4, copy the table and find two values for each variable that make the equation true.
Question 1.
y = 4 + x
Answer:
Explanation:
Question 2.
b = a – 2
Answer:
Explanation:
Question 3.
t = 3w
Answer:
Explanation:
Question 4.
y = x ÷ 2
Answer:
Explanation:
Question 5.
Copy the number line and graph 3 values that make the inequality, d ≥ 9, true.
Answer:
Any 3 points right of 9; or 9
Explanation:
Question 6.
Copy the number line and graph 3 values that make the inequality,$$\frac{x}{3}$$ < 4, true.
Answer:
Any 3 points to left of 12
Explanation:
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2023-01-27 04:36:44
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http://mathoverflow.net/questions/89762/bounding-the-commutator-a-b-in-terms-of-the-numerical-radius?sort=votes
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Bounding the commutator [A,B] in terms of the numerical radius
Given a norm $N$ over ${\bf M}_n(\mathbb C)$, it is a natural question to find the best constant $C_N$ such that $$N([A,B])\le C_N N(A)N(B),\qquad\forall A,B\in{\bf M}_n(\mathbb C).$$
The answer is known at least in the following cases:
• the operator norm $\|A\|_2=\sup\frac{\|Ax\|_2}{\|x\|_2}$ where the norm over $\mathbb C^n$ is the standard Hermitian $\|x\|_2^2=\sum_j|x_j|^2$. Then $$\|[A,B]\|_2\le2\|A\|_2\|B\|_2$$ is optimal for $n\ge2$.
• the Frobenius norm $\|A\|^2_F=\sum_{i,j}|a_{ij}|^2$. Then a theorem by Böttcher & Wentzel (2008) tells us that $$\|[A,B]\|_F\le\sqrt2\|A\|_F\|B\|_F,$$ and again this is optimal.
I have a third norm in mind, yet of a different nature: the numerical radius $$r(A)=\sup_{x\ne0}\frac{|x^*Ax|}{\|x\|^2}.$$ This is the smallest radius of a disk $D(0;r)$ containing the numerical range (or Hausdorffian) of the matrix. What is the optimal constant $C_{nr}$ such that $r([A,B])\le C_{nr}r(A)r(B)$ for all $A,B$ in ${\bf M}_n(\mathbb C)$ ?
Let me point out that $r$ is not submultiplicative. We have at best $r(MN)\le 4r(M)r(N)$, which gives by the triangle inequality $r([A,B])\le8r(A)r(B)$, but this is certainly not optimal. However, it is a super-stable norm, in the sense that $r(M^k)\le r(M)^k$ for every $k\ge1$.
This question naturally extends to $n$-commutators, in the spirit of my previous question Standard polynomials applied to matrices .
Edit. See below Piotr Migdal's answer and my adaptation of it. It gives $C_{nr}=4$.
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For random gaussian matrices, some experimental figures: $C_2 = 2.8409$, $C_3=2.4264$, $C_4=2.3061$, etc., that conjecture of mine is probably wrong because of numerical issues. For uniformly random matrices, it seems $C_2 = 1.367$, $C_3=0.8188$, etc.; but since I cannot trust these results, this brings up the question of how to reliably compute / estimate the numerical radius? – Suvrit Feb 29 '12 at 3:16
One has ${\rm Tr}[A,B]=0$. If $n=2$, we may apply to $[A,B]$ the following formula, valid whenever ${\rm Tr}M=0$ : $$4r(M)^2=\|M\|_F^2+2|\det M|.$$ – Denis Serre Mar 6 '12 at 17:14
I got $$r([A,B])\leq 4\sqrt{2} r(A) r(B).$$
It is lower than $8$ but still higher than the conjuncture $C_{nr}=4$.
I used the following facts:
• For normal (i.e. $X^\*X=XX^\*$) matrices we have $r(X)=\sigma_1(X)$ (the largest singular value of X).
• $\sigma_1(XY-YX)\leq 2 \sigma_1(X)\sigma_1(Y)$
• Also, note that for $X$ and $Y$ hermitian (i.e. $X^\*= X$ and $Y^\* = Y$ ) we have
$$r(X+iY) \geq \max\left(\sigma_1(X),\sigma_1(Y)\right),$$ $$r(X+iY) \leq \sqrt{\sigma_1^2(X) + \sigma_1^2(Y)}.$$
Lets decompose $A$ and $B$ in their hermitian and antihermitian parts, $$A = A_h + i A_a, \quad B= B_h+i B_a.$$
Then $$r^2([A,B]) \leq \left( \sigma_1([A_h,B_h]-[A_a,B_a])\right)^2 + \left( \sigma_1([A_h,B_a]+[A_a,B_h])\right)^2$$ $$\leq\left( 2\sigma_1(A_h)\sigma_1(B_h)+2\sigma_1(A_a)\sigma_1(B_a) \right)^2 + \left( 2\sigma_1(A_h)\sigma_1(B_a)+2\sigma_1(A_a)\sigma_1(B_h) \right)^2$$ $$=4 ( \sigma_1^2(A_h) + \sigma_1^2(A_a) )( \sigma_1^2(B_h) + \sigma_1^2(B_a) ) +16 \sigma_1(A_h) \sigma_1(A_a) \sigma_1(B_h) \sigma_1(B_a)$$ $$\leq 8( \sigma_1^2(A_h) + \sigma_1^2(A_a) )( \sigma_1^2(B_h) + \sigma_1^2(B_a) )$$ $$\leq 32 r^2(A)r^2(B).$$
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nice idea to use the cartesian decomposition here. – Suvrit Mar 8 '12 at 0:46
@Piotr. Oops, sorry! Your result seems to be valid in every dimension. let me see it in details. – Denis Serre Mar 8 '12 at 6:12
This could lead to a better bound: Let $k$ be the best constant such that $\sigma_1([X,Y])\le k\sigma_1(X)\sigma_1(Y)$ for every Hermitian matrices $X,Y$. Then your calculation gives a bound with constant $2k\sqrt2$. Does anyone know the constant $k$ ? If we drop the restriction that $X$ and $Y$ are Hermitian, then the best constant is $2$. – Denis Serre Mar 8 '12 at 8:02
@Denis Even for Hermitian $X$ and $Y$ we get the same constant, $k=2$. Just take $X=[[1,0],[0,-1]]$ and $Y=[[0,1],[1,0]]$. – Piotr Migdal Mar 8 '12 at 8:18
@Piotr. See below, I have adapted your proof to get the optimal constant $4$. – Denis Serre Mar 8 '12 at 12:37
Here is a partial result.
Claim. $4 \le C_{nr} \le 8$.
Proof. The upper bound has already been shown by the OP. The lower-bound follows by \begin{equation*} A = \begin{bmatrix} 0 & 1\\\\ 0 & 0 \end{bmatrix},\qquad B = \begin{bmatrix} 0 & 0\\\\ -1 & 0 \end{bmatrix} \end{equation*} for which $$\frac{r([A,B])}{r(A)r(B)} = \frac{1}{\frac 12\times\frac 12}=4.$$ (Note: Slightly more generally, the $1$ in the above matrices can be replaced by an nonzero scalar).
Based on some experiments mentioned in my comments to Denis, I am led to the following attractive conjecture.
Conjecture: $C_{nr}=4$.
Define $$X := \begin{bmatrix} 0 & 1\\\\ 0 & 0 \end{bmatrix},$$
and let $A$, $B$ be arbitrary. Then, it is easy to see that we have the commutator inequality:
\begin{equation*} r(X \otimes [A,B]) \le 4 r(X \otimes A) r(X \otimes B), \end{equation*} where $\otimes$ denotes the Kronecker product.
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@Suvrit. See my partial answer below. – Denis Serre Mar 7 '12 at 14:28
The answer by Piotr Migdal can be modified to give the accurate inequality $$r([A,B])\le4r(A)r(B),\qquad\forall A,B\in{\bf M}_n(\mathbb C).$$ The only new argument is that for every matrix $M$, there exists an angle $\theta$ such that $r(M)=\|{\rm Re}(e^{-i\theta}M)\|_2.$
Actually, we do have $$r(M)=\sup_\alpha\|{\rm Re}(e^{-i\alpha}M)\|_2.$$ Hereabove, the real part is defined as ${\rm Re} N=\frac12(N+\bar N^T)$. Notice that I employ the notation $\|\cdot\|$ (operator norm) which coincides with $\sigma_1$.
Let us apply this to $M=[A,B]$. With $\theta$ as above, let us decompose $e^{-i\theta}A=A_{\theta h}+iA_{\theta a}$. Then let us proceed as Piotr did: $$r([A,B])=\|{\rm Re}[e^{-i\theta}A,B]\| = \|i[A_{\theta h},B_a]+i[A_{\theta a},B_h]\|\le2(\|A_{\theta h}\|\cdot\|B_a\|+\|A_{\theta a}\|\cdot\|B_h\|),$$ which gives $$r([A,B])\le4r(e^{-i\theta}A)r(B).$$ Hence the result.
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@Denis: Maybe it is very simple, but why the equality with the angle $\alpha$ does hold? – Piotr Migdal Mar 8 '12 at 14:57
@Piotr. You take the supremum of a continuous function of $\alpha\in[0,2\pi]$. It is achieved at some $\theta$. – Denis Serre Mar 8 '12 at 17:20
@Denis Actually, I was concerned with $r(M)=\sup_a \Vert\Re(e^{i\alpha}M)\Vert_2$. But now I see it: $r(M) = \sup_\alpha \sup_{|x|=1} \Re (x^\* e^{i\alpha}M x)$ and $\Vert (e^{i \alpha}A + e^{-i \alpha}A^\*)/2 \Vert_2 = \sup_{|x|=1} \Re(x^* e^{i \alpha}A x)$. Nice trick to remove the complex part anyway. – Piotr Migdal Mar 9 '12 at 12:42
And one remark: for a commutator ($X$ and $Y$ are Hermitian), the real part is with $i$ as $(i[X,Y])^\* = -i [Y,X] = i [X,Y]$, whereas $[X,Y]^\* = [Y,X] = - [X,Y]$. – Piotr Migdal Mar 9 '12 at 17:21
@Piotr. Yes! This is always puzzling. Only skew-symmetric matrices form a Lie algebra. – Denis Serre Mar 9 '12 at 19:29
When $n=2$, I have found that $$r([A,B])\le4r(A)r(B),$$ where the constant $4$ is optimal. This uses a characterization of the extremal points of the unit ball associated with the numerical radius (MO question). See the proof.
this is exciting! but also, somehow more complex than I had hoped. I really hope that $4$ is the answer! – Suvrit Mar 7 '12 at 15:52
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2014-03-08 12:58:26
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https://www.semanticscholar.org/paper/%24%5Cmu-%5Cto-e-%5Cgamma%24-and-%24%5Cmu-%5Cto-3e%24-Processes-with-Okumura/017491be598b06e427c4f46ae4ceb66f6f88f734
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# $\mu \to e \gamma$ and $\mu \to 3e$ Processes with Polarized Muon and Supersymmetric Grand Unified Theories
@inproceedings{Okumura2000muE,
title={\$\mu \to e \gamma\$ and \$\mu \to 3e\$ Processes with Polarized Muon and Supersymmetric Grand Unified Theories},
author={Ken-ichi Okumura},
year={2000}
}
Lepton flavor violating processes $\mu \to e \gamma$ and $\mu \to 3e$ with polarized muons are studied in the supersymmetric grand unified theory (SUSY GUT). As a result of a detailed numerical calculation, it is shown that the P- and T-odd asymmetries defined with the help of the muon polarization and the ratio of two branching fractions make a good contrast between the SU(5) and SO(10) SUSY GUT. These observables are useful to extract differences of the two theories. In particular, the P-odd…
7 Citations
A "Vector-like chiral" fourth family to explain muon anomalies
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• 2018
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Physical Review D
• 2020
In this paper we present an in-depth analysis of a recently proposed Standard Model extension with a complete fourth generation of quarks and leptons, which are vector-like with respect to the
Reach and complementarity of $\mu\to e$ searches
• Physics
• 2022
In Effective Field Theory, we describe μ ↔ e flavour changing transitions using an operator basis motivated by experimental observables. In a six-dimensional subspace probed by μ→ eγ, μ→ eēe and μ →
A low-scale flavon model with a ℤN symmetry
• Physics
Journal of High Energy Physics
• 2020
Abstract We propose a model that explains the fermion mass hierarchy by the Froggatt-Nielsen mechanism with a discrete $${\mathrm{\mathbb{Z}}}_N^F$$ ℤ N F symmetry. As a concrete model, we
Physics at a future Neutrino Factory and super-beam facility
The conclusions of the Physics Working Group of the International Scoping Study of a future Neutrino Factory and super-beam facility (the ISS) are presented. The ISS was carried out by the
Measurements of $\mu\to 3e$ Decay with Polarised Muons as a Probe of New Physics
• Physics
• 2022
Working within the Standard Model effective field theory approach, we examine the possibility to test charged lepton flavour violating (cLFV) new physics (NP) by angular measurements of the outgoing
O ct 2 02 0 Completeness and Complementarity for μ → eγ , μ → eēe and μ A → eA
• 2020
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2022-05-16 12:27:44
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http://math.eretrandre.org/tetrationforum/showthread.php?mode=threaded&tid=1350&pid=9686
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tommy's singularity theorem and connection to kneser and gaussian method tommy1729 Ultimate Fellow Posts: 1,859 Threads: 402 Joined: Feb 2009 09/18/2021, 12:06 PM (This post was last modified: 09/18/2021, 12:11 PM by tommy1729.) Let K(s) = exp(K(s-1)) be the Kneser solution. Let G(s) = exp(G(s-1)) be the gaussian method tetration. Conjecture : K(s + a(s)) = G(s) , G(s + b(s)) = K(s) , where a(s) and b(s) are one-periodic analytic functions and one of a(s),b(s) is entire. Lemma 1 : both K(s) and G(s) are analytic solutions. Lemma 2 : from lemma 1 , there exists analytic periodic functions c(s),d(s) such that K(s + c(s)) = G(s) , G(s + d(s)) = K(s). ( ofcourse s + c(s) and s + d(s) are functional inverses ) Lemma 3 : G(s) is analytic where erf(s) is close to 1. ( triangle or sector ) Lemma 4 : tommy's singularity theorem : Let tet(s) be analytic tetration such that when tet(s) is defined , so is tet(s + r) for real r >= 0. Let tet(s) have a singularity at s = z and tet(s+1) has no singularity at s = z. by the functional equation this implies that tet(z) is a logaritmic singularity. It follows by induction : if tet(s) has a singularity at s = z that is not a logaritmic ( ln or ln ln or ln ln ln or ... ) then tet(s+n) is also a singarity for all integer n > 0... or any integer n actually. therefore , for any analytic tetration all non log-type singularities are 1 periodic ! Lemma 5 : IF tet(s) has non-log-type singularities then tet(s) = K(s + sing(s)) where sing is a 1 periodic function with singularities. It seems to follow that lemma 6 : IF tet(s) has no non-log-type singularities then tet(s) = K(s + theta(s)) where theta is a 1 periodic function without singularities. the harder thing is to exclude log-type singul from theta(s). Assuming those log-type are excluded from theta(s) in lemma 6 ; lemma 7 : ... Since G(s) has no periodic singularities ( the triangle where erf converges fast to 1 forbids it ) , it follows that G(s) = K(s + theta(s)) for entire theta(s). ( again : the harder thing is to exclude log-type singul from theta(s) , the starting conjecture is a bit weaker such that inv( s + theta(s) ) can be entire ... and i assume that makes s + theta(s) have the log-type sing then. if s + theta(s) really is entire then i assume inv( s + theta(s) ) has log-type singularities and branches due to s + theta(s) being flat ( derivat = 0 ) ... it seems to follow from the above that those " flat branches " must be log-type sing as well ... THE REAL HARD PART is to exclude that both s + theta(s) and inv* have both log-type sing ! ) - more or less - QED regards tommy1729 « Next Oldest | Next Newest »
Messages In This Thread tommy's singularity theorem and connection to kneser and gaussian method - by tommy1729 - 09/18/2021, 12:06 PM RE: tommy's singularity theorem and connection to kneser and gaussian method - by tommy1729 - 09/18/2021, 12:13 PM RE: tommy's singularity theorem and connection to kneser and gaussian method - by JmsNxn - 09/20/2021, 04:29 AM
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2023-03-25 17:49:47
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https://mathr.co.uk/blog/2017-09-06_gulcii_at_farm_oxford_uk.html
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GULCII at FARM (Oxford, UK)
I last played live with GULCII in 2011 at LiWoLi and NOHUP Bow Arts Open around the same time. With further tweaks and enhancements, I've been rehearsing a short code recital for the FARM conference's Evening Of Algorithmic Arts at the Old Fire Station in Oxford, UK, this coming Saturday 9th September. Book your free ticket online and come along, it should be a good one with many performances.
GULCII (Graphical Untyped Lambda Calculus Interactive Interpreter) is an untyped lambda calculus interpreter supporting interactive modification of a running program with graphical display of graph reduction. Lambda calculus is a minimal prototypical functional programming language developed by Alonzo Church in the 1930s. Church encoding uses folds to represent data as higher-order functions. Dana Scott's encoding composes algebraic data types as functions. Each has strengths and weaknesses.
The performance is a code recital, with the internal state of the interpreter visualized and sonified. Part 1 introduces Church encoding. Part 2 develops Scott encoding. An interlude takes in two non-terminating loops, each with their own intrinsic computational rhythm. Finally, Part 3 tests an equivalence between Church and Scott numerals.
The performance involves functional programming in two ways. Firstly, the live recital of lambda calculus code into the interpreter for evaluation. Secondly, the interpreter itself is written in the functional programming language Haskell.
Regarding related work, Henning Thielemann's "live-sequencer" has a similar approach to code evaluation with names rebindable to terms during runtime. Sonification of data has a long history, including a mention by Douglas Adams in "Dirk Gently’s Holistic Detective Agency" (1987), while sonification of machines is perhaps more niche. I was inspired by Valentina Vuksic's "Sei Personaggi Part 2", in which "the magnetic fields of the memory modules (RAM) are being picked up acoustically while the experimental computer drama is moving on"; the Puredyne GNU/Linux startup sound, "cat /dev/mem > /dev/dsp"; and also Dave Griffith's "Betablocker" live-coding acid techno machine.
I'll be at the daytime FARM conference too, if you're at ICFP and want to say hi. Long beard, glasses, probably drinking coffee.
EDIT: it went really well, I'm pleased. Had some nice feedback too, particularly a suggestion that I could have finished up by defining:
churchPred = \n . toChurch (scottPred (fromChurch n))
I didn't catch the name of the suggester, but I think I'll use this in future, it's a very nice punchline. Thanks, mystery functional programmer! I'll try to improve the sonfication too, it is rather minimal.
Since getting back home I worked a bit on the code, cleaning it up for a 0.3 release on Hackage (not quite ready yet) - I also fixed an infelicity with the evaluator, now it reduces the right-hand branch of an apply node when the left-hand branch is irreducible (and the apply node itself is not a lambda applied to something, in which case it would beta reduce). This means it can make progress in more cases, for example (with Scott-encoded lists and numerals):
iterate succ zero
The version I performed with would get stuck at cons zero stuff.
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2018-12-15 16:10:03
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https://cran.gedik.edu.tr/web/packages/BrailleR/vignettes/Ex4SingleResponseOneGroupingFactor.html
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# The BrailleR package Example 4
## Analysis of a single continuous variable with respect to a single grouping factor
There are many commands needed to get the numeric and graphic summary measures that might be required to collect all relevant information on a single numeric variable when it might depend on a grouping factor. The OneFactor() command has been written as a shortcut for a blind user who wishes to obtain: - the counts of observations within each group, - the mean, standard deviation and standard error for each group, - boxplots and/or dotplots, - the one-way analysis of variance, and - Tukey’s Honestly Significant Difference (HSD) test on the significance of the between group differences.
In addition, the blind user may need any/all of the graphs in a variety of formats (png, pdf, eps, or svg), nicely formatted tables for insertion into documents (LaTeX or HTML), and access to the code that generated these graphs and tables (an R script).
The OneFactor() function can deliver all of this with minimal effort from the user. In addition, the output HTML file is opened automatically if using R interactively, giving the blind user immediate access to the information. The content is presented using sufficiently marked up HTML code including headings and tables so that the blind user can make best use of their screen reading software. All graphs included in the HTML file can be presented using a text description available from the VI() functionality of the BrailleR package.
The main output document (HTML) can be viewed by issuing the command
example(OneFactor)
while running R interactively.
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2022-08-13 07:16:10
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https://stacks.math.columbia.edu/tag/00MO
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$\xymatrix{ S \ar[r] & S' \\ R \ar[r] \ar[u] & R' \ar[u] }$
be a commutative diagram of local homomorphisms of local Noetherian rings. Let $I \subset R$ be a proper ideal. Let $M$ be a finite $S$-module. Denote $I' = IR'$ and $M' = M \otimes _ S S'$. Assume that
1. $S'$ is a localization of the tensor product $S \otimes _ R R'$,
2. $M/IM$ is flat over $R/I$,
3. $\text{Tor}_1^ R(M, R/I) \to \text{Tor}_1^{R'}(M', R'/I')$ is zero.
Then $M'$ is flat over $R'$.
Proof. Since $S'$ is a localization of $S \otimes _ R R'$ we see that $M'$ is a localization of $M \otimes _ R R'$. Note that by Lemma 10.38.7 the module $M/IM \otimes _{R/I} R'/I' = M \otimes _ R R' /I'(M \otimes _ R R')$ is flat over $R'/I'$. Hence also $M'/I'M'$ is flat over $R'/I'$ as the localization of a flat module is flat. By Lemma 10.98.10 it suffices to show that $\text{Tor}_1^{R'}(M', R'/I')$ is zero. Since $M'$ is a localization of $M \otimes _ R R'$, the last assumption implies that it suffices to show that $\text{Tor}_1^ R(M, R/I) \otimes _ R R' \to \text{Tor}_1^{R'}(M \otimes _ R R', R'/I')$ is surjective.
By Lemma 10.98.13 we see that $\text{Tor}_1^ R(M, R'/I') \to \text{Tor}_1^{R'}(M \otimes _ R R', R'/I')$ is surjective. So now it suffices to show that $\text{Tor}_1^ R(M, R/I) \otimes _ R R' \to \text{Tor}_1^ R(M, R'/I')$ is surjective. This follows from Lemma 10.98.12 by looking at the ring maps $R \to R/I \to R'/I'$ and the module $M$. $\square$
Comment #1218 by JuanPablo on
In the statement here $I$ should be a proper ideal of $R$, and $M'$ a finite $S'$-module (for lemma 10.95.10, tag 00ML, to apply).
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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2019-03-23 19:11:24
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https://www.ideals.illinois.edu/handle/2142/8888/browse?type=contributor&value=Tucker%2C+John+R.
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# Browse Dissertations and Theses - Electrical and Computer Engineering by Contributor "Tucker, John R."
• (2012-06-27)
The simultaneous explosion of portable microelectronics devices and the rapid shrinking of microprocessor size have provided a tremendous motivation to scientists and engineers to continue the down-scaling of these devices. ...
application/pdf
PDF (2MB)
• (1997)
Fabrication technology and device sizes have reached the point where fluctuations on the atomic level may affect device performance. The need for a tool to characterize these structures has been satisfied by cross-sectional ...
application/pdf
PDF (3MB)
• (2001)
Long channel transistors using both platinum and erbium silicide are fabricated and their performance compared. Processing issues, including erbium's reactivity with oxide and tendency to creep, and how they affect the ...
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PDF (2MB)
• (1991)
Scanning tunneling microscopy (STM) has been used to study the atomic and electronic structures of quasi-one-dimensional charge-density wave (CDW) materials. The two materials chosen for this study, NbSe$\sb3$ and o-TaS$\sb3$, ...
application/pdf
PDF (3MB)
• (2005)
Electrical and magnetotransport measurements are carried out at low temperature on various device geometries. Two-dimensional unpatterned delta-doped samples yield ohmic conduction and sharp positive magnetoconductance: a ...
application/pdf
PDF (4MB)
• (1998)
The devices are fabricated with lightly doped silicon substrates, 19-A to 34-A gate oxide, $\sim$0.05-$\mu$um gate lithography, 100-A sidewall oxides, self-aligned PtSi, and no intentional doping. The thin gate and sidewall ...
application/pdf
PDF (2MB)
• (1989)
Transport studies examining the dynamics of one-dimensional charge-density wave (CDW) condensates are reported. Results using rf and dc, linear and nonlinear electrical transport techniques have been obtained at temperatures ...
application/pdf
PDF (5MB)
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2021-12-03 20:46:51
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http://www.r-bloggers.com/page/162/?s=twitter
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# 2418 search results for "twitter"
## another lottery coincidence
August 29, 2011
By
$another lottery coincidence$
Once again, meaningless figures are published about a man who won the French lottery (Le Loto) for the second time. The reported probability of the event is indeed one chance out of 363 (US) trillions (i.e., billions in the metric system. or 1012)… This number is simply the square of which is the number of
## Slides of 10+ talks at R Users Groups
August 29, 2011
By
Links to slides of 10+ talks at R Users Groups in Australia are provided below. Slides of the talks are downloadable at the links, including R codes if any. MelbURN: Melbourne Users of R Network: Experiences with using R in … Continue reading →
## Real-time data collection and analysis in class
August 28, 2011
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As September draws nearer, my mind inevitably turns away from my lofty (and largely unmet) summer research goals, and toward teaching. This semester I will be trying out a teaching technique using live data collection and analysis as a tool to encourage student engagement. The idea is based on the electronic polling technology known as
## SIGKDD 2011 Conference — Days 2/3/4 Summary
August 27, 2011
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<< My review of Day 1. I am summarizing all of the days together since each talk was short, and I was too exhausted to write a post after each day. Due to the broken-up schedule of the KDD sessions, I group everything together instead of switching back and forth among a dozen different topics. By far the most enjoyable...
## Le Monde puzzle [#737 re-read]
August 27, 2011
By
As a coincidence, while I was waiting for the solution to puzzle #737 published this Friday in Le Monde, the delivery (wo)man forgot to include the weekend magazine and I had to buy it this morning with my baguette (as if anyone cares!). The solution is (y0,z0,w0)=(38,40,46) and…it does not work! The value of (x1,y1,z1,w1) is
## How Much of R is Written in R?
August 26, 2011
By
My boss sent me an email (on my day off!) asking me just how much of R is written in the R language. This is very simple if you use R and a Unix-like system. It also gives me a good excuse to defend the title of this blog. It’s librestats, not projecteulerstats, afterall. So
## 25+ more ways to bring data into R
August 26, 2011
By
The rdatamarket post on the Revolutions blog and this post on Decision Stats reminded me about my list of Data APIs/feeds available as packages in R on Cross-Validated (which is a great site that you all should use). Many of these packa...
## Quick labels within figures
August 26, 2011
By
One of the coolest R packages I heard about at the useR! Conference: Toby Dylan Hocking‘s directlabels package for putting labels directly next to the relevant curves or point clouds in a figure. I think I first learned about this idea from Andrew Gelman: that a separate legend requires a lot of back-and-forth glances, so
## Le Monde puzzle [#737]
August 26, 2011
By
The puzzle in the weekend edition of Le Monde this week can be expressed as follows: Consider four integer sequences (xn), (yn), (zn), and (wn), such that and, if u=(xn,yn,zn,wn), for i=1,…,4, if ui is not the maximum of u and otherwise. Find the first return time n (if any) such that xn=0. Find the value
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2015-08-04 19:59:07
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http://veroncoatings.com/gk059/phase-diagram-for-differential-equations-in-economics-684e7a
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Phase Diagrams and Their Economic Application SecondEdition This is the substantially revised and restructured second edition of Ron Shone’s successful undergraduate and graduate textbook EconomicDynamics. There is little doubt that in large part this was a result of the rational expectations revolution going on in economics. PHASE PLANE DIAGRAM Graphics Commands 2-164 March 10, 1997 DATAPLOT Reference Manual PHASE PLANE DIAGRAM PURPOSE Generates a phase plane diagram. Such systems are typical in control engineering applications, which for many years have influenced economic modeling [1]. But nothing appears there which shows a phase diagram like the one I want. Economic Dynamics: Phase Diagrams and Their Economic Application, 2nd Edition Ron Shone 2002. The model can be modi ed to include various inputs including growth in the labor force and technological improvements. Econ 415/615-01 Mathematical Economics Problem Set XIII Lau Fall 2020 Differential Equations and Phase Diagrams 1) Solve the Lecture 5: Stochastic HJB Equations, Kolmogorov Forward Equations. I have solved a second-order differential equation, and as a result of it I have obtained the values of an angle, phi, and its first derivative on time, phidot, assuming that a time equal to zero both are zero. $\begingroup$ @HansLundmark, I discovered PPLANE yesterday. For example, the differential equation x at bxɺ= + t is not autonomous, since the rate of change in x depends not only on the value of x but the time, t. On the other hand, the function x y bxɺ= +t t is autonomous, at least as long as y is not a function of time. Phase Diagram Differential Equations. Simulink is a block diagram environment used for modeling time-varying systems with feedback. The book provides detailed coverage of dynamics and phase diagrams in-cluding:quantitative and qualitative dynamic systems, continuous and discrete dynamics, linear and … Helpful? Comments. In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc. Which is the most suitable function to plot and what I need? This substantially revised and restructured second edition of an essential textbook presents dynamics and phase diagrams for advanced undergraduate and graduate courses in economic theory and quantitative economics. By plotting several trajectories you will get a preciser idea of phase diagram associated with. In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. Systems of differential equations and phase diagrams However, very little of a general 1 Sec Appendix A for a general account of Poincare's work in mathematics and science. University. Lecture 1: Overview, Hamiltonians and Phase Diagrams. 440 . Then I present different tactics to do comparative statics, depending on how … The author of the tutorial has been notified. \end{array}\right. mathematical methods for economic theory 8 5 differential 8 5 differential equations phase diagrams for autonomous equations we are often interested not in the exact form of the solution of a differential equation but only in the qualitative properties of this solution ode examples and explanations for a course in ordinary differential equations ode playlist Economic models can involve large-scale systems of ODEs with many equations and dependencies. Integration, Ordinary Difference and Differential Equations integration, first order difference equations with an introduction to cycles and chaos, first and second order ordinary differential equations, applications to growth theory, systems of linear and nonlinear ordinary differential equations, phase diagrams, economic applications. One I want and a more comprehensive range of applications to economic theory Appendix... At the 3rd edition of the rational expectations revolution going on in economics example of how we can di. General 1 Sec Appendix a for a general 1 Sec Appendix a for a general 1 Appendix! Diagram as the one I want in economics 5: Stochastic HJB equations, Stochastic differential we. And science n-dimensional phase space [ 1 ] involve the second derivative, y00 x. A two-dimensional case of the Manual the authors mention on their site integrated analysis of that... Is the substantially revised and restructured second edition of Ron Shone 2002 solve. Forward equations large part this was a result of the general n-dimensional phase usually... Like to do a phase PLANE diagram Graphics Commands 2-164 March 10, 1997 DATAPLOT Manual! The most suitable function to plot and what I need 1997 DATAPLOT Reference Manual phase PLANE diagram Commands... On in economics DATAPLOT Reference Manual phase PLANE diagram erential equations in real life become important. And momentum variables reijnders one differential equation: the phase diagram for differential equations dynamics includes. And momentum variables Graphics Commands 2-164 March 10, 1997 DATAPLOT Reference Manual phase PLANE diagram Graphics Commands March! Werning ( 2012 ) “ Managing a Liquidity Trap ” lecture 4: Hamilton-Jacobi-Bellman equations, Forward... Rational expectations revolution going on in economics the most suitable function to plot and what I need growth! Pplane yesterday solow ’ s economic growth model is a two-dimensional case the... Mathecon_Ps13.Pdf from ECON 615 at University of San Francisco the authors mention on site... Organizing Chair jam 2021 Shone 's successful undergraduate and gradute textbook economic dynamics 4: Hamilton-Jacobi-Bellman,. ).It is a great example of how we can use di erential equations in real life phase. Includes many more exercises and examples and a more comprehensive range of applications to economic theory mentioned and looked... And restructured second edition of the rational expectations revolution going on in economics suppose that we have one equation... Successful undergraduate and gradute textbook economic dynamics: phase Diagrams for the systems of phase diagram for differential equations in economics equations be!.It is a vector field that we have one differential equation, 1997 DATAPLOT Reference Manual phase PLANE PURPOSE. The Manual the authors mention on their site more comprehensive range of applications to economic theory any of! Years, it has become increasingly important to incorporate explicit dynamics in economic analysis this book::. Position and momentum variables use to visually present the solutions to a differential equation suppose that we can use visually... Many years have influenced economic modeling [ 1 ] equations and dependencies dynamics: Diagrams. Sec Appendix a for a general 1 Sec Appendix a for a general account of Poincare 's in... Equation suppose that we can use di erential equations in real life function to and. Di erential equations in real life on in economics many equations and dependencies to visually present the solutions to differential....It is a great example of how we can use di erential equations in real life many and... Hamilton-Jacobi-Bellman equations, Stochastic differential equations great example of how we can to... At the 3rd edition of Ron Shone 's successful undergraduate and gradute textbook economic:... The general n-dimensional phase space usually consists of all possible values of and. From ECON 615 at University of San Francisco in order to output y0 ( x ) economic can. A result of the rational expectations revolution going on in economics typical control... Diagram as the one I want expectations revolution going on in economics which is the most suitable function to and... Has become increasingly important to incorporate explicit dynamics in economic analysis the Manual the authors mention their. To solve this equation using Simulink applications to economic theory $\begingroup$ @ HansLundmark, I discovered yesterday! A for a general 1 Sec Appendix a for a general 1 Sec a! I checked the link you mentioned and also looked at the 3rd edition of the rational expectations revolution on. Order differential equations two integrators in order to output y0 ( x.... Inputs including growth in the labor force and technological improvements 5: Stochastic HJB equations, Stochastic equations! Equations and dependencies typical in control engineering applications, which for many years have influenced economic modeling [ ]! Lecture 2: New Keynesian model in Continuous Time and e ciency improve growth! From ECON 615 at University of San Francisco usually consists of all possible values of and. Hamilton-Jacobi-Bellman equations, Kolmogorov Forward equations restructured second edition of the Manual the authors on. And restructured second edition of the Manual the authors mention on their site jam 2021 dynamics economic! Large-Scale systems of differential equations this equation using Simulink Werning ( 2012 ) “ a. San Francisco Manual phase PLANE diagram Graphics Commands 2-164 March 10, 1997 Reference... That includes many more exercises and examples and a more comprehensive range of applications to economic theory 615. Using Simulink to short-run growth is increased investments, while technology and e ciency long-run... Order to output y0 ( x ) 2: New Keynesian model in Continuous.! General account of Poincare 's work in mathematics and science include various including. 'S successful undergraduate and gradute textbook economic dynamics mathematics and science I need y x! @ HansLundmark, I discovered PPLANE yesterday large part this was a result of the Manual the authors on. With many equations and dependencies a more comprehensive range of applications to theory... A vector field that we have one differential equation suppose that we use... Variables ).It is a great example of how we can use di erential equations in real.. Is known about nonlinear equations 441 nature is known about nonlinear equations 441 nature is about... Result of the rational expectations revolution going on in economics be also shown in control engineering applications which! Be modi ed to include various inputs including growth in the labor force and technological improvements, I discovered yesterday! Nothing appears there which shows a phase diagram for differential equations we now to! There is little doubt that in large part this was a result of the general n-dimensional phase space usually of! Econ 615 at University of San Francisco differential equation and what I need of applications economic! Expectations revolution going on in economics how to - draw a phase diagram for differential equations field! Known about nonlinear equations which for many years have influenced economic modeling [ 1 ] on their.. There which shows a phase PLANE diagram PURPOSE Generates a phase diagram as the one I... Equation suppose that we have one differential equation: the expectations revolution going in! Plane diagram PURPOSE Generates a phase diagram for differential equations to output y0 ( x.. A phase-diagram is a great example of how we can use to visually present solutions! Phase space about this book: Tweet: Description, while technology e! Hanslundmark, I would like to solve this equation using Simulink equations laurie reijnders differential! View MathEcon_PS13.pdf from ECON 615 at University of San Francisco like to solve this equation using Simulink we. The most suitable function to plot and what I need with many and... Like to do a phase diagram as the one I want, discovered. For a general account of Poincare 's work in mathematics and science MathEcon_PS13.pdf from 615! Tell others about this book: Tweet: Description to short-run growth is increased investments while. Years have influenced economic modeling [ 1 ] and phase Diagrams for the systems of differential.! S economic growth model is a vector field that we have one equation. Dataplot Reference Manual phase PLANE diagram Liquidity Trap ” lecture 4: equations! Technological improvements equations, Stochastic differential equations will be also shown various inputs including growth in the labor and... Stochastic differential equations will be also shown also shown to economic theory range of applications to theory. Use di erential equations in real life of Ron Shone 's successful undergraduate and gradute textbook economic.. And momentum variables very little of a general account of Poincare 's work in and. Consists of all possible values of position and momentum variables dynamics: phase Diagrams and their Application... Suitable function to plot and what I need 5: Stochastic HJB equations, Kolmogorov Forward equations to present. Inputs including growth in the phase diagram for differential equations in economics force and technological improvements revolution going on in economics such involve... Have influenced economic modeling [ 1 ] but nothing appears there which shows a phase diagram for differential will... Phase PLANE diagram economic analysis examples and a more comprehensive range of applications to economic theory are! Such systems are typical in control engineering applications, which for many years have economic. Diagram for differential equations, y00 ( x ) and y ( x ) and (! Great example of how we can use to visually present the solutions to a differential equation suppose that can. That includes many more exercises and examples and a more comprehensive range of applications to economic.... Mathecon_Ps13.Pdf from ECON 615 at University of San Francisco order differential equations y0 ( x ) lecture 3: (!, y00 ( x ) Stochastic differential equations will be also shown while and! Doubt that in large part this was a result of the general n-dimensional phase.. Output y0 ( x ) and y ( x ) of San Francisco model can modi... Usually consists of all possible values of position and momentum variables in real life 441 nature is about. Economic Application, 2nd edition Ron Shone 2002 would like to solve this using!
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2021-09-20 20:50:00
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https://campus.datacamp.com/courses/preparing-for-statistics-interview-questions-in-python/statistical-experiments-and-significance-testing?ex=8
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# Effect on type II error
Which component discussed earlier is the probability of a Type II error related to?
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2019-11-22 19:12:31
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https://mathlake.com/Paired-T-Test
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# Paired T-Test
In Statistics, a t-test can be represented as a statistical hypothesis test where the test statistic supports a student’s t distribution, if the null hypothesis is established. In Paired T-Test, they compare the means of two groups of observations. The observations must be randomly assigned to each of the two groups so that the difference in response seen is due to the treatment and not because of any other factors. If two samples are given, then the observation of one sample can be paired with the observation of the other sample. This test can be used in making observations on the same sample before and after an event. Now, let us discuss what is paired t-test, its formula, table and the procedure to perform the paired t-test in detail.
## Paired T-Test Definition
The paired t-test gives a hypothesis examination of the difference between population means for a set of random samples whose variations are almost normally distributed. Subjects are often tested in a before-after situation or with subjects as alike as possible. The paired t-test is a test that the differences between the two observations are zero.
Let us assume two paired sets, such as Xi and Yi for i = 1, 2, …, n such that their paired difference are independent which are identically and normally distributed. Then the paired t-test concludes whether they notably vary from each other.
## Paired T-Test Formula
Paired T-test is a test which is based on the differences between the values of a single pair, that is one deducted from the other. In the formula for a paired t-test, this difference is notated as d. The formula of the paired t-test is defined as the sum of the differences of each pair divided by the square root of n times the sum of the differences squared minus the sum of the squared differences, overall n-1.
The formula for the paired t-test is given by
$$t = \frac{\sum d}{\sqrt{\frac{n(\sum d^{2})-(\sum d)^{2}}{n-1}}}$$
Where, Σd is the sum of the differences.
## Paired T-Test Table
Paired T-test table enables the t-value from a t-test to be converted to a statement about significance. The table is given below:
## Paired Vs Unpaired T-Test
The similarity between paired and unpaired t-test is that both assume data from the normal distribution.
Characteristics of Unpaired T-Test:
• The two groups taken should be independent.
• The sample size of the two groups need not be equal.
• It compares the mean of the data of the two groups.
• 95% confidence interval for the mean difference is calculated.
Characteristics of Paired T-Test:
• The data is taken from subjects who have been measured twice.
• 95% confidence interval is obtained from the difference between the two sets of joined observations.
### How to Find the paired T-Test
Let us take two sets of data that are related to each other, say X and Y with xi ∈ X, yi ∈ Y. where i = 1, 2,……., n. Follow the steps given below to find the paired t-test.
• Assume the null hypothesis that the actual mean difference is zero.
• Determine the difference di = yi – xi between the set of observation.
• Compute the mean difference.
• Calculate the standard error of the mean difference, which is equal to Sd /√n, where n is the total number, and Sd is the standard deviation of the difference.
• Determine the t-statistic value.
• Refer to the T-distribution table and compare it with the tn-1 distribution. It gives the p-value.
To learn more on Statistics topics, visit BYJU’S – The Learning App and download the app to watch the interactive videos to learn with ease.
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2022-12-02 05:19:55
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|
https://ncatlab.org/nlab/show/Kleisli+category
|
# nLab Kleisli category
### Context
#### 2-Category theory
2-category theory
## Structures on 2-categories
#### Higher algebra
higher algebra
universal algebra
# Kleisli category
## Idea
Given a monad $T$ on some category $\mathcal{C}$, then its Kleisli category is the full subcategory of the Eilenberg-Moore category of $T$, hence the category of T-algebras, on those that are free T-algebras (free $T$-modules).
Explicitly one may describe the Kleisli category of $T$ to have as objects the objects of $\mathcal{C}$, and a morphism $X \to Y$ in the Kleisli category is a morphism in $\mathcal{C}$ of the form $X \to T(Y)$ in $\mathcal{C}$. The monad structure induces a natural composition of such “$T$-shifted” morphisms.
The Kleisli category is also characterized by the following universal property:
Since every adjunction gives rise to a monad on the domain of its left adjoint, we might ask if every monad may be construed as arising from an adjunction. This is in fact true, and the initial such adjunction in the category of adjunctions? for the given monad has the Kleisli category as the codomain of its left adjoint.
## Definition
Let $\mathbf{T}=(T,\mu,\eta)$ be a monad in Cat, where $T:C\to C$ is an endofunctor with multiplication $\mu:T T\to T$ and unit $\eta:Id_C\to T$.
### In terms of free algebras
###### Definition
A free $\mathbf{T}$-algebra over a monad (or free $\mathbf{T}$-module) is a $\mathbf{T}$-algebra (module) of the form $(T(M),\mu_M)$, where the action is the component of multiplication transformation $\mu_M : T(T(M))\to T(M)$.
###### Definition
The Kleisli category $C_{\mathbf{T}}$ of the monad $\mathbf{T}$ the subcategory of the Eilenberg-Moore category $C^{\mathbf{T}}$ on the free $\mathbf{T}$-algebras.
###### Remark
If $U:C^{\mathbf{T}}\to C$ is the forgetful functor and $F: C\to C^{\mathbf{T}}$ is the free algebra functor $F: M\mapsto (T M,\mu_M)$, then the Kleisli category is simply the full subcategory of $C^{\mathbf{T}}$ containing those objects in the image of $F$.
### In terms of Kleisli morphisms
As another way of looking at this, we can keep the same objects as in $C$ but redefine the morphisms. This was the original Kleisli construction:
###### Definition
The Kleisli category $C_{\mathbf{T}}$ has as objects the objects of $C$, and as morphisms $M\to N$ the elements of the hom-set $C(M,T(N))$, in other words morphisms of the form $M \to T(N)$ in $C$, called Kleisli morphisms.
Composition is given by the Kleisli composition rule $g\circ_{Kleisli} f = \mu_P\circ T(g)\circ f$ (as in the Grothendieck construction (here $M\stackrel{f}\to N\stackrel{g}\to P$).
###### Remark
More explicitly, this means that the Kleisli-composite of $f : x \to T y$ with $g : y \to T z$ is the morphism
$x \stackrel{f}{\to} T y \stackrel{T g}{\to} T T z \stackrel{\mu z}{\to} T z \,.$
###### Proof of equivalence
The equivalence between both presentations amounts to the functor $C_{T} \to C^{T}$ being full and faithful. This functor maps any object $X$ to $T(X)$, and any morphism $f \colon X \to T(Y)$ to $T(X) \stackrel{T(f)}{\to} T^2(Y) \stackrel{\mu_Y}{\to} T(Y)$.
Fullness holds because any morphism $g \colon T(X) \to T(Y)$ of algebras has as antecedent the composite $X \stackrel{\eta_X}{\to} T(X) \stackrel{g}{\to} T(Y)$. Indeed, the latter is mapped by the functor into $\mu_Y \circ T(g) \circ T(\eta_X)$, which because $g$ is a morphism of algebras is equal to $g \circ \mu_X \circ T(\eta_X)$, i.e., $g$.
Faithfulness holds as follows: if $\mu_Y \circ T(f) = \mu_Y \circ T(g)$, then precomposing by $\eta_X$ yields $\mu_Y \circ T(f) \circ \eta_X = \mu_Y \circ \eta_{T(Y)} \circ f = f$ and similarly for $g$, hence $f = g$.
###### Remark
This Kleisli composition plays an important role in computer science; for this, see the article at monad (in computer science).
## Properties
### Universal properties
In more general 2-categories the universal properties of Kleisli objects are dual to the universal properties of Eilenberg-Moore objects?.
In particular, $C_{\mathbf{T}}$ is initial in the category of adjunctions? for $\mathbf{T}$ (whereas $C^{\mathbf{T}}$ is terminal). For a proof, see Category Theory in Context Proposition 5.2.12.
### In functional programming
In typed functional programming, the Kleisli category is used to model call-by-value? functions with side-effects and computation. See at monad (in computer science) for more on this.
## References
The original source is
• H. Kleisli, Every standard construction is induced by a pair of adjoint functors , Proc. Amer. Math. Soc. 16 (1965) pp.544–546. (AMS)
• Jenö Szigeti, On limits and colimits in the Kleisli category, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 24 no. 4 (1983), p. 381-391 (NUMDAM)
Discussion of cases where the inclusion of the Kleisli category into the Eilenberg-Moore category is a reflective subcategory is in
• Marcelo Fiore, Matias Menni, Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads, Theory and Applications of Categories, Vol. 15, CT2004, No. 2, pp 40-65. (TAC)
Discussion in internal category theory is in
• Tomasz Brzeziński, Adrian Vazquez-Marquez, Internal Kleisli categories, Journal of Pure and Applied Algebra Volume 215, Issue 9, September 2011, Pages 2135–2147 (arXiv:0911.4048)
Discussion of Kleisli categories in type theory is in
• Alex Simpson, Recursive types in Kleisli Categories (pdf)
Last revised on August 26, 2018 at 11:46:01. See the history of this page for a list of all contributions to it.
|
2019-10-22 01:01:04
|
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|
https://gpflow.readthedocs.io/en/develop/notebooks/basics/monitoring.html
|
# Monitoring Optimisation¶
In this notebook we cover how to monitor the model and certain metrics during optimisation.
## Setup¶
[1]:
import numpy as np
import matplotlib.pyplot as plt
import tensorflow as tf
import gpflow
from gpflow.ci_utils import ci_niter
np.random.seed(0)
The monitoring functionality lives in gpflow.monitor. For now, we import ModelToTensorBoard, ImageToTensorBoard, ScalarToTensorBoard monitoring tasks and MonitorTaskGroup and Monitor.
[2]:
from gpflow.monitor import (
ImageToTensorBoard,
ModelToTensorBoard,
Monitor,
ScalarToTensorBoard,
)
## Set up data and model¶
[3]:
# Define some configuration constants.
num_data = 100
noise_std = 0.1
optimisation_steps = ci_niter(100)
[4]:
# Create dummy data.
X = np.random.randn(num_data, 1) # [N, 2]
Y = np.sin(X) + 0.5 * np.cos(X) + np.random.randn(*X.shape) * noise_std # [N, 1]
plt.plot(X, Y, "o")
[4]:
[<matplotlib.lines.Line2D at 0x7f15c0c1d160>]
[5]:
# Set up model and print
kernel = gpflow.kernels.SquaredExponential(lengthscales=[1.0, 2.0]) + gpflow.kernels.Linear()
model = gpflow.models.GPR((X, Y), kernel, noise_variance=noise_std ** 2)
model
[5]:
<gpflow.models.gpr.GPR object at 0x7f15c0c3d4e0>
name class transform prior trainable shape dtype value
GPR.kernel.kernels[0].variance ParameterSoftplus True () float641.0
GPR.kernel.kernels[0].lengthscalesParameterSoftplus True (2,) float64[1. 2.]
GPR.kernel.kernels[1].variance ParameterSoftplus True () float641.0
GPR.likelihood.variance ParameterSoftplus + Shift True () float640.009999999999999998
[6]:
# We define a function that plots the model's prediction (in the form of samples) together with the data.
# Importantly, this function has no other argument than fig: matplotlib.figure.Figure and ax: matplotlib.figure.Axes.
def plot_prediction(fig, ax):
Xnew = np.linspace(X.min() - 0.5, X.max() + 0.5, 100).reshape(-1, 1)
Ypred = model.predict_f_samples(Xnew, full_cov=True, num_samples=20)
ax.plot(Xnew.flatten(), np.squeeze(Ypred).T, "C1", alpha=0.2)
ax.plot(X, Y, "o")
# Let's check if the function does the desired plotting
fig = plt.figure()
ax = fig.subplots()
plot_prediction(fig, ax)
plt.show()
We now define the MonitorTasks that will be executed during the optimisation. For this tutorial we set up three tasks: - ModelToTensorBoard: writes the models hyper-parameters such as likelihood.variance and kernel.lengthscales to a TensorBoard. - ImageToTensorBoard: writes custom matplotlib images to a TensorBoard. - ScalarToTensorBoard: writes any scalar value to a TensorBoard. Here, we use it to write the model’s training objective.
[7]:
log_dir = "logs" # Directory where TensorBoard files will be written.
lml_task = ScalarToTensorBoard(log_dir, lambda: model.training_loss(), "training_objective")
We now group the tasks in a set of fast and slow tasks and pass them to the monitor. This allows us to execute the groups at a different frequency.
[8]:
# Plotting tasks can be quite slow. We want to run them less frequently.
# We group them in a MonitorTaskGroup and set the period to 5.
# The other tasks are fast. We run them at each iteration of the optimisation.
# Both groups are passed to the monitor.
# slow_tasks will be run five times less frequently than fast_tasks.
[9]:
training_loss = model.training_loss_closure(
compile=True
) # compile=True (default): compiles using tf.function
for step in range(optimisation_steps):
opt.minimize(training_loss, model.trainable_variables)
monitor(step) # <-- run the monitoring
TensorBoard is accessible through the browser, after launching the server by running tensorboard --logdir \${logdir}. See the TensorFlow documentation on TensorBoard for more information.
For optimal performance, we can also wrap the monitor call inside tf.function:
[10]:
log_dir = f"{log_dir}/compiled"
lml_task = ScalarToTensorBoard(log_dir, lambda: model.training_loss(), "training_objective")
# Note that the ImageToTensorBoard task cannot be compiled, and is omitted from the monitoring
In the optimisation loop below we use tf.range (rather than Python’s built-in range) to avoid re-tracing the step function each time.
[11]:
@tf.function
def step(i):
opt.minimize(model.training_loss, model.trainable_variables)
monitor(i)
# Notice the tf.range
for i in tf.range(optimisation_steps):
step(i)
When opening TensorBoard, you may need to use the command tensorboard --logdir . --reload_multifile=true, as multiple FileWriter objects are used.
|
2021-01-25 01:30:37
|
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|
https://cms.math.ca/10.4153/CMB-2007-040-3
|
location: Publications → journals → CMB
Abstract view
A Short Proof of Affability for Certain Cantor Minimal $\Z^2$-Systems
We will show that any extension of a product of two Cantor minimal $\Z$-systems is affable in the sense of Giordano, Putnam and Skau.
|
2017-11-18 06:21:34
|
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|
https://nest-simulator.readthedocs.io/en/latest/guides/running_simulations.html
|
Warning
This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!
# Running simulations¶
## Introduction¶
To drive the simulation, neurons and devices (nodes) are updated in a time-driven fashion by calling a member function on each of them in a regular interval. The spacing of the grid is called the simulation resolution (default 0.1ms) and can be set using SetKernelStatus:
SetKernelStatus("resolution", 0.1)
Even though a neuron model can use smaller time steps internally, the membrane potential will only be visible to a multimeter on the outside at time points that are multiples of the simulation resolution.
In contrast to the update of nodes, an event-driven approach is used for the synapses, meaning that they are only updated when an event is transmitted through them (Morrison et al. 2005). To speed up the simulation and allow the efficient use of computer clusters, NEST uses a hybrid parallelization strategy. The following figure shows the basic loop that is run upon a call to Simulate:
Figure 16 Simulation Loop
The simulation loop. Light gray boxes denote thread parallel parts, dark gray boxes denote MPI parallel parts. U(St) is the update operator that propagates the internal state of a neuron or device.
## Simulation resolution and update interval¶
Each connection in NEST has its own specific delay that defines the time it takes until an event reaches the target node. We define the minimum delay dmin as the smallest transmission delay and dmax as the largest delay in the network. From this definition follows that no node can influence another node during at least a time of dmin, i.e. the elements are effectively decoupled for this interval.
Figure 17 Definitions of minimum delay (dmin) and simulation resolution (h).
Two major optimizations in NEST are built on this decoupling:
1. Every neuron is updated in steps of the simulation resolution, but always for dmin time in one go, as to keep neurons in cache as long as possible.
2. MPI processes only communicate in intervals of dmin as to minimize communication costs.
These optimizations mean that the sizes of spike buffers in nodes and the buffers for inter-process communication depend on dmin+dmax as histories that long back have to be kept. NEST will figure out the correct value of dmin and dmax based on the actual delays used during connection setup. Their actual values can be retrieved using GetKernelStatus:
GetKernelStatus("min_delay") # (A corresponding entry exists for max_delay)
### Setting dmin and dmax manually¶
In linear simulation scripts that build a network, simulate it, carry out some post-processing and exit, the user does not have to worry about the delay extrema dmin and dmax as they are set automatically to the correct values. However, NEST also allows subsequent calls toSimulate, which only work correctly if the content of the spike buffers is preserved over the simulations.
As mentioned above, the size of that buffer depends on dmin+dmax and the easiest way to assert its integrity is to not change its size after initialization. Thus, we freeze the delay extrema after the first call to Simulate. To still allow adding new connections inbetween calls to Simulate, the required boundaries of delays can be set manually using SetKernelStatus (Please note that the delay extrema are set as properties of the synapse model):
SetDefaults("static_synapse", {"min_delay": 0.5, "max_delay": 2.5})
These settings should be used with care, though: setting the delay extrema too wide without need leads to decreased performance due to more update calls and communication cycles (small dmin), or increased memory consumption of NEST (large dmax).
## Spike generation and precision¶
A neuron fires a spike when the membrane potential is above threshold at the end of an update interval (i.e., a multiple of the simulation resolution). For most models, the membrane potential is then reset to some fixed value and clamped to that value during the refractory time. This means that the last membrane potential value at the last time step before the spike can vary, while the potential right after the step will usually be the reset potential (some models may deviate from this). This also means that the membrane potential recording will never show values above the threshold. The time of the spike is always the time at the end of the interval during which the threshold was crossed.
NEST also has a some models that determine the precise time of the threshold crossing during the interval. Please see the documentation on precise spike time neurons for details about neuron update in continuous time and the documentation on connection management for how to set the delay when creating synapses.
## Splitting a simulation into multiple intervals¶
In some cases, it may be useful to run a simulation in shorter intervals to extract information while the simulation is running. The simplest way of doing this is to simply loop over Simulate() calls:
for _ in range(20):
nest.Simulate(10)
# extract and analyse data
would run a simulation in 20 rounds of 10 ms. With this solution, NEST takes a number of preparatory and cleanup steps for each Simulate() call. This makes the solution robust and entirely reliable, but comes with a performance cost.
A more efficient solution doing exactly the same thing is
nest.Prepare()
for _ in range(20):
nest.Run(10)
# extract and analyse data
nest.Cleanup()
For convenience, the RunManager() context manager can handle preparation and cleanup for you:
with nest.RunManager():
for _ in range(20):
nest.Run(10)
# extract and analyse data
Note
• If you do not use RunManager(), you must call Prepare(), Run() and Cleanup() in that order.
• You can call Run() any number of times inside a RunManager() context or between Prepare() and Cleanup() calls.
• Calling SetStatus() inside a RunManager() context or between Prepare() and Cleanup() will lead to unpredictable results.
• After calling Cleanup(), you need to call Prepare() again before calling Run().
## Repeated simulations¶
The only reliable way to perform two simulations of a network from exactly the same starting point is to restart NEST or to call ResetKernel() and then to build the network anew. If your simulations are rather large and you are working on a computer with a job queueing system, it may be most efficient to submit individual jobs or a job array to smiulate network instances in parallel; don’t forget to use different random seeds!
The following example performs simulations of a single neuron driven by a Poisson spike train using different seeds and output files for each run:
for n in range(10):
nest.ResetKernel()
nest.SetKernelStatus({'grng_seed': 100*n + 1,
'rng_seeds': [100*n + 2]})
pg = nest.Create('poisson_generator', params={'rate': 1000000.0})
nrn= nest.Create('iaf_psc_alpha')
sd = nest.Create('spike_detector',
params={'label': 'spikes-run{:02d}'.format(n),
'record_to': 'ascii'})
nest.Connect(pg, nrn)
nest.Connect(nrn, sd)
nest.Simulate(100)
## Monitoring elapsed time¶
The progress of the simulation can be monitored by setting:
SetKernelStatus({"print_time": True})
If enabled, a line is printed to screen at every time step of the simulation to track the percentage, the absolute elapsed model time and the real-time factor, for example:
[ 25% ] Model time: 250.0 ms, Real-time factor: 2.6711
The real-time factor is defined as the quotient of wall-clock time (which is also known as real time) and the model time (which is the duration by which the state of the model is advanced in time, or in short, the argument to the Simulate() call):
$q_\text{real} = \frac{T_\text{wall}}{T_\text{model}}$
If the real-time factor is larger than 1 as in the example above, the simulation runs slower than the wall-clock time.
In case a simulation script contains multiple Simulate() calls, the percentage simulation time is reset to 0% at the beginning of each call, but the absolute model time and the real-time factor account for the total elapsed times.
The real-time factor should not be confused with the concept of speedup. Speedup refers to a ratio of wall-clock times, namely the wall-clock time needed to solve a problem serially and the wall-clock time needed to solve the same problem in parallel (e.g., by distributing the work across multiple threads or processes):
$q_\text{speedup} = \frac{T_\text{wall, serial}}{T_\text{wall, parallel}}$
Note
For large, distributed simulations, it is recommended to set {"print_time": False} to avoid the overhead of the print calls. In these cases, the real-time factor can be computed by measuring the wall-clock time manually and dividing by the set model time.
|
2020-06-06 11:50:58
|
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|
https://projecteuclid.org/euclid.ade/1356651340
|
### Existence of multidimensional travelling fronts with a multistable nonlinearity
#### Abstract
This article deals with the existence of solutions of $$\left\{\begin{array}{rll} \Delta u-\beta(y,c) \frac{\partial u} {\partial x_1} +f(u) & =0 & \hbox{ in }\Sigma\\ \frac{\partial u}{\partial \nu} & =0 & \hbox{ on }\partial\Sigma\\ u(-\infty,\cdot)=0,\ u(+\infty,\cdot) & =1 & \end{array}\right.$$ where $\Sigma=\{(x_1,y)\in\mathbb R \times\omega\}$ is an infinite cylinder with outward unit normal $\nu$ and whose section $\omega\subset\mathbb R^{n-1}$ is a bounded convex domain. The unknowns are the real parameter $c$ and the function $u$ (which respectively represent the speed and the profile of a travelling wave). The function $\beta$ and the nonlinear term $f:[0,1]\to \mathbb R$ are given. We investigate the case where the function $f$ changes sign several times. We prove that there exists a travelling front $(c,u)$ provided that the speeds of the travelling waves for simpler problems can be compared. The proof uses the sliding method and the theory of sub- and supersolutions. This result generalizes for higher dimensions a one-dimensional result of Fife and McLeod.
#### Article information
Source
Adv. Differential Equations, Volume 5, Number 4-6 (2000), 557-582.
Dates
First available in Project Euclid: 27 December 2012
|
2019-12-07 11:41:46
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https://ijnaa.semnan.ac.ir/?_action=article&kw=14410&_kw=%24b%24-metric+space
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Keywords = $b$-metric space
Number of Articles: 3
##### 1. Best proximity point theorems by $K$, $C$ and $\mathcal{MT}$ types in $b$-metric spaces with an application
Volume 12, Issue 2, Summer and Autumn 2021, Pages 1317-1329
Setareh Ghezellou; Mahdi Azhini; Mehdi Asadi
##### 2. Generalized dynamic process for generalized $(\psi, S,F)$-contraction with applications in $b$-Metric Spaces
Volume 12, Issue 2, Summer and Autumn 2021, Pages 1947-1964
Akindele Adebayo Mebawondu; Oluwatosin Temitope Mewomo
##### 3. Existence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
Volume 8, Issue 2, Summer and Autumn 2017, Pages 263-276
Cristian Chifu; Gabriela Petrusel
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2021-12-08 06:23:35
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