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Group Developed Weighing Matrices∗
AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 55 (2013), Pages 205–233 Group developed weighing matrices∗ K. T. Arasu Department of Mathematics & Statistics Wright State University 3640 Colonel Glenn Highway, Dayton, OH 45435 U.S.A. Jeffrey R. Hollon Department of Mathematics Sinclair Community College 444 W 3rd Street, Dayton, OH 45402 U.S.A. Abstract A weighing matrix is a square matrix whose entries are 1, 0 or −1,such that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be devel- oped by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into the existence of matrices with larger weights and orders. 1 Introduction 1.1 Group Developed Weighing Matrices A weighing matrix W = W (n, k) is a square matrix, of order n, whose entries are in t the set wi,j ∈{−1, 0, +1}. This matrix satisfies WW = kIn, where t denotes the matrix transpose, k is a positive integer known as the weight, and In is the identity matrix of size n. Definition 1.1. Let G be a group of order n.Ann×n matrix A =(agh) indexed by the elements of the group G (such that g and h belong to G)issaidtobeG-developed if it satisfies the condition agh = ag+k,h+k for all g, h, k ∈ G. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
James Clerk Maxwell
Conteúdo Páginas Henry Cavendish 1 Jacques Charles 2 James Clerk Maxwell 3 James Prescott Joule 5 James Watt 7 Jean-Léonard-Marie Poiseuille 8 Johann Heinrich Lambert 10 Johann Jakob Balmer 12 Johannes Robert Rydberg 13 John Strutt 14 Michael Faraday 16 Referências Fontes e Editores da Página 18 Fontes, Licenças e Editores da Imagem 19 Licenças das páginas Licença 20 Henry Cavendish 1 Henry Cavendish Referência : Ribeiro, D. (2014), WikiCiências, 5(09):0811 Autor: Daniel Ribeiro Editor: Eduardo Lage Henry Cavendish (1731 – 1810) foi um físico e químico que investigou isoladamente de acordo com a tradição de Sir Isaac Newton. Cavendish entrou no seminário em 1742 e frequentou a Universidade de Cambridge (1749 – 1753) sem se graduar em nenhum curso. Mesmo antes de ter herdado uma fortuna, a maior parte das suas despesas eram gastas em montagem experimental e livros. Em 1760, foi eleito Fellow da Royal Society e, em 1803, um dos dezoito associados estrangeiros do Institut de France. Entre outras investigações e descobertas de Cavendish, a maior ocorreu em 1781, quando compreendeu que a água é uma substância composta por hidrogénio e oxigénio, uma reformulação da opinião de há milénios de que a água é um elemento químico básico. O químico inglês John Warltire (1725/6 – 1810) realizou uma Figura 1 Henry Cavendish (1731 – 1810). experiência em que explodiu uma mistura de ar e hidrogénio, descobrindo que a massa dos gases residuais era menor do que a da mistura original. Ele atribuiu a perda de massa ao calor emitido na reação. Cavendish concluiu que algum erro substancial estava envolvido visto que não acreditava que, dentro da teoria do calórico, o calor tivesse massa suficiente, à escala em análise. -
S.I. and Cgs Units
Some Notes on SI vs. cgs Units by Jason Harlow Last updated Feb. 8, 2011 by Jason Harlow. Introduction Within “The Metric System”, there are actually two separate self-consistent systems. One is the Systme International or SI system, which uses Metres, Kilograms and Seconds for length, mass and time. For this reason it is sometimes called the MKS system. The other system uses centimetres, grams and seconds for length, mass and time. It is most often called the cgs system, and sometimes it is called the Gaussian system or the electrostatic system. Each system has its own set of derived units for force, energy, electric current, etc. Surprisingly, there are important differences in the basic equations of electrodynamics depending on which system you are using! Important textbooks such as Classical Electrodynamics 3e by J.D. Jackson ©1998 by Wiley and Classical Electrodynamics 2e by Hans C. Ohanian ©2006 by Jones & Bartlett use the cgs system in all their presentation and derivations of basic electric and magnetic equations. I think many theorists prefer this system because the equations look “cleaner”. Introduction to Electrodynamics 3e by David J. Griffiths ©1999 by Benjamin Cummings uses the SI system. Here are some examples of units you may encounter, the relevant facts about them, and how they relate to the SI and cgs systems: Force The SI unit for force comes from Newton’s 2nd law, F = ma, and is the Newton or N. 1 N = 1 kg·m/s2. The cgs unit for force comes from the same equation and is called the dyne, or dyn. -
SI and CGS Units in Electromagnetism
SI and CGS Units in Electromagnetism Jim Napolitano January 7, 2010 These notes are meant to accompany the course Electromagnetic Theory for the Spring 2010 term at RPI. The course will use CGS units, as does our textbook Classical Electro- dynamics, 2nd Ed. by Hans Ohanian. Up to this point, however, most students have used the International System of Units (SI, also known as MKSA) for mechanics, electricity and magnetism. (I believe it is easy to argue that CGS is more appropriate for teaching elec- tromagnetism to physics students.) These notes are meant to smooth the transition, and to augment the discussion in Appendix 2 of your textbook. The base units1 for mechanics in SI are the meter, kilogram, and second (i.e. \MKS") whereas in CGS they are the centimeter, gram, and second. Conversion between these base units and all the derived units are quite simply given by an appropriate power of 10. For electromagnetism, SI adds a new base unit, the Ampere (\A"). This leads to a world of complications when converting between SI and CGS. Many of these complications are philosophical, but this note does not discuss such issues. For a good, if a bit flippant, on- line discussion see http://info.ee.surrey.ac.uk/Workshop/advice/coils/unit systems/; for a more scholarly article, see \On Electric and Magnetic Units and Dimensions", by R. T. Birge, The American Physics Teacher, 2(1934)41. Electromagnetism: A Preview Electricity and magnetism are not separate phenomena. They are different manifestations of the same phenomenon, called electromagnetism. One requires the application of special relativity to see how electricity and magnetism are united. -
Technical Units
Reference: www. rockmass.net 620(7(&+1,&$/81,76 7KH,QWHUQDWLRQDO 6, V\VWHPRIXQLWV Its seven basic units, from which other units are derived, are given in the table below. Dimension Symbol SI unit Comment Name Unit Length l metre m Mass m kilogram kg Time t second s Electric current I ampere A Temperature T kelvin K Luminous intensity Iv candela cd Molar heat capacity n mol mol BASIC UNITS IN SI SYSTEM Angle a radian rad Additional unit Frequency f hertz Hz s-1 Force F newton N 1 N = 1 kgm/s2 Pressure, stress p, σ, pascal Pa 1 Pa = 1 N/m² UNITS Energy, work, heat E, W, Q joule J 1 J = 1 N × m DIVERTED SI- Effect P watt W 1 W = 1 J/s 'HFDGHSUHIL[HV prefix symbol value prefix symbol value tera T 1012 deci d 10-1 giga G 109 centi c 10-2 mega M 106 milli m 10-3 kilo k 103 micro µ 10-6 hecto h 102 nano n 10-9 deca da 101 pico p 10-12 7KH*UHHNDOSKDEHW Α α, ∝ ∗) alpha (a) Ι ι iota (i) Ρ ρ rho (r, rh) Β β beta (b) Κ κ kappa (k) Σ σ sigma (s) Γ γ gamma (g, n) Λ λ lambda (l) Τ τ tau (t) ∆ δ, ∂ ∗) delta (d) Μ µ mu (m) Υ υ upsilon (y, u) Ε ε epsilon (e) Ν ν nu (n) Φ φ, ϕ*) phi (ph) Ζ ζ zeta (z) Ξ ξ xi (x) X χ chi (ch, h) Η η ëta (e, ë) Ο ο omicron (o) Ψ ψ psi (ps) Θ θ, ϑ ∗) theta (th) Π π pi (p) Ω ω omega (o, õ) *) Old-style character 2 9DULRXVXQLWVDQGFRQYHUVLRQV 'LPHQVLRQ 1DPH 6\PERO 8QLW &RQYHUVLRQ Time minute min s 1 h = 60 s hour h h 1 h = 60 min day day day 1 day = 24 h week wk wk 1 wk = 7 days year yr yr 1 yr = 365.242 days = 52.17 wk Length Angstrom A m 1 A = 10-10 m nautical mile n mile 1 n mile = 1852 m wave length λ m Force load G (P,W) N 1 kp = 9.807 N 2 o o 2 gravity g N 1 gn = 9.80665 m/s (exact, at 45 N; at 60 N g = 9.82 m/s ) atmosphere atm 1 atm Modulus elasticity modulus E Pa 1 kPa = 0.1 N/cm = 0.102 ton/m2 deformation modulus G Pa 1 MPa = 10,2 kg/cm2 shear modulus K Pa Density mass density ρ kg/m3 force density γ kN/m3 Flow Lugeon Lugeon l/min/m 1 Lugeon = approx. -
DIMENSIONS and UNITS to Get the Value of a Quantity in Gaussian Units, Multiply the Value Ex- Pressed in SI Units by the Conversion Factor
DIMENSIONS AND UNITS To get the value of a quantity in Gaussian units, multiply the value ex- pressed in SI units by the conversion factor. Multiples of 3 intheconversion factors result from approximating the speed of light c =2.9979 1010 cm/sec × 3 1010 cm/sec. ≈ × Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units t2q2 Capacitance C l farad 9 1011 cm ml2 × m1/2l3/2 Charge q q coulomb 3 109 statcoulomb t × q m1/2 Charge ρ coulomb 3 103 statcoulomb 3 3/2 density l l t /m3 × /cm3 tq2 l Conductance siemens 9 1011 cm/sec ml2 t × 2 tq 1 9 1 Conductivity σ siemens 9 10 sec− 3 ml t /m × q m1/2l3/2 Current I,i ampere 3 109 statampere t t2 × q m1/2 Current J, j ampere 3 105 statampere 2 1/2 2 density l t l t /m2 × /cm2 m m 3 3 3 Density ρ kg/m 10− g/cm l3 l3 q m1/2 Displacement D coulomb 12π 105 statcoulomb l2 l1/2t /m2 × /cm2 1/2 ml m 1 4 Electric field E volt/m 10− statvolt/cm t2q l1/2t 3 × 2 1/2 1/2 ml m l 1 2 Electro- , volt 10− statvolt 2 motance EmfE t q t 3 × ml2 ml2 Energy U, W joule 107 erg t2 t2 m m Energy w, ϵ joule/m3 10 erg/cm3 2 2 density lt lt 10 Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units ml ml Force F newton 105 dyne t2 t2 1 1 Frequency f, ν hertz 1 hertz t t 2 ml t 1 11 Impedance Z ohm 10− sec/cm tq2 l 9 × 2 2 ml t 1 11 2 Inductance L henry 10− sec /cm q2 l 9 × Length l l l meter (m) 102 centimeter (cm) 1/2 q m 3 Magnetic H ampere– 4π 10− oersted 1/2 intensity lt l t turn/m × ml2 m1/2l3/2 Magnetic flux Φ weber 108 maxwell tq t m m1/2 Magnetic -
ACM-8RF Connected to the EIA-485 Port
G PN 50362:C0 ECN 01-155 Control Relay Module ACM-8RF Instruction Manual Document 50362 03/21/2001 Rev: C While a fire alarm system may lower insurance Fire Alarm System Limitations rates, it is not a substitute for fire insurance! An automatic fire alarm system–typically made up Heat detectors do not sense particles of combustion of smoke detectors, heat detectors, manual pull and alarm only when heat on their sensors increases stations, audible warning devices, and a fire alarm at a predetermined rate or reaches a predetermined control with remote notification capability–can provide level. Rate-of-rise heat detectors may be subject to early warning of a developing fire. Such a system, reduced sensitivity over time. For this reason, the however, does not assure protection against property rate-of-rise feature of each detector should be tested damage or loss of life resulting from a fire. at least once per year by a qualified fire protection specialist. Heat detectors are designed to protect The Manufacturer recommends that smoke and/or property, not life. heat detectors be located throughout a protected premise following the recommendations of the current IMPORTANT! Smoke detectors must be installed in edition of the National Fire Protection Association the same room as the control panel and in rooms Standard 72 (NFPA 72), manufacturer's recommenda- used by the system for the connection of alarm tions, State and local codes, and the recommenda- transmission wiring, communications, signaling, and/or tions contained in the Guide for Proper Use of System power. If detectors are not so located, a developing Smoke Detectors, which is made available at no fire may damage the alarm system, crippling its ability charge to all installing dealers. -
Computer Simulation of an Unsprung Vehicle, Part I C
Agricultural and Biosystems Engineering Agricultural and Biosystems Engineering Publications 1967 Computer Simulation of an Unsprung Vehicle, Part I C. E. Goering University of Missouri Wesley F. Buchele Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/abe_eng_pubs Part of the Agriculture Commons, and the Bioresource and Agricultural Engineering Commons The ompc lete bibliographic information for this item can be found at https://lib.dr.iastate.edu/ abe_eng_pubs/960. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Agricultural and Biosystems Engineering at Iowa State University Digital Repository. It has been accepted for inclusion in Agricultural and Biosystems Engineering Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Computer Simulation of an Unsprung Vehicle, Part I Abstract The mechanics of unsprung wheel tractors has received extensive study in the last 40 years. The quantitative approach to the problem essentially began with the work of McKibben (7) in the 1920s. Twenty years later, Worthington (12) analyzed the effect of pneumatic tires on tractor stabiIity. Later, Buchele (3) drew on land- locomotion theory to introduce soil variables into the equations for tractor stability. Differential equations were avoided in these analyses by assuming that the tractor moved with zero or constant acceleration. Thus, vibration and actual tipping of the tractor were beyond the scope of the analyses. Disciplines Agriculture | Bioresource and Agricultural Engineering Comments This article is published as Goering, C. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Erste Arbeiten Mit Zuse-Computern
HERMANN FLESSNER ERSTE ARBEITEN MIT ZUSE-COMPUTERN BAND 1 Erste Arbeiten mit Zuse-Computern Mit einem Geleitwort von Prof. Dr.-Ing. Horst Zuse Band 1 Rechnen, Planen und Konstruieren mit Computern Von Prof. em. Dr.-Ing. Hermann Flessner Universit¨at Hamburg Mit 166 Abbildungen Prof. em. Dr.-Ing. Hermann Flessner Geboren 1930 in Hamburg. Nach Abitur 1950 – 1952 Zimmererlehre in Dusseldorf.¨ 1953 – 1957 Studium des Bauingenieurwesens an der Technischen Hochschule Hannover. 1958 – 1962 Statiker undKonstrukteurinderEd.Zublin¨ AG. 1962 Wiss. Mitarbeiter am Institut fur¨ Massivbau der TH Hannover; dort 1964 Lehrauftrag und 1965 Promotion. Ebd. 1966 Professor fur¨ Elektronisches Rechnen im Bauwesen. 1968 – 1978 Professor fur¨ Angewandte Informatik im Ingenieurwesen an der Ruhr-Universit¨at Bochum; 1969 – 70 zwischenzeitlich Gastprofessor am Massachusetts Institute of Technology (M.I.T.), Cambridge, USA. Ab 1978 Ordentl. Professor fur¨ Angewandte Informatik in Naturwissenschaft und Technik an der Universit¨at Hamburg. Dort 1994 Emeritierung, danach beratender Ingenieur. Biografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliothek; detaillierte bibliografische Daten sind im Internet uber¨ http://dnb.d-nb.de abrufbar uber:¨ Flessner, Hermann: Erste Arbeiten mit ZUSE-Computern, Band 1 Dieses Werk ist urheberrechtlich geschutzt.¨ Die dadurch begrundeten¨ Rechte, insbesondere die der Ubersetzung,¨ des Nachdrucks, der Entnahme von Abbildungen, der Wiedergabe auf photomechani- schem oder digitalem Wege und der Speicherung in Datenverarbeitungsanlagen bzw. Datentr¨agern jeglicher Art bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. c 2016 H. Flessner, D - 21029 Hamburg 2. Auflage 2017 Herstellung..und Verlag:nBoD – Books on Demand, Norderstedt Text und Umschlaggestaltung: Hermann Flessner ISBN: 978-3-7412-2897-1 V Geleitwort Hermann Flessner kenne ich, pr¨aziser gesagt, er kennt mich als 17-j¨ahrigen seit ca. -
CAR-ANS PART 05 Issue No. 2 Units of Measurement to Be Used In
CIVIL AVIATION REGULATIONS AIR NAVIGATION SERVICES Part 5 Governing UNITS OF MEASUREMENT TO BE USED IN AIR AND GROUND OPERATIONS CIVIL AVIATION AUTHORITY OF THE PHILIPPINES Old MIA Road, Pasay City1301 Metro Manila INTENTIONALLY LEFT BLANK CAR-ANS PART 5 Republic of the Philippines CIVIL AVIATION REGULATIONS AIR NAVIGATION SERVICES (CAR-ANS) Part 5 UNITS OF MEASUREMENTS TO BE USED IN AIR AND GROUND OPERATIONS 22 APRIL 2016 EFFECTIVITY Part 5 of the Civil Aviation Regulations-Air Navigation Services are issued under the authority of Republic Act 9497 and shall take effect upon approval of the Board of Directors of the CAAP. APPROVED BY: LT GEN WILLIAM K HOTCHKISS III AFP (RET) DATE Director General Civil Aviation Authority of the Philippines Issue 2 15-i 16 May 2016 CAR-ANS PART 5 FOREWORD This Civil Aviation Regulations-Air Navigation Services (CAR-ANS) Part 5 was formulated and issued by the Civil Aviation Authority of the Philippines (CAAP), prescribing the standards and recommended practices for units of measurements to be used in air and ground operations within the territory of the Republic of the Philippines. This Civil Aviation Regulations-Air Navigation Services (CAR-ANS) Part 5 was developed based on the Standards and Recommended Practices prescribed by the International Civil Aviation Organization (ICAO) as contained in Annex 5 which was first adopted by the council on 16 April 1948 pursuant to the provisions of Article 37 of the Convention of International Civil Aviation (Chicago 1944), and consequently became applicable on 1 January 1949. The provisions contained herein are issued by authority of the Director General of the Civil Aviation Authority of the Philippines and will be complied with by all concerned.