A4, Empower3 Processing Tips and Tricks
|
|
|
- Willa O’Connor’
- 9 years ago
- Views:
Transcription
1 A4, Empower3 Processing Tips and Tricks Rune Buhl Frederiksen, Manager, Waters Educational Services 2012 Waters Corporation 1
2 Content Basic Chromatography Workflow Processing Workflow Integration Theory Traditional Integration Algorithm ApexTrack Algorithm Exercise 1 Break System Suitability & Noise and Drift Calculations Managing Manually Adjusted Results Exercise Waters Corporation 2
3 Basic Chromatography Workflow Sampling/Login Method Setup Sequence/Run Samples Empower Database Process Data Review/Preview Print Report 2012 Waters Corporation 3
4 Processing Workflow Create Processing Method Run Sample Set Bring Sample Set To review Check/ Adjust Method Save the Changes Process Sample Set 2012 Waters Corporation 4
5 Processing Workflow (continued) Bring Results Set To review Adjust Integration/ Identification Save Changes Preview Results Set Sign Off Results Print Results Set 2012 Waters Corporation 5
6 Creating a Processing Method Optimizing Integration Component table System Suitability Calculations Noise & Drift Calculations 2012 Waters Corporation 6
7 Integration Integration requires three operations: 1. Find the peak (peak detection) 2. Find the baseline of the peak 3. Compute the peak s area and height The first two are the challenge Empower has two different algorithms to perform integration Traditional Apex Track 2012 Waters Corporation 7
8 Traditional Integration 4 Global Parameters Traditional Integration Peak Width and Threshold work together to detect the peaks from the baseline. 4 Global Parameters Peak Width Threshold Minimum Area Minimum Height 2012 Waters Corporation 8
9 Traditional Integration Peak Width Determination Peak Width Peak width is measured at the baseline of the narrowest peak of interest and is used to determine a bunching factor Bunching Factor= Peak Width x Sampling Rate 15 =4 B1 B2 B3 B4 B5 B Waters Corporation 9
10 Traditional Integration Determining peak start Threshold Specifies the liftoff and touchdown values (minimum rate of change of the detector signal) for peak detection. Empower averages the signal slope across 3 data bunch intervals and compares to the liftoff threshold When the average slope of the signal between the 3 bunches is the liftoff threshold value, point B1 is flagged as possible peak start Individual points in bunch B1 is then examined to determine peak start = data point with lowest Y- value slope 1 = B2 - B1 t2 - t1 slope 2 = B3- B2 t3 - t2 average slope = slope1+ slope Waters Corporation 10
11 Traditional Integration Determining peak apex Signal is monitored until slope sign changes from positive to negative Bunch where the slope change occurs (B12 in the figure) is analyzed. Data point which is farthest away from the baseline is tentatively assigned as peak apex Final apex is determined after integration and baseline assignment 2012 Waters Corporation 11
12 Traditional Integration Determining peak end Slope of the signal is compared to the touchdown threshold When 2 consecutive slopes are < threshold, last point in the last bunch is flagged as possible peak end Individual points in this bunch and the next bunch to determine actual peak end = data point with lowest Y-value 2012 Waters Corporation 12
13 Traditional Integration Minimum Height or Minimum Area Minimum Height or Minimum Area Defines minimum peak area (mv*sec) or minimum peak height (µv) that Empower will report Used to reject unwanted peaks once integration has been optimized Empower use 95% of the peak s area/ height so that it can report peaks that approach the selected peak s size 2012 Waters Corporation 13
14 Traditional Integration Timed Events Parameters Timed Events a time-based action to adjust peak detection and/or integration in specified sections of a chromatogram There are 20 integration events that can be used to fine-tune integration across selected regions of a chromatogram You might need to apply one or more timed events when the default peak detection and integration parameters do not adequately detect and integrate all peaks in the chromatogram Waters Corporation 14
15 Traditional Integration Timed Events II Inhibit Integration SPW Set Peak Width SLO Set Liftoff STD Set Touchdown SMA Set Minimum Area SMH Set Minimum Height SMxA Set Maximum Area SMxH Set Maximum Height VV Valley to Valley ES Exponential Skim TS Tangential Skim ANP Allow Negative Peaks FDL Force Drop Line FBT Force Baseline by Time FBP Force Baseline by Peak FHP Forward Horizontal by Peak FHT Forward Horizontal by Time RHP Reverse Horizontal by Peak RHT Reverse Horizontal by Time FP Force Peak 2012 Waters Corporation 15
16 ApexTrack Integration A New Approach to the Integration of Chromatographic Peaks Easier than traditional integration Better than traditional integration Based on measuring the curvature (the rate of change of slope) of the chromatogram (2 nd derivative) Traditional integration detects peaks by initially looking for a peak start ApexTrack integration detects peaks by initially looking for the peak apex 2012 Waters Corporation 16
17 ApexTrack Integration Easier: Automatically determines appropriate integration parameter settings Auto Peak Width Auto Threshold Usually integrates well at first pass using default and automatic parameters Better: Integrates negative peaks effectively Integrates small peaks in noisy or drifting baseline effectively Peak shoulders are easily detected Gaussian skimming available 2012 Waters Corporation 17
18 Basis of ApexTrack: Curvature Threshold Detects the peak apex when the curvature is above the threshold Effective: Detects shoulders Baseline slope does not affect detection of peaks Peak detection and baseline determination are decoupled o Baseline placement can be modified without affecting the number of peaks detected and vise versa 2012 Waters Corporation 18
19 Second Derivative Measures Curvature Gaussian peak 1 2 Curvature Apex High (-) Second derivative Inflection points 3. Liftoff/TD Zero High (+) Baseline Zero 2012 Waters Corporation 19
20 Apex Track Integration Apex detection parameters Start (min) (Start Detection/Integration Time) End (min) (End Detection/Integration Time) Peak Width (sec) (Peak 5% Height) AUTO o Recommended range= 0.5 to 2 times Auto PW value Detection Threshold (Peak Detection Threshold) AUTO Baseline determination parameters Liftoff % Baseline start threshold %. Default:0 Touchdown % Baseline end threshold %. Default:0.5 Peak acceptance criteria Minimum Area (works in the same way as in traditional int.) Minimum Height (works in the same way as in traditional int.) 2012 Waters Corporation 20
21 ApexTrack Peak Detection Peak detection is controlled by the Peak Width and Threshold parameters Peak Width: measured in seconds, Auto Peak width sets it to 5% height of the largest peak in the second derivative (determined by using the inflection point width and calculating the gaussian peak width); used as a filter similar to traditional integration. Threshold: measured in units of height, Auto Threshold sets it to the peak to peak noise; used as a threshold for peak detection in the 2 nd derivative 2012 Waters Corporation 21
22 PeakWidth 2nd derivative plot AutoWidth 2012 Waters Corporation 22
23 Threshold 2nd derivative plot AutoThreshold AutoWidth Peak to peak noise 2012 Waters Corporation 23
24 Apex detection 2nd derivative plot Apex Detection Apex Detection AutoThreshold Considered as noise AutoWidth 2012 Waters Corporation 24
25 Apex Track Integration What happens? 1. Acquire the data 2. Obtain chromatogram s second derivative 3. Determine peak width (AutoPeakWidth) 4. Determine threshold (AutoThreshold) 5. Detect peaks - Second Derivative 6. Identify inflection points Apex Detection 2nd derivative plot Apex Detection AutoThreshold AutoWidth Considered as noise 2012 Waters Corporation 25
26 Apex Track Integration Baseline Resolved Peak Fused Peaks (Valley) Fused Peaks (Shoulder) Fused Peaks (Round) Unprocessed Chromatogram Second Derivative Plot Integrated Chromatogram 2012 Waters Corporation 26
27 Apex Track Integration Baseline Determination What about Baseline determination? ApexTrack uses percentage slope threshold. o o The slope threshold depends on peak height The baseline is the same for all peaks Why? Baselines change when concentration changes and the location of touchdown is most sensitive. What happens? User specifies baseline threshold as a percentage of peak height. Algorithm computes a separate slope threshold for each peak Slope threshold is then proportional to peak height o o Big peaks have big threshold Small peaks have small threshold 2012 Waters Corporation 27
28 Baseline Determination 1. Initially draws baseline between the inflection points 2. Determines slope differences ( m)using tangents to the inflection points Peak start = m 1 x Liftoff%/100 Peak stop = m 2 x Tuchdown%/100 m 1 m 2 3. Determines slope thresholds using Baseline % Thresholds from processing method and slope differences. Baseline % Thresholds scale inflection point slope differences to determine liftoff and touchdown points Waters Corporation 28
29 Baseline Determination 4. Baselines start at the inflection point baseline 5. Baselines are expanded until the slope threshold criteria are met 6. A Baseline % Threshold of 100 % yields baseline at inflection points 7. A Baseline % Threshold of 0 % yields baseline that is tangent to baseline noise 2012 Waters Corporation 29
30 Concentration Change: Traditional Approach Height ratios of 1: 1/10 : 1/100 Times of liftoff and touchdown change Biggest peak: Touchdown far down in tail 2012 Waters Corporation 30
31 Concentration Change: Zoom In Focus on 1/10 peak Middle peak: Touchdown is well positioned 2012 Waters Corporation 31
32 Concentration Change: Zoom In Again Focus on 1/100 peak Smallest peak: Touchdown is high up the tail Relative area of smallest peak is reduced! 2012 Waters Corporation 32
33 Concentration Change: ApexTrack Height ratios of 1: 1/10 : 1/100 Liftoff is the same for each peak. Touchdown is the same for each peak Biggest peak: Touchdown is well positioned 2012 Waters Corporation 33
34 Concentration Change: Zoom In Focus on 1/10 peak Middle peak: Touchdown is well positioned 2012 Waters Corporation 34
35 Concentration Change: Zoom In Again Focus on 1/100 peak Smallest peak: Touchdown is well positioned Note different slope thresholds 2012 Waters Corporation 35
36 Changing %Touchdown Focus on Big peak A small change in the %Touchdown will have a big impact on the slope for the big peak because it is a percentage of the peak height This will have very little effect on the middle peak and NO effect on the small peak 2012 Waters Corporation 36
37 Apex Track Integration Timed Events ANP - Allow Negative Peaks DS - Detect Shoulders GS - Gaussian Skim TS - Tangential Skim II - Inhibit Integration MP - Merge Peaks (for GPC only) SL% - Set Liftoff % ST% - Set Touchdown % SMA - Set Minimum Area SMH - Set Minimum Height SMxH - Set Maximum Height SMxA - Set Maximum Area VV - Valley-to-Valley SPW - Set Peak Width SDT - Set Detection Threshold 2012 Waters Corporation 37
38 Integration events Comparison: Traditional Apex Track 2012 Waters Corporation 38
39 Conclusions Advantages over other Integration Packages 1. Automatic parameter determination, for rapid method development 2. Default parameters superior to those of Traditional 3. Curvature detection, for reproducible detection of difficult peaks and shoulders 4. Internally adjusted slope threshold, for accurate baseline determination, does not affect peak detection 5. Gaussian Skimming 2012 Waters Corporation 39
40 Processing Method Default values 2012 Waters Corporation 40 40
41 Developing an ApexTrack method Peak width & Detection Threshold is automatically Determined (14.69 & 4.5) Limit the Apex Detection time zone ( min) Default settings 2012 Waters Corporation 41 41
42 Developing an ApexTrack method Lower the Touchdown% to Waters Corporation 42 42
43 Developing an ApexTrack method Lower the Touchdown% to Waters Corporation 43 43
44 Developing an ApexTrack method Setting min. Area 2012 Waters Corporation 44 44
45 Developing an ApexTrack method Adding Gaussian skim event 2012 Waters Corporation 45 45
46 Developing an ApexTrack method Adding Detect shoulders event 2012 Waters Corporation 46 46
47 Questions 2012 Waters Corporation 47
48 Exercise 1 Optimize existing processing method Optimize integration Adjust retention times 2012 Waters Corporation 48
49 System Suitability Calculations 2012 Waters Corporation 49
50 System Suitability Tab New in Empower Waters Corporation 50
51 Use Noise Centered on Peak Region in Blank Injection Blank Injection Half height multiplier for EP s/n region = Waters Corporation 51
52 Choosing the Blank Injection 2012 Waters Corporation 52
53 2012 Waters Corporation 53
54 Setting System Suitability Limits 2012 Waters Corporation 54
55 2012 Waters Corporation 55
56 Noise & Drift Calculations 2012 Waters Corporation 56
57 Empower Noise and Drift Calculations There are 8 different calculations that can be performed: Detector Noise Peak-to-Peak Noise Detector Drift Average Detector Noise Average Peak-to-Peak Noise Average Drift Baseline Noise Baseline Drift 2012 Waters Corporation 57
58 Enabling 2012 Waters Corporation 58
59 Visual Representation of the Least-squares line 2012 Waters Corporation 59
60 Detector Drift Detector drift is the slope of the least-squares line. Drift is expressed in detector units per hour. For example, the drift calculation for a UV detector would be expressed in absorbance units (AU) per hour. Average Drift is calculated by dividing the data into segments (specified in the processing method) and averaging the values for each segments Waters Corporation 60
61 Detector Noise The root mean square (RMS) noise of the data is calculated using the least-squares line. The formula for Detector Noise is: ( y n i Where y i = the y value of the data point y pi = the y value of the data point predicted by the line n = the number of datapoints 2 y pi ) 2 AU -1.2x x x x x x x x x x x10-5 Residual= y i -y pi 3.49X10-6 AU Minutes 2012 Waters Corporation 61
62 Average Detector Noise 2.43X10-6 AU AU -1.2x x x x x x x x x x x X X X X Minutes 2012 Waters Corporation 62
63 Peak to Peak Noise Peak to Peak Noise is defined to be the algebraic difference of the maximum and minimum residuals between each data point and the least-square line. The residual is determined by subtracting the y value of the data point predicted by the line from the y value of the data point. The formula for Peak to Peak Noise is: Peak to Peak Noise = Max residual Min. residual Where Residual = i pi y y AU -1.2x x x x x x x x x x x X X X10-5 AU Minutes 2012 Waters Corporation 63
64 Average Peak to Peak Noise? 1.15X10-5 AU AU -1.2x x x x x x x x x x x X X X X Minutes 2012 Waters Corporation 64
65 Baseline Noise and Drift Calculations Baseline Noise setup in System Suitability Peak to Peak Calculation 30 second segments (not adjustable) Set time range and percent of run time Waters Corporation 65
66 Waters Corporation 66
67 Viewing the Calculated Results 2012 Waters Corporation 67
68 Managing Manually Integrated Results in a Result Set 2012 Waters Corporation 68
69 Managing Manually Integrated Results in a Result Set, Samples and Controls Process Sample Set Uses Sample Set Information (bracketing) Use Acquisition Method Set (recommended) Review Result Set Manual changes to integration Click Quantitate only DO NOT change standards or click Calibrate Save Result Print Result Set Will ensure that only latest results will be printed 2012 Waters Corporation 69
70 Managing Manually Integrated Results in a Result Set, Samples and Controls Process Sample Set Review & Manual integrate Result Set Sample Set Result Set 1 Result Set 1 Channel 1046 Result 2033 Result 2033 Channel 1054 Channel 1073 Result 2039 Result 2063 Result 2039 Manual Result 3741 New Version of Result Waters Corporation 70
71 Managing Manually Integrated Results in a Result Set, Standards (& Samples/Controls) Process Sample Set Uses Sample Set Information (bracketing) Use Acquisition Method Set (recommended) Review Result Set Manual changes to integration only DO NOT Calibrate or change proc. method Save Result Reprocess Result Set Select Use Existing Integration Calibrate and Quantitate Print Result Set Will ensure that only latest results will be printed 2012 Waters Corporation 71
72 Managing Manually Integrated Results in a Result Set, Standards (& Samples/Controls) Process Sample Set Review & Manual integrate Result Set Re-Process Result Set Use Existing Integration Sample Set Result Set 1 Result Set 1 Result Set 2 Channel 1046 Result 2033 Result 2033 Result 3834 Channel 1054 Channel 1073 Result 2039 Result 2063 Result 2039 Manual Result 3741 Manual Result 3836 Result 3849 Result 2063 New Version of 2012 Waters Corporation 72
73 What happens if you do NOT follow this procedure Sample set Process Result set Modified result set Change std Change sample!! 2012 Waters Corporation 73
74 Questions 2012 Waters Corporation 74
75 Exercise 2 System Suitability Calculations Noise and Drift Calculations Process Sample Set Review and Adjust Results 2012 Waters Corporation 75
Empower Software Data Acquisition and Processing
Empower Software Data Acquisition and Processing Theory Guide 34 Maple Street Milford, MA 01757 71500031209, Revision B NOTICE The information in this document is subject to change without notice and should
INTRODUCTION. The principles of which are to:
Taking the Pain Out of Chromatographic Peak Integration Shaun Quinn, 1 Peter Sauter, 1 Andreas Brunner, 1 Shawn Anderson, 2 Fraser McLeod 1 1 Dionex Corporation, Germering, Germany; 2 Dionex Corporation,
Empower PDA Software. Getting Started Guide. 34 Maple Street Milford, MA 01757 71500031503, Revision A
Empower PDA Software Getting Started Guide 34 Maple Street Milford, MA 01757 71500031503, Revision A NOTICE The information in this document is subject to change without notice and should not be construed
Evaluating System Suitability CE, GC, LC and A/D ChemStation Revisions: A.03.0x- A.08.0x
CE, GC, LC and A/D ChemStation Revisions: A.03.0x- A.08.0x This document is believed to be accurate and up-to-date. However, Agilent Technologies, Inc. cannot assume responsibility for the use of this
Quick Start Guide Chromeleon 7.2
Chromeleon 7.2 7229.0004 Revision 1.0 July 2013 Table of Contents 1 Introduction... 1 1.1 About this Document... 1 1.2 Other Documentation... 2 2 Using Chromeleon... 3 2.1 Overview... 3 2.2 Starting Chromeleon...
PDA Software Getting Started Guide
PDA Software Getting Started Guide 34 Maple Street Milford, MA 01757 WAT053020TP, Revision 1 NOTICE The information in this document is subject to change without notice and should not be construed as a
Signal, Noise, and Detection Limits in Mass Spectrometry
Signal, Noise, and Detection Limits in Mass Spectrometry Technical Note Chemical Analysis Group Authors Greg Wells, Harry Prest, and Charles William Russ IV, Agilent Technologies, Inc. 2850 Centerville
STANDARD OPERATING PROCEDURES
PAGE: 1 of 33 CONTENTS 1.0 SCOPE AND APPLICATION 2.0 METHOD SUMMARY 3.0 SAMPLE PRESERVATION, CONTAINERS, HANDLING, AND STORAGE 4.0 INTERFERENCES AND POTENTIAL PROBLEMS 5.0 EQUIPMENT/APPARATUS 6.0 REAGENTS
Alignment and Preprocessing for Data Analysis
Alignment and Preprocessing for Data Analysis Preprocessing tools for chromatography Basics of alignment GC FID (D) data and issues PCA F Ratios GC MS (D) data and issues PCA F Ratios PARAFAC Piecewise
Learning Objectives:
Proteomics Methodology for LC-MS/MS Data Analysis Methodology for LC-MS/MS Data Analysis Peptide mass spectrum data of individual protein obtained from LC-MS/MS has to be analyzed for identification of
ANALYTICAL METHODS INTERNATIONAL QUALITY SYSTEMS
VALIDATION OF ANALYTICAL METHODS 1 GERT BEUVING INTERNATIONAL PHARMACEUTICAL OPERATIONS TASKS: - Internal auditing - Auditing of suppliers and contract manufacturers - Preparing for and guiding of external
Data Analysis Software
Data Analysis Software for VISION, BioCAD 700E, SPRINT, and INTEGRAL Workstations Version 3 Series Software Getting Started Guide DRAFT August 10, 2001 2:47 pm DASgsg_Title.fm Copyright 1998, 2001, Applied
Characterizing Digital Cameras with the Photon Transfer Curve
Characterizing Digital Cameras with the Photon Transfer Curve By: David Gardner Summit Imaging (All rights reserved) Introduction Purchasing a camera for high performance imaging applications is frequently
Strategies for Developing Optimal Synchronous SIM-Scan Acquisition Methods AutoSIM/Scan Setup and Rapid SIM. Technical Overview.
Strategies for Developing Optimal Synchronous SIM-Scan Acquisition Methods AutoSIM/Scan Setup and Rapid SIM Technical Overview Introduction The 5975A and B series mass selective detectors (MSDs) provide
TotalChrom Workstation User s Guide - Volume II
TotalChrom Workstation User s Guide - Volume II Release History Part Number Release Publication Date N515-6024 B December 2004 User Assistance PerkinElmer 710 Bridgeport Avenue Shelton, CT 06484-4794 Or
AMINO ACID ANALYSIS By High Performance Capillary Electrophoresis
AMINO ACID ANALYSIS By High Performance Capillary Electrophoresis Analysis of Amino Acid Standards Label free analysis using the HPCE-512 ABSTRACT Capillary electrophoresis using indirect UV detection
Signal to Noise Instrumental Excel Assignment
Signal to Noise Instrumental Excel Assignment Instrumental methods, as all techniques involved in physical measurements, are limited by both the precision and accuracy. The precision and accuracy of a
Longitudinal Relaxation Time (T 1 ) Measurement for 1 H on VnmrJ2.2D (use on Ra, Mut, and Isis)
Longitudinal Relaxation Time (T 1 ) Measurement for 1 H on VnmrJ2.2D (use on Ra, Mut, and Isis) Knowledge of the T 1 's of a molecule is important in the setup of many 1D and 2D experiments, in which the
ChromQuest 5.0 Chromatography Data System
ChromQuest 5.0 Chromatography Data System User Guide CHROM-97252 Revision A March 2008 2008 Thermo Fisher Scientific Inc. All rights reserved. Surveyor is a registered trademark of Thermo Fisher Scientific
Algebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only
Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: A-APR.3: Identify zeros of polynomials
Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1
Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1 What are the multiples of 5? The multiples are in the five times table What are the factors of 90? Each of these is a pair of factors.
Intro to Excel spreadsheets
Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using
Analysis of Liquid Samples on the Agilent GC-MS
Analysis of Liquid Samples on the Agilent GC-MS I. Sample Preparation A. Solvent selection. 1. Boiling point. Low boiling solvents (i.e. b.p. < 30 o C) may be problematic. High boiling solvents (b.p. >
Step-by-Step Analytical Methods Validation and Protocol in the Quality System Compliance Industry
Step-by-Step Analytical Methods Validation and Protocol in the Quality System Compliance Industry BY GHULAM A. SHABIR Introduction Methods Validation: Establishing documented evidence that provides a high
What's New in ADP Reporting?
What's New in ADP Reporting? Welcome to the latest version of ADP Reporting! This release includes the following new features and enhancements. Use the links below to learn more about each one. What's
Alerts & Filters in Power E*TRADE Pro Strategy Scanner
Alerts & Filters in Power E*TRADE Pro Strategy Scanner Power E*TRADE Pro Strategy Scanner provides real-time technical screening and backtesting based on predefined and custom strategies. With custom strategies,
Uses of Derivative Spectroscopy
Uses of Derivative Spectroscopy Application Note UV-Visible Spectroscopy Anthony J. Owen Derivative spectroscopy uses first or higher derivatives of absorbance with respect to wavelength for qualitative
Analyses: Statistical Measures
Application Note 129 APPLICATION NOTE Heart Rate Variability 42 Aero Camino, Goleta, CA 93117 Tel (805) 685-0066 Fax (805) 685-0067 [email protected] www.biopac.com 05.22.14 Analyses: Statistical Measures
Fundamentals of modern UV-visible spectroscopy. Presentation Materials
Fundamentals of modern UV-visible spectroscopy Presentation Materials The Electromagnetic Spectrum E = hν ν = c / λ 1 Electronic Transitions in Formaldehyde 2 Electronic Transitions and Spectra of Atoms
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B)
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) Question 4 Let f be a function defined on the closed interval 5 x 5 with f ( 1) = 3. The graph of f, the derivative of f, consists of two semicircles and
Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.
Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data
TotalChrom Workstation User s Guide - Volume I
TotalChrom Workstation User s Guide - Volume I Release History Part Number Release Publication Date N515-6023 B December 2004 User Assistance PerkinElmer 710 Bridgeport Avenue Shelton, CT 06484-4794 Or
How Far is too Far? Statistical Outlier Detection
How Far is too Far? Statistical Outlier Detection Steven Walfish President, Statistical Outsourcing Services [email protected] 30-325-329 Outline What is an Outlier, and Why are
Thermo Scientific Dionex Chromeleon 7 Chromatography Data System Software
Thermo Scientific Dionex Chromeleon 7 Chromatography Data System Software Frank Tontala, Thermo Fisher Scientific, Germering, Germany Technical Note 708 Key Words Chromeleon Chromatography Data System,
Function Guide for the Fourier Transformation Package SPIRE-UOL-DOC-002496
Function Guide for the Fourier Transformation Package SPIRE-UOL-DOC-002496 Prepared by: Peter Davis (University of Lethbridge) [email protected] Andres Rebolledo (University of Lethbridge) [email protected]
Activitity (of a radioisotope): The number of nuclei in a sample undergoing radioactive decay in each second. It is commonly expressed in curies
Activitity (of a radioisotope): The number of nuclei in a sample undergoing radioactive decay in each second. It is commonly expressed in curies (Ci), where 1 Ci = 3.7x10 10 disintegrations per second.
FREE FALL. Introduction. Reference Young and Freedman, University Physics, 12 th Edition: Chapter 2, section 2.5
Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities
Disclaimer: The authors of the articles in this guide are simply offering their interpretation of the concepts. Information, charts or examples
Disclaimer: The authors of the articles in this guide are simply offering their interpretation of the concepts. Information, charts or examples contained in this lesson are for illustration and educational
Lecture - 4 Diode Rectifier Circuits
Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits
Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization
Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization 2.1. Introduction Suppose that an economic relationship can be described by a real-valued
MultiQuant Software Version 3.0 for Accurate Quantification of Clinical Research and Forensic Samples
MultiQuant Software Version 3.0 for Accurate Quantification of Clinical Research and Forensic Samples Fast and Efficient Data Review, with Automatic Flagging of Outlier Results Adrian M. Taylor and Michael
The Center for Teaching, Learning, & Technology
The Center for Teaching, Learning, & Technology Instructional Technology Workshops Microsoft Excel 2010 Formulas and Charts Albert Robinson / Delwar Sayeed Faculty and Staff Development Programs Colston
Perthometer. Surface Texture Parameters New Standards DIN EN ISO / ASME
Perthometer. Surface Texture Parameters New Standards DIN EN ISO / ASME MAHR GMBH, Germany - EDITION 09/01/99 Contents Real surface... Geometrical Product Specification Definition Profile filter P t Profile
Excel 2010: Create your first spreadsheet
Excel 2010: Create your first spreadsheet Goals: After completing this course you will be able to: Create a new spreadsheet. Add, subtract, multiply, and divide in a spreadsheet. Enter and format column
Mass Frontier 7.0 Quick Start Guide
Mass Frontier 7.0 Quick Start Guide The topics in this guide briefly step you through key features of the Mass Frontier application. Editing a Structure Working with Spectral Trees Building a Library Predicting
Analyst 1.6 Software. Software Reference Guide
Analyst 1.6 Software Software Reference Guide Release Date: August 2011 This document is provided to customers who have purchased AB SCIEX equipment to use in the operation of such AB SCIEX equipment.
Enhancing GCMS analysis of trace compounds using a new dynamic baseline compensation algorithm to reduce background interference
Enhancing GCMS analysis of trace compounds using a new dynamic baseline compensation algorithm to reduce background interference Abstract The advantages of mass spectrometry (MS) in combination with gas
Jitter Measurements in Serial Data Signals
Jitter Measurements in Serial Data Signals Michael Schnecker, Product Manager LeCroy Corporation Introduction The increasing speed of serial data transmission systems places greater importance on measuring
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
TI-83/84 Plus Graphing Calculator Worksheet #2
TI-83/8 Plus Graphing Calculator Worksheet #2 The graphing calculator is set in the following, MODE, and Y, settings. Resetting your calculator brings it back to these original settings. MODE Y Note that
Project 5: Scoville Heat Value of Foods HPLC Analysis of Capsaicinoids
Willamette University Chemistry Department 2013 Project 5: HPLC Analysis of Capsaicinoids LABORATORY REPORT: Formal Writing Exercises PRE-LAB ASSIGNMENT Read the entire laboratory project and section 28C
Solving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
Method To Solve Linear, Polynomial, or Absolute Value Inequalities:
Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with
Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds
Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative
Introduction to Microsoft Excel 2010
Introduction to Microsoft Excel 2010 Screen Elements Quick Access Toolbar The Ribbon Formula Bar Expand Formula Bar Button File Menu Vertical Scroll Worksheet Navigation Tabs Horizontal Scroll Bar Zoom
Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
1.1 This test method covers the qualitative and quantitative determination of the content of benzene and toluene in hydrocarbon wax.
Standard Method for Analysis of Benzene and Toluene Content in Hydrocarbon Waxes by Headspace Gas Chromatography EWF METHOD 002/03 (Version 1 Reviewed 2015) 1 Scope 1.1 This test method covers the qualitative
Heart Rate Data Collection Software Application User Guide
Y O R K B I O F E E D B A C K w w w. y o r k - b i o f e e d b a c k. c o. u k G l y n B l a c k e t t Heart Rate Data Collection Software Application User Guide Table of Contents 1 Introduction...1 2
Acceleration of Gravity Lab Basic Version
Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration
Selecting RJ Bandwidth in EZJIT Plus Software
Selecting RJ Bandwidth in EZJIT Plus Software Application Note 1577 Introduction Separating jitter into its random and deterministic components (called RJ/DJ separation ) is a relatively new technique
Simple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
Expense Management. Configuration and Use of the Expense Management Module of Xpert.NET
Expense Management Configuration and Use of the Expense Management Module of Xpert.NET Table of Contents 1 Introduction 3 1.1 Purpose of the Document.............................. 3 1.2 Addressees of the
EXPERIMENT NUMBER 5 BASIC OSCILLOSCOPE OPERATIONS
1 EXPERIMENT NUMBER 5 BASIC OSCILLOSCOPE OPERATIONS The oscilloscope is the most versatile and most important tool in this lab and is probably the best tool an electrical engineer uses. This outline guides
Session 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares
Two Correlated Proportions (McNemar Test)
Chapter 50 Two Correlated Proportions (Mcemar Test) Introduction This procedure computes confidence intervals and hypothesis tests for the comparison of the marginal frequencies of two factors (each with
How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
Computer Training Centre University College Cork. Excel 2013 Pivot Tables
Computer Training Centre University College Cork Excel 2013 Pivot Tables Table of Contents Pivot Tables... 1 Changing the Value Field Settings... 2 Refreshing the Data... 3 Refresh Data when opening a
OPTOFORCE DATA VISUALIZATION 3D
U S E R G U I D E - O D V 3 D D o c u m e n t V e r s i o n : 1. 1 B E N E F I T S S Y S T E M R E Q U I R E M E N T S Analog data visualization Force vector representation 2D and 3D plot Data Logging
Impact Analysis for Software changes in OpenLAB CDS A.01.04
Impact Analysis for Software changes in OpenLAB CDS A.01.04 Document Information: Filename Product Identifier Product Revision Project Identifier Document Revision Impact_Analysis_OpenLAB_CDS_A0104 OpenLAB
Chemistry 321, Experiment 8: Quantitation of caffeine from a beverage using gas chromatography
Chemistry 321, Experiment 8: Quantitation of caffeine from a beverage using gas chromatography INTRODUCTION The analysis of soft drinks for caffeine was able to be performed using UV-Vis. The complex sample
ALGEBRA I (Common Core)
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................
Fractional Distillation and Gas Chromatography
Fractional Distillation and Gas Chromatography Background Distillation The previous lab used distillation to separate a mixture of hexane and toluene based on a difference in boiling points. Hexane boils
SOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The Odd-Root Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
Data Reporting in Chromeleon
Technical Note 70 Data Reporting in Chromeleon 1. Introduction One of the most important functions of any Chromatography application is the reporting of processed data. If it is not possible to use the
Electrical Resonance
Electrical Resonance (R-L-C series circuit) APPARATUS 1. R-L-C Circuit board 2. Signal generator 3. Oscilloscope Tektronix TDS1002 with two sets of leads (see Introduction to the Oscilloscope ) INTRODUCTION
Roots of Equations (Chapters 5 and 6)
Roots of Equations (Chapters 5 and 6) Problem: given f() = 0, find. In general, f() can be any function. For some forms of f(), analytical solutions are available. However, for other functions, we have
Background Information
1 Gas Chromatography/Mass Spectroscopy (GC/MS/MS) Background Information Instructions for the Operation of the Varian CP-3800 Gas Chromatograph/ Varian Saturn 2200 GC/MS/MS See the Cary Eclipse Software
ICH Topic Q 2 (R1) Validation of Analytical Procedures: Text and Methodology. Step 5
European Medicines Agency June 1995 CPMP/ICH/381/95 ICH Topic Q 2 (R1) Validation of Analytical Procedures: Text and Methodology Step 5 NOTE FOR GUIDANCE ON VALIDATION OF ANALYTICAL PROCEDURES: TEXT AND
Positive Feedback and Oscillators
Physics 3330 Experiment #6 Fall 1999 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active
Section 1. Inequalities -5-4 -3-2 -1 0 1 2 3 4 5
Worksheet 2.4 Introduction to Inequalities Section 1 Inequalities The sign < stands for less than. It was introduced so that we could write in shorthand things like 3 is less than 5. This becomes 3 < 5.
Solving Systems of Two Equations Algebraically
8 MODULE 3. EQUATIONS 3b Solving Systems of Two Equations Algebraically Solving Systems by Substitution In this section we introduce an algebraic technique for solving systems of two equations in two unknowns
Shimadzu UV-VIS User s Guide
Shimadzu UV-VIS User s Guide 1) Push the F4 button on the UV-VIS instrument keypad. This will enable PC control. Push the F4 Button 2) Log into the UV-VIS software with your username and password. 3) After
Math 1. Month Essential Questions Concepts/Skills/Standards Content Assessment Areas of Interaction
Binghamton High School Rev.9/21/05 Math 1 September What is the unknown? Model relationships by using Fundamental skills of 2005 variables as a shorthand way Algebra Why do we use variables? What is a
Analyst 1.6.1 Software
MAX cover image size 4.8 inches X 7.8 inches In Body page mode, draw a graphic frame to match this section and then go to the next step. Delete this text from the Front Cover Master page. View>Master Pages,
Review and Approve Results in Empower Data, Meta Data and Audit Trails
Review and Approve Results in Empower Data, Meta Data and Audit Trails 2013 Waters Corporation 1 What is an audit trail? Systematic story of the data from creation, through interpretation and final assessment
6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
Unique Software Tools to Enable Quick Screening and Identification of Residues and Contaminants in Food Samples using Accurate Mass LC-MS/MS
Unique Software Tools to Enable Quick Screening and Identification of Residues and Contaminants in Food Samples using Accurate Mass LC-MS/MS Using PeakView Software with the XIC Manager to Get the Answers
Mathematics. What to expect Resources Study Strategies Helpful Preparation Tips Problem Solving Strategies and Hints Test taking strategies
Mathematics Before reading this section, make sure you have read the appropriate description of the mathematics section test (computerized or paper) to understand what is expected of you in the mathematics
Basic Excel Handbook
2 5 2 7 1 1 0 4 3 9 8 1 Basic Excel Handbook Version 3.6 May 6, 2008 Contents Contents... 1 Part I: Background Information...3 About This Handbook... 4 Excel Terminology... 5 Excel Terminology (cont.)...
SPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
Setting up a Quantitative Analysis MS ChemStation
Setting up a Quantitative Analysis MS ChemStation Getting Ready 1. Use the tutorial section "Quant Reports" on the MSD Reference Collection CD-ROM that came with your ChemStation software. 2. Know what
Definition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
Trigonometric functions and sound
Trigonometric functions and sound The sounds we hear are caused by vibrations that send pressure waves through the air. Our ears respond to these pressure waves and signal the brain about their amplitude
Understanding the market
Understanding the market Technical Analysis Approach: part I Xiaoguang Wang President, Purdue Quantitative Finance Club PhD Candidate, Department of Statistics Purdue University [email protected] Outline
Student Performance Q&A:
Student Performance Q&A: 2008 AP Calculus AB and Calculus BC Free-Response Questions The following comments on the 2008 free-response questions for AP Calculus AB and Calculus BC were written by the Chief
QIAGEN Rotor Gene Q: Software V2.0
QIAGEN Rotor Gene Q: Software V2.0 Instrument Setup Instructions for RT 2 Profiler PCR Arrays Preparation Before the Experiment (Presetting the Machine will save time for your run): Please make note of
Properties of Real Numbers
16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should
The Measurement of Sensitivity in Fluorescence Spectroscopy
The Measurement of Sensitivity in Fluorescence Spectroscopy Among instrumental techniques, fluorescence spectroscopy is recognized as one of the more sensitive. In fluorescence, the intensity of the emission
