A Guide to Networking Terminology
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Completeness in Quasi-Pseudometric Spaces—A Survey
mathematics Article Completeness in Quasi-Pseudometric Spaces—A Survey ¸StefanCobzas Faculty of Mathematics and Computer Science, Babe¸s-BolyaiUniversity, 400 084 Cluj-Napoca, Romania; [email protected] Received:17 June 2020; Accepted: 24 July 2020; Published: 3 August 2020 Abstract: The aim of this paper is to discuss the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of right K-Cauchy net in a quasi-metric space for which the corresponding completeness is equivalent to the sequential completeness. In this way we complete some results of R. A. Stoltenberg, Proc. London Math. Soc. 17 (1967), 226–240, and V. Gregori and J. Ferrer, Proc. Lond. Math. Soc., III Ser., 49 (1984), 36. A discussion on nets defined over ordered or pre-ordered directed sets is also included. Keywords: metric space; quasi-metric space; uniform space; quasi-uniform space; Cauchy sequence; Cauchy net; Cauchy filter; completeness MSC: 54E15; 54E25; 54E50; 46S99 1. Introduction It is well known that completeness is an essential tool in the study of metric spaces, particularly for fixed points results in such spaces. The study of completeness in quasi-metric spaces is considerably more involved, due to the lack of symmetry of the distance—there are several notions of completeness all agreing with the usual one in the metric case (see [1] or [2]). Again these notions are essential in proving fixed point results in quasi-metric spaces as it is shown by some papers on this topic as, for instance, [3–6] (see also the book [7]). -
Bit & Baud Rate
What’s The Difference Between Bit Rate And Baud Rate? Apr. 27, 2012 Lou Frenzel | Electronic Design Serial-data speed is usually stated in terms of bit rate. However, another oft- quoted measure of speed is baud rate. Though the two aren’t the same, similarities exist under some circumstances. This tutorial will make the difference clear. Table Of Contents Background Bit Rate Overhead Baud Rate Multilevel Modulation Why Multiple Bits Per Baud? Baud Rate Examples References Background Most data communications over networks occurs via serial-data transmission. Data bits transmit one at a time over some communications channel, such as a cable or a wireless path. Figure 1 typifies the digital-bit pattern from a computer or some other digital circuit. This data signal is often called the baseband signal. The data switches between two voltage levels, such as +3 V for a binary 1 and +0.2 V for a binary 0. Other binary levels are also used. In the non-return-to-zero (NRZ) format (Fig. 1, again), the signal never goes to zero as like that of return- to-zero (RZ) formatted signals. 1. Non-return to zero (NRZ) is the most common binary data format. Data rate is indicated in bits per second (bits/s). Bit Rate The speed of the data is expressed in bits per second (bits/s or bps). The data rate R is a function of the duration of the bit or bit time (TB) (Fig. 1, again): R = 1/TB Rate is also called channel capacity C. If the bit time is 10 ns, the data rate equals: R = 1/10 x 10–9 = 100 million bits/s This is usually expressed as 100 Mbits/s. -
"Mathematics for Computer Science" (MCS)
“mcs” — 2016/9/28 — 23:07 — page i — #1 Mathematics for Computer Science revised Wednesday 28th September, 2016, 23:07 Eric Lehman Google Inc. F Thomson Leighton Department of Mathematics and the Computer Science and AI Laboratory, Massachussetts Institute of Technology; Akamai Technologies Albert R Meyer Department of Electrical Engineering and Computer Science and the Computer Science and AI Laboratory, Massachussetts Institute of Technology 2016, Eric Lehman, F Tom Leighton, Albert R Meyer. This work is available under the terms of the Creative Commons Attribution-ShareAlike 3.0 license. “mcs” — 2016/9/28 — 23:07 — page ii — #2 “mcs” — 2016/9/28 — 23:07 — page iii — #3 Contents I Proofs Introduction 3 0.1 References4 1 What is a Proof? 5 1.1 Propositions5 1.2 Predicates8 1.3 The Axiomatic Method8 1.4 Our Axioms9 1.5 Proving an Implication 11 1.6 Proving an “If and Only If” 13 1.7 Proof by Cases 15 1.8 Proof by Contradiction 16 1.9 Good Proofs in Practice 17 1.10 References 19 2 The Well Ordering Principle 29 2.1 Well Ordering Proofs 29 2.2 Template for Well Ordering Proofs 30 2.3 Factoring into Primes 32 2.4 Well Ordered Sets 33 3 Logical Formulas 47 3.1 Propositions from Propositions 48 3.2 Propositional Logic in Computer Programs 51 3.3 Equivalence and Validity 54 3.4 The Algebra of Propositions 56 3.5 The SAT Problem 61 3.6 Predicate Formulas 62 3.7 References 67 4 Mathematical Data Types 93 4.1 Sets 93 4.2 Sequences 98 4.3 Functions 99 4.4 Binary Relations 101 4.5 Finite Cardinality 105 “mcs” — 2016/9/28 — 23:07 — page iv — #4 Contentsiv 5 Induction 125 5.1 Ordinary Induction 125 5.2 Strong Induction 134 5.3 Strong Induction vs. -
MTH 304: General Topology Semester 2, 2017-2018
MTH 304: General Topology Semester 2, 2017-2018 Dr. Prahlad Vaidyanathan Contents I. Continuous Functions3 1. First Definitions................................3 2. Open Sets...................................4 3. Continuity by Open Sets...........................6 II. Topological Spaces8 1. Definition and Examples...........................8 2. Metric Spaces................................. 11 3. Basis for a topology.............................. 16 4. The Product Topology on X × Y ...................... 18 Q 5. The Product Topology on Xα ....................... 20 6. Closed Sets.................................. 22 7. Continuous Functions............................. 27 8. The Quotient Topology............................ 30 III.Properties of Topological Spaces 36 1. The Hausdorff property............................ 36 2. Connectedness................................. 37 3. Path Connectedness............................. 41 4. Local Connectedness............................. 44 5. Compactness................................. 46 6. Compact Subsets of Rn ............................ 50 7. Continuous Functions on Compact Sets................... 52 8. Compactness in Metric Spaces........................ 56 9. Local Compactness.............................. 59 IV.Separation Axioms 62 1. Regular Spaces................................ 62 2. Normal Spaces................................ 64 3. Tietze's extension Theorem......................... 67 4. Urysohn Metrization Theorem........................ 71 5. Imbedding of Manifolds.......................... -
General Topology
General Topology Tom Leinster 2014{15 Contents A Topological spaces2 A1 Review of metric spaces.......................2 A2 The definition of topological space.................8 A3 Metrics versus topologies....................... 13 A4 Continuous maps........................... 17 A5 When are two spaces homeomorphic?................ 22 A6 Topological properties........................ 26 A7 Bases................................. 28 A8 Closure and interior......................... 31 A9 Subspaces (new spaces from old, 1)................. 35 A10 Products (new spaces from old, 2)................. 39 A11 Quotients (new spaces from old, 3)................. 43 A12 Review of ChapterA......................... 48 B Compactness 51 B1 The definition of compactness.................... 51 B2 Closed bounded intervals are compact............... 55 B3 Compactness and subspaces..................... 56 B4 Compactness and products..................... 58 B5 The compact subsets of Rn ..................... 59 B6 Compactness and quotients (and images)............. 61 B7 Compact metric spaces........................ 64 C Connectedness 68 C1 The definition of connectedness................... 68 C2 Connected subsets of the real line.................. 72 C3 Path-connectedness.......................... 76 C4 Connected-components and path-components........... 80 1 Chapter A Topological spaces A1 Review of metric spaces For the lecture of Thursday, 18 September 2014 Almost everything in this section should have been covered in Honours Analysis, with the possible exception of some of the examples. For that reason, this lecture is longer than usual. Definition A1.1 Let X be a set. A metric on X is a function d: X × X ! [0; 1) with the following three properties: • d(x; y) = 0 () x = y, for x; y 2 X; • d(x; y) + d(y; z) ≥ d(x; z) for all x; y; z 2 X (triangle inequality); • d(x; y) = d(y; x) for all x; y 2 X (symmetry). -
Continuity Properties and Sensitivity Analysis of Parameterized Fixed
Continuity properties and sensitivity analysis of parameterized fixed points and approximate fixed points Zachary Feinsteina Washington University in St. Louis August 2, 2016 Abstract In this paper we consider continuity of the set of fixed points and approximate fixed points for parameterized set-valued mappings. Continuity properties are provided for the fixed points of general multivalued mappings, with additional results shown for contraction mappings. Further analysis is provided for the continuity of the approxi- mate fixed points of set-valued functions. Additional results are provided on sensitivity of the fixed points via set-valued derivatives related to tangent cones. Key words: fixed point problems; approximate fixed point problems; set-valued continuity; data dependence; generalized differentiation MSC: 54H25; 54C60; 26E25; 47H04; 47H14 1 Introduction Fixed points are utilized in many applications. Often the parameters of such models are estimated from data. As such it is important to understand how the set of fixed points aZachary Feinstein, ESE, Washington University, St. Louis, MO 63130, USA, [email protected]. 1 changes with respect to the parameters. We motivate our general approach by consider applications from economics and finance. In particular, the solution set of a parameterized game (i.e., Nash equilibria) fall under this setting. Thus if the parameters of the individuals playing the game are not perfectly known, sensitivity analysis can be done in a general way even without unique equilibrium. For the author, the immediate motivation was from financial systemic risk models such as those in [10, 8, 4, 12] where methodology to estimate system parameters are studied in, e.g., [15]. -
The Three Myths of Optical Capacity Scaling How to Maximize and Monetize Subsea Cable Capacity
WHITE PAPER The Three Myths of Optical Capacity Scaling How to Maximize and Monetize Subsea Cable Capacity MYTH 1 Scaling BAUD RATE increases spectral efficiency, thereby increasing total subsea fiber capacity MYTH 2 Scaling MODULATION ORDER increases spectral efficiency, thereby increasing total subsea fiber capacity MYTH 3 Scaling INTEGRATION has no effect on spectral efficiency or subsea fiber capacity AXES OF SCALABILITY Capacity/wave Capacity/device Baud G/Wave 100 Gbaud 800 Gb/s+ 2.4 Tb/s 600 Gb/s 66 Gbaud 1.2 Tb/s 200 Gb/s 500 Gb/s 33 Gbaud 100 Gb/s Modulation Fiber capacity 6 Carrier SC 1.2 @ 16QAM QPSK 8QAM 16QAM 237.5 GHz 64QAM CS-64QAM Multi-channel Super-channel Gb/s/unit FigureFigure 1: 1: Three The Three axes Axes of opticalof Optical scalability Scaling The Three Axes of Optical Scaling Figure 1 shows the three axes that are needed for optical scaling—baud rate, modulation order and integration. This paper will discuss scaling along each of these axes, but it is important to clarify exactly what is being scaled. There are at least three interpretations: • Increasing the data rate per wavelength • Increasing the capacity per line card or appliance • Increasing the total fiber capacity, or spectral efficiency These can potentially be scaled independently, or in concert as transponder technology evolves. In subsea deployments total fiber capacity, or spectral efficiency, is usually the dominant factor in determining overall network economics, so it becomes extremely important to understand the most effective way to achieve total capacity, especially when scaling baud rate has become a focal point for many dense wavelength-division multiplexing (DWDM) vendors today. -
Quadrature Amplitude Modulation (QAM) Or Amplitude Phase Shift Keying (APSK) S(T ) = a Sin(2Π F T + )
ΕΠΛ 427: ΚΙΝΗΤΑ ΔΙΚΤΥΑ ΥΠΟΛΟΓΙΣΤΩΝ (MOBILE NETWORKS) Δρ. Χριστόφορος Χριστοφόρου Πανεπιστήμιο Κύπρου - Τμήμα Πληροφορικής Modulation Techniques (Τεχνικές Διαμόρφωσης) Recall (Process and Elements of Radio Transmission) 1 Modulation Demodulation Topics Discussed 2 Digital Modulation Bit rate, Baud rate Basic Digital Modulation Techniques (ASK, FSK, PSK, QAM) Constellation diagrams Factors that influence the choice of Digital Modulation Scheme – Power Efficiency, Bandwidth Efficiency Modulation 3 Message Signal (Data to be transmitted) Carrier signal with frequency fc Controlling the Amplitude of the carrier signal (ASK) Controlling the Frequency of the carrier signal (FSK) Controlling the Phase of the Modulated Signals Modulated carrier signal (PSK) Analog and Digital Signals Αναλογικά και Ψηφιακά Σήματα 4 Means by which data are propagated over a medium (Οι τρόποι με τους οποίους τα δεδομένα διαδίδονται μέσω κάποιου μέσου). An Analog Signal is a continuously varying electromagnetic wave (ένα συνεχόμενο εναλλασσόμενο ηλεκτρομαγνητικό κύμα) that may be propagated over a variety of media: Wire, fiber optic, coaxial, space (wireless) A digital signal is a sequence of discrete voltage pulses (είναι μια αλληλουχία διακριτών παλμών τάσης) that can be transmitted over a wire medium: E.g., a constant positive level of voltage to represent bit 1 and a constant negative level to represent bit 0. Modulation for Wireless Digital Modulation 5 Digital modulation is the process by which an analog carrier wave is modulated to include a discrete (digital) signal. (Ψηφιακή διαμόρφωση είναι η διαδικασία κατά την οποία ένας μεταφορέας αναλογικού σήματος διαμορφώνεται έτσι ώστε να συμπεριλάβει ένα διακριτό (ψηφιακό) σήμα (π.χ., 1 or 0)) Digital modulation methods can be considered as Digital-to- Analog conversion, and the corresponding Demodulation (e.g., at the Receiver) as Analog-to-Digital conversion. -
Inspector's Handbook: Subbase Construction
INSPECTOR'S HANDBOOK SUBBASE CONSTRUCTION IOWA STATE HIGHWAY COMMISSION AMES, IOWA 1969 r 17:_:H53 s~sl4 1969 \------ -- "- SUBBASE CONSTRUCTION Walter Schneider Jerry Rodibaugh INTRODUCTION This handbook is an inspector's aid. It was written by two inspectors to bring together a 11 of the most of ten-needed information involved in their work. Much care has been taken to detai I each phase of construction, with particular attention to the r.equire ments and limitations of specifications. All applicable specification interpretations in Instructions to Resident Engineers have been included. The beginning inspector should look to the hand book as a reference for standards of good practice. The Standard.Specifications and Special Provisions should not, however, be overlooked as the basic sources of information on requirements and restrictions concerning workmanship and materials. I . CONTENTS SUBBASE CONSTRUCTION Page 1 Definition 1 Types 1 Figure 1 - Typical Section 1 INSPECTION 1 Plans, Proposals, and Specifications · 1 Preconstruction Detai Is 2 I l. STAKING 2 Purpose 2 Techniques 2 -- SUBGRADE CORRECTION 3 Application 3 Profile and Cross-Section Requirements 4 Figure 2 - Flexible Base Construction 5 INSPECTING DIFFERENT TYPES OF ROLLERS USED IN SUBBASE CONSTRUCTION 5 Tamping Rollers . s· Self-Propelled, Steel-Tired Rollers 5 Self-Propelled and Pull-Type Pneumatic Tire Roi lers 6 Figure 3 - Pneumatic-Tired Roller 6 SPREAD RA TES AND PLAN QUANTITIES 6 Spread Chart 6 Fig.ure 4 - Typical Spr~ad chart 7 Figure 5 - scale Ti ck 8 et -- Granular -
A Guide to Networking Terminology. INSTITUTION National Bureau of Standards (DOC), Washington, D.C
DOCUMENT RESUME ED 092 160 IR 000 721 AUTHOR Neumann, A. J. TITLE A Guide to Networking Terminology. INSTITUTION National Bureau of Standards (DOC), Washington, D.C. SPONS AGENCY National Science Foundation, Washington, D.C. REPORT NO NBS-TN-803 PUB DATE Mar 74 NOTE 33p. AVAILABLE FROM Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (SD Cat. No. 013.46:803, $0.80) EDRS PRICE MF-$0.75 HC-$1.85 PLUS POSTAGE DESCRIPTORS Computers; *Computer Science; Definitions; *Glossaries; *Information Networks; Information Processing; Information Systems; *Telecommunication; *Vocabulary IDENTIFIERS *Computer Networks ABSTRACT A selected set of terms and definitions relating to computer networking is presented in a coherent manner. An introduction gives the rationale for the glossary, defies the scope by a brief tutorial overview, and states the glossary format and conventions. The glossary is arranged alphabetically and contains about 140-definitions and associated terms. The sources ofmany terms are cited and modifiers indicate the status of definitions. A complete listing of source material is appended. (Author) NBS TECHNICAL NOTE803 I. I I D U.S. DEPARTMENT OF COMMERCE National Bureau of Standards NATIONAL BUREAU OF STANDARDS Hie National limean of Standards' was established by an act of Congress March 3. 1901. 1111.. lillfl:111.111\ i1.111p,4.1111 to strengthen and ikh.ince the Nation's science and technology facilitate their ellective iipplication for public heneln To this end, the Bureau conducts research and provides. (It a h;isis (or the Nations physical measurement system, 12) scientific and technological services for industry and government, {It a technical basis for equity in trade. -
De-Mystifying Spectral Compatibility of Bonded Copper Systems - Why DMT Is Superior to SHDSL
White Paper De-Mystifying Spectral Compatibility of Bonded Copper Systems - Why DMT is Superior to SHDSL July 2010 Copyright © 2010 Positron Access Solutions, Inc. All rights reserved. Information in this document is subject to change without notice. Doc#: WP-2001-0710 White Paper: De-Mystifying Spectral Compatibility Table of Contents Abstract ....................................................................................... 3 Introduction ................................................................................. 4 The Basic Mechanism of Spectral Impact .................................. 6 Legacy HDSL/SHDSL Systems Confined by Overlap Spectra Design ...................................................................... 7 DMT’s Simplicity, Performance and Predictability Mitigate It’s Impact on ADSL/ADSL2+ ....................................................... 10 Why Enhanced SHDSL also Falls Short ..................................... 13 Proving it with Numbers – Data Supporting DMT’s Superiority .. 16 Conclusion ................................................................................... 19 References ................................................................................... 20 Doc#: WP-2001-0710 2 White Paper: De-Mystifying Spectral Compatibility Abstract This paper compares the spectral impact of symmetric DMT and SHDSL systems and provides clear evidence as to why DMT systems provide superior spectral compatibility, especially when they’re enhanced with MIMO on DMT functionality. It discusses the major -
Multiplexing with NMEA 0183 You Don’T Need State-Of-The-Art Gear to Build a Cost-Effective Onboard Network
ELECTRONICS The MiniPlex Lite multiplexer allows you to link wind instruments (above) and AIS data (right) to your computer. Multiplexing with NMEA 0183 You don’t need state-of-the-art gear to build a cost-effective onboard network. n the last three years, PS has looked autopilots, wind sensors, Automatic NMEA 0183 PRIMER Iat several ways to integrate per- Identification System (AIS) devices, NMEA 0183 is a serial protocol nor- sonal computers into our navigation etc.—still use it to communicate. New mally transmitting at 4,800 baud. For routine. In July 2006, we looked at and expensive devices meeting the comparison, this is about one-tenth of building a custom mini-computer for NMEA 2000 standard (see “Market the speed of a basic dial-up Internet onboard duties. In September 2006, Notes,” page 29) are readily available, connection. we carried out a broad review of nav but in the spirit of doing more with NMEA 0183 is based on the Elec- software with several updates in 2007 less, this article looks at ways we can tronic Industry Association’s RS-422 and 2008. get the most of our existing electronic standard, a close cousin of the RS-232 This is a fast-moving target, and equipment. standard. RS-422 uses differential several recent technological advances When it comes time to add more voltages while RS-232 is single-ended. are changing the playing field. The sensors to your navigation system This means that RS-422 is much more mainstream introduction of solid (such as an AIS unit) or integrate your resistant to electrical noise and can state memory (no more spinning hard PC into the system, making connec- transmit over much longer wire runs.