AG-7.1, Industrial Automation Glossary
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Intrinsic Parity of Neutral Pion
Intrinsic Parity of Neutral Pion Taushif Ahmed 13th September, 2012 1 2 Contents 1 Symmetry 4 2 Parity Transformation 5 2.1 Parity in CM . 5 2.2 Parity in QM . 6 2.2.1 Active viewpoint . 6 2.2.2 Passive viewpoint . 8 2.3 Parity in Relativistic QM . 9 2.4 Parity in QFT . 9 2.4.1 Parity in Photon field . 11 3 Decay of The Neutral Pion 14 4 Bibliography 17 3 1 Symmetry What does it mean by `a certain law of physics is symmetric under certain transfor- mations' ? To be specific, consider the statement `classical mechanics is symmetric under mirror inversion' which can be defined as follows: take any motion that satisfies the laws of classical mechanics. Then, reflect the motion into a mirror and imagine that the motion in the mirror is actually happening in front of your eyes, and check if the motion satisfies the same laws of clas- sical mechanics. If it does, then classical mechanics is said to be symmetric under mirror inversion. Or more precisely, if all motions that satisfy the laws of classical mechanics also satisfy them after being re- flected into a mirror, then classical mechanics is said to be symmetric under mirror inversion. In general, suppose one applies certain transformation to a motion that follows certain law of physics, if the resulting motion satisfies the same law, and if such is the case for all motion that satisfies the law, then the law of physics is said to be sym- metric under the given transformation. It is important to use exactly the same law of physics after the transfor- mation is applied. -
An Interpreter's Glossary at a Conference on Recent Developments in the ATLAS Project at CERN
Faculteit Letteren & Wijsbegeerte Jef Galle An interpreter’s glossary at a conference on recent developments in the ATLAS project at CERN Masterproef voorgedragen tot het behalen van de graad van Master in het Tolken 2015 Promotor Prof. Dr. Joost Buysschaert Vakgroep Vertalen Tolken Communicatie 2 ACKNOWLEDGEMENTS First of all, I would like to express my sincere gratitude towards prof. dr. Joost Buysschaert, my supervisor, for his guidance and patience throughout this entire project. Furthermore, I wanted to thank my parents for their patience and support. I would like to express my utmost appreciation towards Sander Myngheer, whose time and insights in the field of physics were indispensable for this dissertation. Last but not least, I wish to convey my gratitude towards prof. dr. Ryckbosch for his time and professional advice concerning the quality of the suggested translations into Dutch. ABSTRACT The goal of this Master’s thesis is to provide a model glossary for conference interpreters on assignments in the domain of particle physics. It was based on criteria related to quality, role, cognition and conference interpreters’ preparatory methodology. This dissertation focuses on terminology used in scientific discourse on the ATLAS experiment at the European Organisation for Nuclear Research. Using automated terminology extraction software (MultiTerm Extract) 15 terms were selected and analysed in-depth in this dissertation to draft a glossary that meets the standards of modern day conference interpreting. The terms were extracted from a corpus which consists of the 50 most recent research papers that were publicly available on the official CERN document server. The glossary contains information I considered to be of vital importance based on relevant literature: collocations in both languages, a Dutch translation, synonyms whenever they were available, English pronunciation and a definition in Dutch for the concepts that are dealt with. -
Switches and Relays for the Power Industry
Switches and Relays For the Power Industry E L E C T R O NEVER S W I T A DOUBT C H U T I L I T Y ELECTROSWITCH Corporation 180 King Avenue P Weymouth, MA 02188 R TEL: (781) 335-5200 O FAX: (781) 335-4253 www.electroswitch.com D U C T S 5M 113 Printed in USA U.2.D THE ELECTRO SWITCH CORPORATion Family… PROVIDING INTELLIGENT SOLUTIONS FOR SWITCHING AND CONTROL Complete line of electrically and manually activated Rotary Switches and Relays POWER SWITCHES & RELAYS for electric utility, defense, and industrial monitoring and control applications The Best Rotary Switches, Relays, and Electrical Systems Products... Backed by the industry’s most www.electroswitch.com knowledgeable and responsive Rotary Switches; Miniature Toggle, Paddle, Rocker, Power Toggle, and Push- ELECTRONIC PRODUCTS Button Switches; Hall Effect, and Mechanical Encoders; Illuminated Switch engineering and customer Products; and Power Transformers service professionals... Any way you want them... Delivered when you need them. www.electro-nc.com DIGITRAN Digital and Rotary Switch Products designed for aviation, defense, and industrial DIGITAL & ROTARY SWITCHES switch applications ELECTROSWITCH www.digitran-switches.com ARGA CONTROLS Electric utility, industrial and military-grade Power Meters, Battery Monitors, MEASUREMENT & CONTROL INSTRUMENTATION and Transducers for precision measurement applications NEVER www.argacontrols.com Sunrise Technologies Wireless Communication Systems for Smart Grid applications and a complete A DOUBT OUTDOOR LIGHTING CONTROLS & MONITORING line -
Helicity of the Neutrino Determination of the Nature of Weak Interaction
GENERAL ¨ ARTICLE Helicity of the Neutrino Determination of the Nature of Weak Interaction Amit Roy Measurement of the helicity of the neutrino was crucial in identifying the nature of weak interac- tion. The measurement is an example of great ingenuity in choosing, (i) the right nucleus with a specific type of decay, (ii) the technique of res- onant fluorescence scattering for determining di- rection of neutrino and (iii) transmission through Amit Roy is currently at magnetised iron for measuring polarisation of γ- the Variable Energy rays. Cyclotron Centre after working at Tata Institute In the field of art and sculpture, we sometimes come of Fundamental Research across a piece of work of rare beauty, which arrests our and Inter-University attention as soon as we focus our gaze on it. The ex- Accelerator Centre. His research interests are in periment on the determination of helicity of the neutrino nuclear, atomic and falls in a similar category among experiments in the field accelerator physics. of modern physics. The experiments on the discovery of parity violation in 1957 [1] had established that the vi- olation parity was maximal in beta decay and that the polarisation of the emitted electron was 100%. This im- plies that its helicity was −1. The helicity of a particle is a measure of the angle (co- sine) between the spin direction of the particle and its momentum direction. H = σ.p,whereσ and p are unit vectors in the direction of the spin and the momentum, respectively. The spin direction of a particle of posi- tive helicity is parallel to its momentum direction, and for that of negative helicity, the directions are opposite (Box 1). -
Product Manual Heat Recovery Ventilation Units EN
EN HMB/HMBE aura-t & auralite® compatible HRV units HRV20 Q Plus ECO TP650HMB HRV20 HE Q Plus ECO TP652HMB B/BC/BE aura compatible HRV units HRV20 Q Plus ECO TP651B HRV20 HE Q Plus ECO TP653B Cold Climate HRV units HRV20 Q Plus ECO* TP651BC HRV20 HE Q Plus ECO* TP653BC *Special Order Only Heat Recovery Ventilation Units Product Manual ventilation systems Warnings, Safety Information and Guidance Important Information Important: read these instructions fully before the installation of this appliance 1. Installation of the appliance and accessories must be carried out by a qualified and suitable competent person and be carried out in clean, dry conditions where dust and humidity are at minimal levels. 2. This manual covers the installation of the Heat Recovery Ventilation (HRV) unit 3. All wiring must conform to current I.E.E. Wiring Regulations and all applicable standards and Building Regulations. 4. Inspect the appliance and electrical supply cord. If the supply cord is damaged, it must be replaced by the manufacturer, their service agent or similarly qualified persons in order to avoid a hazard. 5. The unit is supplied with a mains rated 3 core flexible cord (PVC sheathed, brown, blue and green/yellow 0.75mm²). 6. The appliance must be connected to a local double pole isolation switch with a contact separation of at least 3mm. 7. The appliance must be earthed.. 8. HRV20 Q Plus suitable for 230V ~ 50/60Hz single phase with a fuse rating of 5A. 9. auralite® & aurastat®, control & communication cable access is via the fitted cable gland(s) which are suitable for Ø3- 6mm cable. -
Parity Alternating Permutations Starting with an Odd Integer
Parity alternating permutations starting with an odd integer Frether Getachew Kebede1a, Fanja Rakotondrajaob aDepartment of Mathematics, College of Natural and Computational Sciences, Addis Ababa University, P.O.Box 1176, Addis Ababa, Ethiopia; e-mail: [email protected] bD´epartement de Math´ematiques et Informatique, BP 907 Universit´ed’Antananarivo, 101 Antananarivo, Madagascar; e-mail: [email protected] Abstract A Parity Alternating Permutation of the set [n] = 1, 2,...,n is a permutation with { } even and odd entries alternatively. We deal with parity alternating permutations having an odd entry in the first position, PAPs. We study the numbers that count the PAPs with even as well as odd parity. We also study a subclass of PAPs being derangements as well, Parity Alternating Derangements (PADs). Moreover, by considering the parity of these PADs we look into their statistical property of excedance. Keywords: parity, parity alternating permutation, parity alternating derangement, excedance 2020 MSC: 05A05, 05A15, 05A19 arXiv:2101.09125v1 [math.CO] 22 Jan 2021 1. Introduction and preliminaries A permutation π is a bijection from the set [n]= 1, 2,...,n to itself and we will write it { } in standard representation as π = π(1) π(2) π(n), or as the product of disjoint cycles. ··· The parity of a permutation π is defined as the parity of the number of transpositions (cycles of length two) in any representation of π as a product of transpositions. One 1Corresponding author. n c way of determining the parity of π is by obtaining the sign of ( 1) − , where c is the − number of cycles in the cycle representation of π. -
Title: Parity Non-Conservation in Β-Decay of Nuclei: Revisiting Experiment and Theory Fifty Years After
Title: Parity non-conservation in β-decay of nuclei: revisiting experiment and theory fifty years after. IV. Parity breaking models. Author: Mladen Georgiev (ISSP, Bulg. Acad. Sci., Sofia) Comments: some 26 pdf pages with 4 figures. In memoriam: Prof. R.G. Zaykoff Subj-class: physics This final part offers a survey of models proposed to cope with the symmetry-breaking challenge. Among them are the two-component neutrinos, the neutrino twins, the universal Fermi interaction, etc. Moreover, the broken discrete symmetries in physics are very much on the agenda and may occupy considerable time for LHC experiments aimed at revealing the symmetry-breaking mechanisms. Finally, an account of the achievements of dual-component theories in explaining parity-breaking phenomena is added. 7. Two-component neutrino In the previous parts I through III of the paper we described the theoretical background as well as the bulk experimental evidence that discrete group symmetries break up in weak interactions, such as the β−decay. This last part IV will be devoted to the theoretical models designed to cope with the parity-breaking challenge. The quality of the proposed theories and the accuracy of the experiments made to check them underline the place occupied by papers such as ours in the dissemination of symmetry-related matter of modern science. 7.1. Neutrino gauge In the general form of β-interaction (5.6) the case Ck' = ±Ck (7.1) is of particular interest. It corresponds to interchanging the neutrino wave function in the parity-conserving Hamiltonian ( Ck' = 0 ) with the function ψν' = (! ± γs )ψν (7.2) In as much as parity is not conserved with this transformation, it is natural to put the blame on the neutrino. -
MHPAEA-Faqs-Part-45.Pdf
CCIIO OG MWRD 1295 FAQS ABOUT MENTAL HEALTH AND SUBSTANCE USE DISORDER PARITY IMPLEMENTATION AND THE CONSOLIDATED APPROPRIATIONS ACT, 2021 PART 45 April 2, 2021 The Consolidated Appropriations Act, 2021 (the Appropriations Act) amended the Mental Health Parity and Addiction Equity Act of 2008 (MHPAEA) to provide important new protections. The Departments of Labor (DOL), Health and Human Services (HHS), and the Treasury (collectively, “the Departments”) have jointly prepared this document to help stakeholders understand these amendments. Previously issued Frequently Asked Questions (FAQs) related to MHPAEA are available at https://www.dol.gov/agencies/ebsa/laws-and- regulations/laws/mental-health-and-substance-use-disorder-parity and https://www.cms.gov/cciio/resources/fact-sheets-and-faqs#Mental_Health_Parity. Mental Health Parity and Addiction Equity Act of 2008 MHPAEA generally provides that financial requirements (such as coinsurance and copays) and treatment limitations (such as visit limits) imposed on mental health or substance use disorder (MH/SUD) benefits cannot be more restrictive than the predominant financial requirements and treatment limitations that apply to substantially all medical/surgical benefits in a classification.1 In addition, MHPAEA prohibits separate treatment limitations that apply only to MH/SUD benefits. MHPAEA also imposes several important disclosure requirements on group health plans and health insurance issuers. The MHPAEA final regulations require that a group health plan or health insurance issuer may -
Relativistic Quantum Mechanics 1
Relativistic Quantum Mechanics 1 The aim of this chapter is to introduce a relativistic formalism which can be used to describe particles and their interactions. The emphasis 1.1 SpecialRelativity 1 is given to those elements of the formalism which can be carried on 1.2 One-particle states 7 to Relativistic Quantum Fields (RQF), which underpins the theoretical 1.3 The Klein–Gordon equation 9 framework of high energy particle physics. We begin with a brief summary of special relativity, concentrating on 1.4 The Diracequation 14 4-vectors and spinors. One-particle states and their Lorentz transforma- 1.5 Gaugesymmetry 30 tions follow, leading to the Klein–Gordon and the Dirac equations for Chaptersummary 36 probability amplitudes; i.e. Relativistic Quantum Mechanics (RQM). Readers who want to get to RQM quickly, without studying its foun- dation in special relativity can skip the first sections and start reading from the section 1.3. Intrinsic problems of RQM are discussed and a region of applicability of RQM is defined. Free particle wave functions are constructed and particle interactions are described using their probability currents. A gauge symmetry is introduced to derive a particle interaction with a classical gauge field. 1.1 Special Relativity Einstein’s special relativity is a necessary and fundamental part of any Albert Einstein 1879 - 1955 formalism of particle physics. We begin with its brief summary. For a full account, refer to specialized books, for example (1) or (2). The- ory oriented students with good mathematical background might want to consult books on groups and their representations, for example (3), followed by introductory books on RQM/RQF, for example (4). -
Dirac Equation
Particle Physics Dr. Alexander Mitov µ+ µ+ e- e+ e- e+ µ- µ- µ+ µ+ e- e+ e- e+ µ- µ- Handout 2 : The Dirac Equation Dr. A. Mitov Particle Physics 45 Non-Relativistic QM (Revision) • For particle physics need a relativistic formulation of quantum mechanics. But first take a few moments to review the non-relativistic formulation QM • Take as the starting point non-relativistic energy: • In QM we identify the energy and momentum operators: which gives the time dependent Schrödinger equation (take V=0 for simplicity) (S1) with plane wave solutions: where •The SE is first order in the time derivatives and second order in spatial derivatives – and is manifestly not Lorentz invariant. •In what follows we will use probability density/current extensively. For the non-relativistic case these are derived as follows (S1)* (S2) Dr. A. Mitov Particle Physics 46 •Which by comparison with the continuity equation leads to the following expressions for probability density and current: •For a plane wave and «The number of particles per unit volume is « For particles per unit volume moving at velocity , have passing through a unit area per unit time (particle flux). Therefore is a vector in the particle’s direction with magnitude equal to the flux. Dr. A. Mitov Particle Physics 47 The Klein-Gordon Equation •Applying to the relativistic equation for energy: (KG1) gives the Klein-Gordon equation: (KG2) •Using KG can be expressed compactly as (KG3) •For plane wave solutions, , the KG equation gives: « Not surprisingly, the KG equation has negative energy solutions – this is just what we started with in eq. -
On the Parity of the Number of Multiplicative Partitions and Related Problems
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 140, Number 11, November 2012, Pages 3793–3803 S 0002-9939(2012)11254-7 Article electronically published on March 15, 2012 ON THE PARITY OF THE NUMBER OF MULTIPLICATIVE PARTITIONS AND RELATED PROBLEMS PAUL POLLACK (Communicated by Ken Ono) Abstract. Let f(N) be the number of unordered factorizations of N,where a factorization is a way of writing N as a product of integers all larger than 1. For example, the factorizations of 30 are 2 · 3 · 5, 5 · 6, 3 · 10, 2 · 15, 30, so that f(30) = 5. The function f(N), as a multiplicative analogue of the (additive) partition function p(N), was first proposed by MacMahon, and its study was pursued by Oppenheim, Szekeres and Tur´an, and others. Recently, Zaharescu and Zaki showed that f(N) is even a positive propor- tion of the time and odd a positive proportion of the time. Here we show that for any arithmetic progression a mod m,thesetofN for which f(N) ≡ a(mod m) possesses an asymptotic density. Moreover, the density is positive as long as there is at least one such N. For the case investigated by Zaharescu and Zaki, we show that f is odd more than 50 percent of the time (in fact, about 57 percent). 1. Introduction Let f(N) be the number of unordered factorizations of N,whereafactorization of N is a way of writing N as a product of integers larger than 1. For example, f(12) = 4, corresponding to 2 · 6, 2 · 2 · 3, 3 · 4, 12. -
The ℓ-Parity Conjecture Over the Constant Quadratic Extension
THE `-PARITY CONJECTURE OVER THE CONSTANT QUADRATIC EXTENSION KĘSTUTIS ČESNAVIČIUS Abstract. For a prime ` and an abelian variety A over a global field K, the `-parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton-Dyer, the Z`-corank of the `8-Selmer group and the analytic rank agree modulo 2. Assuming that char K ¡ 0, we prove that the `-parity conjecture holds for the base change of A to the constant quadratic extension if ` is odd, coprime to char K, and does not divide the degree of every polarization of A. The techniques involved in the proof include the étale cohomological interpretation of Selmer groups, the Grothendieck–Ogg–Shafarevich formula, and the study of the behavior of local root numbers in unramified extensions. 1. Introduction 1.1. The `-parity conjecture. The Birch and Swinnerton-Dyer conjecture (BSD) predicts that the completed L-function LpA; sq of an abelian variety A over a global field K extends meromorphically to the whole complex plane, vanishes to the order rk A at s “ 1, and satisfies the functional equation LpA; 2 ´ sq “ wpAqLpA; sq; (1.1.1) where rk A and wpAq are the Mordell–Weil rank and the global root number of A. The vanishing assertion combines with (1.1.1) to give “BSD modulo 2,” namely, the parity conjecture: ? p´1qrk A “ wpAq: Selmer groups tend to be easier to study than Mordell–Weil groups, so, fixing a prime `, one sets 8 rk` A :“ dimQ` HompSel` A; Q`{Z`q bZ` Q`; where Sel 8 A : lim Sel n A ` “ ÝÑ ` is the `8-Selmer group, notes that the conjectured finiteness of the Shafarevich–Tate group XpAq implies rk` A “ rk A, and instead of the parity conjecture considers the `-parity conjecture: ? p´1qrk` A “ wpAq: (1.1.2) 1.2.