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# 200 Recent Changes in LHCb Web retrieved at 08:00 (GMT)

YouhuaYang 2019 12 11
This page contains information on column testing. The full test protocol is available at https://www.overleaf.com/read/mrqtdxndrrck First checks by experts Check...
Daily WLCG Operations calls :: collection of LHCb reports Starting from April 2009, this twiki collects all the LHCb reports given to the daily WLCG calls at 3pm...
AntonioFalabella 08 Dec 2011 Working Groups Customized Productions Introduction LHCbDIRAC is used to run centralized processing tasks on selected datasets. A processing...
Run 2 Turbo PV refitting issue The issue In order to obtain an unbiased (or less biased) measure of the displacement of a particle wrt a PV (eg, flight distance,...
LHCb Run 1 2 Performance Working Group New Performance WG encompassing PID, Calo Objects, Tracking and Alignment (and Trigger) for LHCb Run 1 and 2 Mailing list of...
Cooling Common primary chiller requirements (April 2016) (28 June 2016) of refrigeration options (M. Doubek) cooling meeting (13 October...
When logging on a HEPIX enabled machine like those in the lxplus.cern.ch cluster, the user environment is customized with experiment specific settings (AKA group...
TCK
TCK Trigger Configuration Key The HLT is configured via a unique key, named Trigger Configuration Key (TCK), that defines the sequence of algorithms, and the cuts...
Platforms and compilers supported by LHCb production software Source code and binaries for supported platforms are available in CVMFS (directory /cvmfs/lhcb.cern.ch...
TrackCalib Package TrackCalib was created as tool for creating tracking efficiency correction tables allowing for user defined track quality cuts, binning and variable...
Making ntuples from Turbo data This page shows you how to configure DaVinci to process Turbo data. Due to the historical development cycle of the Turbo processing...
onferences Upcoming Conferences Name Where Date url Topic Abstract deadline Conferences with SciFi participation Conference...
Physics Software Release Schedules This page documents release schedules agreed at the Applications Coordination meetings. Details of the contents of future releases...
SciFi Module Assembly and Quality Assurance tests Access and Contacts Grey Room in LHCB Hall (ask for keys LHCb secretariat) It has airconditioning/heating...
The LHCb Upgrade II LHCb Upgrade II Organisation Upgrade Ib (LS2) and Upgrade II (LS3) matters are overseen by the U2PG: Membership: Spokesperson Passaleva...
Friday Relax Every Thursday at point 8, starting around 18:00 to subscribe to the email list: https://e groups.cern.ch/e groups/EgroupsSubscription.do?egroupName...
PIDCalib Packages This page provides information on how to use the package for extracting PID performance results from both collision data and MC. Questions or comments...
This page contains information on how to configure the system and to take data in the ComLab. Setup the system from scratch Switch on the file server storerich...
Welcome to the home of b TWiki.LHCb /b . This is a web based collaboration area for ... LHCbComputing LHCb FAQs LHCbPhysics LHCbPhysicsPerformance LHCbVELO...
Unbinned PID resampling using kernel density estimation Introduction PIDGen is a set of scripts within PIDCalib package to correct the PID response for MC signal...
Preparing a software project for release This wiki explains the procedure to be used by software release managers to prepare a project for release. It assumes the...
Photos photos in CERNBox SciFi Google Photos Album CERN article 2019 11 12 https://cds.cern.ch/record/2701306# Posters OpenDays 2019 SciFi posters (svg and...
Status SciFi Module 11.11.2019 CF1 12: 14 12 5 13 10 17 11 8 9 6 30 27 CF2 12: 21 27 15 16 20 19 22 23 29 24 28 20 CF3 10: 67 68 70 66 65 64 61...
LHCb User Enviroment (LbEnv) Motivations and design The current tool to set the LHCb User Environment (LbLogin) uses the SetupProject tool to look for the various...
GEOC 2018 shifts This page lists qualified LHCb GEOCs for 2018 and shift stats. The authoritative numbers are in the Database and this page summarises whats there...
Introduction The rationale and the basics of the use of Git in LHCb have been presented and discussed in a few places: Analysis and Software Week (2016 01...
SciFi Tracker Test Beam July 2018 Logbook Runlogbook.ods: Logbook of the settings for each recorded run Instructions for Shifters yes Test beam is...
OPC UA communication The OPC UA server will run on the ELMBs CCPC (TBC). In the ComLab, the pclhcb33 machine is emulating this CCPC. The OPC UA client is running on...
The R2HV1 project is running on lbrichecs01. Port number are shown here https://twiki.cern.ch/twiki/bin/view/LHCb/WinCCProjects Channels configuration The lbRichHV...
Machines used in the SysLab and ComLab The following machines are running CentOS 7, in compliance with the architecture foreseen during the upgrade. storerich01...
TestBeamOct2019 @ DESY This section will summarize the main documents, informations and results of the October/November 2019 testbeam. A fiber based telescope was...
LHCb plots for 2018 data X(3872) in pPb/Pbp: Fit to the Jpsi pi pi invariant mass distributions to determine the yields of X(3872) in pPb/Pbp at 8.16 TeV. The invariant...
MuDAQ MuDAQ (micro DAQ) is a readout environment that performs similar functions to the LHCb miniDAQ environment. It is a lower cost alternative intended for smaller...
The LHCb Upgrade Silicon Strip Common ASIC SALT (Silicon ASIC for LHCb Tracking) People Activity conveners: Idzik (AGH UST UT PI and SALT Project Coordinator...
Project Scope Development of an SiPM based multichannel array photon detector for the SciFi Tracker upgrade. The detector part includes also a flexible PCB and connectors...
Tracking and Alignment Plots for Conferences Tracking Muon tracking efficiency Plot Description Track reconstruction efficiency for 2012 and...
Precision Timing ECAL for Upgrade II Talks Upgrade Ib/II calorimeter meeting. 23rd, 2018 (By A.Davis) Upgrade Ib/II calorimeter meeting. 8th, 2018...
LHCb Software Training LHCb Starterkit StarterKit: First Steps in LHCb LHCb data flow, DST exploration, LoKi Functors, DaVinci and Ganga introductions....
A list of talks at Tracking, Alignment and Vertexing conferences can be found in this table Year Conference Speaker Title Talk/Poster...
System Twiki Mailing list Reconstruction Alignment/Calibration VELO Hutchcroft Borghi, Giulio Dujany TT LHCbST lhcb inner...
Welcome to the LHCb Computing page Do you have a question and are looking for an answer? Try the Q A website Project Management Computing Project Management...
This page is describe the main differences between the old LbScripts/LbLogin environment and the new LbEnv one. Use Case LbScripts LbEnv change current...
LHCb Nightly Build System The System The LHCb Nightly Build System is a collection of tools and scripts that allow automation of build and test tasks for LHCb software...
Naming conventions and port numbers Install the MiniDAQ (ECS DAQ) project from scratch Create a new WinCC project. Copy the fwInstallation folder into the project...
Reference manual Chimaera2 is a readout board designed to receive binary hit data from 128 digital channels through a high density connector. The readout logic is...
LHCb Operations This page is essentially a set of links. Operations Planning Group The OPG meets on Thursdays at 9h30. See here for agendas and minutes. The archives...
Usage The access to the results is done by going to special page. Additionally the previous results are available on this page A few points should be explained to...
OPC UA servers General information and the links to the installers for the OPC UA servers, compatible with CentOS 7, can be found at http://lhcb online.web.cern.ch...
BEWARE This page is obsolete and has been superseded by the new Release Guide. Software Release Guide Special Instructions and troubleshooting Installation on AFS...
List of approved plots for WP2 Title Link in CDS Date Evolution of the upgrade LHCb HLT1 throughput https://lhcbproject.web.cern.ch/lhcbproject/Publications...
List of approved plots for WP4 Title Link in CDS Date First study of the VELO pixel 2 half alignment https://cds.cern.ch/record/2688231?ln en Sep...
The procedure to archive LHCb software release can be found here
List of approved plots for WP6 Title Link in CDS Date
List of approved plots for WP1 Title Link in CDS Date
List of approved plots for WP5 Title Link in CDS Date Tracking efficiencies prior to alignment corrections from 1st Data challenges https://cds.cern...
List of approved plots for WP3 Title Link in CDS Date Breakdown of the current Hlt 2 reconstruction throughput rate for the LHCb upgrade. http:...
Differences between Sim09 versions Below is a list of all Sim09 versions, quickly describing new features and known issues. Fixes to problems of previous versions...
Talks Model Discussion Meeting. 2019.09.03 Internal Discussion 2019.05.15 Useful Links Calo Event Model Calo Software container toturial Array of structures and...
LHCb Conditions Database Browser Table of Contents Introduction The Conditions Database Browser (CondDBBrowser) is a Graphical User Interface (GUI) that can be...
LHCb Conditions Database Browser (OBSOLETE, COOL version) WARNING : This page refers to the version of the CondDBBrowser shipped with LHCb CondDB Browser main window...
LHCb detector performance paper Status of LHCb sub system detector performance paper Sub System Contact Person Number Link Reviewer Reviewer...
The prototype FSM is running on pclhcb33 in the elmb project GiovanniCavallero 2019 09 05
Introduction Detailed development conventions are descrived at https://edms.cern.ch/ui/#master/navigator/document?P:1414255486:100275477:subDocs, summarised in the...
AlessandroPetrolini 2019 07 27 HW commissioning HV crates Currently there is one crate from production registered on the network database: LBRICH CAEN SY4527...
PDMDB The information provided here complements the information found in Documents motherboard TCM/DTM plug ins The RICH PDMDB provides the configuration and...
ParasNaik 2017 05 16 ClaireProuve 2015 07 18 Running the Online RICH mirror alignment How to run the Alignment from the PVSS panel Before running XML file...
ParasNaik 2017 05 16 ClaireProuve 2015 07 18 Code for the Online RICH mirror alignment RICH mirror alignment project and package overview The alignment package...
Talks WP4 5 meeting, 2019.08.22 Internal Discussions http://hep.tsinghua.edu.cn/indico/event/117/contribution/4/attachments/240/291/report.pdf 2019.05.15...
DIRAC Grid Storage Quota A similar tutorial on working with your grid quota in ganga is given in GridAndDataManagement. Before executing the commands in this tutorial...
RICH Upgrade Database Inventory, Bookkeeping and Connectivity Database project A note describing the functionalities of the database (DB) is available at https:/...
This documentation is a documentation for Gaudi based project maintainers. If you are only a user or a developer, you should have a look at GaudiCMake315Configuration...
Version controlled LaTeX documents in LHCb This is about git based solutions. svn is being retired on 21 February 2019. The obsolete documentation for svn can be found...
This documentation is the updated version of https://twiki.cern.ch/twiki/bin/view/LHCb/GaudiCMakeConfiguration and is based on 3.15. It was written after the modernization...
This page contains information on how to configure the system and to take data in the SysLab. Setup the system from scratch Switch on lbminidaq2 13. Type lspci...
LHCb Computing Upgrade This is the entry point for all activities related to Computing for the LHCb Upgrade. Upgrade Software Planning Group (USPG) The USPG was formed...
Optical fibres for ComLab These sketches show the proposed fibre connections for the full column commissioning set up. To zoom in with your browser it is best to right...
Test data Web pages are under development which wil provide summaries of the test results. They are likely to change without warning and are not likely to contain...
This documentation is deprecated since Gaudi v33r0. See instead: https://twiki.cern.ch/twiki/bin/view/LHCb/GaudiCMake315Configuration Introduction CMake is an Open...
Test Beam for the LHCb Upgrade Silicon Tracker This page is about Test Beam for the LHCb Upgrade Silicon Tracker. The dates are scheduled in this presentation: meeting...
Run 2 trigger changelog This page tries to collect the key changes that occurred in the L0, HLT1, and HLT2 systems throughout Run 2 that may be particularly relevant...
Idea To be able to process data at 30 MHz, the possibility of running the full HLT1 on GPUs is currently being studied. The repository of the project is Allen. A...
LHCbPR Performance and Regression Tests Introduction LHCbPR is responsible for systematically running the regression tests, collecting and comparing results of these...
Recommended LoKi::Hybrid Functors This lists the filters recommended for use in the HLT and the selections. See DaVinciTutorial4 for a hands on tutorial. A longer...
This page is obsolete. See the Starterkit for getting started with LHCbDIRAC: https://lhcb.github.io/starterkit lessons/first analysis steps/bookkeeping.html
Vac Configuration for LHCb This page explains how to run LHCb virtual machines on Vac factory machines. Please see the website for Vacs Admin Guide and man pages...
LHCbSAM for ETF This page describes how to maintain the LHCbSAM probes used with Nagios within ETF. The results of these probes are used to generate the monthly WLCG...
TestFileDB, a database of test files for use in automated software tests The TestFileDB is a small python database of PFNs of files used for automated software tests...
Work package: Frames and Infrastructure Chairs: Blake Leverington (Frames), Sune Jakobsen (Services) C Frame Integration Engineer: Thomas Mittelstaedt Documents...
Building the statistics tables for Monte Carlo simulations. Foreword The user of a Monte Carlo sample is interested in a number of efficiency values to make sense...
Muon Alignment Links to past presentations detector spatial alignment with 2016 collision data Stefania Vecchi June, 6th 2016 detector spatial alignment...
LHCbDirac Data Management commands This page describes the usage of the LHCbDirac data management (DMS) commands. As they interface may vary with time and introduction...
PatriziaDeSimone 2019 07 04 Tools Packages Muon/MuonMoni{Sim, Digi, Rec} are available in order to monitor the sim/digi/rec phase of the production for what...
LHCb MuonID General informations This page is intended to be a repository of documents, discussions and meetings about the LHCb Muon Identification Procedure Mailing...
PatriziaDeSimone 2019 07 04 Muon LHCb geometry General informations This page is intended to be a repository of documents about the LHCb Muon Geometry. The most...
PatriziaDeSimone 2019 07 04 Muon LHCb Simulation General informations This page is intended to be a repository of documents about the LHCb Muon Simulation. One of...
PatriziaDeSimone 2019 07 04 Muon LHCb ReadOut maps General informations The upgrade phase 1 foresees for the muon system a different granularity readout: 1) new...
LHCb Vcycle LHCb uses Vcycle to manage resources on the CERN and Yandex OpenStack sites. Currently lbvobox200 hosts the Vcycle agent. Vcycle is not part of DIRAC and...
Welcome to the LHCb UT electronics test page This twiki collects information about the UT electronics slice test and 8 channel prototype SALT ASIC Collection of related...
Particle Selection Toolkit Introduction This wiki explains the use of new python wrapper classes that are intended to simplify both the writing and use of particle...
Simulation in LHCb This page is intended to hold fast evolving information on the simulation and to allow contributions by all. More information is available from...
LHCb U2 Calorimeter Upgrade Page Introduction UNDER CONSTRUCTION Ongoing studies What Who Where Precision Timing ECAL for Upgrade II Z. Xu, P. Robbe...
Code Analysis Tools This page contain a guide to using various code profiling and analysis tools on the LHCb software. Please feel free to add any information to this...
Apr 2006 12971 113 2 2096 WebRss 315 RareDecays 299 LHCbComputing 274 Production 263 LHCbTaskForce 261 DiracProject 224 ComputingModel...
Gen/GenTune Monte Carlo (MC) Generators tuning with Rivet in Gauss For an introduction to RIVET , Professor and their current state of implementation in LHCb please...
Welcome to the LHCb Alignment Web Page Alignment Subtasks Former conveners: Lucia Grillo, Agnieszka Dziurda, Francesco Polci, Giulio Dujany Alignment software...
General LHCb Tracking Wiki Page Run 1 2 Performance WG The tracking alignment WG has been merged with the PID CO WG to form the Run 1 2 Performance WG. Please...
Muon Tracking Efficiencies RenataKopecna1 MichelDeCian Electron Detection and Reconstruction Efficiencies (For details see Electron tracking efficiencies...
Ultra Fast Simulation of LHCb Review of the beta version The aim of the review is to evaluate the status of the software in view of a beta release of Delphes in Gauss...
SciFi test procedures and commissioning Module Assembly and QA at CERN https://twiki.cern.ch/twiki/bin/view/LHCb/SciFiFibreModulesQA Cframe Commissioning The goal...
PID Plots for Conference Run 2 Muon ID with MVAs Contact: Kazeev Plot Description Muon efficiency vs pion rejection after applying IsMuon IsMuonUnbiased...
OBSOLETE Prototype of LHCb Software installation with RPM/YUM Introduction In order to test possible alternatives to install project for the release of LHCb software...
RICH Organization Project leader: DAmbrosio Deputy project leaders: McCann, Rob Jones Operations Coordinator: Gambetta Institutes participating in RICH project...
During the LHCb Core Software meeting of the 12/12/2018 (https://indico.cern.ch/event/779237/), in view of the upcoming deployment of the new environment configuration...
Three testing phases: 1. Viisual inspection and basic powering test using Philips board connected to testing edge connector. 1. Basic set up of board....
Top level PC Microcontroller commands RESET Command for doing general reset of test system. Cutoff all power, end all tests, re initialise TEST BOARD RESET...
Oxford tester board commands Always acknowledge commands Command format Line by line Sequence number Command Data 0000 Command Response\n Match...
Amplitude Analyses of B hadron decays to Open Charm This is the B2OC subgroup focusing on amplitude analyses of B decays to charm final states. Your current sub group...
Tracking Alignment Liaisons page The LHCb liaisons page can be found here Mandate The tasks or a liaison for the Tracking Alignment group includes: Attend...
IllyaShapoval 21 Mar 2013 LHCb Conditions Database pages Introduction GitCondDB Getting started (obsolete) CondDB FAQ (needs revision) Publications...
Reporting bugs in LHCb software You should report bugs, make feature requests, or track your own tasks using one of the following Jira trackers: https://its...
Work package: Front End tester Scope Develops, manufactures and fully characterizes the Read Out Box electronics tester. incl. the specification, user descriptions...
LbSoftConfDb2 Architecture LbSoftConfDb2 is web service that provides a Neo4j database used to store the dependencies of the LHCb software projects. The project is...
Goals As fast as possible and complementary to forward.... Responsible/Proponents Sevda Esen (sevda.esen at cern.ch) Michel De Cian (michel.de.cian at cern.ch) Software...
How to create a new Data Management transformation Introduction dirac dms add transformation is a script allowing to create many types of DMS transformations such...
LHCbDirac transformation plugins Introduction The LHCbDirac transformation system provides a large set of plugins that are used to create tasks from a list of files...
ParasNaik 2014 10 24 AnatolySolomin 2009 07 16 RICH mirror alignment monitoring via software by the use of real data (Online, in real time) Introduction History...
Task List for New Arrivals For newly arriving people at the Point 8 Assembly Hall (Bldg 3852) the following items should be completed BEFORE arrival, if possible...
Delivery Information Note: Deliveries cannot be made directly to Point 8, but have to go via the CERN Pr...
Technical criteria for LHCb T2 D sites: The criteria that T2 D sites agree to meet are set out in the LHCb internal note on T2 D sites, and are reproduced here:...
OBSOLETE LHCb Nightly build slots lhcb future URL https://lhcb nightlies.cern.ch/nightly/?slot lhcb future Definition svn ssh://svn.cern.ch/reps/lhcb...
Please discuss with the Moore release manager (Rosen), before proceeding to these steps Prerequisite You should already have created the new TCKs after following...
LHCb plots for 2018 data PbPb annd PbNe Plots (approved 27th November 2018) Plot Description The invariant mass distribution of $\mu^ \mu^$ reconstructed...
IllyaShapoval 28 Aug 2012 Welcome to the LHCb Conditions Database Web Portal page Introduction The CondDB web portal interface is built on top of the Release Notes...
RICH Run 2 performance paper Here we will list the progress towards a RICH performance paper for Run 2 General structure We need to talk about the things that go...
TupleToolGeometry: vertex, impact parameter, flight distance, etc. info Decay vertex (ENDVERTEX) location for reconstructed particles Primary vertex (OWNPV...
web site page LHCb RICH TWiki page Welcome to the LHCb RICH TWiki web page Here are some links to help you quickly navigate: RICH Organization Reports...
Analysis preservation and reproducibility CERN Central Analysis Preservation The central analysis preservation services and https://reana.readthedocs.io/en/latest...
Module test board Test board modifications This is a list of modifications made to the test boards to correct hardware bugs. They must be implemented on new boards...
LHCb Conditions Database Browser (for COOL/SQLite) Since end of Run2 LHCb does not support COOL based Conditions Databases . All active branches support GitCondDB...
Recommended DataBase tags Introduction This is based on Thomas Rufs at T rec on 13/7/09. Which database tags should I use? As a general rule, for real data it should...
Note: when finalised. this should all be documented in an EDMS document All major items (e.g. modules, cold boxes, electronics, cables, etc.) shall be identified...
RicardoVazquezGomez 2015 06 03 Stripping project description The stripping project has been moved to gitlab: https://gitlab.cern.ch/lhcb/Stripping and contains the...
TurboSP paper The TurboSP paper describes the evolution of the Turbo processing model since the paper. This page gives some information on the document. The source...
This is obsolete SVN will be retired. This is the old documentation. Refer this page instead. https://twiki.cern.ch/twiki/pub/LHCb/OldLHCbDocs/LHCbDocs.jpg Using...
LoKis Particle Functions This lists a lot of the LoKi Functors. See DaVinciTutorial4 for a hands on tutorial. A list with examples of use in CombineParticles can...
T2 D Commissioning procedure This page outlines the administrative and technical steps needed to commission a site as a T2 D (a Tier 2 with Data). The site...
LHCb Stripping page Processing passes for all Stripping productions An exhaustive list of the processing passes including database tags, DaVinci versions etc can...
RicardoVazquezGomez 2016 09 07 Test a Stripping line with git (work in progress) # PLEASE DO NOT USE THESE INSTRUCTIONS, INSTEAD FOLLOW https://its.cern.ch/jira...
Calorimeter Upgrade II Full Simulation Study Ecal background study The materials of 5/11/2018 meeting: 25ns background.pdf: the species, energy flow, transverse...
!!! PAGE NO LONGER MAINTAINED. KEPT FOR HISTORICAL REASONS !!! Physics Analysis Software Packages Introduction The table below lists all packages used in physics...
!!! PAGE NO LONGER MAINTAINED. KEPT FOR HISTORICAL REASONS !!! DaVinci Configuration Introduction Since DaVinci v22r0 the run configuration can only be done using...
Simulation studies to investigate the effects of radiation dose on the LHCb SciFi detectorOle Gerber (Masterarbeit, TU Dortmund,2018) Study of the angle dependent...
PatLongLivedTracking Goal Description for PatLongLivedTracking, used to reconstruct Downstream tracks in Run II of LHCb. Proponents Adam Davis, Michel De Cian, Adam...
Introduction GitCondDB is the new backend for condition data in LHCb. Concept The idea is simple: map time evolution of conditions data on a filesystem hierarchy...
Review RICH electronics review Indico page Contains links to review documents and reviewers report. RICH PDMDB EDR Indico page Contains links to review documents...
Layout and coverage Title Description Graphic / links (click image for full size) Station layout Title Description Graphic / links (click...
TWeeder info for LHCb Total Number of topics: 2912 29 Topics updated during the last 7 days Days Web Topic Date S7 LHCb RichTestBeamMiniDaq...
Work package: Fibre Procurement and QA WP leader: Christian.Joram #64;cernNOSPAMPLEASE.ch Team at CERN: Ana Barbara Cavalcante (until August 2016), Biplab...
SebastianBachmann 2016 04 27 The link to the Production Database is https://scifi.physi.uni heidelberg.de/db/prod/ . Informations on registration and usage of the...
Fibre Mat Inventory Overview of fibre mats good mats mats that are used in modules etc or which are meant to Name Nickname Fibres used Winding...
Documents Fibre Mat Production Bible : v1, April 2016 v2, Jun 2016 v3, Sep 2016 Link to Thomas Kirns website: http://accms04.physik.rwth aachen...
Work package: Fibre Mats and Module WP leader: Blake Leverington (b.leverington at cern.ch) WP deputy leader: Thomas Kirn (kirn at physik.rwth aachen.de) Scope...
TestBeamOct2018 This section will summarize the main documents, informations and results of the October 2018 testbeam. A fiber based telescope was installed in...
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# Can matter undergo phase transitions?

Jul 18, 2017

...If it is matter, then I hope so. If it is matter, it should be describable by a phase diagram (at least, in principle).

Benzene is a fine example:

• If we start at $\text{280 K}$ and $\text{30 torr}$, and increase the pressure at constant temperature past roughly $\text{40 torr}$...

...We condense the gas into a liquid. (If we reverse the process we just did, we vaporize the liquid into a gas.)

• If we start at $\text{273 K}$ and $\text{10 torr}$, and increase the pressure at constant temperature, we move vertically upwards in the phase diagram.

We consequently transform the gas into a solid, i.e. deposition, past roughly $\text{30 torr}$. (If we reverse the process, we perform sublimation.)

• And if we look closely, the solid-liquid coexistence curve has a negative slope (is not perfectly vertical).

So if we start at roughly $\text{280 K}$ and $\text{40 torr}$ (to the left of the triple point) and increase the pressure at constant temperature, past roughly $\text{50 torr}$ we would melt the solid into a liquid. (The reverse process would be freezing the liquid.)

format: plain


text:
RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Guidelines for authors Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 J. Sib. Fed. Univ. Math. Phys.: Year: Volume: Issue: Page: Find

 Determination of source functions in composite type system of equationsYury Ya. Belov, Vera G. Kopylova 275 Limit theorem for the joint distribution in the $Q$-processesAzam A. Imomov 289 New periodic Gibbs measures for $q$-state Potts model on a Cayley treeRustamjon M. Khakimov 297 The Bergman and Cauchy–Szego kernels for matrix ball of the second typeGulmirza Kh. Khudayberganov, Uktam S. Rakhmonov 305 Asymptotic behavior at infinity of the Dirichlet problem solution of the $2k$ order equation in a layerMikhail S. Kildyushov, Valery A. Nikishkin 311 On minimal cubature formulas exact for Haar polynomials of low degrees in the two-dimensional caseKirill A. Kirillov 318 Generator of solutions for $2D$ Navier–Stokes equationsAlexander V. Koptev 324 Univalent differentials of integer order on variable torusTatyana S. Krepizina 331 Conditions for convergence of the Mellin–Barnes integral for solution to system of algebraic equationsVladimir R. Kulikov 339 Risk aversion for defining elliptic acceptance sets in the model of generalized coherent risk measuresTatyana A. Kustitskaya 347 Problems on structure for quasifields of orders $16$ and $32$Vladimir M. Levchuk, Polina K. Shtukkert 362 New approaches to the analysis of the elementary reactions kineticsMaxim N. Nazarov 373 On a new embedding theorem in analytic Bergman type spaces in bounded strictly pseudoconvex domains of $n$-dimensional complex spaceRomi F. Shamoyan, Sergey M. Kurilenko 383 Determination of mechanical force between two planar inductors in the problem of electrodynamic excitation of seismic wavesAlexander A. Shchitnikov 389 On creeping motion of binary mixture in a tube with rectangular cross-sectionAlexandra E. Silaeva 398


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# React Typescript Boilerplate

I'm trying to build a React Boilerplate Using multiple tools. They are all: React, TypeScript, ESLint, Webpack, Babel, Prettier, VSCode and with Airbnb's code style guide.

Actually, this is my first Boilerplate. I don't know if there's a redundant dependency or unnecessary codes inside. Can you please review it? The devDependencies looks so many compared to my previous projects.

All I want to do is create a boilerplate that uses the stacks I mentioned above, so that I can use it whenever I want to start a new project. Something like a handmade create-react-app. The content of the App doesn't really matter, as long as it follows the rules, just like create-react-app. I came here to find out the quality of my configurations, since sometimes, those tools are fighting each other and I want know when and why are they fighting again. Just like 1 hour ago, I added the Airbnb style guide and it collided with prettier's indentation. I resolved it using the last 3 eslint rules below, but I don't know if there's any hidden conflict left.

Here's the link to my boilerplate: https://github.com/SnekNOTSnake/react-typescript-boilerplate

And here's my quick .eslintrc.json file:

{
"parser": "@typescript-eslint/parser",
"extends": [
"plugin:@typescript-eslint/recommended", // Typescript rules
"plugin:prettier/recommended", // Sets the prettier/prettier rule to "error"
"plugin:react/recommended", // React rules
"plugin:react-hooks/recommended", // React Hooks rules
"airbnb-typescript" // Airbnb code stylings
],
"parserOptions": {
"ecmaVersion": 2020, // ES11 New features are enabled!
"sourceType": "module", // Tell ESLint that everything is a module
"project": "./tsconfig.json" // Location of the Parser config file
},
// Runs Prettier as an ESLint rule and reports differences as individual ESLint issues.
"plugins": ["prettier"],
"rules": {
"@typescript-eslint/no-var-requires": "off", // Off for webpack config files
"react/jsx-indent": [2, "tab"], // Use tabs
"@typescript-eslint/indent": "off", // Use prettier indentation instead
"no-tabs": "off" // Use tabs
}
}

Another quick package.json file:

{
"scripts": {
"build": "NODE_ENV=production webpack --config webpack.prod.js",
"start": "webpack-dev-server --open --config webpack.dev.js",
"check-types": "tsc"
},
"dependencies": {
"react": "^16.13.1",
"react-dom": "^16.13.1"
},
"devDependencies": {
"@babel/core": "^7.11.1",
"@babel/preset-env": "^7.11.0",
"@babel/preset-react": "^7.10.4",
"@babel/preset-typescript": "^7.10.4",
"@types/react": "^16.9.45",
"@types/react-dom": "^16.9.8",
"@types/webpack-env": "^1.15.2",
"@typescript-eslint/eslint-plugin": "^3.8.0",
"@typescript-eslint/parser": "^3.8.0",
"clean-webpack-plugin": "^3.0.0",
"eslint": "^7.6.0",
"eslint-config-airbnb-typescript": "^9.0.0",
"eslint-config-prettier": "^6.11.0",
"eslint-plugin-import": "^2.22.0",
"eslint-plugin-jsx-a11y": "^6.3.1",
"eslint-plugin-prettier": "^3.1.4",
"eslint-plugin-react": "^7.20.5",
"eslint-plugin-react-hooks": "^4.0.8",
"html-webpack-plugin": "^4.3.0",
"prettier": "^2.0.5",
"typescript": "^3.9.7",
"webpack": "^4.44.1",
"webpack-cli": "^3.3.12",
"webpack-dev-server": "^3.11.0",
"webpack-merge": "^5.1.1"
},
"engines": {
"node": "^12.16.3"
}
}

For the sake of completeness: .babelrc.json

{
"presets": [
[
"@babel/preset-env",
{
"targets": {
"edge": 17,
"firefox": 60,
"chrome": 67,
"safari": "11.1"
},
"corejs": "3",
"useBuiltIns": "usage"
}
],
"@babel/preset-react",
"@babel/preset-typescript"
]
}

tsconfig.json

{
"compilerOptions": {
"baseUrl": ".",
"paths": {
"Utils/*": ["src/utils/*"]
},

"allowSyntheticDefaultImports": true,
"noImplicitAny": true,
"moduleResolution": "node",
"sourceMap": true,
"module": "esnext",
"target": "esnext",
"jsx": "react",
"allowJs": true,
"noEmit": true,
"noImplicitThis": true,
"strictNullChecks": true,
"lib": ["es6", "dom"]
}
}

.prettier.json

{
"useTabs": true,
"singleQuote": true,
"trailingComma": "all",
"semi": true,
"tabWidth": 2,
"endOfLine": "lf",
"arrowParens": "avoid",
"bracketSpacing": true
}

• Maybe you missed the text on the right side when typing your question : "Your question must contain code that is already working correctly, and the relevant code sections must be embedded in the question." Questions must include the code to be reviewed. Links to code hosted on third-party sites are permissible, but the most relevant excerpts must be embedded in the question itself. – cliesens Aug 13 at 15:41
• Should I put all of the files inside this question? There's like 12 of them. And I think those two are what I need the most to be reviewed. – SnekNOTSnake Aug 13 at 15:46
• I'm not sure, you're the one asking the question; only include all the files you want to be reviewed, and only those. If the two files you've put in your question are the only ones, then you're fine. You can look at some other questions to have a better idea of what is/isn't acceptable, but in general, more code is better, so don't be afraid to add more. – cliesens Aug 13 at 15:51
• Ahh, got it. I'll include all of the config files only. – SnekNOTSnake Aug 13 at 15:51
• All I want to do is create a boilerplate that uses the stacks I mentioned above, so that I can use it whenever I want to start a new project. Something like a handmade create-react-app. The content of the App doesn't really matter, as long as it follows the rules, just like create-react-app. I came here to find out the quality of my codes, since sometimes, those tools are fighting each other and I want know when and why are they fighting again. Just like 1 hour ago, I added the Airbnb style guide and it collided with prettier's indentation. – SnekNOTSnake Aug 13 at 16:05


text:
# Egyptian Pyramids

The Great Pyramid of Giza, the largest pyramid in Egypt, is not only the oldest of the Seven Wonders of the Ancient World, but it is also the only one to remain largely intact. The Egyptian Pyramids can take up to 20 years to build and are so big that Al-Aziz Uthman, son of the great Saladin who crushed the Crusaders, had to give up demolishing the Great pyramids of Giza because it was deemed too great a task. The Egyptian pyramids were mostly built as tombs for the country's Pharaohs and their consorts during the Old and Middle Kingdom periods (c. 2686–1690 BCE), and as of 2008, 138 Egyptian pyramids have been discovered.

The task is to create a program which inputs a sequence of distances separated by a space, and produces 10×10 text pyramids separated by those distances. A distance of 1 is equal to two characters.

A text pyramid will look like this:

         /\
/--\
/----\
/------\
/--------\
/----------\
/------------\
/--------------\
/----------------\
/------------------\

If the input consists of only a line break, then one pyramid will be produced, as above. For each pyramid, pyramids to the left are displayed as if they were in front.

## Example I

Input:

4 3 1

Output:

         /\      /\    /\/\
/--\    /--\  /--\-\
/----\  /----\/----\-\
/------\/------\-----\-\
/--------\-------\-----\-\
/----------\-------\-----\-\
/------------\-------\-----\-\
/--------------\-------\-----\-\
/----------------\-------\-----\-\
/------------------\-------\-----\-\

## Example II

Input:

0 9

Output:

         /\                /\
/--\              /--\
/----\            /----\
/------\          /------\
/--------\        /--------\
/----------\      /----------\
/------------\    /------------\
/--------------\  /--------------\
/----------------\/----------------\
/------------------\-----------------\

## Example III

Input:

11

Output:

         /\                    /\
/--\                  /--\
/----\                /----\
/------\              /------\
/--------\            /--------\
/----------\          /----------\
/------------\        /------------\
/--------------\      /--------------\
/----------------\    /----------------\
/------------------\  /------------------\

The application to fulfill these requirements in the fewest amount of characters is the winner.

Reference: Wikipedia.org

• I presume that additional whitespace at the end of the line is permitted? – Peter Taylor Jun 1 '11 at 18:33
• Depends who you ask. In the strictest reading of the spec, there is no whitespace following the output. But given that this is for fun, I have no problem with it. – nharren Jun 1 '11 at 22:32
• So command line arguments for taking input is allowed? – Joey Jun 3 '11 at 14:07
• As long as it meets the requirements. I do see now that Whitledge's solution is actually not able to handle linebreaks as input (I cannot undo my upvote), it simply works around it by producing a pyramid if there is no input. But if you can find a solution that can handle linebreak inputs (\r or \n is fine) as command line args, then it is okay with me. – nharren Jun 4 '11 at 2:38

~]0-:|;10,{:§9\-" "*"/""-"§2**+"\\"+:&|{.§>{§-(2*" "*1$}{-2*&>}if}%n}%  Direct port of my Ruby solution, so I'm sure it's possible to shorten this by quite a few characters. ## Windows PowerShell, 122 132133139 $d=@(-split$input)-gt0 0..9|%{' '*(9-($x=$_))+($a="/$('--'*$_)\")+-join($d|%{' '*(($_-$x-1)*($x-lt$_))$a[(-2*$_)..-1]})}  Random input also makes for nice images: • It works if I add $input=Read-Host at the top, otherwise it doesn't ask for input. How should this be run? – nharren Jun 1 '11 at 2:07
• @nharren: echo 0 3 4 1|powershell -noprofile -file pyramids.ps1 Or from PowerShell '0 1 4 3' | .\pyramids.ps1. This is a frequent problem with golfing in PowerShell, sadly, as you can only accept either piped-in input or interactive input. PowerShell doesn't really have the notion of stdin other languages and environments have and this shows sometimes. I usually go for piped input, unless the task explicitly calls for interactivity, like Guess the number. – Joey Jun 1 '11 at 9:45
• Ah yes, now it works. My button mashing wasn't yielding any results, and I couldn't figure out why. – nharren Jun 1 '11 at 11:39

r=replicate
p d=map(\k->foldr(\n i->r(9-k)' '++'/':r(2*k)'-'++"\\"++drop(11+k)(r(2*n)' '++i))""$d++[0])[0..9] main=interact$unlines.p.map read.words

I'm quite unsatisfied with this! It just feels way too long. Ideas?

• Inside the lambda, you could change the big pile of ++'s to a single list and use concat aka >>=id. I don't know whether it will help. Another point would be using foldr1 instead of foldr. – FUZxxl Jun 1 '11 at 13:51
• Thanks for the ideas. Neither helps in this case: Converting ++ sequences only saves you one character per item, and the overhead of the final concat is too high here. The foldr can't use the foldr1 form as the result time is String whereas the list type is [Int] (The 1 variants fold require them to be the same.) – MtnViewMark Jun 5 '11 at 0:04

## Python, 123 characters

N=[10]+map(int,raw_input().split())
for y in range(10):print''.join((2*n*' '+'/'+2*y*'-'+'\ ')[-2*n-1:-1]for n in N)[9-y:]

• Out of curiosity, is this python 2.5? To get this to work in python 3.2, I wrapped the map function in a list function, changed raw_input() to input(), and changed print to print(). – nharren Jun 2 '11 at 6:33
• @nharren: works in both 2.4.4 and 2.5.2 for me. – Keith Randall Jun 2 '11 at 6:44

## Ruby 1.9, 116 characters

d=gets.split-[?0]
10.times{|i|puts [?\s*(9-i),l=?/+?-*2*i+?\\,d.map{|r|i<(r=r.to_i)??\s*2*(r+~i)+l :l[-2*r,99]}]*""}

$_=<>;$s=" "x9;map{$k.="/\\"." "x($_-1)if$_}split;$_="$s$k/\$s\n";fori(0..9){print;s%\\-%-\\%g;s%\\/%-\\%g;s%\\ %-\\%g;s% /%/-%g}  Slightly shorter version which takes input as command-line arguments rather than from stdin: s=" "x9;map{k.="/\\"." "x(_-1)if_}@ARGV;_="sk/\$s\n";for$i(0..9){print;s%\\-%-\\%g;s%\\/%-\\%g;s%\\ %-\\%g;s% /%/-%g}  Can't believe no-one did a regex solution yet. Perl is a long way from being my best language, so this can probably lose a lot more. I'd be interested to see a sed implementation, if someone's up for the challenge. (Thanks, @mbx, for 4 chars). • foreach==for -> save 4 chars – mbx Jun 2 '11 at 2:36 • have you tested your version with the given testcases?! – mbx Jun 2 '11 at 2:45 • @mbx, yes, works for me. Perl 5.10.1, Ubuntu. What bug are you seeing? – Peter Taylor Jun 2 '11 at 5:42 • @Peter Taylor - on my ubuntu and win32 it works also fine. I first tried it on ideone which is running perl 5.12.1. – mbx Jun 2 '11 at 9:08 • »If the input consists of only a line break« hints at standard input, actually. – Joey Jun 2 '11 at 11:13 ## JavaScript, 396 bytes function p(a){for(u=0;u<10;u++){t[u+a][9-u]="/";for(k=9-u+1+a;k<10+u+a;k++)t[k][u]="-"; t[10+u+a][u]="\\"}}function _(a){t=[];for(i=0;i<50;i++){t[i]=[];for(j=0;j<10;j++)t[i][j]=" " }var a=a.split(" "),b=a.reduce(function(a,b){return a-0+(b-0)})*2;for(i=a.length-1;i>=0; i--)p(b),b-=a[i]*2-0;p(0);a="";for(j=0;j<10;j++){b="";for(i=0;i<50;i++)b+=t[i][j]; a+=b.replace(/\s+$/,"")+(j<9?"\n":"")}return a}

I'm not going to win with JavaScript, but there is a JavaScript entry now :)

Usage: _("1 2 3") etc.

## Ruby (112)

Slightly shorter than Ventero's Ruby solution, with a different approach. I just started learning Ruby, so this can probably be reduced quite a bit.

s=' '*9+r='/\\';gets.split.map{|i|s+=' '*2*(i.to_i-1)+r}
10.times{puts s;s.gsub!' /','/-';s.gsub!(/\\.?/,'-\\')}

# Powershell, 105 98 bytes, the strictest reading of the spec

($a=' '+-join(,5+$args-gt0|%{'  '*--$_+'/\'})) 1..9|%{($a=$a-replace' /','/-'-replace'\\.?','-\')}  Test script: $f = {

($a=' '+-join(,5+$args-gt0|%{'  '*--$_+'/\'})) 1..9|%{($a=$a-replace' /','/-'-replace'\\.?','-\')} } @( ,(@" /\ /--\ /----\ /------\ /--------\ /----------\ /------------\ /--------------\ /----------------\ /------------------\ "@) ,(@" /\ /\ /\/\ /--\ /--\ /--\-\ /----\ /----\/----\-\ /------\/------\-----\-\ /--------\-------\-----\-\ /----------\-------\-----\-\ /------------\-------\-----\-\ /--------------\-------\-----\-\ /----------------\-------\-----\-\ /------------------\-------\-----\-\ "@, 4,3,1) ,(@" /\ /\ /--\ /--\ /----\ /----\ /------\ /------\ /--------\ /--------\ /----------\ /----------\ /------------\ /------------\ /--------------\ /--------------\ /----------------\/----------------\ /------------------\-----------------\ "@, 0,9) ,(@" /\ /\ /--\ /--\ /----\ /----\ /------\ /------\ /--------\ /--------\ /----------\ /----------\ /------------\ /------------\ /--------------\ /--------------\ /----------------\ /----------------\ /------------------\ /------------------\ "@, 11) ) | % {$expected, $a =$_
$result = &$f @a
($result-join"n")-eq$expected
$result }  Output: True /\ /--\ /----\ /------\ /--------\ /----------\ /------------\ /--------------\ /----------------\ /------------------\ True /\ /\ /\/\ /--\ /--\ /--\-\ /----\ /----\/----\-\ /------\/------\-----\-\ /--------\-------\-----\-\ /----------\-------\-----\-\ /------------\-------\-----\-\ /--------------\-------\-----\-\ /----------------\-------\-----\-\ /------------------\-------\-----\-\ True /\ /\ /--\ /--\ /----\ /----\ /------\ /------\ /--------\ /--------\ /----------\ /----------\ /------------\ /------------\ /--------------\ /--------------\ /----------------\/----------------\ /------------------\-----------------\ True /\ /\ /--\ /--\ /----\ /----\ /------\ /------\ /--------\ /--------\ /----------\ /----------\ /------------\ /------------\ /--------------\ /--------------\ /----------------\ /----------------\ /------------------\ /------------------\  # Powershell, 101 94, fun with one leading whitespace ($a=-join(,6+$args-gt0|%{' '*--$_+'/\'}))
1..9|%{($a=$a-replace' /','/-'-replace'\\.?','-\')}

I couldn't get the C#3 version any shorter than this. I don't know the character count exactly, but I suspect that I have lost. :-(

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace PyramidRenderer
{
/// <summary>
/// Generates ASCII-art pyramids at user-specified horizontal locations to
/// the standard output stream.
/// </summary>
public class Program
{
/// <summary>
/// Generates one or more ASCII-art pyramids at the locations specified and
/// sends them to the standard output stream.
/// </summary>
/// <param name="args">The command-line arguments. These should be non-negative
/// integers that specify the horizontal distance of each additional pyramid from the
/// preceeding pyramid. Whether or not any distances are suppplied, a pyramid
/// is rendered at the starting location.</param>
public static void Main(string[] args)
{
try
{
AppDomain.CurrentDomain.UnhandledException += new UnhandledExceptionEventHandler(CurrentDomain_UnhandledException);

int[] pyramidDistances = ParsePyramidLocationsFromCommandLine(args).ToArray();
PyramidCollection pyramids = new PyramidCollection(pyramidDistances);
pyramids.RenderToText(Console.Out);
}
catch (ArgumentException ex)
{
Console.Error.WriteLine(ex.Message);
}
}

/// <summary>
/// Handler for the unhandled exception. This just displays the error message to
/// the standard error stream.
/// </summary>
/// <param name="sender">Required but unnecessary sender object for the event handler.</param>
/// <param name="e">The object that represents the exception.</param>
private static void CurrentDomain_UnhandledException(object sender, UnhandledExceptionEventArgs e)
{
Debug.Assert(e.ExceptionObject != null);

string exceptionText;
Exception ex = e.ExceptionObject as Exception;
if (ex == null)
exceptionText = e.ExceptionObject.ToString();
else
exceptionText = ex.Message;
Console.Error.WriteLine(exceptionText);
}

/// <summary>
/// Takes the command-line arguments and converts them to a sequence of
/// non-negative integers.
/// </summary>
/// <param name="args">The command-line arguments as supplied to Main.</param>
/// <returns>A sequence of integers that represent the user’s distance selections.</returns>
/// <exception cref="ArgumentException">An invalid argument was supplied.</exception>
private static IEnumerable<int> ParsePyramidLocationsFromCommandLine(string[] args)
{
Debug.Assert(args != null);

foreach (string arg in args)
{
int result;
if (int.TryParse(arg, out result))
{
if (result < 0)
throw new ArgumentException(string.Format("Invalid distance specified: {0}", arg));

yield return result;
}
else
{
throw new ArgumentException(string.Format("Invalid option: {0}", arg));
}
}
}
}

/// <summary>
/// Represents a single pyramid to be rendered.
/// </summary>
internal class Pyramid
{
/// <summary>
/// The height of the pyramids in text rows. The width of each pyramid will be
/// twice the height.
/// </summary>
internal const int Height = 10;

/// <summary>
/// The length in characters of the horizontal unit distance in which the user
/// specifies the pyramid distances.
/// </summary>
internal const int PyramidUnits = 2;

/// <summary>
/// The character to output as the background of the pyramids.
/// </summary>
private const char backgroundChar = ' ';

/// <summary>
/// The character to output as the left edge of the pyramids.
/// </summary>
private const char leftEdgeChar = '/';

/// <summary>
/// The character to output within each pyramid, between the edges.
/// </summary>
private const char brickChar = '-';

/// <summary>
/// The character to output as the right edge of the pyramids.
/// </summary>
private const char rightEdgeChar = '\\';

/// <summary>
/// The absolute horizonal location of the pyramid’s bottom left corner as
/// specified in PyramidUnits.
/// </summary>
private int position;

/// <summary>
/// Constructs a new pyramid object at the specified location.
/// </summary>
/// <param name="position">The absolute horizonal location of the pyramid’s bottom
/// left corner in PyramidUnits.</param>
internal Pyramid(int position)
{
Debug.Assert(position >= 0);

this.position = position;
}

/// <summary>
/// Renders a single row the pyramid to the supplied text stream starting at
/// the indicated location.
/// </summary>
/// <param name="textWriter">The output stream to which the pyramid is to
/// be rendered.</param>
/// <param name="row">The row of the pyramid to render. Zero is the top row,
/// and Height - 1 is the bottom row.</param>
/// <param name="startingPosition">The text character position—indexed at zero—at
/// which the rendering is to begin. If non-zero, this identifies the column one
/// past the ending location of the previous pyramid.</param>
/// <returns>The horizontal location (in characters) at which the next item
/// may be rendered.</returns>
internal int RenderRow(TextWriter textWriter, int row, int startingPosition)
{
Debug.Assert(textWriter != null);
Debug.Assert(row >= 0);
Debug.Assert(startingPosition >= 0);

int leftBoundary = Height - 1 - row + position * PyramidUnits;
int rightBoundary = Height + row + position * PyramidUnits;

startingPosition = RenderField(textWriter, backgroundChar, startingPosition, leftBoundary);
startingPosition = RenderField(textWriter, leftEdgeChar, startingPosition, leftBoundary + 1);
startingPosition = RenderField(textWriter, brickChar, startingPosition, rightBoundary);
startingPosition = RenderField(textWriter, rightEdgeChar, startingPosition, rightBoundary + 1);
return startingPosition;
}

/// <summary>
/// Outputs a sequence of repeated characters from the indicated starting position to
/// just before the ending position, unless the starting position is already equal to
/// or greater than the ending position.
/// </summary>
/// <param name="textWriter">The output stream to which the field is to be rendered.</param>
/// <param name="character">The character to be repeated in the output.</param>
/// <param name="startingPosition">The location at which rendering may begin in
/// characters indexed at zero.</param>
/// <param name="endingPosition">The location one past the location at which rendering
/// is to end.</param>
/// <returns>The position at which the next field may begin.</returns>
private static int RenderField(TextWriter textWriter, char character, int startingPosition, int endingPosition)
{
Debug.Assert(textWriter != null);
Debug.Assert(startingPosition >= 0);
Debug.Assert(endingPosition >= 0);

int charCount = endingPosition - startingPosition;
if (charCount <= 0)
return startingPosition;
textWriter.Write(new string(character, charCount));
return endingPosition;
}
}

/// <summary>
/// A collection of pyramids to be displayed.
/// </summary>
internal class PyramidCollection
{
/// <summary>
/// A left-to-right ordered list of the pyramids that the user has
/// requested to be rendered.
/// </summary>
List<Pyramid> allPyramids = new List<Pyramid>();

/// <summary>
/// Constructs a new pyramid collection.
/// </summary>
/// <param name="distances">The distances of each non-leftmost pyramid (in PyramidUnits) after
/// the previous pyramid. The total number of pyramids will be one greater than the length of
/// the distances array.</param>
internal PyramidCollection(int[] distances)
{
Debug.Assert(distances != null);

int nextPosition = 0;
foreach (int nextDistance in distances)
{
Debug.Assert(nextDistance >= 0);

try
{
checked
{
nextPosition += nextDistance;
int endLocation = nextPosition * Pyramid.PyramidUnits + Pyramid.Height * 2;
}
}
catch (OverflowException)
{
// Ignore any pyramids specified beyond the integer maximum distance.
break;
}
}
}

/// <summary>
/// Outputs ASCII-art images of the pyramids in this collection to the
/// provided output stream.
/// </summary>
/// <param name="textWriter">The output stream to which the pyramids
/// are to be rendered.</param>
internal void RenderToText(TextWriter textWriter)
{
Debug.Assert(textWriter != null);

for (int row = 0; row < Pyramid.Height; row++)
{
int startingPosition = 0;
foreach (Pyramid pyramid in allPyramids)
{
startingPosition = pyramid.RenderRow(textWriter, row, startingPosition);
}
textWriter.WriteLine();
}
}
}

}
`
• Did you confuse Code Bowling and Code Golf by any chance? – Joey Jun 2 '11 at 17:53
• At least pretend to try. People won't hold a verbose language against you if you golf it. – dmckee Jun 3 '11 at 0:51
• I guess that is your verbose version to explain your nifty tricks. It seems you forgot to post the golf version of it. – mbx Jun 5 '11 at 14:59
• @Joey, @dmckee - I thought about doing a golf version, but haven't got around to it. I am terrible at this game anyway. Obscure code goes completely against my nature. I should probably stay away from the golf puzzles! - @mbx - Sadly, there are no nifty tricks. – Jeffrey L Whitledge Jun 6 '11 at 14:40


text:
What is this type of digits-only LCD called?

I've seen this type of LCD many times in weigh scales, calculators, gauges, micrometers, etc. I know it's a fairly traditional display but I really like its compactness, simplicity, and maybe it even costs less, versus TFTs or smartphone-type touch displays.

[What is it called? Answered by @kevlar1818 and @stevenvh: "Seven-segment display"]

I would like to work with this type of LCD, for example, I just found this 8-digit one called VIM-878 from the Digikey catalog; here is its datasheet.

How do I interface with it? I would like to know what would be a good/common way of interfacing with it from a simple AVR microcontroller like an Atmega8 -- preferably with interfacing circuitry/parts that aren't too physically large.

• I presume some sort of driver or multiplexer would be necessary? I guess I'm looking for some beginning perspective from others who may have better experience interfacing with this type of LCD.
• Thank you for adding the requested information. Please be careful that you don't undo previous edits in the process, however. – Chris Laplante Aug 29 '12 at 13:27
• That is exactly what I did, didn't I, oops! Could you or someone help put the image back please? – boardbite Aug 29 '12 at 13:28
• You could try rolling back to edit 2, and then adding your information to that. I don't have the rep to do rollbacks so I'll flag it. – Chris Laplante Aug 29 '12 at 13:29

It's a 7-segments display. Unlike the dot-matrix character displays kevlar refers to these are most often not intelligent module. Most dot matrix displays have an HD44780-compatible controller which you simply can write ASCII codes to, but a 7-segment LCD will often be just the glass, with connections for segments and a number of backplanes (often up to 4).

Driving LCDs can be awkward since they don't use just two levels, so you can't drive them with common digital logic.

The best thing you can do is select a microcontroller with integrated LCD controller, which you can connect the display directly to, like the TI MSP430x4xx. Like most controllers this one also knows just segments; it isn't aware of digits or anything. (Great, first we had a dumb display, now we have a dumb driver as well!) There's reason for this. These LCD drivers are often used to drive custom LCDs which may be a mix of a numeric part, bar graphs and custom symbols. Such a symbol is also a single segment, so it makes no sense to talk about digits.

This display has symbols like "battery" and "alarm clock", but also all text fields, like "AM", "PM" and "SNOOZE" are symbols consisting of a single segment (i.e. controlled by a single bit).

MSP430x4xx Family User's Guide. LCD controller is covered on p.709 ff.

• Assuming segments mean the number of parts used to construct a character/digit on my LCD, I think that microcontroller would be great - it can support 96, and it has only 200 uA current draw. Are you suggesting replacing my AVR with the TI microcontroller, or just communicating VIA it with the LCD? I'd prefer the latter, because of my AVR-based experience (also limited!); so can you comment on that? – boardbite Aug 29 '12 at 13:34
• @Inga - I'm not aware of any AVR with an LCD driver on board. Using the MSP430 as display driver may be a good idea: your AVR can stick to its main task, and the program for the MSP430 can be kept simple (if you don't have much experience with it) or advanced (if you want to make it an intelligent driver, which you can supply with commands like "increment"). – stevenvh Aug 29 '12 at 13:39
• That sounds very doable; I'm about to order one of the TI chips! By the way, in case my programming attempts with that microcontroller fail, can I use a simple multiplexer or LED driver, e.g. an IC like this one I just found from Maxim ? I am foreseeing trouble because of what you stated about the multiple levels. – boardbite Aug 29 '12 at 13:43
• @Inga - No, you can't use the MAX7219, that's a LED driver. For one thing they multiplex much too fast for LCDs. The multiple levels shouldn't be a problem; that's what you've got a driver for. That takes care of everything. What do you think of the intelligent driver which keeps count of the number to display? You could use commands like "load value", "increment count", "reset count", etc. – stevenvh Aug 29 '12 at 13:47
• Haha, it really has commands like that?! I surely have to write code to implement those functions myself, don't I? – boardbite Aug 29 '12 at 13:50

What you are thinking of is called a 7 segment LCD. If you know how to light up a regular LED then your 1/8th of the way there.

Here is the Wiki to it. It has some theory on how you would create numbers by lighting up different arrays of the LED's: http://en.wikipedia.org/wiki/Seven-segment_display

(de)Multiplexing is a good method for lighting up a large 7-Segment panel, although not necessary. If your I/O ports are limited then it's the way to go. The basic's of demuxing work like this (assuming you know binary here). Look at this picture:

With a 3 bit binary number like 000 we can represent up to the number 7 (I.E. to select port 5 we'd have ABC be 101). What would happen in the demux in your situation is one input is something like a high signal, and AB&C are I/O ports. The 0 to 7 are connect to each segment of the LCD and by writing to ABC from your controller you can light up a segment. You may be saying wait but if I want to light up a number I need many segments lit, not just the 5th segment. Well after that you can look into two roads to get the LCD to display a number. The first is add more demux's for additional needed segments. The second is a software approach which involves very very quickly flashing each of the segment required to create the illusion that the panel is completely lit. The AVR chip in your mega is operating in the Megahertz range if you write a loop to display ABGED (from the wiki pic) you will end up seeing something that looks like a number 2. Hope this gets you started.

• I like the first approach that you suggested: more demux's. But if I were to go that route, how can one cut down on physical size of components? In my case, I would need 8 digits = 56 segments, you know? – boardbite Aug 29 '12 at 13:53
• Err well you're not going to have enough I/0 to drive 8 digits with a nothing but hardware approach. Here is a link, it's scary I know but I don't think I can draw/explain an easier breakdown. doctronics.co.uk/4511.htm. That's the theory though. In practicality I would consider the scanning method, I know it may seem like it would not provide a nice image or would be complicated but it's a very common practice in industry. Best of luck. – Nimjox Aug 29 '12 at 15:12
• @Inga - even 64 if you also count decimal points! There are two reasons you won't find those non-multiplexed. One is just the sheer number of pins, both on the display and the microcontroller. The microcontroller would need at least 80 pins and more pins = more cost. But there's also routing. If you have a multiplexed display you will have the routing of one segment going via an adjacent segment, but if they're all separate you can't do a thing like that. That's also an extra cost. – stevenvh Aug 29 '12 at 15:26

A seven-segment display or dot matrix display are what you're referring to I believe.

Here's an example on Sparkfun with the relevant datasheet. Found this AVR example/tutorial in the "Documents" section of the product page. Isn't Sparkfun great?

Given this 14-segment display, and its datasheet, let's figure out how to use it.

Let's take the example of showing a 7 in the first (leftmost) segment cluster.

To write a 7, we need to assert segments 1A, 1B, and 1C, as seen in the datasheet. These segments all map to pin 35 of the device, but on different COM lines. With such a cryptic datasheet, my best guess would be that these COM lines map to pins 17 through 20, given the table in the datasheet.

Thus, to assert each segment above, you would hold pin 35 high while quickly cycling between asserting COM1, COM2, and COM3 via pins 18, 19, and 20 respectively. The three segments would all appear lit simultaneously, creating a 7.

This being said, well-written code simply will use some sort of map for any given character to be displayed. The challenge is to make this map work for ANY of the segment clusters.

I still recommend a dot-matrix display like the first one I linked to; there are certainly more lightweight designs out there. The benefit to using a dot-matrix display is that most have a data register built-in, so you can just pass it 8-bit ASCII characters, no funky implementation issues like in the 14-seg example above.

• Incidentally, I have an LCD very similar to the example you posted! But it is a very thick module and it isn't very readable without its backlight on. Whereas the one I posted is visible much better despite no backlight, and somehow seems cleaner (no shadowy-remnant-type of appearance of the non-displayed digits). Any thoughts? Are there sub-categories within these displays? – boardbite Aug 29 '12 at 13:09
• Using "seven-segment display" as my search term, I found this one: Digikey page I would like to work with this one, for example. And this is its datasheet. – boardbite Aug 29 '12 at 13:15
• I was actually going to say (based on your explanation) that the 14-segment one seems SIMPLER, no? Well, OK, not simpler than just passing ASCII characters, but fairly simple in terms of logic and the amount of control (e.g., just lighting up one segment). BTW, in the approach you recommended above, how does it deal with what stevenvh said in his Answer about there not being two levels of logic for these displays? – boardbite Aug 29 '12 at 13:48
• @Inga It doesn't seem to me like there would need to be more than two logic levels in this particular 14-segment display, as it has such a verbose pinout. I'm still not positive though, because the datasheet and Digikey page say nothing about voltage/logic levels. Honestly, it's usually not good practice to buy such a poorly documented device. – kevlar1818 Aug 29 '12 at 13:52
• Why not use some of the LCD drivers, that interface over I2C, such as Holtek 1632 or similar? (I hope I got the part correct!) – Vaibhav Garg Sep 4 '12 at 7:56


text:
# Kozhasov Khazhgali: On complete monotonicity of inverse powers of elementary symmetric polynomials

Tid: On 2019-11-27 kl 10.15 - 11.00

Plats:

Abstract: Sufficiently high inverse powers \$p^a\$, \$a<0\$, of some real
stable polynomials \$p\$ (among which are basis generating polynomials of
certain classes of matroids) turn out to be completely monotone, that
is, the coefficients of the Taylor expansion of \$y \mapsto p(x-y)^a\$ are
nonnegative for any \$x\$ in the positive orthant. I will discuss this
phenomenon for the class of elementary symmetric polynomials. The talk
is based on a joint work with M. Mikhalek and B. Sturmfels.

Innehållsansvarig:webmaster@math.kth.se
Tillhör: Institutionen för matematik


text:
Mertens' function in time $O(\sqrt x)$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T06:22:09Z http://mathoverflow.net/feeds/question/95726 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95726/mertens-function-in-time-o-sqrt-x Mertens' function in time $O(\sqrt x)$ Charles 2012-05-02T05:38:57Z 2012-05-10T21:13:50Z
This MathOverflow question seems to indicate that the state of the art in computing $$M(x)=\sum_{n\le x}\mu(n)$$ takes time $\Theta(n^{2/3}(\log\log n)^{1/3}),$ which matches my understanding. Recently I came across a paper [1] which gives, almost as an afterthought, an algorithm for computing $M(x)$ in $O(\sqrt x)$ time (in section 3.2).

The algorithm itself seems to be correct, being derived in a straightforward way from the identity $$M(x)=1-\sum_{d\ge2}M(x/d).$$ But the claim that is runs in time $O(\sqrt x),$ or even $O(x^{1/2+\varepsilon}),$ seems unusual enough for me to ask for verification.

First, this would be a major breakthrough in computing $M(x),$ enough that I would think it would merit more mention than a substep of another algorithm. At the least, I would expect a mention that previous algorithms were slower.

Second, the algorithm is very simple, so that if the time is as indicated the implied constant should be low and the algorithm should be practical. In any case it is not hard to program.

Third, on coding the algorithm I found it to be very slow. In fact, it was slower for those values tested than sum(n=1, 10^7, moebius(n)) in GP which involves factoring each number up to $10^7.$ The time needed to factor numbers of those sizes is about $\sqrt x/\log x$ on average, so that's a $\Theta(n^{3/2}/\log n)$ algorithm (admittedly, well-optimized) beating a $\Theta(n^{1/2})$ algorithm. The constants would have to be worse by a factor of $5\cdot10^6$ for that to happen, and there's nothing in the algorithm to suggest anything that bad.

Of course I may have miscoded it (though I obtained the correct answer) or there may be reasons why the constant factors would be so high for this algorithm. But in any case this seemed suspicious enough to bring up here that I might be enlightened in any case.

Of course even if the result claimed is not correct this is no mark against the author, as the paper is only a preprint and the claim is peripheral in any case.

[1]: Jakub Pawlewicz, Counting square-free numbers (2011), arXiv:1107.4890.
 http://mathoverflow.net/questions/95726/mertens-function-in-time-o-sqrt-x/95767#95767 Answer by Anthony Quas for Mertens' function in time $O(\sqrt x)$ Anthony Quas 2012-05-02T13:38:58Z 2012-05-02T13:38:58Z
I am totally not an expert here, but at first sight, it looks as though the issue is the phrase in the preprint "having all values $M(x/d)$ for $d\ge 2$". I take this to mean that you're supposed to have a pre-computed list of those values. If you did not do this, but your code was recursive instead then this would end up being much slower because for numbers with many divisors, you would end up computing $M(n)$ many times over.
 http://mathoverflow.net/questions/95726/mertens-function-in-time-o-sqrt-x/95769#95769 Answer by Johan Andersson for Mertens' function in time $O(\sqrt x)$ Johan Andersson 2012-05-02T13:49:09Z 2012-05-02T16:00:19Z
Well,

Although this does not answer your particular question of whether the paper is right, it seems rather straightforward to obtain the $O(x^{1/2+\epsilon})$ result for calculating the sum $\sum_{n \leq x} \mu(n)$ by using the same idea as in my answer to http://mathoverflow.net/questions/81443/fastest-algorithm-to-compute-the-sum-of-primes/81545#81545. Let as in that answer $\Phi(x)$ be a smooth test function such that $\Phi(x)=1$ for $x<0$ and $\Phi(x)=0$ for $x>1$. The difference here is that we consider a sum $$\sum_{n\leq x} \mu(n) =\sum_{n=1}^\infty \mu(n)\Phi \left( \frac {n-x} {\sqrt x} \right ) - \sum_{x< n < x + \sqrt x } \mu(n) \Phi \left(\frac {n-x} {\sqrt x} \right)$$ over the Möbius function instead of a sum over primes. The first sum can be calculated by the integral $$\sum_{n=1}^\infty \mu(n)\Phi \left( \frac {n-x} {\sqrt x} \right )= \frac 1 {2 \pi i} \int_{c-\infty i}^{c+\infty i} \frac 1 {\zeta(s)} \int_0^\infty \Phi \left(\frac{y-x}{\sqrt x} \right)f(y) y^{s-1} dyds, (c>1)$$ which can be calculated by the Odlyzko-Schönhage algorithm in time $O(x^{1/2+\epsilon})$ in the same way as in that answer. The remaining sum will be over an interval of length $\sqrt x$. Sieving techniques can determine the Möbius function for all these numbers fast and the time it will take to calculate that sum is of the order of $O(\sqrt x \log x)$.

Update: I looked at Lagarias-Odlyzkos 1987 paper "Computing $\pi(x)$ an analytic method". On page 8 at the bottom of the page I quote "The basic ideas underlying analytic $\pi(x)$ algorithms can be used for computing other arithmetical functions, such as $$M(x) =\sum_{n\leq x} \mu(n).$$ Thus they were certainly aware of the $O(x^{1/2+\epsilon})$ time complexity for calculating $M(x)$. What I describe above is indeed a variant of the Lagarias-Odlyzko method.
 http://mathoverflow.net/questions/95726/mertens-function-in-time-o-sqrt-x/96602#96602 Answer by Johan Andersson for Mertens' function in time $O(\sqrt x)$ Johan Andersson 2012-05-10T18:45:06Z 2012-05-10T21:13:50Z
This is really a response to Dror Speiser's comment (but it is too long to give as a comment), and gives an analytic $O(n^{1/3+\epsilon})$ time and $O(n^{1/6+\epsilon})$ space algorithm to count the number of square free numbers less than $x$ (thus improving on the complexity of the algorithm given in the Jakub Pawlewicz paper cited in the question). If we do exactly in the same way as in my other answer for $$\sum_{n\leq x} |\mu(n)|$$ instead of $$\sum_{n\leq x} \mu(n)$$ by using the fact that $$\frac{\zeta(s)}{\zeta(2s)} = \sum_{n=1}^\infty |\mu(n)| n^{-s}$$ it is true that the time complexity will be $O(x^{1/2+\epsilon})$. There is however a way to combine the analytic method (which is essentially the same as in Lagarias-Odlyzkos 1987 paper "Computing $\pi(x)$ an analytic method" http://www.dtc.umn.edu/~odlyzko/doc/arch/analytic.pi.of.x.pdf) with the elementary identity $$S(n)=\sum_{d=1}^{\lfloor \sqrt n\rfloor} \mu(d) \lfloor \frac n {d^2} \rfloor$$ that is Pawleviec's starting point in obtaining his algorithm. Let $\Phi$ be defined as in my other answer, i.e. let $\Phi(x)$ be a smooth test function such that $\Phi(x)=1$ for $x<0$ and $\Phi(x)=0$ for $x>1$. Consider the identity $$\sum_{n\leq x} |\mu(n)| =\sum_{n=1}^\infty |\mu(n)| \Phi \left( \frac {n-x} {x^{2/3}} \right ) - \sum_{x< n < x + x^{2/3} } |\mu(n)| \Phi \left(\frac {n-x} {x^{2/3}} \right)$$

The first sum can be estimated by a complex integral of length $x^{1/3+\epsilon}$ and by the Odlyzko-Schönhage algorithm it can be calculated in $O(x^{1/3+\epsilon})$ time (and $O(x^{1/6+\epsilon})$ space). The remaining sum will have length $O(x^{2/3})$ so might at first glance not be so simple to treat. I claim however that in fact it can be calculated in $O(x^{1/3+\epsilon})$ time. This is where using the elementary identity is handy. Let $\Psi(x)=0$ for $x<0$ and $\Psi(x)=\Phi(x)$ for $x \geq 0$ (this will have a discontinuity at $x=0$) By a similar elementary identity we obtain

$$\sum_{x< n < x + x^{2/3} } |\mu(n)| \Phi \left(\frac {n-x} {x^{2/3}} \right) = \sum_{d=1}^{\lfloor \sqrt {x+x^{2/3}}\rfloor} \mu(d) \sum_{k=1}^\infty \Psi \left(\frac {d^2k-x} {x^{2/3}} \right).$$ For any $d$ the inner sum can be calculated fast (certainly in $O(x^\epsilon)$ time), by either noticing that the sum is empty, just contains one element or the Poisson summation formula. The trick now is to see that there will only be $O(x^{1/3})$ integers $d$ where the inner sum (in $k$) is non empty, namely $d$ must either be $O(x^{1/3})$ or belong to an interval $(\sqrt{ x/k},\sqrt{(x+x^{2/3})/k})$ for $k \leq x^{1/3}$ and there are only $O(x^{1/3})$ such $d$. Now if we can calculate the values of $\mu(d)$ fast (simple sieving seems more difficult in this case) we obtain the desired algorithm. Determining $\mu(d)$ basically comes down to factoring the number. However it is sufficient to determine the factors less than $d^{1/3}$ since if we know that all prime factors are greater than $d^{1/3}$, then either it has one or two prime factors. We can determine if it is a prime fast by the Agrawal-Kayal-Saxena algorithm, then of course $\mu(d)=-1$. If it has two prime factors either $\mu(d)=0$, but then it has to be a square, and it can be easily checked, or $\mu(d)=1$. Now factoring the $O(x^{1/3})$ numbers of size $O(x^{1/2})$ into all prime factors less than $x^{1/6}$ will take $O(x^{1/3+\epsilon})$ time and $O(x^{1/6+\epsilon})$ space by Bernstein's algorithm http://cr.yp.to/papers/sf.pdf. I might possibly write up this answer as a paper proper. If anyone has seen these arguments anywhere else or have references I would be interested.


text:
# Separation of variables

Separation of variables

In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

## Ordinary differential equations (ODE)

Suppose a differential equation can be written in the form

$\frac{d}{dx} f(x) = g(x)h(f(x)),\qquad\qquad (1)$

which we can write more simply by letting y = f(x):

$\frac{dy}{dx}=g(x)h(y).$

As long as h(y) ≠ 0, we can rearrange terms to obtain:

${dy \over h(y)} = {g(x)dx},$

so that the two variables x and y have been separated. dx (and dy) can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations. A formal definition of dx as a differential (infinitesimal) is somewhat advanced.

### Alternative notation

Some who dislike Leibniz's notation may prefer to write this as

$\frac{1}{h(y)} \frac{dy}{dx} = g(x),$

but that fails to make it quite as obvious why this is called "separation of variables".

Integrating both sides of the equation with respect to x, we have

$\int \frac{1}{h(y)} \frac{dy}{dx} \, dx = \int g(x) \, dx, \qquad\qquad (2)$

or equivalently,

$\int \frac{1}{h(y)} \, dy = \int g(x) \, dx$

because of the substitution rule for integrals.

If one can evaluate the two integrals, one can find a solution to the differential equation. Observe that this process effectively allows us to treat the derivative $\frac{dy}{dx}$ as a fraction which can be separated. This allows us to solve separable differential equations more conveniently, as demonstrated in the example below.

(Note that we do not need to use two constants of integration, in equation (2) as in

$\int \frac{1}{h(y)} \, dy + C_1 = \int g(x) \, dx + C_2,$

because a single constant C = C2C1 is equivalent.)

### Example (I)

The ordinary differential equation

$\frac{d}{dx}f(x)=f(x)(1-f(x))$

may be written as

$\frac{dy}{dx}=y(1-y).$

If we let g(x) = 1 and h(y) = y(1 − y), we can write the differential equation in the form of equation (1) above. Thus, the differential equation is separable.

As shown above, we can treat dy and dx as separate values, so that both sides of the equation may be multiplied by dx. Subsequently dividing both sides by y(1 − y), we have

$\frac{dy}{y(1-y)}=dx.$

At this point we have separated the variables x and y from each other, since x appears only on the right side of the equation and y only on the left.

Integrating both sides, we get

$\int\frac{dy}{y(1-y)}=\int dx,$

which, via partial fractions, becomes

$\int\frac{1}{y} \, dy + \int\frac{1}{1-y}\,dy=\int 1 \, dx,$

and then

ln  | y | − ln  | 1 − y | = x + C

where C is the constant of integration. A bit of algebra gives a solution for y:

$y=\frac{1}{1+Be^{-x}}.$

One may check our solution by taking the derivative with respect to x of the function we found, where B is an arbitrary constant. The result should be equal to our original problem. (One must be careful with the absolute values when solving the equation above. It turns out that the different signs of the absolute value contribute the positive and negative values for B, respectively. And the B = 0 case is contributed by the case that y = 1, as discussed below.)

Note that since we divided by y and (1 − y) we must check to see whether the solutions y(x) = 0 and y(x) = 1 solve the differential equation (in this case they are both solutions). See also: singular solutions.

### Example (II)

Population growth is often modeled by the differential equation

$\frac{dP}{dt}=kP\left(1-\frac{P}{K}\right)$

where P is the population with respect to time t, k is the rate of growth, and K is the carrying capacity of the environment.

Separation of variables may be used to solve this differential equation.

$\frac{dP}{dt}=kP\left(1-\frac{P}{K}\right)$
$\int\frac{dP}{P\left(1-\frac{P}{K}\right)}=\int k\,dt$

To evaluate the integral on the left side, we simplify the fraction

$\frac{1}{P\left(1-\frac{P}{K}\right)}=\frac{K}{P\left(K-P\right)}$

and then, we decompose the fraction into partial fractions

$\frac{K}{P\left(K-P\right)}=\frac{1}{P}+\frac{1}{K-P}$

Thus we have

$\int\left(\frac{1}{P}+\frac{1}{K-P}\right)\,dP=\int k\,dt$

$\ln\begin{vmatrix}P\end{vmatrix}-\ln\begin{vmatrix}K-P\end{vmatrix}=kt+C$

$\ln\begin{vmatrix}K-P\end{vmatrix}-\ln\begin{vmatrix}P\end{vmatrix}=-kt-C$

$\ln\begin{vmatrix}\cfrac{K-P}{P}\end{vmatrix}=-kt-C$

$\begin{vmatrix}\cfrac{K-P}{P}\end{vmatrix}=e^{-kt-C}$

$\begin{vmatrix}\cfrac{K-P}{P}\end{vmatrix}=e^{-C}e^{-kt}$

$\frac{K-P}{P}=\pm e^{-C}e^{-kt}$

Let $A=\pm e^{-C}$.

$\frac{K-P}{P}=Ae^{-kt}$

$\frac{K}{P}-1=Ae^{-kt}$

$\frac{K}{P}=1+Ae^{-kt}$

$\frac{P}{K}=\frac{1}{1+Ae^{-kt}}$

$P=\frac{K}{1+Ae^{-kt}}$

Therefore, the solution to the logistic equation is

$P\left(t\right)=\frac{K}{1+Ae^{-kt}}$

To find A, let t = 0 and $P\left(0\right)=P_0$. Then we have

$P_0=\frac{K}{1+Ae^0}$

Noting that e0 = 1, and solving for A we get

$A=\frac{K-P_0}{P_0}$

## Partial differential equations

The method of separation of variables are also used to solve a wide range of linear partial differential equations with boundary and initial conditions, such as heat equation, wave equation, Laplace equation and Helmholtz equation.

### Homogeneous case

Consider the one-dimensional heat equation.The equation is

$\frac{\partial u}{\partial t}-\alpha\frac{\partial^{2}u}{\partial x^{2}}=0$

(1)

The boundary condition is homogeneous, that is

$u\big|_{x=0}=u\big|_{x=L}=0$

(2)

Let us attempt to find a solution which is not identically zero satisfying the boundary conditions but with the following property: u is a product in which the dependence of u on x, t is separated, that is:

u(x,t) = X(x)T(t).

(3)

Substituting u back into equation,

$\frac{T'(t)}{\alpha T(t)} = \frac{X''(x)}{X(x)}.$

(4)

Since the right hand side depends only on x and the left hand side only on t, both sides are equal to some constant value − λ. Thus:

T'(t) = − λαT(t),

(5)

and

X''(x) = − λX(x).

(6)

− λ here is the eigenvalue for both differential operators, and T(t) and X(x) are corresponding eigenfunctions.

We will now show that solutions for X(x) for values of λ ≤ 0 cannot occur:

Suppose that λ < 0. Then there exist real numbers B, C such that

$X(x) = B e^{\sqrt{-\lambda} \, x} + C e^{-\sqrt{-\lambda} \, x}.$

From (2) we get

X(0) = 0 = X(L),

(7)

and therefore B = 0 = C which implies u is identically 0.

Suppose that λ = 0. Then there exist real numbers B, C such that

X(x) = Bx + C.

From (7) we conclude in the same manner as in 1 that u is identically 0.

Therefore, it must be the case that λ > 0. Then there exist real numbers A, B, C such that

T(t) = Ae − λαt,

and

$X(x) = B \sin(\sqrt{\lambda} \, x) + C \cos(\sqrt{\lambda} \, x).$

From (7) we get C = 0 and that for some positive integer n,

$\sqrt{\lambda} = n \frac{\pi}{L}.$

This solves the heat equation in the special case that the dependence of u has the special form of (3).

In general, the sum of solutions to (1) which satisfy the boundary conditions (2) also satisfies (1) and (3). Hence a complete solution can be given as

$u(x,t) = \sum_{n = 1}^{\infty} D_n \sin \frac{n\pi x}{L} \exp\left(-\frac{n^2 \pi^2 \alpha t}{L^2}\right),$

where Dn are coefficients determined by initial condition.

Given the initial condition

$u\big|_{t=0}=f(x),$

we can get

$f(x) = \sum_{n = 1}^{\infty} D_n \sin \frac{n\pi x}{L}.$

This is the sine series expansion of f(x). Multiplying both sides with $\sin \frac{n\pi x}{L}$ and integrating over [0,L] result in

$D_n = \frac{2}{L} \int_0^L f(x) \sin \frac{n\pi x}{L} \, dx.$

This method requires that the eigenfunctions of x, here $\left\{\sin \frac{n\pi x}{L}\right\}_{n=1}^{\infty}$, are orthogonal and complete. In general this is guaranteed by Sturm-Liouville theory.

### Nonhomogeneous case

Suppose the equation is nonhomogeneous,

$\frac{\partial u}{\partial t}-\alpha\frac{\partial^{2}u}{\partial x^{2}}=h(x,t)$

(8)

with the boundary condition the same as (2).

Expand h(x,t) ,u(x,t) and f(x,t) into

$h(x,t)=\sum_{n=1}^{\infty}h_{n}(t)\sin\frac{n\pi x}{L},$

(9)

$u(x,t)=\sum_{n=1}^{\infty}u_{n}(t)\sin\frac{n\pi x}{L},$

(10)

$f(x)=\sum_{n=1}^{\infty}b_{n}\sin\frac{n\pi x}{L},$

(11)

where hn(t) and bn can be calculated by integration, while un(t) is to be determined.

Substitute (9) and (10) back to (8) and considering the orthogonality of sine functions we get

$u'_{n}(t)+\alpha\frac{n^{2}\pi^{2}}{L^{2}}u_{n}(t)=h_{n}(t),$

which are a sequence of linear differential equations that can be readily solved with, for instance, Laplace transform,or Integrating factor. Finally, we can get

$u_{n}(t)=e^{-\alpha\frac{n^{2}\pi^{2}}{L^{2}}} \left (b_{n}+\int_{0}^{L}h_{n}(s)e^{\alpha\frac{n^{2}\pi^{2}}{L^{2}} s} \, ds \right).$

If the boundary condition is nonhomogeneous, then the expansion of (9) and (10) is no longer valid. One has to find a function v that satisfies the boundary condition only, and subtract it from u. The function u-v then satisfies homogeneous boundary condition, and can be solved with the above method.

In orthogonal curvilinear coordinates, separation of variables can still be used, but in some details different from that in Cartesian coordinates. For instance, regularity or periodic condition may determine the eigenvalues in place of boundary conditions. See spherical harmonics for example.

## Matrices

The matrix form of the separation of variables is the Kronecker sum.

As an example we consider the 2D discrete Laplacian on a regular grid:

$L = \mathbf{D_{xx}}\oplus\mathbf{D_{yy}}=\mathbf{D_{xx}}\otimes\mathbf{I}+\mathbf{I}\otimes\mathbf{D_{yy}}, \,$

where $\mathbf{D_{xx}}$ and $\mathbf{D_{yy}}$ are 1D discrete Laplacians in the x- and y-directions, correspondingly, and $\mathbf{I}$ are the identities of appropriate sizes. See the main article Kronecker sum of discrete Laplacians for details.

## References

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• Separation des variables — Séparation des variables En mathématiques, la séparation des variables constitue l une des méthodes de résolution des équations différentielles partielles et ordinaires, dont l algèbre permet de réécrire l équation de sorte chacune des deux… …   Wikipédia en Français

• Séparation de variables — Séparation des variables En mathématiques, la séparation des variables constitue l une des méthodes de résolution des équations différentielles partielles et ordinaires, dont l algèbre permet de réécrire l équation de sorte chacune des deux… …   Wikipédia en Français

• Séparation des variables — En mathématiques, la séparation des variables constitue l une des méthodes de résolution des équations différentielles partielles et ordinaires, lorsque l algèbre permet de réécrire l équation de sorte que chacune des deux variables apparaisse… …   Wikipédia en Français

• separation of variables — kintamųjų atskyrimas statusas T sritis fizika atitikmenys: angl. separation of variables vok. Separierung der Variablen, f; Variablentrennung, f rus. разделение переменных, n pranc. séparation des variables, f …   Fizikos terminų žodynas

• séparation des variables — kintamųjų atskyrimas statusas T sritis fizika atitikmenys: angl. separation of variables vok. Separierung der Variablen, f; Variablentrennung, f rus. разделение переменных, n pranc. séparation des variables, f …   Fizikos terminų žodynas

• separation of variables — Math. 1. a grouping of the terms of an ordinary differential equation so that associated with each differential is a factor consisting entirely of functions of the independent variable appearing in the differential. 2. a process of finding a… …   Universalium

• separation of variables — a regrouping of the terms of a differential equation so that each differential has as a factor a function of the corresponding independent variable * * * Math. 1. a grouping of the terms of an ordinary differential equation so that associated… …   Useful english dictionary

• method of separation of variables — kintamųjų atskyrimo metodas statusas T sritis fizika atitikmenys: angl. method of separation of variables vok. Veränderlichentrennmethode, f; Veränderlichentrennungsmethode, f rus. метод разделения переменных, m pranc. méthode de séparation des… …   Fizikos terminų žodynas

• méthode de séparation des variables — kintamųjų atskyrimo metodas statusas T sritis fizika atitikmenys: angl. method of separation of variables vok. Veränderlichentrennmethode, f; Veränderlichentrennungsmethode, f rus. метод разделения переменных, m pranc. méthode de séparation des… …   Fizikos terminų žodynas

• method of incomplete separation of variables — nevisiško kintamųjų atskyrimo metodas statusas T sritis fizika atitikmenys: angl. method of incomplete separation of variables vok. unvollständige Veränderlichentrennmethode, f; unvollständige Veränderlichentrennungsmethode, f rus. метод… …   Fizikos terminų žodynas

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text:
## College Algebra (11th Edition)

Published by Pearson

# Chapter 2 - Section 2.7 - Graphing Techniques - 2.7 Exercises - Page 256: 61

#### Answer

See the picture below.

#### Work Step by Step

By calculating the values of $f(x)=2x^2-1$ (with blue) and $g(x)=x^2$ (with red) we can see that the following equation is true: $2g(x)-1=f(x)$ In order to graph the parent function , here is the table of values: $g(-2)=-2^2=4$ $g(-1)=-1^2=1$ $g(0)=0^2=0$ $g(1)=1^2=1$ $g(2)=2^2=4$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but is wider (is stretched vertically by a factor of 2) and is translated 1 unit down.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text: - Optimal Newton-type methods for nonconvex smooth optimization problems Coralia Cartis(coralia.cartised.ac.uk) Nicholas I. M. Gould(nick.gouldstfc.ac.uk) Philippe L. Toint (philippe.tointfundp.ac.be) Abstract: We consider a general class of second-order iterations for unconstrained optimization that includes regularization and trust-region variants of Newton's method. For each method in this class, we exhibit a smooth, bounded-below objective function, whose gradient is globally Lipschitz continuous within an open convex set containing any iterates encountered and whose Hessian is $\alpha-$Holder continuous (for given $\alpha\in [0,1]$) on the path of the iterates, for which the method in question takes at least $\epsilon^{-(2+\alpha)/(1+\alpha)}$ function-evaluations to generate a first iterate whose gradient is smaller than $\epsilon$ in norm. This provides a lower bound on the evaluation complexity of second-order methods in our class when applied to smooth problems satisfying our assumptions. Furthermore, for $\alpha=1$, this lower bound is of the same order in $\epsilon$ as the upper bound on the evaluation complexity of cubic regularization, thus implying cubic regularization has optimal worst-case evaluation complexity within our class of second-order methods. Keywords: nonlinear optimization, global complexity bounds, optimal algorithms Category 1: Nonlinear Optimization Citation: ERGO Technical Report 11-009, School of Mathematics, University of Edinburgh, 2011. Download: [PDF]Entry Submitted: 06/22/2011Entry Accepted: 06/22/2011Entry Last Modified: 06/22/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.


text:
# [Trilinos-Users] Anasazi: Generalized eigenproblems

Nils Wagner nwagner at mecha.uni-stuttgart.de
Tue Mar 15 01:41:49 MST 2005

Hi all,

I am wondering if someone has written a program
to solve generalized non-Hermitian eigenvalue problems

A x = \lambda B x,

where A and B are given in Harwell Boeing format.

An example for the standard eigenvalue problem

A x = \lambda x

trilinos-5.0/LINUX_SERIAL/packages/anasazi/example/BlockKrylovSchur/BlockKrylovSchurEpetraExHB.exe

Usage: ./BlockKrylovSchurEpetraExHB.exe HB_filename
where:
HB_filename        - filename and path of a Harwell-Boeing data set

Any pointer would be appreciated.


text:
de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch

Hilfe Wegweiser Impressum Kontakt Einloggen

# Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Zeitschriftenartikel

#### Why a splitting in the final state cannot explain the GSI-Oscillations

##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons30806

Merle,  A.
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

##### Volltexte (frei zugänglich)

0907.3554
(Preprint), 219KB

##### Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
##### Zitation

Merle, A. (2009). Why a splitting in the final state cannot explain the GSI-Oscillations. Physical Review C, 80(5): 054616, pp. 1-9. doi:10.1103/PhysRevC.80.054616.

Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000E-F95A-0
##### Zusammenfassung
In this paper, I give a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive Quantum Field Theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the Double Slit experiment using photons, $e^+ e^- \to \mu^+ \mu^-$ scattering, and charged pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only Standard Model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the Quantum Beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.


text:
# American Institute of Mathematical Sciences

ISSN:
1078-0947

eISSN:
1553-5231

All Issues

## Discrete & Continuous Dynamical Systems - A

2005 , Volume 12 , Issue 3

Select all articles

Export/Reference:

2005, 12(3): 377-385 doi: 10.3934/dcds.2005.12.377 +[Abstract](169) +[PDF](197.5KB)
Abstract:
We consider conformal structures invariant under a volume-preserving Anosov system. We show that if such a structure is in $L^p$ for sufficiently large $p$, then it is continuous.
2005, 12(3): 387-402 doi: 10.3934/dcds.2005.12.387 +[Abstract](175) +[PDF](249.8KB)
Abstract:
The well-posedness of the Cauchy problem for a generalized nonlinear dispersive equation is studied. Local well-posedness for data in $H^s(\mathbb R)(s>-\frac{1}{8})$ and the global result for data in $L^{2}(\mathbb{R})$ are obtained if $l=2$. Moreover, for $l=3$, the problem is locally well-posed for data in $H^s(s>\frac{1}{4}).$ The main idea is to use the Fourier restriction norm method.
2005, 12(3): 403-412 doi: 10.3934/dcds.2005.12.403 +[Abstract](145) +[PDF](212.8KB)
Abstract:
In this note we derive an upper bound for the Hausdorff and box dimension of the stable and local stable set of a hyperbolic set $\Lambda$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold. As a consequence we obtain that dim$_H W^s(\Lambda)=n$ is equivalent to the existence of a SRB-measure. We also discuss related results for expanding maps.
Dong Ye and Feng Zhou
2005, 12(3): 413-424 doi: 10.3934/dcds.2005.12.413 +[Abstract](150) +[PDF](234.2KB)
Abstract:
We consider semilinear elliptic equations $\Delta u \pm \rho(x)f(u) = 0$, or more generally $\Delta u + \varphi(x, u) = 0$, posed in $\R^N$ ($N\geq 3$). We prove that the existence of entire bounded positive solutions is closely related to the existence of bounded solution for $\Delta u + \rho(x) = 0$ in $\mathbb R^N$. Many sufficient conditions which are invariant under the isometry group of $\mathbb R^N$ are established. Our proofs use the standard barrier method, but our results extend many earlier works in this direction. Our ideas can also be applied for the existence of large solutions, for the exterior domain problem and for the system situations.
2005, 12(3): 425-436 doi: 10.3934/dcds.2005.12.425 +[Abstract](172) +[PDF](212.5KB)
Abstract:
We consider the coupled Euler-Bernoulli viscoelastic system with boundary damping. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method.
2005, 12(3): 437-463 doi: 10.3934/dcds.2005.12.437 +[Abstract](155) +[PDF](265.3KB)
Abstract:
In this article we study a class of robust control problems in fluid mechanics recently proposed in [5]. Using a method of [23], we provide another proof of the existence and the uniqueness of solutions to the robust control problems under weaker assumptions as compared to [5]. We also study the Newton method for the numerical solution of these control problems. We prove the convergence of the method and we obtain an estimate of the convergence rate.
2005, 12(3): 465-480 doi: 10.3934/dcds.2005.12.465 +[Abstract](123) +[PDF](244.8KB)
Abstract:
Let $f: M \rightarrow M$ denote a diffeomorphism of a smooth manifold $M$. Let $p \in M$ be its hyperbolic fixed point with stable and unstable manifolds $W_S$ and $W_U$ respectively. Assume that $W_S$ is a curve. Suppose that $W_U$ and $W_S$ have a degenerate homoclinic crossing at a point $B\ne p$, i.e., they cross at $B$ tangentially with a finite order of contact.
It is shown that, subject to $C^1$-linearizability and certain conditions on the invariant manifolds, a transverse homoclinic crossing will arise arbitrarily close to $B$. This proves the existence of a horseshoe structure arbitrarily close to $B$, and extends a similar planar result of Homburg and Weiss [10].
2005, 12(3): 481-500 doi: 10.3934/dcds.2005.12.481 +[Abstract](149) +[PDF](258.3KB)
Abstract:
For a scalar delayed differential equation $\dot x(t)=f(t,x_t)$, we give sufficient conditions for the global attractivity of its zero solution. Some technical assumptions are imposed to insure boundedness of solutions and attractivity of non-oscillatory solutions. For controlling the behaviour of oscillatory solutions, we require a very general condition of Yorke type, together with a 3/2-condition. The results are particularly interesting when applied to scalar differential equations with delays which have served as models in populations dynamics, and can be written in the general form $\dot x(t)=(1+x(t))F(t,x_t)$. Applications to several models are presented, improving known results in the literature.
2005, 12(3): 501-522 doi: 10.3934/dcds.2005.12.501 +[Abstract](199) +[PDF](264.5KB)
Abstract:
We analyze the asymptotic behavior of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial differential equations, with a retardation of the maturation variable and a time delay depending on this maturity. We show that the stability of this system depends strongly on the behavior of the immature cell population. We obtain conditions for the global stability and the instability of the trivial solution.
2005, 12(3): 523-530 doi: 10.3934/dcds.2005.12.523 +[Abstract](146) +[PDF](207.4KB)
Abstract:
We prove that the following properties are $C^0$ generic in the space of discrete dynamical systems on a compact smooth manifold $M$: periodic shadowing (Theorem 1.1) and, assuming dim$M\leq 3$, $\mathcal T_C$-inverse shadowing (Theorem 1.2).
2005, 12(3): 531-554 doi: 10.3934/dcds.2005.12.531 +[Abstract](128) +[PDF](510.8KB)
Abstract:
We study a singularly perturbed scalar reaction-diffusion equation on a bounded interval with a spatially inhomogeneous bistable nonlinearity. For certain nonlinearities, which are piecewise constant in space on $k$ subintervals, it is possible to characterize all stationary solutions for small $\varepsilon$ by means of sequences of $k$ symbols, indicating the behavior of the solution in each subinterval. Determining also Morse indices and zero numbers of the equilibria in terms of the symbol sequences, we are able to give a criterion for heteroclinic connections and a description of the associated global attractor for all $k$.
2005, 12(3): 555-565 doi: 10.3934/dcds.2005.12.555 +[Abstract](296) +[PDF](232.6KB)
Abstract:
We establish lower bounds for the topological entropy expressed in terms of the exponential growth rate of $k$-volumes. This approach provides the sharpest possible bounds when no further geometric information is available. In particular, our methods apply to (partially) volume-expanding dynamics with not necessarily compact phase space, including a large class of geodesic flows. As an application, we conclude that the topological entropy of these systems is positive.

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