Recommended Unit Symbols, SI Prefixes, and Abbreviations
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Db Math Marco Zennaro Ermanno Pietrosemoli Goals
dB Math Marco Zennaro Ermanno Pietrosemoli Goals ‣ Electromagnetic waves carry power measured in milliwatts. ‣ Decibels (dB) use a relative logarithmic relationship to reduce multiplication to simple addition. ‣ You can simplify common radio calculations by using dBm instead of mW, and dB to represent variations of power. ‣ It is simpler to solve radio calculations in your head by using dB. 2 Power ‣ Any electromagnetic wave carries energy - we can feel that when we enjoy (or suffer from) the warmth of the sun. The amount of energy received in a certain amount of time is called power. ‣ The electric field is measured in V/m (volts per meter), the power contained within it is proportional to the square of the electric field: 2 P ~ E ‣ The unit of power is the watt (W). For wireless work, the milliwatt (mW) is usually a more convenient unit. 3 Gain and Loss ‣ If the amplitude of an electromagnetic wave increases, its power increases. This increase in power is called a gain. ‣ If the amplitude decreases, its power decreases. This decrease in power is called a loss. ‣ When designing communication links, you try to maximize the gains while minimizing any losses. 4 Intro to dB ‣ Decibels are a relative measurement unit unlike the absolute measurement of milliwatts. ‣ The decibel (dB) is 10 times the decimal logarithm of the ratio between two values of a variable. The calculation of decibels uses a logarithm to allow very large or very small relations to be represented with a conveniently small number. ‣ On the logarithmic scale, the reference cannot be zero because the log of zero does not exist! 5 Why do we use dB? ‣ Power does not fade in a linear manner, but inversely as the square of the distance. -
Appendix A: Symbols and Prefixes
Appendix A: Symbols and Prefixes (Appendix A last revised November 2020) This appendix of the Author's Kit provides recommendations on prefixes, unit symbols and abbreviations, and factors for conversion into units of the International System. Prefixes Recommended prefixes indicating decimal multiples or submultiples of units and their symbols are as follows: Multiple Prefix Abbreviation 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 10 deka da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y Avoid using compound prefixes, such as micromicro for pico and kilomega for giga. The abbreviation of a prefix is considered to be combined with the abbreviation/symbol to which it is directly attached, forming with it a new unit symbol, which can be raised to a positive or negative power and which can be combined with other unit abbreviations/symbols to form abbreviations/symbols for compound units. For example: 1 cm3 = (10-2 m)3 = 10-6 m3 1 μs-1 = (10-6 s)-1 = 106 s-1 1 mm2/s = (10-3 m)2/s = 10-6 m2/s Abbreviations and Symbols Whenever possible, avoid using abbreviations and symbols in paragraph text; however, when it is deemed necessary to use such, define all but the most common at first use. The following is a recommended list of abbreviations/symbols for some important units. -
Calculating Growing Degree Days by Jim Nugent District Horticulturist Michigan State University
Calculating Growing Degree Days By Jim Nugent District Horticulturist Michigan State University Are you calculating degree day accumulations and finding your values don't match the values being reported by MSU or your neighbor's electronic data collection unit? There is a logical reason! Three different methods are used to calculate degree days; i.e., 1) Averaging Method; 2) Baskerville-Emin (BE) Method; and 3) Electronic Real-time Data Collection. All methods attempt to calculate the heat accumulation above a minimum threshold temperature, often referred to the base temperature. Once both the daily maximum and minimum temperatures get above the minimum threshold temperature, (i.e., base temperature of 42degrees, 50degrees or whatever other base temperature of interest) then all methods are fairly comparable. However, differences do occur and these are accentuated in an exceptionally long period of cool spring temperatures, such as we experienced this year. Let me briefly explain: 1. Averaging Method: Easy to calculate Degree Days(DD) = Average daily temp. - Base Temp. = (max. + min.) / 2 - Base temp. If answer is negative, assume 0. Example: Calculate DD Base 50 given 65 degrees max. and 40 degrees min. Avg. = (65 + 40) / 2 = 52.5 degrees DD base 50 = 52.5 - 50 = 2.5 degrees. But look what happens given a maximum of 60 degrees and a minimum of 35 degrees: Avg. = (60 + 35) / 2 = 47.5 DD base 50 = 47.5 - 50 = -2.5 = 0 degrees. The maximum temperature was higher than the base of 50° , but no degree days were accumulated. A grower called about the first of June reporting only about 40% of the DD50 that we have recorded. -
An Atomic Physics Perspective on the New Kilogram Defined by Planck's Constant
An atomic physics perspective on the new kilogram defined by Planck’s constant (Wolfgang Ketterle and Alan O. Jamison, MIT) (Manuscript submitted to Physics Today) On May 20, the kilogram will no longer be defined by the artefact in Paris, but through the definition1 of Planck’s constant h=6.626 070 15*10-34 kg m2/s. This is the result of advances in metrology: The best two measurements of h, the Watt balance and the silicon spheres, have now reached an accuracy similar to the mass drift of the ur-kilogram in Paris over 130 years. At this point, the General Conference on Weights and Measures decided to use the precisely measured numerical value of h as the definition of h, which then defines the unit of the kilogram. But how can we now explain in simple terms what exactly one kilogram is? How do fixed numerical values of h, the speed of light c and the Cs hyperfine frequency νCs define the kilogram? In this article we give a simple conceptual picture of the new kilogram and relate it to the practical realizations of the kilogram. A similar change occurred in 1983 for the definition of the meter when the speed of light was defined to be 299 792 458 m/s. Since the second was the time required for 9 192 631 770 oscillations of hyperfine radiation from a cesium atom, defining the speed of light defined the meter as the distance travelled by light in 1/9192631770 of a second, or equivalently, as 9192631770/299792458 times the wavelength of the cesium hyperfine radiation. -
Time and Frequency Users' Manual
,>'.)*• r>rJfl HKra mitt* >\ « i If I * I IT I . Ip I * .aference nbs Publi- cations / % ^m \ NBS TECHNICAL NOTE 695 U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards Time and Frequency Users' Manual 100 .U5753 No. 695 1977 NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, a technical (3) basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the Office of Experimental Technology Incentives Program. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essen- tial services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics -
Illumination and Distance
PHYS 1400: Physical Science Laboratory Manual ILLUMINATION AND DISTANCE INTRODUCTION How bright is that light? You know, from experience, that a 100W light bulb is brighter than a 60W bulb. The wattage measures the energy used by the bulb, which depends on the bulb, not on where the person observing it is located. But you also know that how bright the light looks does depend on how far away it is. That 100W bulb is still emitting the same amount of energy every second, but if you are farther away from it, the energy is spread out over a greater area. You receive less energy, and perceive the light as less bright. But because the light energy is spread out over an area, it’s not a linear relationship. When you double the distance, the energy is spread out over four times as much area. If you triple the distance, the area is nine Twice the distance, ¼ as bright. Triple the distance? 11% as bright. times as great, meaning that you receive only 1/9 (or 11%) as much energy from the light source. To quantify the amount of light, we will use units called lux. The idea is simple: energy emitted per second (Watts), spread out over an area (square meters). However, a lux is not a W/m2! A lux is a lumen per m2. So, what is a lumen? Technically, it’s one candela emitted uniformly across a solid angle of 1 steradian. That’s not helping, is it? Examine the figure above. The source emits light (energy) in all directions simultaneously. -
Decibels, Phons, and Sones
Decibels, Phons, and Sones The rate at which sound energy reaches a Table 1: deciBel Ratings of Several Sounds given cross-sectional area is known as the Sound Source Intensity deciBel sound intensity. There is an abnormally Weakest Sound Heard 1 x 10-12 W/m2 0.0 large range of intensities over which Rustling Leaves 1 x 10-11 W/m2 10.0 humans can hear. Given the large range, it Quiet Library 1 x 10-9 W/m2 30.0 is common to express the sound intensity Average Home 1 x 10-7 W/m2 50.0 using a logarithmic scale known as the Normal Conversation 1 x 10-6 W/m2 60.0 decibel scale. By measuring the intensity -4 2 level of a given sound with a meter, the Phone Dial Tone 1 x 10 W/m 80.0 -3 2 deciBel rating can be determined. Truck Traffic 1 x 10 W/m 90.0 Intensity values and decibel ratings for Chainsaw, 1 m away 1 x 10-1 W/m2 110.0 several sound sources listed in Table 1. The decibel scale and the intensity values it is based on is an objective measure of a sound. While intensities and deciBels (dB) are measurable, the loudness of a sound is subjective. Sound loudness varies from person to person. Furthermore, sounds with equal intensities but different frequencies are perceived by the same person to have unequal loudness. For instance, a 60 dB sound with a frequency of 1000 Hz sounds louder than a 60 dB sound with a frequency of 500 Hz. -
The Impact of the Speed of Light on Financial Markets and Their Regulation
When Finance Meets Physics: The Impact of the Speed of Light on Financial Markets and their Regulation by James J. Angel, Ph.D., CFA Associate Professor of Finance McDonough School of Business Georgetown University 509 Hariri Building Washington DC 20057 USA 1.202.687.3765 [email protected] The Financial Review, Forthcoming, May 2014 · Volume 49 · No. 2 Abstract: Modern physics has demonstrated that matter behaves very differently as it approaches the speed of light. This paper explores the implications of modern physics to the operation and regulation of financial markets. Information cannot move faster than the speed of light. The geographic separation of market centers means that relativistic considerations need to be taken into account in the regulation of markets. Observers in different locations may simultaneously observe different “best” prices. Regulators may not be able to determine which transactions occurred first, leading to problems with best execution and trade- through rules. Catastrophic software glitches can quantum tunnel through seemingly impregnable quality control procedures. Keywords: Relativity, Financial Markets, Regulation, High frequency trading, Latency, Best execution JEL Classification: G180 The author is also on the board of directors of the Direct Edge stock exchanges (EDGX and EDGA). I wish to thank the editor and referee for extremely helpful comments and suggestions. I also wish to thank the U.K. Foresight Project, for providing financial support for an earlier version of this paper. All opinions are strictly my own and do not necessarily represent those of Georgetown University, Direct Edge, the U.K. Foresight Project, The Financial Review, or anyone else for that matter. -
Angles ANGLE Topics • Coterminal Angles • Defintion of an Angle
Angles ANGLE Topics • Coterminal Angles • Defintion of an angle • Decimal degrees to degrees, minutes, seconds by hand using the TI-82 or TI-83 Plus • Degrees, seconds, minutes changed to decimal degree by hand using the TI-82 or TI-83 Plus • Standard position of an angle • Positive and Negative angles ___________________________________________________________________________ Definition: Angle An angle is created when a half-ray (the initial side of the angle) is drawn out of a single point (the vertex of the angle) and the ray is rotated around the point to another location (becoming the terminal side of the angle). An angle is created when a half-ray (initial side of angle) A: vertex point of angle is drawn out of a single point (vertex) AB: Initial side of angle. and the ray is rotated around the point to AC: Terminal side of angle another location (becoming the terminal side of the angle). Hence angle A is created (also called angle BAC) STANDARD POSITION An angle is in "standard position" when the vertex is at the origin and the initial side of the angle is along the positive x-axis. Recall: polynomials in algebra have a standard form (all the terms have to be listed with the term having the highest exponent first). In trigonometry, there is a standard position for angles. In this way, we are all talking about the same thing and are not trying to guess if your math solution and my math solution are the same. Not standard position. Not standard position. This IS standard position. Initial side not along Initial side along negative Initial side IS along the positive x-axis. -
Using Microsecond Single-Molecule FRET to Determine the Assembly
Using microsecond single-molecule FRET to determine PNAS PLUS the assembly pathways of T4 ssDNA binding protein onto model DNA replication forks Carey Phelpsa,b,1, Brett Israelsa,b, Davis Josea, Morgan C. Marsha,b, Peter H. von Hippela,2, and Andrew H. Marcusa,b,2 aDepartment of Chemistry and Biochemistry, Institute of Molecular Biology, University of Oregon, Eugene, OR 97403; and bDepartment of Chemistry and Biochemistry, Oregon Center for Optical, Molecular and Quantum Science, University of Oregon, Eugene, OR 97403 Edited by Stephen C. Kowalczykowski, University of California, Davis, CA, and approved March 20, 2017 (received for review December 2, 2016) DNA replication is a core biological process that occurs in pro- complete coverage of the exposed ssDNA templates at the precisely karyotic cells at high speeds (∼1 nucleotide residue added per regulated concentration of protein that needs to be maintained in millisecond) and with high fidelity (fewer than one misincorpora- the infected Escherichia coli cell (8, 9). The gp32 protein has an tion event per 107 nucleotide additions). The ssDNA binding pro- N-terminal domain, a C-terminal domain, and a core domain. tein [gene product 32 (gp32)] of the T4 bacteriophage is a central The N-terminal domain is necessary for the cooperative binding integrating component of the replication complex that must con- of the gp32 protein through its interactions with the core domain of tinuously bind to and unbind from transiently exposed template an adjacent gp32 protein. To bind to ssDNA, the C-terminal domain strands during DNA synthesis. We here report microsecond single- of the gp32 protein must undergo a conformational change that molecule FRET (smFRET) measurements on Cy3/Cy5-labeled primer- exposes the positively charged region of its core domain, which in template (p/t) DNA constructs in the presence of gp32. -
2.1 Definition of the SI
CCPR/16-53 Modifications to the Draft of the ninth SI Brochure dated 16 September 2016 recommended by the CCPR to the CCU via the CCPR president Takashi Usuda, Wednesday 14 December 2016. The text in black is a selection of paragraphs from the brochure with the section title for indication. The sentences to be modified appear in red. 2.1 Definition of the SI Like for any value of a quantity, the value of a fundamental constant can be expressed as the product of a number and a unit as Q = {Q} [Q]. The definitions below specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit. By fixing the exact numerical value the unit becomes defined, since the product of the numerical value {Q} and the unit [Q] has to equal the value Q of the constant, which is postulated to be invariant. The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or ratios of defining constants. The International System of Units, the SI, is the system of units in which the unperturbed ground state hyperfine splitting frequency of the caesium 133 atom Cs is 9 192 631 770 Hz, the speed of light in vacuum c is 299 792 458 m/s, the Planck constant h is 6.626 070 040 ×1034 J s, the elementary charge e is 1.602 176 620 8 ×1019 C, the Boltzmann constant k is 1.380 648 52 ×1023 J/K, 23 -1 the Avogadro constant NA is 6.022 140 857 ×10 mol , 12 the luminous efficacy of monochromatic radiation of frequency 540 ×10 hertz Kcd is 683 lm/W. -
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.