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# Maxwell Relations Ppt

Our courses are free of charge and accessible 24/7. To practice integrity means seeking out the best for your employees. They were derived by mathematician James Clerk Maxwell, who first published them in 1861 and in 1862. See the complete profile on LinkedIn and discover Kurt’s connections and jobs at similar companies. formulated by Maxwell, may be expressed easily in integral form. Ham Society of Character. Discretionary Authority. Addison February 25, 2003 Introduction In this lecture we introduce other thermodynamic potentials and Maxwell relations. Inspiring stories, instructive interviews and life-changing strategies. 141,440 views. Animations to view in class and at home:. Relation Networks for Object Detection is described in an CVPR 2018 oral paper. 3 Maxwell relations The diﬀerentiability of the thermodynamic potentials leads to various Maxwell relations, such as the one given by Eq. In 2010, Chile's Asociación Chilena de Seguridad (ACHS), a workers' insurance non-profit corporation, was facing rising accident rates and falling financial returns. FaceBook post by Simon Sinek from Dec 25, 2015. A reliable kinetic description of relativistic non-equilibrium plasma sheaths—besides its interest from a fundamental point of view—is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Maxwell determined the distribution of velocities among the molecules of a gas. Don’t think of success as a place. On this site, you’ll find: You can get a series of hints to help you solve the problem, or you can see. Page Link: Maxwell Relations - Posted By: seminar class Created at: Wednesday 23rd of March 2011 12:27:40 PM Last Edited Or Replied at :Wednesday 23rd of March 2011 12:27:40 PM [:=Show Contents=:] maxwell thermodynamic relations ppt, how to use the maxwell relations, ppt of new topics in thermodynamics in chemistry, chemistry seminar on maxwell. The Helmholtz equation is closely related to the Maxwell system (for time-harmonic elds). Office of Personnel Management, Accountability and Workforce Relations (AWR), sponsors training for human resources practitioners, such as labor relations specialists who represent federal agencies. Photon Model of Light. the thought that everyone doing business is blessed, because. 9979 X 108 m/s, from this Maxwell concluded that light itself is an EM wave [1,2,3]. At that time, electricity and magnetism had been extensively studied, and it was known since 1831 that electric current produces magnetism. Interior permanent magnet synchronous motor (IPM motor) is a motor that is highly efficient and has a wide operation range, wherein this motor uses a rare earth-sintered permanent magnet having a strong magnetic force and uses a reluctance torque that is caused by the inductance difference of d- and q-axes, in addition to a magnet torque due to the magnetic. All the different kinds of electromagnetic radiation are essentially the same "stuff" as light: they're forms of energy that travel in straight lines, at the speed of light (300,000 km or 186,000 miles per second), when electrical and magnetic vibrations wiggle from side to side. (See the magnifying glass at the top right of the page. The changing nature of work and society, it is. It can only change forms. Discovering and Creating Possibilities. The definitions, canonical state variables and Maxwell relations for all four functions are summarised in Table 4. 2 Linear Pulse Propagation in Isotropic Me-dia For dielectric non magnetic media, with no free charges and currents due. Perhaps because he was a minister for 25 years, Maxwell is somewhat overly fond of well-worn anecdotes and even ditties, but some readers will find that his charts, pull-quotes, bulleted lists and cartoons help make his ideas easily. Auburn University has developed into one of the largest universities in the South, remaining in the educational forefront with its traditional blend of arts and applied science and changing with the needs of today while living with a respect for the traditions and spirit that are Auburn. pdf), Text File (. Download CSS Notes in all formats, video, audio, ppt, pdf. Since the order in which a second partial derivative is taken is unimportant, it follows that, Maxwell’s relations:. See the complete profile on LinkedIn and discover Kurt’s connections and jobs at similar companies. Maxwell's right hand grip rule Assume that the current carrying conductor is held in the right hand so that the fingers wrap around the conductor and the thumb is stretched (as shown in the figure at left). Maxwell, leaders who fail to grasp this fact are often hampered by ego, insecurity, or temperament. Abstract: The purpose of this paper is to describe the most relevant features of qualitative research in order to show how, from the Epistemology of the Known Subject perspective I propose, it is necessary to review first the ontological and then the. BHP released its 2019 Annual Reporting Suite, an in-depth look at BHP's operations and performance over the 2019 financial year. Stay up to date with Google company news and products. He is the only child of Isabella Mary (Abbott), a secretary to the Dean of Sciences at McGill University, and John Orme Plummer, who sold securities and stocks. 1-day read. The process of tissue repair is a complex series of cascaded, chemically mediated events that lead to the production of scar tissue that constitutes an effective material to restore the continuity of the damaged tissue. The Ampere-Maxwell law Integral formReminder that the Dot product tells you to findmagnetic field is a the part of H parallel to dlvector (along path C) The rate of change An incremental The electric current with time segment of path in amperes C 𝑑 𝐻h𝑑 𝑙 = 𝐼 𝑒𝑛𝑐 + 𝜀0 𝐸h𝑛 𝑑𝑎 𝐶 𝑑𝑡 𝑠 The electric. Displaying maxwell equation PowerPoint Presentations Lecture 6: Maxwell’s Equations Cerkio Srl PPT Presentation Summary : Together with the Maxwell’s equations, the constitutive relations completely describe the electromagnetic field. Interior permanent magnet synchronous motor (IPM motor) is a motor that is highly efficient and has a wide operation range, wherein this motor uses a rare earth-sintered permanent magnet having a strong magnetic force and uses a reluctance torque that is caused by the inductance difference of d- and q-axes, in addition to a magnet torque due to the magnetic. Occasion: Georgia Public Library Service's "Georgia Cataloging Summit" Location: Unicoi Lodge & Conference Center, Helen, GA USA Date: August 9-10, 2011. Physics UCLA 1979. These equations were mostly known prior to Maxwell and their names are given, but Maxwell combined them into a single theory. We’re software experts who invest in growth. would change the view of light is, Maxwell's equations are still valid within it. When you talk with Critical Carl about his negative attitude, give him a goal: Tell him that if he has a problem with a plan, a person, or a situation, you would like to hear something positive he’s found as well. The power delivered from an alternating current source is also alternating, and it is known as AC power. John J has 5 jobs listed on their profile. This is an official implementation for Relation Networks for Object Detection based on MXNet. One can apply Onsager's fluctuation theory to a mass-transfer system with various driving forces, such as gradients of mole fraction, concentration, or chemical potential, and obtain a proper reciprocal. It's a Bible resource that The people, events, and teachings of the Bible are a treasury of wisdom and guidance for anyone who has been called to be a leader, to develop leaders, or to work with leaders-in church, business. Maxwell Relations (2) - Free download as Powerpoint Presentation (. Submit questions for earnings call. Take the right people with you on your success journey. 0001637459-20-000027. The role of ethics in. The signs are accumulated on the. They will make you ♥ Physics. Setting boundary and initial conditions: these are invoked so that solutions to Maxwell’s equations are uniquely solved for a particular application. The wave equation is a partial differential equation. Scientific realism is a positive epistemic attitude toward the content of our best theories and models, recommending belief in both observable and unobservable aspects of the. For doctors and hospitals, prescribing represents an important source of clinical risk and cost, and is. Lecture 6: Maxwell’s Equations Cerkio Srl PPT. Abstract: The problem of induction refers to the difficulties involved in the process of justifying experience-based scientific conclusions. The current enclosed is the same as for surface 1. This complementary, or dual, role for the behavior of light can be employed to describe all of the known characteristics that have been observed experimentally, ranging from refraction, reflection, interference, and diffraction, to the results with polarized light and the photoelectric effect. Direction of the circular magnetic field lines can be given by Maxwell's right hand grip rule or Right handed cork screw rule. Figure 1 lists the basic steps involved in all DNA extraction methods. News, email and search are just the beginning. In the second section the electric Maxwell equations are derived from a scalar wave equation showing a hidden structure and unifying the electricity and the magnetism. Introduction. The spatial dependence of these components are the same as for the TE-waves E x˘cos mˇx a sin nˇy b e jkzz E y˘sin mˇx a cos nˇy b. No, the equation dU = TdS - PdV applies to irreversible processes as well. Life is beautiful not because of the things we see or do. In this dis-cussion, vectors are denoted by bold-faced underscored lower-case letters, e. Heaviside restructured Maxwell's original 20 equations to be the four equations that we now recognize as Maxwell's equations. Seventh-day Adventists Believe. ()-() using Gauss' theorem and Stokes' theoremEquation () is called Gauss' law, and says that the flux of the electric field out of a closed surface is proportional to the enclosed electric charge. 1 Vector Operations Any physical or mathematical quantity whose amplitude may be decomposed into "directional" components often is represented conveniently as a vector. Join Tims™ Rewards and start earning rewards today. Visit us at embedded world 2020, Booth #4A-606. Maxwell's equations govern all of electricity and magnetism, so it is no surprise that they yield the wave equation. There are furthermore four Maxwell relations relating T, respectively S to P respectively V. Office 365 provides many productivity and collaboration services to the BSU community, online hosted email, additional online storage with OneDrive, Office in the cloud and so much more. The communication process includes clarifying expectations, setting objectives, identifying goals, providing feedback, and reviewing results. We have so far come across three thermodynamic potentials, two of them only briefly. The wave equation follows, along with the wave speed equal to that of light (3 x 10^8), suggesting (correctly) that light is an electromagnetic wave. Thus, according to Maxwell's equations the total loss or core loss is P C =Ph+ Pe (9) where Ph is the hysteresis loss and Pe is the eddy-current loss. It represents the beginning of the far field. Maxwell’s first equation in differential form. 1905 - Albert Einstein uses Maxwell's equations to a start his theory of special relativity. 1) be replaced by a new set of equations that would apply to time varying fields. I would think that there would be 6 Maxwell relations because when using the Legendre transformations, there are 6 choices of two variables from these 4 for me to create a function dependent on these two variables. co last update = 17Sep2015. The simplest solutions are plane waves in inﬂnite media, and we shall explore these now. 7), do not look manifestly covariant with respect to Lorentz transformations. quantities a ^Table of Mendeleyev _ based on their respective relations? It is the purpose of this research to find an answer to the above questions which could result in a classification of the physical quantities and their respective relations. Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow. Miles and Huberman (1994) defined a conceptual framework as a visual or written product,. Consider the disciples. We discuss some of the tactics for solving such equations on the site Differential Equations. The relation between the point impulse and the field impulse is a key point for the UT. Working in HR means being a leader by way of cultivating leadership in the workplace. Since whenever there is current there is charge, both electric and magnetic fields exist. Welcome to the Health and Safety Authority's portal for health and safety courses on-line. 15A, except that they are placed in series. In effect, Maxwell's equations are a set of relations linking the values of a number of quantities that describe. download the script: Maxwell Relations At first, we will deal the Internal energy u, Enthalpy h, Gibbs function g and Free energy or Helmholtz function f. Oren Etzioni, a world-renowned researcher and professor in the field of artificial intelligence. To make the Lorentz transformations. By Becky Rameden Physical Chemistry I. Volume: 573,031. Maxwell determined the distribution of velocities among the molecules of a gas. The field equations ()-() can be deduced from Eqs. web; books; video; audio; software; images; Toggle navigation. Anywhere, Today. They are named after James Clerk Maxwell, the Scottish physicist whose pioneering work during the second half of the 19th century unified the theories of electricity, magnetism, and light. Bain Capital, LP is one of the world’s leading multi-asset alternative investment firms. Author (s): Prof. The goal of successful Investor Relation (IR) is to achieve a fair valuation for a company’s shares, suitable. Maxwell has done exactly that in The 21 Irrefutable Laws of Leadership. (AKRON, Ohio – April 30, 2020) – Babcock & Wilcox Vølund A/S (Vølund), a subsidiary of Babcock & Wilcox Enterprises, Inc. • The previous relation is called as Integral form of Maxwell's equation derived from Gauss's law for the electric field. Published by Cambridge University Press, it goes for. 022 Spring 2005 Lecture 19: Displacement current. 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The Pareto Principle is an observation, not a law of nature. that leadership is a multi-directional influence relation, while management is a unidirectional authority relationship (Katz, 1955). The stress-strain relation in a crystal is a more complex situation that can also be described in terms of tensors. Solar Roof Conference Call Webcast. In that context, a contract may be described as an agreement that the law (the Courts) will enforce. The value of our lives is not determined by what we do for ourselves. Alexandre Kolomenski Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist. They are all extremely useful in that the quantity on the right-hand side is virtually impossible to measure directly, while the quantity on the left-hand side is easily measured in the laboratory. Other articles where Maxwell relations is discussed: thermodynamics: Entropy as an exact differential: This is one of four Maxwell relations (the others will follow shortly). Together they had only one child. Williams and Hazer (1986) found a direct link between job satisfaction and organizational commitment, whereby job satisfaction is an antecedent of organizational commitment. Ampère initially considered steady electric currents and this was later expanded by Maxwell to included time varying currents. pdf), Text File (. Starting from ∂U ∂S! V,N = T, and ∂U ∂V! S,N = −p, we can calculate ∂2U ∂V∂S = ∂T ∂V! S,N, and ∂2U ∂S∂V = − ∂p ∂S! V,N. ppt [Mode de compatibilité]. Maxwell's equations are the basic equations of electromagnetism which are a collection of Gauss's law for electricity, Gauss's law for magnetism, Faraday's law of electromagnetic induction and Ampere's law for currents in conductors. It will also cover everything in the \Advanced Quantum Field Theory" course, much of the \Standard Model" course, and will serve you well if you go on to do research. He attended high school in Edinburgh – Edinburgh Academy – where he published his first academic paper, Oval Curves at the age of just 14. ppt Author: dmittlem Created Date: 2/26/2016 9:48:20 AM. We drop in the following the dependence on the number of particles N. The 5 Levels of Leadership are:. This covers the basics of FRBR, including its development and contents. " We should remark, however, that there is an interesting consequence to this additional assumption: we are removing the symmetry with respect to time that exists. People search: find Photos, Location, Education, Job! William Dickerson. , PRL 2008; Valentini and Veltri, PRL 2009 Vienna WPI - Valentini The ion-bulk waves Boltzmanian electrons Debye length Vlasov – Yukawa (VY) model Proton distribution function Valentini et al. 141,440 views. Listen to webcast. Discover stories about our culture, philosophy, and how Google technology is impacting others. 1 Maxwell's Relations; There are 4 laws to thermodynamics, and they are some of the most important laws in all of physics. 4{2 Chi-square: Testing for goodness of t The χχ2 distribution The quantity ˜2 de ned in Eq. In 2010, the SEC's Enforcement Division created a specialized unit to further enhance its enforcement of the FCPA, which prohibits companies issuing stock in the U. Here, is a closed surface enclosing a volume. Speaker Training (Youth Certification Edition) Roddy Galbraith. Supporting Materials. In the discipline of international relations there are contending general theories or theoretical perspectives. Tesla, Inc. It will also cover everything in the \Advanced Quantum Field Theory" course, much of the \Standard Model" course, and will serve you well if you go on to do research. Stakeholders is a broad term and refers to an individual or group of people who has/have an interest in a business. In the second section the electric Maxwell equations are derived from a scalar wave equation showing a hidden structure and unifying the electricity and the magnetism. Displaying maxwell equation PowerPoint Presentations Lecture 6: Maxwell's Equations Cerkio Srl PPT Presentation Summary : Together with the Maxwell's equations, the constitutive relations completely describe the electromagnetic field. This book covers the following topics: Probability and Statistics, The Maxwell-Boltzmann Distribution, Collision Rates, Diffusion and Viscosity, Collision Theory of the Rate Constant, First Law of Thermodynamics, Thermochemistry, Ideal Gas Carnot Engines and Efficiency, The Second Law of Thermodynamics, The Clausius Inequality and the Mathematical Statement of. 13 Heat Capacities Previous: 2. 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Analysis We do not have exact analytical property relations for refrigerant-134a, and thus we need to replace the differential quantities in the last Maxwell relation with the corresponding finite quantities. I would think that there would be 6 Maxwell relations because when using the Legendre transformations, there are 6 choices of two variables from these 4 for me to create a function dependent on these two variables. Definition and concept. A Mnemonic to Remember the Maxwell Relations. & Maxwell, C. You can’t change how he thinks. txt) or view presentation slides online. Tesla has agreed to buy energy storage company Maxwell Technologies for 218 million US in an all-stock deal that could help the electric car maker produce batteries that hold more energy and last. It is the integral form of Maxwell’s 1st equation. Thermodynamic Potentials and Maxwell's Relations Stephen R. 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One can apply Onsager's fluctuation theory to a mass-transfer system with various driving forces, such as gradients of mole fraction, concentration, or chemical potential, and obtain a proper reciprocal. 11 Available work 2. One of its most famous aspects concerns objects moving. In the radiative area, the fields begin to radiate. Sandra has 1 job listed on their profile. Maxwell's Equations for Electromagnetic Waves 6. Book summary by Regine P. Definition and concept. When collaborating with our customers, we leverage our deep knowledge of material science, our i6 Innovation Process™, and our industry-leading packaging and services portfolio to create impactful customized solutions that build stronger brands. It was Maxwell's idea that by substituting J with J+!D!t in Ampère's law (and therefore modifying it) the aforementioned inconsistency could be erased. Home of Canada's favourite coffee. 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Inova is Northern Virginia’s leading nonprofit healthcare provider, recognized in 2019 by U. 1947) Main goals - To develop constitutive models that can describe non-linear phenomena such as rod climbing - To use the equations in practical applications such as polymer processing and soft tissue mechanics Ranges of viscoelasticity: the Deborah number. Beautiful, People, Life Is Beautiful. 022 141 5 x 1023 particles/mole. Jesus came with the purpose of reclaiming the world with the Gospel. Browse our courses and find one that suits you whether you're in education or work. In any process, the total energy of the universe remains the same. The Cauchy’s integral theorem indicates the intimate relation between simply connectedness and existence of a continuous antiderivative. And I thought that this would mean there are 6 relations. Properties of Light • Waves, particles and EM spectrum • Interaction with matter • Absorption • Reﬂection, refraction and scattering • Polarization and diffraction • Reading foci: pp 175-185, 191-199 not responsible for boxes 7. It is usually contrasted with idealism or liberalism, which tends to emphasize cooperation. International Affairs is a leading journal of international relations. Looking for a specialist? Looking for an urgent care? Find One Near You SEE ALL LOCATIONS. We have so far established that the total flux of electric field out of a closed surface is just the total enclosed charge multiplied by 1 / ε 0, ∫ E → ⋅ d A → = q / ε 0. 6022 × 10–19 C. The process of tissue repair is a complex series of cascaded, chemically mediated events that lead to the production of scar tissue that constitutes an effective material to restore the continuity of the damaged tissue. The stress-strain relation in a crystal is a more complex situation that can also be described in terms of tensors. In thermodynamics, the Maxwell equations are a set of equations derived by application of Euler's reciprocity relation to the thermodynamic characteristic functions. There are a variety of memo template styles available to explore. Come to E-Day February 22. Email: [email protected] Listen to webcast. Download CSS Notes in all formats, video, audio, ppt, pdf. Created Date: 11/1/2005 9:34:41 PM. Subscribe today. LECTURE NOTES 6 ELECTROMAGNETIC WAVES IN MATTER Electromagnetic Wave Propagation in Linear Media We now consider EM wave propagation inside linear matter, but only in regions where there are NO free charges free 0 and/or free currents Kfree 0 (i. Maxwell Relations Idea: Each thermodynamic potential gives rise to several identities among its second derivatives, known as Maxwell relations, which express the integrability of the fundamental identity of thermodynamics for that potential, or equivalently the fact that the potential really is a thermodynamical state function. web; books; video; audio; software; images; Toggle navigation. 12–19) for steam at 250°C and 300 kPa. of Kansas Dept. In Section 8. Newton showed that his laws explained Kepler’s Laws of planetary motion where the planet orbits are elliptical rather than circular. The literature on social exclusion is, obviously, not for the abstemious. By the 1850’s, various difficulties with the existing theories of heat, such as the caloric theory, caused some rethinking, and people took another look at the kinetic theory of Bernoulli, but little real progress was made until Maxwell attacked the problem in 1859. MAXWELL CENTER FOR INTERNATIONAL COMMUNICATIONS Donate To Support The Maxwell Center's Educational Efforts Our Mission. 4 Mass Transfer and Chemical Reaction inside a Porous Catalyst Pellet 6. A team is any group of people organized to work together, both interdependently and cooperatively to accomplish a purpose or a goal. James Clerk Maxwell collected all that was known about electricity and magnetism and summarized it in 4 equations. Perhaps because he was a minister for 25 years, Maxwell is somewhat overly fond of well-worn anecdotes and even ditties, but some readers will find that his charts, pull-quotes, bulleted lists and cartoons help make his ideas easily. 3 Gas Absorption into a Falling Liquid Film 5. Definition and concept. Clerk Maxwell's career will be recounted in the following brief sketch, and the reader who wishes to obtain further and more detailed information or to study his character in its social relations may consult the interesting work to which reference has been made. James Clerk Maxwell (1831-1879). Call 1-855-MY-INOVA (855-694-6682) Common Questions. It is the level at which the leader has achieved the right to lead in an organisation without any difficulty. 2 shows the mean free path of a molecule, the impingement rate (molecules/cm 2 /sec at 25°C) and the time to form one ML of adsorbed species (assuming a unity sticking coefficient) at room temperature as a function of pressure. The content may be incomplete. The first equation allows you to calculate the electric field created by a charge. Every day, leaders are making countless decisions and facing problems they've never encountered before. 4) The vacuum velocity of light is c 0 = s 1 µ 0 0. Maxwell Equations (a brief reminder of electromagnetism) Basic Facts - Maxwell Equations obtained by generalizing of observations intrinsically relativistic can be made compatible with QM- quantum electrodynamics this lecture: "classical" electric and magnetic field Maxwell Equations Maxwell Equations Maxwell Equations Potentials General solutions Multipole Expansions Multipole expansion. It depends on the nature, size, and composition of the system. See the complete profile on LinkedIn and discover Kurt’s connections and jobs at similar companies. In this dis-cussion, vectors are denoted by bold-faced underscored lower-case letters, e. This theory of mass communication was formally introduced in 1972 by Maxwell McCombs and Donald Shaw, two professors who documented a significant correlation between issues citizens of Chapel Hill, N. The Labor Relations Professional Development Series I (LR-PDS I. For thermodynamic relations, see Maxwell relations. 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Updates from Dr. At that time, electricity and magnetism had been extensively studied, and it was known since 1831 that electric current produces magnetism. This is a fundamental relationship, and it is never violated for systems at equilibrium. The value of our lives is determined by what we do for others. Maxwell Relations 1 - Free download as Powerpoint Presentation (. Maxwell's centroid asymmetry measured by the control cohort. Covariant Formulation of Electrodynamics. Maxwell's Equations are commonly written in a few different ways. Think of it as a path. Between Newton and Einstein, James Clerk Maxwell Stands Alone In his Principia Mathematica (1687), Sir Isaac Newton gave the foundations of classical mechanics and gravity. This distribution was first set forth by the Scottish physicist James Clerk Maxwell in 1859, on the basis of probabilistic arguments, and gave the distribution of velocities among the molecules of a gas. The permittivity and permeability μ are related to the electric and magnetic susceptibilities of the material as follows. She enjoys helping businesses with the startup spirit grow. • To relate D with del operator to convert surface integral into volume integral using Divergence theorem as:- • Comparing two integrals, we can say that,. Helmholtz free energy From Wikipedia, the free encyclopedia In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the "useful" work obtainable from a closed thermodynamic system at a constant temperature Maxwell relations Table of thermodynamic equations. download the script: Maxwell Relations At first, we will deal the Internal energy u, Enthalpy h, Gibbs function g and Free energy or Helmholtz function f. This graphics illustration was prepared by JOHAN SJÖHOLM and KRISTOFFER PALMER as part of their undergraduate Diploma Thesis. We begin by re-viewing Maxwell's equations and their physical signiﬁcance. 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Some quantity A is a function of two variables, B and C (just for the sake of briefness|the actual number of variables can be. transverse waves Derivation of wave equation from Maxwell's Equations Why light waves are transverse waves – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Perceptions are formed through customers’ assessment of the quality of service provided by a company and whether they are satisfied with the overall service (Zeithaml and Bitner, 2003, p. how much he loves helping people with the actual gardening. Walgreens is your home for Pharmacy, Photo and Health & Wellness products. Heaviside restructured Maxwell's original 20 equations to be the four equations that we now recognize as Maxwell's equations. And I thought that this would mean there are 6 relations. No, the equation dU = TdS - PdV applies to irreversible processes as well. 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A reliable kinetic description of relativistic non-equilibrium plasma sheaths—besides its interest from a fundamental point of view—is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Maxwell's Equations. 1 Maxwell's Equations The equations developed by James Clerk Maxwell describe the behavior of electric and magnetic fields and their interaction with matter. Orson Bean passed away on February 7, 2020. Organization Development Models: A Critical Review 29 ISSN 2057-5238(Print), ISSN 2057-5246(Online) and Implications for Creating Learning Organizations Maxwell. Other articles where Maxwell relations is discussed: thermodynamics: Entropy as an exact differential: This is one of four Maxwell relations (the others will follow shortly). 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Standard Costing and Variance Analysis Topic Gateway Series 3. 4{2 Chi-square: Testing for goodness of t The χχ2 distribution The quantity ˜2 de ned in Eq. Instead, it is to ground your proposed study in the relevant previous work, and to give the reader a clear sense of your theoretical approach to the phenomena that you propose to study” (p. The webcast addresses, through an exploration of RDA itself, how FRBR lies at the foundation of RDA’s structure, and what. The 21 Irrefutable Laws of Leadership is a powerful, definitive statement of the timeless laws you simply must follow if you want to be a great leader—at home, on the job, in church, or whenever you are called on to lead. It’s a big responsibility and one that is constantly evolving. Agenda-setting theory refers to how the media’s news coverage determines which issues become the focus of public attention. 19), taking their rotation, and combining the two resulting equations we obtain. 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However, the fundamental question of what factors make a fores. Cynthia Stevens Kent (ret. News & World Report which named Inova Fairfax Hospital the #1 hospital in the Washington, DC region. Ampère initially considered steady electric currents and this was later expanded by Maxwell to included time varying currents. We can use a Maxwell Relation to change these into ones we can more readily measure, -(\frac{\partial V}{\partial T})_P $for this example. From motherhood through menopause, Yale New Haven Hospital is committed to meeting the specialized health care needs of women. They were published by Maxwell in 1864 and in its original form comprised of 20 equations in 20 unknowns. When the calibrated components are a. Cars on demand. Maxwell's Equations for Electromagnetic Waves 6. Please try the A to Z Directory here or use the search tool. Gauss's theorem states that the surface integral of the electrostatic field D over a closed surface is equal to the charge. 1 The Internal Energy U. Gnosticism embraces numerous general attitudes toward life: it encourages non-attachment and non-conformity to the world, a “being in the world, but not of the world”; a lack of egotism; and a respect for the freedom and dignity of other beings. Zeroth law of thermodynamics - If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. On this site, you'll find: Complete solutions to every problem in the book. Page Link: Maxwell Relations - Posted By: seminar class Created at: Wednesday 23rd of March 2011 12:27:40 PM Last Edited Or Replied at :Wednesday 23rd of March 2011 12:27:40 PM [:=Show Contents=:] maxwell thermodynamic relations ppt, how to use the maxwell relations, ppt of new topics in thermodynamics in chemistry, chemistry seminar on maxwell. 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Job satisfaction and organizational commitment Past research has found a positive correlation between job satisfaction and organizational commitment (Mathieu & Zajac, 1990). ppt), PDF File (. Marine Corps University (MCU) Interior and exterior of MCU new construction. Hertz is also the man whose peers honored by attaching his name to the unit of frequency; a cycle per second is one hertz. 2 Introduction Formulations of electromagnetic problems ♦ Maxwell equations, material relations ♦ Electrostatics, electrokinetics, magnetostatics, magnetodynamics ♦ Strong and weak formulations Discretization of electromagnetic problems ♦ Finite elements, mesh, constraints ♦ Very rich content of weak finite element formulations. The stress-strain relation in a crystal is a more complex situation that can also be described in terms of tensors. Maxwell Relations 1 - Free download as Powerpoint Presentation (. 30 – May 2009. 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Presentation Summary : Chapter 31 Serway & Jewett 6th Ed. • (a) The relation between U and q • The total energy of the system relative to the energy of the lowest state • Because the most probable configuration is so strongly dominating, use the Boltzmann distribution for the populations • A form involving only q. Agenda setting theory (Maxwell McCombs and Donald L. 9 million in Canada; - 66% (~17. Communication is the most important skill in life. At that time, electricity and magnetism had been extensively studied, and it was known since 1831 that electric current produces magnetism. Millikan (1868-1953) devised a method known as oil drop experiment (1906-14), to determine the charge on the electrons. Yet he did more than anyone else to shape how James Clerk Maxwell’s electromagnetic theory was understood and applied in the 50 years after Maxwell’s death. Submit questions for earnings call. Parameters for both torsional and nonbonded energetics have been derived, while the bond stretching and angle bending parameters have been adopted mostly from the AMBER all-atom force field. His second wife was Carolyn Maxwell, whom he married in 1965. Investor Relations Sustainability & Corporate Responsibility Sales & Channel Effectiveness. It describes the magnetic fields that result from a transmitter wire or loop in electromagnetic surveys. His first wife was actress Jacqueline De Sibour, to whom he married in 1956. '石证书,'石认证,'石火彩,'石鉴定,'石等级,'石光性能,珠宝实验室. Office of Personnel Management, Accountability and Workforce Relations (AWR), sponsors training for human resources practitioners, such as labor relations specialists who represent federal agencies. 2 The Maxwell - Stefan Relations. It was Maxwell's idea that by substituting J with J+!D!t in Ampère's law (and therefore modifying it) the aforementioned inconsistency could be erased. However, the Maxwell equations as they stand, written in the form given in equation (1. (AKRON, Ohio – April 30, 2020) – Babcock & Wilcox Vølund A/S (Vølund), a subsidiary of Babcock & Wilcox Enterprises, Inc. The major contributors of this repository include Dazhi Cheng, Jiayuan Gu, Han Hu and Zheng Zhang. Change management is the discipline that guides how we prepare, equip and support individuals to successfully adopt change in order to drive organizational success and outcomes. & Maxwell, C. One can thus apply of the criterion of exact differential for these functions. Cooper clearly implicates Zechariah Sitchin in relation to Maxwells work. He is the founder of The John Maxwell Company, The John Maxwell Team. The speed is relentless, the stakes are high, but the rewards are great for those who can lead a team to consistently achieve extraordinary results. Joy Maxwell Director of Legacy Relations at KU Alumni. ppt Author: dmittlem Created Date: 2/26/2016 9:48:20 AM. Please try the A to Z Directory here or use the search tool. 1 Maxwell's Equations The equations developed by James Clerk Maxwell describe the behavior of electric and magnetic fields and their interaction with matter. txt) or view presentation slides online. 4 Plane Electromagnetic Waves To examine the properties of the electromagnetic waves, let's consider for simplicity an electromagnetic wave propagating in the +x-direction, with the electric field E G pointing in the +y-direction and the magnetic field B G in the +z-direction, as shown in Figure 13. Prior to building her own, Mackenzie worked with small businesses and organizations to create effective marketing - from churches to insurance companies. Seth Godin is an Author, Entrepreneur and Most of All, A teacher Seth is an entrepreneur, best-selling author, and speaker. The CSS Point | The Best Place for All CSS Aspirants. An ALCTSwebcast. 03 - Lect 13 - Electromagnetic Waves, Solutions to Maxwell's Equations, Polarization - Duration: 1:15:11. Office 365 provides many productivity and collaboration services to the BSU community, online hosted email, additional online storage with OneDrive, Office in the cloud and so much more. Maxwell’s equations describe large-scale electric and magnetic ﬁelds and also—as Maxwell discovered—the propagation of light waves, at a characteristic velocity, the speed of light. ppt Author: dmittlem Created Date: 2/26/2016 9:48:20 AM. Maxwell understood the significance of Faraday's work and realised that the speed of an electromagnetic waves travelled at the speed of light. This is a fundamental relationship, and it is never violated for systems at equilibrium. It has gotten 167 views and also has 4. Mark Cole Mentorship. Disclaimer. of Kansas Dept. Refill your prescriptions online, create memories with Walgreens Photo, and shop products for delivery or in-store pickup. 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Break times for me are often times to do some coding, and this summer was no exception. I decided to start working on a new version of Cedile, dubbed Cedille Omega because the change to the core type theory is so large as to warrant skipping an infinite number of version numbers from Cedille 1. Ha. Naturally, I was expecting to have something working by the end of the summer, and I do! I can correctly process comments.

Oh my. Did I really spend a month or so on comments? Well, my work time is in a vise due to childcare under the pandemic, but still that seems extravagant. And there is more than just comment support, because I set up an emacs mode communicating with a backend written in Haskell, from scratch. Some things I did not know too well how to do, like set up a bigger Haskell codebase with cabal (with my own nested modules, for example). This was not hard but engineering takes time. The elisp side is more “interesting” because of dynamic typing and elisp weirdness.

But to comments: in Cedille Omega, there are three kinds of comments:

• comment to end of line
• comment to start of line
• nestable comment

Comment to end of line begins with –, as in Haskell. It can also begin with -., to match comment to start of line, which ends with .- and is thus the mirror image. Nestable comments are with {- and -} as in Haskell.  I have not seen comment to start of line, but it seems like an obvious complement to comment to end of line.

I implemented, in the Haskell backend, what I am calling “blanking semantics” for comments. Blanking means to replace the whole comment, including start- and end-comment characters, with spaces. This is handy for indentation-sensitive parsing of non-comment text. There are some conflicts between the three kinds of comments, which are resolved by applying blanking to the different types of comment in order.  So first we blank comments to end of line.  This will erase start- and end-comment characters for all types of comments.  So if you have a line like

hi — there .-

the — will win out over the .-, and blanking will leave only the “hi”.

Finally, dangling start- or end-characters for nestable comments (which can indeed be nested, as in Haskell) comment to end of file or beginning of file, respectively.

This semantics was easy to implement in three passes in Haskell.  Because blanking comments to start of line seemed easier with the string reversed, my code just uses one core function to blank comments to end of line and reverse the string as a result.  So you blank -. comments getting a reversed string, then blank -. again which has the desired effect of blanking comments to start of line.  Then a recursive function blanks nestable comments still standing.  A little extra logic is needed to watch for dangling end-characters for nestable comments.

During blanking, the code builds up character ranges for the different kinds of comments.  The backend then communicates these to the front end, also indicating which kind of comment it is.  The latter information is useful for setting stickiness of text properties in emacs.  You can assign characters text properties, which are retained as text is manipulated (moved, copied, etc.).  I decided to try using the category property, which gives a layer of indirection: you assign the properties you want (like face, which controls the display of the character) to an elisp symbol, and then make that symbol the value of the category property for a piece of text.  Then all the properties you bound to the symbol are applied to the text.  Nifty.  All comments get the same face for comment highlighting.  But I made different categories for the different kinds of comments, so I could set the stickiness of text properties differently for them.  Text properties in emacs can be front- or rear-sticky, which means that they are inherited by new characters inserted just before or just after, respectively, the text with the properties.  Comments to end of line should be rear sticky but not front sticky, and vice versa for comments to beginning of line.  Nestable comments should be front and rear sticky inside the delimiters, but start-characters should not be front sticky and end characters should not be rear-sticky.  So when you type new text right next to a comment , the comment highlighting is inherited or not, appropriately.

Just posting this in case you, too, care to comment.

A little while ago, I posted a challenge to come up with examples where optimal beta-reduction would reduce a term efficiently, but call-by-need evaluation in Haskell (with optimizations on) would be inefficient. A little while ago? Wow, it was last summer! Well, summer time for me has become time to think about optimal beta-reduction. What a hobby, right? And the semester is ending here at U. Iowa, so here it goes again.

Anyhow, I have a little bit of a new challenge — and this time a solution to it (instead of needing help to find a solution: thank you friends!). The examples I got last time (from Victor Maia, many thanks) were all ones that reduce efficiently with optimal beta, but not with call-by-need. You can watch Haskell grind and grind on examples that are instantaneous with optimal beta. But these examples are — or should be; more on that shortly — efficiently executable with normal-order reduction [edit: actually the strategy is a little more than that; see below]. This means that theorem provers like Coq and Agda should be able to reduce them efficiently.

Ok, so the new challenge is to find an example that is inefficient with normal-order reduction (and hence would certainly also be in Haskell), but would be efficient with optimal beta. In a sense Victor already solved this challenge with his very inspiring Medium posts of a couple years back (like this one), as these are examples that execute asymptotically much faster with optimal beta than with call-by-need, and normal-order reduction does not help as they are actually not higher order. But I am hoping for a little simpler example, exhibiting exponential behavior under normal-order reduction. Also, I would like to compare with normal-order reduction explicitly.

The solution (suggested by Victor) to my first challenge is this one:

busy :: Int -> Int -> Int
busy 0 = \ x -> x
busy n = \ x ->
let f = busy (n - 1)
in f (f x)

Asking ghc to evaluate something like busy 34 0 will take a while; call-by-need evaluation is exponential in n. But busy n is always just the identity function, and optimal-beta will take take time linear in n. But (and this realization is what spurred my interest in the new challenge), normal-order evaluation will also be linear in n, because we will reduce busy (n – 1) to the identity function, and then f (f x) reduces in just two beta-reductions to x. [edit: for this to work, we need to use a version of normal-order reduction that evaluates let-terms strictly; let x = t1 in t2 needs t1 to be evaluated first, then t2]

I tried this out in Cedille, which implements [this version of] normal-order evaluation, and sure enough, the runtime is extremely fast, linear in n. Our interpreter is very naive, so evaluating busy 64 would definitely explode if evaluation were exponential — but it completes in a second or two.

Now what surprised me is that this example takes exponential time in both Coq and Agda! Weird, right? Why is that? I am puzzled, and emailed the Agda list to see if anyone has any ideas. [edit: Agda inlines let-definitions, causing the example to blow up.]

But here is a modified version of the example that makes Cedille choke (and certainly Coq, Agda, and I confirmed Haskell as well):

type Id = forall a . a -> a

busy :: Int -> Id -> Id
busy 0 = \ x -> x x
busy n = \ x ->
let f = busy (n - 1)
in f (f x)

Evaluating busy n builds a lambda term which takes in x and then builds a balanced binary tree of depth O(n) of applications of x. For example, Cedille’s normal-order evaluator will show this result for busy 2:

λ x . x x (x x) (x x (x x)) (x x (x x) (x x (x x)))

Here we see a nice example of the power of optimal-beta, because optimal-beta will represent this exponential-sized term in linear space! And applying busy n to the identity function will reduce in linear time. The key point about this example beyond the first version of busy, is that it copies what the Asperti and Guerrini book call “virtual redexes”, namely applications of variables. Those variables could become instantiated later, creating redexes, and we better not copy any redexes (ever!) if we want to be optimal. So copying a virtual redex could lead to non-optimality.

On many PL researchers’ lists of most important ever papers in PL is “Types, Abstraction, and Parametric Polymorphism” by the great John C. Reynolds.  I have been studying the paper rather intensively the past month or so, and would like to share some thoughts (and even a legend for the paper’s notation, at the end of the post!).

In this paper, Reynolds sets out to characterize mathematically what parametric polymorphism is.  Part of the idea is the familiar goal (in Computer Science) that different implementations of the same interface should be interchangeable: as long as they behave the same with respect to the interface, then no other piece of code should be able to tell the difference between them.  Another part of the idea is that type polymorphism can be used to enforce this, as different clients of some interface cannot discover details about the implementation that are hidden behind some type abstraction.

To move these ideas from the realm of intuition to theorems, Reynolds defines two semantics for types.  The first interprets types as sets.  For example, a type like $\textit{Nat} \to \textit{Nat}$ is interpreted as the set of all set-theoretic (mathematical) functions from natural numbers to natural numbers (assuming the type Nat gets interpreted as the set of natural numbers).  Programs in the polymorphic typed lambda calculus he considers are then interpreted as elements of those sets.  For example, $\lambda\ x : \textit{Nat}.\ x$ will be interpeted as the set-theoretic identity function on the set of natural numbers.  This part of the paper is not too surprising.  The type structure of the language enables a straightforward set-theoretic semantics for typed lambda calculus, at least until it comes to impredicative polymorphism.  Here Reynolds speculates in the paper that the semantics will work out, but discovers the next year that it does not (a problem shortly corrected by others who use a different background mathematical theory which avoids the problems raised by impredicativity).  But the paper actually starts out just with a simply typed language, where things work out cleanly, and then adds on polymorphism (where things do not).

The second semantics for types interprets them as binary relations on the sets given by the first semantics.  The relations are the ones familiar from the setting of logical relations.  For example, the relation associated with $\textit{Nat} \to \textit{Nat}$ relates two unary operations on the set of natural numbers iff those functions map related inputs to related outputs (related by the relation for Nat, which Reynolds will take to be the identity relation).  So they should map equal numeric inputs to equal numeric outputs.

The part of the paper that was driving me crazy is the Identity Extension Lemma.  This says that if you have a type and you interpret all its free type variables as identity relations (on the sets that the first interpretation assigns to those type variables), then the interpretation of that type will also be the identity relation.  So identity relations are extended by the semantics from type variables to all types.

Now, the vexing question to me was, why are we setting up all this machinery to define a bunch of identity relations?  There is one formalistic answer, which is that when it comes to polymorphism, Reynolds achieves Identity Extension by the expedient (not to say hack) of making the first interpretation of types invoke the second one (i.e., the relational one), to say that the set interpretation of a polymorphic type is the set of set-theoretic functions which satisfy Identity Extension.  Voila, Identity Extension holds now for polymorphic types!

But now the real answer — and I wish Reynolds had given more hints about this, or if he did, that I noticed them better: the point of the paper is not the relational semantics, though this is technically the most interesting part.  Really, we are just trying to define the set-theoretic semantics for polymorphic types, in such a way that all the functions we intend to be extensionally equivalent are soundly mapped down to the exact same mathematical object.  So we want to interpret mergesort and quicksort as the unique set-theoretic list-sorting function.  This is why Identity Extension is so important: it shows we did this correctly!  All the interesting equivalence has gotten squashed down in that first semantics.  Thus, the second semantics doesn’t have anything interesting to add.  But it is there as a specification of what we were trying to achieve.  For it is the description of the extensional equality we are trying to mash down with the first semantics.

The fact that the relational semantics is required by the set interpretation of polymorphism is, to me, a total cop-out.  It means that we only achieved the squashing down we wanted by including that extensional equality in our set interpretations.  So for the difficult part of the matter (i.e., polymorphism), it is as if we just said that the set interpretation of type A is the set of equivalence classes of terms, where the equivalence in question is the one given by the relational semantics.  If our goal was to achieve a set interpretation that satisfied that extensional equivalence (i.e., Identity Extension) but was independent of it, then at this point we failed.

Now, this is just the seminal paper in a pretty technically involved line of research.  It looks, though, in more modern treatments, as if the basic set-up is accepted: two semantics, mutually dependent.  That is clearly flawed, if the goal is as I just described (set interpretations which are independent of but satisfy the relational interpretations).  But perhaps that is not the goal of these more recent works?

If you think I am mistaken in any of the above, please perform your charitable deed of the day and correct me!  I am not an expert, just someone trying to understand…

As a service to other students of this paper, I am providing a short legend (reynolds-key) of notation for the first bit of it.  I will probably update this after our next reading-group meeting, when another member of the group is planning to add to it.

Victor Maia, of course.  I called for a simple example that shows non-optimality of ghc -O2, and Victor shared with me several awesome examples.  I modified the first of these to get something similar to what I was trying out in the previous post:

module Main where
import System.Environment

powstr :: Integer -> String
powstr x = show (x ^ x)

digit :: Int -> Int -> Char
digit x n = powstr (fromIntegral x) !! n

str :: Int -> String
str x = fmap (digit x) [0..(x-1)]

main :: IO ()
main = do
(a : _ ) <- getArgs
let n = read a :: Int

putStrLn $str n This program repeatedly (by fmap’ing over [0..(x-1)]) computes the string representation of x ^ x to get the n’th digit of that representation, and rebuilds that string representation from all those digits. This is not a good way to compute that string, of course, but compiling with ghc -O2 (version 8.6.5), I see this behavior: $ time ./Another 5000 > /dev/null

real 0m2.051s
user 0m2.042s
sys 0m0.009s

Now compare with a different version of that program, which computes the string representation of x ^ x just once, and then rebuilds that by selecting each digit:

module Main where
import System.Environment

powstr :: Integer -> String
powstr x = show (x ^ x)

str :: Int -> String
str x =
let s = powstr (fromIntegral x) in
fmap ((!!) s) [0..(x-1)]

main :: IO ()
main = do
(a : _ ) <- getArgs
let n = read a :: Int

putStrLn $str n Compiling this with -O2, I then see: $ time ./Anotherl 5000 > /dev/null

real 0m0.075s
user 0m0.063s
sys 0m0.013s

But with optimal beta, the first version will run in exactly the same time as the second, as the string representation of x ^ x will only get computed once across all those calls (in the first program) to ‘digit’.

So the basic idea of this path to displaying non-optimality is: repeatedly compute something rather big (in this case, the string representation of x ^ x) extracting something from it.  The big thing you compute needs to be the same across your many extractions.  Optimal will compute the big thing once, but at least in this case, we manage to get ghc -O2 to compute it again and again.

The second program Victor sent is more artificial but also cooler:

module Main where

busy :: Int -> Int -> Int
busy 0 = \ x -> x
busy n = \ x ->
let f = busy (n - 1)
in f (f x)

main :: IO ()
main = print $busy 32 0 Compiling with ghc -O2 I find: antioch:~/optimal-beta/haskell$ time ./Busy
0

real 0m10.492s
user 0m10.491s
sys 0m0.000s

But with optimal reduction, this takes time linear (as opposed to exponential) in n: inductively, busy (n – 1) is the identity, and then busy n reduces to the identity.  Critically, we must reduce under the lambda in the body of busy for this to work; ghc won’t do that but optimal will.

Many thanks to Victor, Adam, and Lukasz for contributing to this discussion.  I hope you found it interesting.  Please comment if you have further thoughts on these experiments or optimal reduction vs mainstream compilation technology.

Optimal beta reduction is the most amazing technology you have (probably) never heard of.  Through more complex graph representations of lambda terms, optimal beta reduction schemes (and there are a couple) guarantee that normal forms for terms are reached in the optimal number of steps.  There is no duplication of work: any redex needed on the way to a normal form is guaranteed to be reduced just once.

Now, depending on how much you have heard of this before (and if you haven’t, please check out the awesome posts by Victor Maia), and your background, you may be thinking: but come on, the functional programming community has worked on efficient execution of languages based on lambda calculus for many decades.  Some of the most brilliant Computer Scientists in the world have studied this and developed very efficient ways to compile and execute programs in such languages.  And isn’t Haskell optimal anyway?  It implements call-by-need reduction so that should be the best you can do, right?

Wrong.  Algorithms for optimal beta reduction were developed starting with Lamping’s 1990 POPL paper (sorry, paywall) — so have not been around as long.  The literature is much sparser, possibly because the algorithms are very intricate and their correctness rests on quite technical work of Jean-Jacques Levy in the late 1970s, who managed to define a form of parallel reduction that he proved guaranteed optimality (but for which he did not have a proposal for implementation).  But unlike the efficient execution schemes implemented by the compiler for your favorite functional programming language, optimal beta reduction algorithms (and here I count just Lamping’s and an algorithm called lambdascope — these are the only ones I am aware of that claim optimality) are optimal.  You cannot trick them into computing redexes multiple times.

To help show the difference — and as I have been trying to understand the relationship between the rich literature in FP on compilation and optimal beta reduction — I performed a little experiment with Haskell.  Consider the following tiny Haskell program [modified from original post of a couple days ago]:

module Main where
import System.Environment

f x y _ = x ^ y
g x y = let r = x ^ y in \ _ -> r

main :: IO ()
main = do
(a0 : a1 : a2 : a3 : _ ) <- getArgs
let w = read a0 :: Bool
let n = read a1 :: Integer
let m = read a2 :: Integer
let k = read a3 :: Integer
let s = sum $map (if w then (f n m) else (g n m)) [0..k] putStrLn$ if even s then "even" else "odd"

This program reads in a Bool that controls whether the code calls function f or function g.  Both those functions return x ^ y, ignoring z; but g lifts that computation of x ^ y out of the lambda z, and f does not lift it. Then the code maps the chosen function, applied to n and m, over a list of the numbers 0 through k.  There is a summation to force evaluation.

The critical point here is that when the code for ‘main’ calls f n m, the value of n ^ m could be pre-computed, before f n m is mapped over the list.  Optimal beta reduction would do this, only computing n ^ m once despite many applications of f n m.  If the ghc-produced executable were doing this, too, then the cost of running the program with inputs n, m, and k should be equal (roughly) to the cost of computing n to the m, plus the cost of traversing the list.  On the other hand, if ghc cannot manage to precompute n ^ m, then we would expect to see the cost to equal more like k times the cost for n ^ m.  Let’s see what happens (on my laptop).

First compile with ghc with default optimization:

$ghc --make Main [1 of 1] Compiling Main ( Main.hs, Main.o ) Linking Main ... Now run with function f: $ time ./Main True 1000001 100000 1000 2
odd

real    0m8.103s
user    0m7.777s
sys 0m0.325s

Now with function g:

\$ time ./Main False 1000001 100000 1000 2
odd

real    0m0.071s
user    0m0.053s
sys 0m0.018s

We see that running with g is much faster than running with f.

So what have we learned?  Executables produced by ghc with its default optimizations do not implement optimal reduction (they were not claimed to, just to be clear), and we can expose this with a simple example.

Now maybe you think this is a lesson with no leasing: just showing that compiler X is not as fast as you can imagine it could be from the comfort of your armchair is neither sporting nor informative.  For surely one can cherry pick this or that weird example and see something imperfect?

But this example is relying on a very basic feature of higher-order programming, namely the ability for functions to make use of variables bound outside their scopes.  Indeed, that lengthy literature I was mentioning is largely concerned exactly with how to implement this efficiently.  And guess what: those methods fall short on exactly the kind of test they should be able to handle well.  Dealing with open lambda terms (ones which contain variables bound outside their scopes) is also the chief source of difficulty for optimal beta reduction.  But those algorithms, despite their difficulties, actually solve the problem completely.

So why aren’t people using optimal beta?  The simple answer is that the machinery proposed to deal with open terms in those algorithms adds quite a bit of overhead to reduction (and makes implementation a scary prospect).  So almost for sure you would need heroic engineering to get anywhere close to ghc and other awesome compilers on examples outside this class where optimal easily crushes them.

What I am working on currently is how to solve the problem of open terms in optimal beta with a lot less machinery, to get something that could compete with those tools with just a realistic (for me!) amount of engineering.  No results yet, but some promising leads…

A final important update: this example does not exhibit different behavior if we compile with -O2 (thanks to commenter Adam for pointing this out).  I could not find a way to tweak the example to show non-optimality with -O2, despite some (maybe not sufficiently expert?) twiddling.

So this is an open call for small Haskell programs that exhibit non-optimal behavior with -O2.

Thanks for reading!  Feedback very welcome (particularly if you think I am out to lunch on this — please challenge/correct me).

format: plain


text:
# IMO 1979 problem

The question is $$\text{If }\, p, \ q\in \mathbb{N}, \;1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}=\frac{p}{q}.\qquad \text{Prove that } 1979\mid p.$$

So my solution went like this:

$$S=1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}\Rightarrow S=\sum_{k=1}^{1319}\frac{1}{k}-2\sum_{k=1}^{659}\frac{1}{2k}=\sum_{k=660}^{1319}\frac{1}{k}$$ Now this is equivalent to finding the sum of the roots of the equation $$\left(x-\frac{1}{660}\right)\left(x-\frac{1}{661}\right)\dots \left(x-\frac{1}{1319}\right)=0$$.

Rewriting this equation, we get $(660x-1)(661x-1)\dotsc(1319x-1)=0$ (we can discard the $\displaystyle \frac{1319!}{659!}$ since $1979$ is a prime). Calculating the sum of the roots, we get the required value to be equal to $(1320+659)\times 330$ which is obviously divisible by $1979$ (again discarding the coeffecient of $x^{660}$).

Now my question is: Using the same method of converting the problem into finding the sum of roots of a polynomial, we get from the original equation something like this: $$(x-1)\left(x+\frac{1}{2}\right)\dots \left(x-\frac{1}{1319}\right)=0 \Rightarrow (x-1)(2x+1)\dotsc(1319x-1)=0$$

So, the sum of roots would be $-1+2-3+4-\dotsc+1318-1319=-660$ But this is not divisible by $1979$. Why does the former solution work while the latter doesn't? Is there a flaw in my reasoning?

Note: I know that the question can be solved by some other methods. Please only explain my given doubts and don't instead give another solution

I realised my mistake after some hours of pondering over it.

(In the 1st equation) To get the required sum I would need to take calculate $\displaystyle -\frac{\text{coeffecient of }x^{659}\,}{\text{coeffecient of }x^{660}}$. However what I've done is calculate this: $\displaystyle -\frac{\text{ coeffecient of }x}{\text{coeffecient of }x^{660}}$ which is actually equal to $\text{sum of roots taken }659 \text{ at a time}$. It was just a coincidence that the value I calculated was divisible by $1979$.

The correct way, indeed, would be through the link supplied above

• How is the sum of the roots $(1320+659)\cdot 330$ or $-660$? – Hagen von Eitzen Jan 11 '14 at 16:01
• The first formula should have a negative sign for $1/4$, rigth? – leonbloy Jan 11 '14 at 16:04
• I believe that what user117913 doing is finding the coefficient of the second term in the polynomial, and using the reasoning that that coefficient must be the negative of the sum of the roots multiplied by the leading coefficient. So what is being calculated is the product of the sum of roots and the leading coefficient, and since the leading coefficient isn't divisible by 1979, the sum of roots must be. – Glen O Jan 11 '14 at 16:18
• @GlenO But that second term is way bigger. It is the sum of $>600$ positive integers, each of which is at least $\frac{1318!}{659!}$. – Hagen von Eitzen Jan 11 '14 at 16:24
• @HagenvonEitzen - yeah, I just realised I made a mistake. The calculation is for the second-last term, not the second term. I have to think about it a bit more. – Glen O Jan 11 '14 at 16:25


text:
# All Questions

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### Bobcat hash, trying to find a 48-bit hash collision for x

I am trying to find a collision with the Bobcat hash of the 48-bit hash. I am a beginner coder so please point out any flaws in my modification of the bobcat program. It does find a truncated 12-bit ...
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### Are the values of Tate and Ate pairing the same?

Assume we have a Baretto Naehrig curve over $GF(p)$ and a field extension $GF(p^{12})$ given by a minimum polynomial. Let $G \in GF(p)$ and $Q \in GF(p^{12})$ from the trace 0 subgroup. Do then the ...
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### Limit the number of private key uses for RSASSA-PKCS1-v1_5 with SHA-256 signature?

Assuming all messages and their signatures are available to the attacker, is it secure to use the same RSA private key to sign many messages (roughly $10^{6}$) via PKCS#11 ...
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### Is there a way to slow down collision attacks using iteration?

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### Detecting steganography by analysing non-significant data entropy?

I am not thinking only steganography in images, I think it is also possible to encode data for example into the length of spaces of a clear html text. I suspect, the steganography changes (elevates) ...
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### Is Shoup's Practical Threshold Signatures considered secure?

I am planning to use threshold cryptography in a Java application. So far, I have only found ThresSig and a ECDSA implementation used in TwoFactorBtcWallet. However, ThresSig is based on a 15-years ...
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### How does FileVault2 Recovery actually work?

I'm a crypto-enthusiast but no expert at all, that'll explain why i didn't understand. Also please consider english isn't my native language :) I am about to enable FileVault2 FDE on the new macbook ...
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### How did G.H. Hardy's work contribute to today's public-key cryptography?

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### Test vectors for TLS PRF function

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text:
# Acoustic Destabilization of Vortices

E. G. Broadbent, D. W. Moore

## Abstract

A line vortex which has uniform vorticity 2$\Omega _{0}$ in its core is subjected to a small two-dimensional disturbance whose dependence on polar angle is e$^{\text{i}m\theta}$. The stability is examined according to the equations of compressible, inviscid flow in a homentropic medium. The boundary condition at infinity is that of outgoing acoustic waves, and it is found that this capacity to radiate leads to a slow instability by comparison with the corresponding incompressible vortex which is stable. Numerical eigenvalues are computed as functions of the mode number m and the Mach number M based on the circumferential speed of the vortex. These are compared with an asymptotic analysis for the m = 2 mode at low Mach number in which it is found that the growth rate is ($\pi$/32)M$^{4}\Omega _{0}$ in good agreement with the numerical results.


text:
# How do you solve 10(2x + 4) = - (-8 -9x) + 3x?

Jan 25, 2016

x = - 4

#### Explanation:

First 'distribute' the brackets :

ie 20x + 40 = 8 + 9x + 3x

( collect x terms to left side and numbers to the right )

20x - 9x - 3x = 8 - 40

hence : 8x = - 32

( divide both sides by 8 )

so x = - 4


text:
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