Fourier transforms in NMR, optical, and mass spectrometry: a user's handbook
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
1990
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Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVI, 450 S. Ill., graph. Darst. |
ISBN: | 0444873600 0444874127 |
Internformat
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245 | 1 | 0 | |a Fourier transforms in NMR, optical, and mass spectrometry |b a user's handbook |c Alan G. Marshall and Francis R. Verdun |
264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 1990 | |
300 | |a XVI, 450 S. |b Ill., graph. Darst. | ||
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adam_text | IMAGE 1
FOURIER TRANSFORMS IN
NMR, OPTICAL, AND MASS SPECTROMETRY
A USER S HANDBOOK
ALAN G. MARSHALL AND FRANCIS R. VERDUN DEPARTMENTS OF CHEMISTRY AND
BIOCHEMISTRY, THE OHIO STATE UNIVERSITY, COLUMBUS, OH43210-1173, U.S.A.
ELSEVIER AMSTERDAM - OXFORD - NEW YORK - TOKYO 1990
IMAGE 2
C O N T E N TS
DEDICATION XIII
PREFACE XV
ACKNOWLEDGMENTS XVI
CHAPTER 1 SPECTRAL LINE SHAPE DERIVED FROM THE MOTION OF A DAMPED MASS
ON A SPRING 1.1 TERMINOLOGY 1
1.2 TRANSIENT RESPONSE TO A SUDDEN IMPULSE: RELAXATION 4
1.3 STEADY-STATE RESPONSE TO A SINUSOIDAL DRIVING FORCE 7
1.3.1 ABSORPTION AND DISPERSION SPECTRA 7
1.3.2 MAGNITUDE AND POWER SPECTRA 11
1.3.3 HUBERT TRANSFORM AND DISPA 11
1.3.4 PHYSICAL MEANING OF MATHEMATICALLY COMPLEX QUANTITIES 13
1.4 TRANSIENT VS. STEADY-STATE EXPERIMENTS 14
1.4.1 FOURIER TRANSFORM RELATION BETWEEN THE TWO EXPERIMENTS 14
1.4.2 ZERO-FRICTION LIMIT: THOMSON AND RAYLEIGH SCATTERING 17
1.4.3 ZERO-MASS LIMIT: DIELECTRIC OR ULTRASONIC RELAXATION 18
FURTHER READING 21
PROBLEMS 21
SOLUTIONS TO PROBLEMS 25
CHAPTER 2 FOURIER TRANSFORMS FOR ANALOG (CONTINUOUS) WAVEFORMS
2.1 COSINE, SINE, AND COMPLEX FOURIER TRANSFORMS: LIBRARY OF FT PAIRS 27
2.1.1 SINUSOID/8-FUNCTION: EVEN, ODD, SIGNUM, AND CAUSAL FUNCTIONS 27
2.1.2 KECTANGLE/SINC: EFFECT OF OFF-RESONANCE EXCITATION 30
2.1.3 EXPONENTIAL/LORENTZ 32
2.1.4 GAUSSIAN/GAUSSIAN 33
2.1.5 COMB/COMB 33
2.1.6 CHIRP/FREQUENCY-SWEEP 35
2.1.7 RANDOM NOISE/WHITE SPECTRUM 37
2.2 CONVOLUTION 38
2.2.1 IDEAL VS. OBSERVED RESPONSE 38
2.2.2 CONVOLUTION AND FOURIER TRANSFORMS: THE CONVOLUTION THEOREM 40
2.2.2.1 EXPANSION OF THE LIBRARY OF FT PAIRS 42
2.2.2.2 COMPENSATION FOR AN IMPERFECT EXPERIMENT 44
2.2.3 CROSS-CORRELATION AND AUTO-CORRELATION 46
IMAGE 3
2.3 APODIZATION (WINDOWING): TAILORING OF SPECTRAL PEAK SHAPE 47
2.3.1 DIRICHLET (RECTANGLE, BOXCAR) 47
2.3.2 OTHERS: TRIANGLE, TRAPEZOID, HAMMING, BLACKMAN-HARRIS, BESSEL,
ETC. 47
2.3.3 LINE SHAPE TRANSFORMATIONS (FOURIER SELF-DECONVOLUTION) 48
2.4 TIME DELAY AND PHASE SHIFT 51
2.4.1 SHIFT THEOREM: RELATION BETWEEN TIME DELAY AND SPECTRAL PHASE 51
2.4.2 FREQUENCY-DOMAIN PHASE CORRECTION 53
FURTHER READING 56
PROBLEMS 57
SOLUTIONS TO PROBLEMS 64
CHAPTER 3 FOURIER TRANSFORMS OF DIGITAL (DISCRETE) WAVEFORMS
3.1 NUMERICAL ALGORITHMS 69
3.1.1 FOURIER SERIES AND FAST FOURIER TRANSFORM 69
3.1.2 DISCRETE CONVOLUTION AND FAST ALGORITHM 72
3.2 NYQUIST CRITERION 74
3.2.1 FOLDOVER (ALIASING) 75
3.2.2 DIGITAL SPECTRAL RESOLUTION 76
3.3 VERTICAL DYNAMIC RANGE 77
3.3.1 FIXED-POINT VERSUS FLOATING-POINT ARITHMETIC 77
3.3.2 CLIPPED DATA SETS 78
3.4 USES FOR ZERO 80
3.4.1 ZERO-FILLING 80
3.4.2 DIGITAL FILTERS 82
3.5 PHASE CORRECTION AND ITS ARTIFACTS 83
3.5.1 ZERO- AND FIRST-ORDER PHASE CORRECTION 83
3.5.2 ARTIFACTS 86
3.6 SCALING OF DISCRETE FT ENERGY AND POWER SPECTRA 86
FURTHER READING 88
PROBLEMS 89
SOLUTIONS TO PROBLEMS 91
CHAPTER 4 FOURIER TRANSFORM SPECTROMETRY: COMMON FEATURES
4.1 MULTICHANNEL SPECTROMETRY 95
4.1.1 SINGLE-CHANNEL SPECTROMETRY 95
4.1.2 MULTIDETECTORS 95
4.1.3 MULTIPLEX METHODS (FELLGETT ADVANTAGE) 98
4.1.3.1 HADAMARD CODE 100
4.1.3.2 FOURIER CODE 101
IMAGE 4
4.2 ABSORPTION, DISPERSION, MAGNITUDE, AND POWER SPECTRA 102
4.2.1 DIGITAL VS. ANALOG RESOLUTION 105
4.2.2 TIME-DOMAIN AND FREQUENCY-DOMAIN EXCITATION MAGNITUDE 106
4.2.3 INVERSE FT: TAILORED (STORED WAVEFORM) EXCITATION 107
4.3 LINEAR VERSUS CIRCULAR POLARIZATION 109
4.3.1 NEGATIVE-FREQUENCY COMPONENTS 110
4.3.2 QUADRATURE EXCITATION AND DETECTION 113
4.3.2.1 BASELINE OFFSET BETWEEN QUADRATURE CHANNELS: THE CENTER GLITCH
114 4.3.2.2 GAIN DIFFERENCE BETWEEN QUADRATURE CHANNELS: IMAGE PEAKS 114
4.3.2.3 TIME DELAY BETWEEN QUADRATURE CHANNELS: ALTERNATE VS.
SIMULTANEOUS SAMPLING 116
4.3.2.4 PHASE CYCLING 119
4.4 NON-LINEAR EFFECTS 120
4.4.1 ORIGIN OF HARMONIC AND INTERMODULATION FREQUENCIES 120
4.4.2 MIXERS AND DOUBLERS: HETERODYNE DETECTION 122
4.4.3 AMPLITUDE MODULATION 125
4.4.4 FREQUENCY AND PHASE MODULATION 127
FURTHER READING 131
PROBLEMS 131
SOLUTIONS TO PROBLEMS 137
CHAPTER 5 NOISE
5.1 NOISE IN THE DETECTED SPECTRUM 141
5.1.1 SOURCE-LIMITED VS. DETECTOR-LIMITED NOISE 142
5.1.2 NOISE, DATA WORD LENGTH, SIGNAL-AVERAGING, AND DYNAMIC RANGE 144
5.1.3 QUANTIZATION NOISE AND OVERSAMPLING 147
5.1.4 PRECISION IN DETERMINATION OF PEAK POSITION, WIDTH, AND HEIGHT AS
A FUNCTION OF PEAK SHAPE, SIGNAL-TO-NOISE RATIO, AND DIGITAL RESOLUTION
150 5.1.5 EFFECT OF APODIZATION ON SPECTRAL SIGNAL-TO-NOISE RATIO AND
RESOLUTION 155 5.2 NOISE AS A SPECTRAL SOURCE: FOURIER ANALYSIS OF
RANDOM MOTIONS 157
5.2.1 RANDOM NOISE: AUTOCORRELATION FUNCTION AND POWER SPECTRUM 157
5.2.2 PSEUDORANDOM NOISE: SHIFT REGISTER AND HADAMARD S-MATRIX SEQUENCES
165
FURTHER READING 167
PROBLEMS 168
SOLUTIONS TO PROBLEMS 174
IMAGE 5
CHAPTER 6 NON-FT METHODS FOR PROCEEDING FROM TIME- TO FREQUENCY-DOMAIN
6.1 WHAT S WRONG WITH FOURIER TRANSFORMS? 179
6.2 NEW WAYS TO REPRESENT AN ANALOG SPECTRUM: THE (CONTINUOUS) TRANSFER
FUNCTION AND THE (CONTINUOUS) LAPLACE TRANSFORM FOR A MASS-ON-A-SPRING
180 6.3 DIFFERENCE EQUATION, DISCRETE TRANSFER FUNCTION AND DISCRETE
Z-TRANSFORM FOR THE MASS-ON-A-SPRING 186
6.3.1 LINEAR PREDICTION: THE AUTOREGRESSION (AR) MODEL 193
6.3.1.1 LEAST SQUARES CRITERION 193
6.3.1.2 AUTOCORRELATION METHOD 194
6.3.2 MOVING AVERAGE (MA), AUTOREGRESSION/MOVING AVERAGE (ARMA) METHODS
204
6.4 MAXIMUM ENTROPY METHODS 206
6.4.1 AGREEMENT BETWEEN TRIAL AND ACTUAL TIME-DOMAIN DATA SETS 206
6.4.2 PROBABILITY PEAKING: MOST PROBABLE RESULT 208
6.4.3 ENTROPY, PROBABILITY, AND SPECTRAL SMOOTHNESS 211
6.4.4 RELATION BETWEEN MEM AND AUTOREGRESSION METHODS 215
FURTHER READING 216
PROBLEMS 217
SOLUTIONS TO PROBLEMS 221
CHAPTER 7 FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETRY
7.1 NATURAL MOTIONS OF AN ION IN A STATIC ELECTROMAGNETIC TRAP 225
7.1.1 CYCLOTRON MOTION: ICR ORBITAL FREQUENCY, RADIUS, VELOCITY, AND
ENERGY225 7.1.2 TRAPPING OSCILLATION 229
7.1.3 MAGNETRON MOTION 230
7.2 STATIC ELECTROMAGNETIC ION TRAPS 232
7.2.1 EXCITATION OF A COHERENT TIME-DOMAIN ICR SIGNAL 232
7.2.2 DETECTION OF AN ICR SIGNAL 233
7.2.3 ICR ION TRAPS (CUBIC, CYLINDRICAL, HYPERBOLIC, ORTHORHOMBIC,
SCREENED), AND THEIR EFFECT ON MASS RESOLUTION AND UPPER MASS LIMIT 234
7.2.4 ION FORMATION AT HIGH PRESSURE WITH DETECTION AT LOW PRESSURE:
DUAL-TRAP; EXTERNAL INJECTION OF IONS 239
7.3 DAMPING OF THE TIME-DOMAIN ICR SIGNAL 239
7.3.1 TYPES OF DAMPING: HOMOGENEOUS VS. INHOMOGENEOUS 239
7.3.2 DAMPING ( RELAXATION ) MECHANISMS 240
7.3.3 COULOMB (SPACE-CHARGE) ION-ION REPULSIONS: ICR FREQUENCY SHIFT AND
MASS SPECTRAL PEAK BROADENING 243
IMAGE 6
7.4 FT ASPECTS OF ICR 243
7.4.1 MASS RESOLUTION, MASS ACCURACY, AND MASS CALIBRATION 243
7.4.2 PULSED SINGLE-FREQUENCY, FREQUENCY-SWEEP, AND STORED WAVEFORM
INVERSE FT (SWIFT) EXCITATION 246
7.4.3 DIRECT-MODE VS. HETERODYNE-MODE EXPERIMENTS; MULTIPLE FOLDOVER 246
7.4.4 PHASING OF BROADBAND PHASE-WRAPPED FT/ICR SPECTRA 249
7.4.5 HARMONICS 250
7.4.6. QUADRATURE ICR EXCITATION AND DETECTION 253
7.5 FT/ICR FEATURES, EXPERIMENTS, AND APPLICATIONS 254
7.5.1 FT/ICR EXPERIMENTAL EVENTS [ION FORMATION, ION EXCITATION OR
EJECTION, ION DE-EXCITATION, ION FRAGMENTATION OR CHEMICAL REACTION, ION
DETECTION, ION REMOVAL (QUENCH)] 254
7.5.2 FT/ICR EXPERIMENTAL EVENT SEQUENCES: THE GAS-PHASE CHEMICAL
LABORATORY 260
7.5.2.1 NORMAL BROAD-BAND OR HETERODYNE DETECTION 260
7.5.2.2 ION-MOLECULE REACTION PATHWAYS, RATE CONSTANTS, EQUILIBRIUM
CONSTANTS, AND ENERGETICS 261
7.5.2.3 FOURIER AND HADAMARD MULTIPLEX DETECTION OF ION-MOLECULE
COLLISION OR REACTION PRODUCTS: TWO-DIMENSIONAL MS/MS 267
FURTHER READING 272
PROBLEMS 273
SOLUTIONS TO PROBLEMS 275
CHAPTER 8 FOURIER TRANSFORM NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
8.1 NATURAL MOTION OF A MAGNETIC MOMENT IN A MAGNETIC FIELD: LARMOR
PRECESSION 279
8.1.1 CLASSICAL MECHANICAL MOTION AND ENERGY OF A MAGNETIC MOMENT IN A
STATIC MAGNETIC FIELD: LABORATORY AND ROTATING-FRAME REPRESENTATIONS 279
8.1.2 QUANTUM MECHANICAL MAGNETIC NUCLEI 281
8.2 NMR PARAMETERS 283
8.2.1 CHEMICAL SHIFT: IDENTIFICATION OF CHEMICAL BONDS 283
8.2.2 SCALAR (J-) COUPLING THROUGH CHEMICAL BONDS: DIHEDRAL ANGLES 285
8.2.3 DIPOLAR COUPLING THROUGH SPACE: INTRA- AND INTERMOLECULAR
DISTANCES 287 8.3 SPIN MANIPULATIONS 288
8.3.1 90 PULSE: FT/NMR EXCITATION, TI RELAXATION, AND DETECTION 288
8.3.2 180 PULSE: SPIN-LATUECE [TSS RELAXATION; RELATION BETWEEN T AND TI
291 8.3.3 SPIN-ECHO: ELIMINATION OF CHEMICAL SHIFT DIFFERENCES;
DOUBLE-SIDED FT 295
8.3.4 MULTIPLE-PULSE EXCITATION AND NON-LINEAR PHENOMENA: SOLVENT
SUPPRESSION 295
IMAGE 7
8.4 NMR TIME SCALES 3 00
8.4.1 CHEMICAL EXCHANGE 3 00
8.4.2 DECOUPLING: ELIMINATION OF J - C O U P L I NG 3 02
8.4.3 MOLECULAR MOTION: SOLIDS VS. LIQUIDS 3 03
8.5 TWO-DIMENSIONAL NMR 3 06
8.5.1 SPIN-ECHO P L US DECOUPLING: J - M O D U L A T I O N; DEFT 3 06
8.5.2 OTHER 2D-FT/NMR EXPERIMENTS 3 12
8.5.2.1 COSY 3 12
8.5.2.2 NOESY 3 12
8.5.2.3 COHERENCES: D O U B L E - Q U A N T UM NMR (INADEQUATE) 3 14
8.6 NMR IMAGING 3 15
8.6.1 SPATIAL ENCODING METHODS: SLICE SELECTION, P H A S E- A ND
FREQUENCY-ENCODING 3 17
8.6.2 IMAGE C O N T R A S T: T -, T2-, A ND P - W E I G H T I NG 3 19
8.6.3 FLOW IMAGING 3 20
8.6.4 CHEMICAL SHIFT IMAGING 3 21
FURTHER READING 3 24
PROBLEMS 3 25
SOLUTIONS TO PROBLEMS 3 27
CHAPTER 9 FT/INTERFEROMETRY
9.1 NATURAL MOTIONS OF VIBRATING MOLECULES 3 31
9.1.1 NORMAL MODES: INFRARED SPECTRA 3 31
9.1.2 COUPLING OF N U C L E AR A ND ELECTRONIC MOTIONS: R A M AN SPECTRA
3 37
9.1.3 INFRARED-ACTIVE US. RAMAN-ACTIVE VIBRATIONS: SELECTION RULES 3 40
9.2 THE MICHELSON INTERFEROMETER 3 41
9.2.1 GENERATION OF AN INTERFEROGRAM: REFLECTIVE VS. REFRACTIVE OPTICS 3
41
9.2.2 SAMPLING CALIBRATION BY COUNTING LASER FRINGES 3 47
9.2.3 TRANSMITTANCE A ND ABSORBANCE FT SPECTRA FROM SINGLE-BEAM M E A S
U R E M E N TS 3 47
9.2.4 PHASING 3 48
9.2.5 DYNAMIC RANGE: GAIN-RANGING, CHIRPING 3 50
9.2.6 OPENING THE EXIT A ND E N T R A N CE SLITS: FELLGETT
(MULTICHANNEL) A ND JACQUINOT (THROUGHPUT, ETENDUE) ADVANTAGES 3 51
9.3 APPLICATIONS OF FT/INTERFEROMETRY 3 52
9.3.1 FT/INFRARED S P E C T R O M E T RY 3 52
9.3.1.1 MOLECULAR S T R U C T U RE FROM VIBRATIONAL GROUP FREQUENCIES 3
52
9.3.1.2 GC/FT/IR ANALYSIS OF MIXTURES 3 54
IMAGE 8
9.3.2 ULTRAVIOLET/VISIBLE INTERFEROMETRY 354
9.3.2.1 RESOLUTION, BANDWIDTH, AND FOLDOVER 355
9.3.2.2 SOURCE-LIMITED VS. DETECTOR-LIMITED NOISE: MULTIPLEX
DISADVANTAGE FOR SPARSE SPECTRA 357
9.3.3 RAMAN SPECTROSCOPY: THE CENTERBAND DYNAMIC RANGE PROBLEM 357
9.3.3.1 FT/RAMAN SPECTROSCOPY 358
9.3.3.2 HADAMARD TRANSFORM RAMAN SPECTROSCOPY 360
9.3.3.3 HADAMARD ENCODEMENT FOR SPATIAL IMAGING 363
FURTHER READING 365
PROBLEMS 365
SOLUTIONS TO PROBLEMS 366
CHAPTER 10 EPILOG: FOURIER TRANSFORMS IN OTHER TYPES OF SPECTROSCOPY 369
APPENDIX A INTEGRALS AND THEOREMS FOR FT APPLICATIONS 373
APPENDDI * THE DIRAC AFUNCTIONAL 385
APPENDDI * THE FFT ALGORITHM: CONCEPTUAL BASIS AND PROGRAM LISTINGS 389
FURTHER READING 406
APPENDDI D FOURIER TRANSFORM PROPERTIES AND PICTORIAL ATLAS OF FOURIER
TRANSFORM PAIRS 407
APPENDDI E PHYSICAL CONSTANTS AND UNITS 431
INDEX 433
|
any_adam_object | 1 |
author | Marshall, Alan G. Verdun, Francis R. |
author_facet | Marshall, Alan G. Verdun, Francis R. |
author_role | aut aut |
author_sort | Marshall, Alan G. |
author_variant | a g m ag agm f r v fr frv |
building | Verbundindex |
bvnumber | BV006114834 |
classification_rvk | SK 950 UH 5400 VE 8600 |
classification_tum | CHE 236f CHE 160f |
ctrlnum | (OCoLC)246688092 (DE-599)BVBBV006114834 |
dewey-full | 543/.0877 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 543 - Analytical chemistry |
dewey-raw | 543/.0877 |
dewey-search | 543/.0877 |
dewey-sort | 3543 3877 |
dewey-tens | 540 - Chemistry and allied sciences |
discipline | Chemie / Pharmazie Physik Chemie Mathematik |
format | Book |
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id | DE-604.BV006114834 |
illustrated | Illustrated |
indexdate | 2024-07-09T16:40:30Z |
institution | BVB |
isbn | 0444873600 0444874127 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003862977 |
oclc_num | 246688092 |
open_access_boolean | |
owner | DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 |
owner_facet | DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-188 |
physical | XVI, 450 S. Ill., graph. Darst. |
publishDate | 1990 |
publishDateSearch | 1990 |
publishDateSort | 1990 |
publisher | Elsevier |
record_format | marc |
spelling | Marshall, Alan G. Verfasser aut Fourier transforms in NMR, optical, and mass spectrometry a user's handbook Alan G. Marshall and Francis R. Verdun Amsterdam [u.a.] Elsevier 1990 XVI, 450 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier NMR-Spektroskopie (DE-588)4075421-2 gnd rswk-swf Massenspektrometrie (DE-588)4037882-2 gnd rswk-swf Fourier-Spektroskopie (DE-588)4135413-8 gnd rswk-swf Massenspektrometrie (DE-588)4037882-2 s DE-604 NMR-Spektroskopie (DE-588)4075421-2 s Fourier-Spektroskopie (DE-588)4135413-8 s Verdun, Francis R. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003862977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Marshall, Alan G. Verdun, Francis R. Fourier transforms in NMR, optical, and mass spectrometry a user's handbook NMR-Spektroskopie (DE-588)4075421-2 gnd Massenspektrometrie (DE-588)4037882-2 gnd Fourier-Spektroskopie (DE-588)4135413-8 gnd |
subject_GND | (DE-588)4075421-2 (DE-588)4037882-2 (DE-588)4135413-8 |
title | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook |
title_auth | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook |
title_exact_search | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook |
title_full | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook Alan G. Marshall and Francis R. Verdun |
title_fullStr | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook Alan G. Marshall and Francis R. Verdun |
title_full_unstemmed | Fourier transforms in NMR, optical, and mass spectrometry a user's handbook Alan G. Marshall and Francis R. Verdun |
title_short | Fourier transforms in NMR, optical, and mass spectrometry |
title_sort | fourier transforms in nmr optical and mass spectrometry a user s handbook |
title_sub | a user's handbook |
topic | NMR-Spektroskopie (DE-588)4075421-2 gnd Massenspektrometrie (DE-588)4037882-2 gnd Fourier-Spektroskopie (DE-588)4135413-8 gnd |
topic_facet | NMR-Spektroskopie Massenspektrometrie Fourier-Spektroskopie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003862977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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