Foundations of fluid mechanics with applications: problem solving using Mathematica
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1999
|
| Series: | Modeling and simulation in science, engineering and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 575 S. graph. Darst. 25 cm |
| ISBN: | 3764339950 0817639950 |
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MARC
| LEADER | 00000nam a22000001c 4500 | ||
|---|---|---|---|
| 001 | BV013032703 | ||
| 003 | DE-604 | ||
| 005 | 20050810 | ||
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| 008 | 000208s1999 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 958300984 |2 DE-101 | |
| 020 | |a 3764339950 |c (Basel ...) Pp. : sfr 138.00 |9 3-7643-3995-0 | ||
| 020 | |a 0817639950 |c (Boston) Pp. |9 0-8176-3995-0 | ||
| 035 | |a (OCoLC)246113850 | ||
| 035 | |a (DE-599)BVBBV013032703 | ||
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| 100 | 1 | |a Kiselev, Sergej P. |d 1956- |e Verfasser |0 (DE-588)121731146 |4 aut | |
| 245 | 1 | 0 | |a Foundations of fluid mechanics with applications |b problem solving using Mathematica |c Sergey P. Kiselev ; Evgenii V. Vorozhtsov ; Vasily M. Fomin |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1999 | |
| 300 | |a XIV, 575 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Modeling and simulation in science, engineering and technology | |
| 630 | 0 | 4 | |a Mathematica (Computer file) |
| 650 | 4 | |a Strömungsmechanik - Lehrbuch | |
| 650 | 4 | |a Strömungsmechanik - Mathematica 3.0 | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Fluid mechanics | |
| 650 | 4 | |a Fluid mechanics |x Data processing | |
| 650 | 0 | 7 | |a Mathematica |g Programm |0 (DE-588)4268208-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Strömungsmechanik |0 (DE-588)4077970-1 |D s |
| 689 | 0 | 1 | |a Mathematica |g Programm |0 (DE-588)4268208-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Vorožcov, Evgenij V. |d 1946- |e Verfasser |0 (DE-588)121730611 |4 aut | |
| 700 | 1 | |a Fomin, Vasilij M. |d 1940- |e Verfasser |0 (DE-588)121731189 |4 aut | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008878535 | |
Record in the Search Index
| _version_ | 1807319931713224704 |
|---|---|
| adam_text |
CONTENTS
PREFACE
XI
1
DEFINITIONS
OF
CONTINUUM
MECHANICS
1
1.1
VECTORS
AND
TENSORS
.
1
1.1.1
COVARIANT
DIFFERENTIATION
.
5
1.1.2
THE
LEVI-CIVITA
TENSOR
.
7
1.1.3
DIFFERENTIAL
OPERATIONS
.
9
1.1.4
PHYSICAL
COMPONENTS
OF
VECTORS
AND
TENSORS
.
9
1.1.5
EIGENVALUES
AND
EIGENVECTORS
OF
A
SYMMETRIC
TENSOR
.
10
1.1.6
THE
OSTROGRADSKY-GAUSS
THEOREM
.
12
1.1.7
THE
STOKES
THEOREM
.
14
1.1.8
THE
WEYL
FORMULA
.
15
1.2
EULERIAN
AND
LAGRANGIAN
DESCRIPTION
OF
A
CONTINUUM:
STRAIN
TENSOR
.
24
1.2.1
LAGRANGIAN
AND
EULERIAN
DESCRIPTION
OF
A
CONTINUUM
.
24
1.2.2
STRAIN
TENSOR
.
28
1.2.3
A
CONDITION
FOR
COMPATIBILITY
OF
DEFORMATIONS
.
.
35
1.2.4
RATE-OF-STRAIN
TENSOR:
CAUCHY-HELMHOLTZ
THEOREM
.
37
1.3
STRESS
TENSOR
.
55
1.3.1
THE
CAUCHY
STRESS
TENSOR
IN
THE
ACCOMPANYING
COORDINATE
SYSTEM
.
55
1.3.2
PIOLA-KIRCHHOFF
STRESS
TENSORS
IN
THE
REFERENCE
FRAME
AND
IN
THE
EULERIAN
COORDINATES
.
59
1.3.3
PRINCIPAL
VALUES
AND
INVARIANTS
OF
THE
STRESS
TENSOR
.
61
1.3.4
DIFFERENTIATION
OF
THE
STRESS
TENSOR
WITH
RESPECT
TO
TIME
.
63
REFERENCES
.
73
VI
CONTENTS
2
FUNDAMENTAL
PRINCIPLES
AND
LAWS
OF
CONTINUUM
MECHANICS
75
2.1
EQUATIONS
OF
CONTINUITY,
MOTION,
AND
ENERGY
FOR
A
CONTINUUM
.
75
2.1.1
CONTINUITY
EQUATION
.
76
2.1.2
EQUATIONS
OF
MOTION
AND
OF
MOMENTUM
MOMENT
.
78
2.1.3
THE
ENERGY
CONSERVATION
LAW:
THE
FIRST
AND
SECOND
LAWS
OF
THERMODYNAMICS
.
84
2.1.4
EQUATION
OF
STATE
(GENERAL
RELATIONS)
.
92
2.1.5
EQUATIONS
OF
AN
IDEAL
AND
VISCOUS,
HEAT-CONDUCTING
GAS
.
95
2.2
THE
HAMILTON-OSTROGRADSKY
'
S
VARIATIONAL
PRINCIPLE
IN
CONTINUUM
MECHANICS
.
115
2.2.1
EULER-LAGRANGE
EQUATIONS
IN
LAGRANGIAN
COORDINATES
.
115
2.2.2
HAMILTON
'
S
EQUATIONS
IN
LAGRANGIAN
COORDINATES
.
121
2.2.3
EULER-LAGRANGE
EQUATIONS
IN
EULERIAN
COORDINATES
AND
MURNAGHAN
'
S
FORMULA
.
125
2.3
CONSERVATION
LAWS
FOR
ENERGY
AND
MOMENTUM
IN
CONTINUUM
MECHANICS
.
135
2.3.1
CONSERVATION
LAWS
IN
CARTESIAN
COORDINATES
.
.
.
135
2.3.2
CONSERVATION
LAWS
IN
AN
ARBITRARY
COORDINATE
SYSTEM
.
144
REFERENCES
.
152
3
THE
FEATURES
OF
THE
SOLUTIONS
OF
CONTINUUM
MECHANICS
PROBLEMS
155
3.1
SIMILARITY
AND
DIMENSION
THEORY
IN
CONTINUUM
MECHANICS
.
155
3.2
THE
CHARACTERISTICS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
.
.
.
163
3.3
DISCONTINUITY
SURFACES
IN
CONTINUUM
MECHANICS
.
171
REFERENCES
.
185
4
IDEAL
FLUID
187
4.1
INTEGRALS
OF
MOTION
EQUATIONS
OF
IDEAL
FLUID
AND
GAS
.
.
.
187
4.1.1
MOTION
EQUATIONS
IN
THE
GROMEKA-LAMB
FORM
.
.
188
4.1.2
THE
BERNOULLI
INTEGRAL
.
188
4.1.3
THE
LAGRANGE
INTEGRAL
.
189
4.2
PLANAR
IRROTATIONAL
STEADY
MOTIONS
OF
AN
IDEAL
INCOMPRESSIBLE
FLUID
.
193
4.2.1
THE
GOVERNING
EQUATIONS
OF
PLANAR
FLOWS
.
193
4.2.2
THE
POTENTIAL
FLOW
PAST
THE
CYLINDER
.
202
CONTENTS
VII
4.2.3
THE
METHOD
OF
CONFORMAL
MAPPINGS
.
208
4.2.4
THE
PROBLEM
OF
THE
FLOW
AROUND
A
SLENDER
PROFILE
.
219
4.3
AXISYMMETRIC
AND
THREE-DIMENSIONAL
POTENTIAL
IDEAL
INCOMPRESSIBLE
FLUID
FLOWS
.
223
4.3.1
AXIALLY
SYMMETRIC
FLOWS
.
223
4.3.2
THE
METHOD
OF
SOURCES
AND
SINKS
.
231
4.3.3
THE
PROGRAM
PROG4-5.NB
.
233
4.3.4
THE
TRANSVERSE
FLOW
AROUND
THE
BODY
OF
REVOLUTION:
THE
PROGRAM
PROG4-6.NB
.
235
4.4
NONSTATIONARY
MOTION
OF
A
SOLID
IN
THE
FLUID
.
242
4.4.1
FORMULATION
OF
A
PROBLEM
ON
NONSTATIONARY
BODY
MOTION
IN
IDEAL
FLUID
.
242
4.4.2
THE
HYDRODYNAMIC
REACTIONS
AT
THE
BODY
MOTION
.
244
4.4.3
EQUATIONS
OF
SOLID
MOTION
IN
A
FLUID
UNDER
THE
ACTION
OF
GIVEN
FORCES
.
247
4.5
VORTICAL
MOTIONS
OF
IDEAL
FLUID
.
250
4.5.1
THE
THEOREMS
OF
THOMSON,
LAGRANGE,
AND
HELMHOLTZ
.
250
4.5.2
MOTION
EQUATIONS
IN
FRIEDMANN
'
S
FORM
.
257
4.5.3
THE
BIOT
-SAVART
FORMULAS
AND
THE
STRAIGHT
VORTEX
FILAMENT
.
258
REFERENCES
.
265
5
VISCOUS
FLUID
267
5.1
GENERAL
EQUATIONS
OF
VISCOUS
INCOMPRESSIBLE
FLUID
.
268
5.1.1
THE
NAVIER-STOKES
EQUATIONS
.
268
5.1.2
FORMULATION
OF
PROBLEMS
FOR
THE
SYSTEM
OF
THE
NAVIER-STOKES
EQUATIONS
.
275
5.2
VISCOUS
FLUID
FLOWS
AT
SMALL
REYNOLDS
NUMBERS
.
276
5.2.1
EXACT
SOLUTIONS
OF
THE
SYSTEM
OF
EQUATIONS
FOR
A
VISCOUS
FLUID
.
277
5.2.2
VISCOUS
FLUID
MOTION
BETWEEN
TWO
ROTATING
COAXIAL
CYLINDERS
.
280
5.2.3
THE
VISCOUS
INCOMPRESSIBLE
FLUID
FLOW
AROUND
A
SPHERE
AT
SMALL
REYNOLDS
NUMBERS
.
282
5.3
VISCOUS
FLUID
FLOWS
AT
LARGE
REYNOLDS
NUMBERS
.
287
5.3.1
PRANDTL
'
S
THEORY
OF
BOUNDARY
LAYERS
.
288
5.3.2
BOUNDARY
LAYER
OF
A
FLAT
PLATE
.
293
5.4
TURBULENT
FLUID
FLOWS
.
298
5.4.1
BASIC
PROPERTIES
OF
TURBULENT
FLOWS
.
298
5.4.2
LAMINAR
FLOW
STABILITY
AND
TRANSITION
TO
TURBULENCE
.
300
VIII
CONTENTS
5.4.3
TURBULENT
FLUID
FLOW
.
302
REFERENCES
.
309
6
GAS
DYNAMICS
311
6.1
ONE-DIMENSIONAL
STATIONARY
GAS
FLOWS
.
311
6.1.1
GOVERNING
EQUATIONS
FOR
QUASI-ONE-DIMENSIONAL
GAS
FLOW
.
311
6.1.2
GAS
MOTION
IN
A
VARIABLE
SECTION
DUCT:
ELEMENTARY
THEORY
OF
THE
LAVAL
NOZZLE
.
313
6.1.3
PLANAR
SHOCK
WAVE
IN
IDEAL
GAS
.
321
6.1.4
SHOCK
WAVE
STRUCTURE
IN
GAS
.
329
6.2
NONSTATIONARY
ONE-DIMENSIONAL
FLOWS
OF
IDEAL
GAS
.
334
6.2.1
PLANAR
ISENTROPIC
WAVES
.
334
6.2.2
GRADIENT
CATASTROPHE
AND
SHOCK
WAVE
FORMATION
.
342
6.3
PLANAR
IRROTATIONAL
IDEAL
GAS
MOTION
(LINEAR
APPROXIMATION)
.
346
6.3.1
GOVERNING
EQUATIONS
AND
THEIR
LINEARIZATION
.
.
.
346
6.3.2
THE
PROBLEM
OF
THE
FLOW
AROUND
A
SLENDER
PROFILE
.
348
6.4
PLANAR
IRROTATIONAL
STATIONARY
IDEAL
GAS
FLOW
(GENERAL
CASE)
.
354
6.4.1
CHARACTERISTICS
OF
STATIONARY
IRROTATIONAL
FLOWS
OF
IDEAL
GAS,
SIMPLE
WAVE:
THE
PRANDTL-MEYER
FLOW
.
355
6.4.2
CHAPLYGIN
'
S
EQUATIONS
AND
METHOD
.
366
6.4.3
OBLIQUE
SHOCK
WAVES
.
377
6.4.4
INTERFERENCE
OF
STATIONARY
SHOCK
WAVES
.
382
6.5
THE
FUNDAMENTALS
OF
THE
GASDYNAMIC
DESIGN
TECHNOLOGY
.
386
6.5.1
THE
BASIC
ALGORITHM
.
387
6.5.2
THE
SUPERPOSITION
PROCEDURE
.
391
6.5.3
THE
COMPLEMENT
PROCEDURE
.
395
REFERENCES
.
399
7
MULTIPHASE
MEDIA
401
7.1
MATHEMATICAL
MODELS
OF
MULTIPHASE
MEDIA
.
403
7.1.1
GENERAL
EQUATIONS
OF
THE
MECHANICS
OF
MULTIPHASE
MEDIA
.
403
7.1.2
EQUATIONS
OF
A
TWO-PHASE
MEDIUM
OF
THE
TYPE
OF
GAS-SOLID
PARTICLES
.
407
7.1.3
EQUATIONS
OF
A
BICOMPONENT
MEDIUM
OF
GAS
MIXTURE
TYPE
.
415
CONTENTS
IX
7.2
CORRECTNESS
OF
THE
CAUCHY
PROBLEM:
RELATIONS
AT
DISCONTINUITIES
IN
MULTIPHASE
MEDIA
.
417
7.2.1
THE
CHARACTERISTICS
OF
A
SYSTEM
OF
EQUATIONS
FOR
GAS-PARTICLE
MIXTURES
AND
CORRECTNESS
OF
THE
CAUCHY
PROBLEM
.
417
7.2.2
JUMP
RELATIONS
.
431
7.3
QUASI-ONE-DIMENSIONAL
FLOWS
OF
A
GAS-PARTICLE
MIXTURE
IN
LAVAL
NOZZLES
.
442
7.3.1
THE
EQUATIONS
OF
THE
QUASI-ONE-DIMENSIONAL
FLOW
OF
A
GAS-PARTICLE
MIXTURE
.
442
7.3.2
THE
FLOW
OF
A
GAS-PARTICLE
MIXTURE
IN
THE
LAVAL
NOZZLE
WITH
SMALL
VELOCITY
AND
TEMPERATURE
LAGS
OF
PARTICLES
.
447
7.4
THE
CONTINUAL-DISCRETE
MODEL
AND
CAUSTICS
IN
THE
PSEUDOGAS
OF
PARTICLES
.
456
7.4.1
THE
EQUATIONS
OF
THE
CONTINUAL-DISCRETE
MODEL
OF
A
GAS-PARTICLE
MIXTURE
AT
A
SMALL
VOLUME
CONCENTRATION
OF
PARTICLES
.
456
7.4.2
INVESTIGATION
OF
CAUSTICS
IN
THE
PSEUDOGAS
OF
PARTICLES
.
460
7.5
NONSTATIONARY
PROCESSES
IN
GAS-PARTICLE
MIXTURES
.
471
7.5.1
INTERACTION
OF
A
SHOCK
WAVE
WITH
A
CLOUD
OF
PARTICLES
.
471
7.5.2
ACOUSTIC
APPROXIMATION
IN
THE
PROBLEM
OF
SHOCK
WAVE
INTERACTION
WITH
A
PARTICLE
'
S
CLOUD
AT
A
SMALL
VOLUME
CONCENTRATION
.
478
7.6
THE
FLOWS
OF
HETEROGENEOUS
MEDIA
WITHOUT
REGARD
FOR
INERTIAL
EFFECTS
.
486
7.6.1
THE
BROWNIAN
MOTION
OF
PARTICLES
IN
A
FLUID
.
.
.
486
7.6.2
FLUID
FILTRATION
IN
A
POROUS
MEDIUM
.
493
7.7
WAVE
PROCESSES
IN
BUBBLY
LIQUIDS
.
500
7.7.1
EQUATIONS
OF
THE
MOTION
OF
A
BUBBLY
LIQUID
.
500
7.7.2
EQUATIONS
FOR
WEAK
NONLINEAR
DISTURBANCES
IN
BUBBLY
LIQUIDS
.
507
7.7.3
PROGRESSIVE,
WEAK
NONLINEAR
WAVES
IN
BUBBLY
LIQUIDS
.
512
REFERENCES
.
522
APPENDIX
A:
MATHEMATICA
FUNCTIONS
526
APPENDIX
B:
GLOSSARY
OF
PROGRAMS
550
INDEX
565 |
| any_adam_object | 1 |
| author | Kiselev, Sergej P. 1956- Vorožcov, Evgenij V. 1946- Fomin, Vasilij M. 1940- |
| author_GND | (DE-588)121731146 (DE-588)121730611 (DE-588)121731189 |
| author_facet | Kiselev, Sergej P. 1956- Vorožcov, Evgenij V. 1946- Fomin, Vasilij M. 1940- |
| author_role | aut aut aut |
| author_sort | Kiselev, Sergej P. 1956- |
| author_variant | s p k sp spk e v v ev evv v m f vm vmf |
| building | Verbundindex |
| bvnumber | BV013032703 |
| callnumber-first | Q - Science |
| callnumber-label | QA901 |
| callnumber-raw | QA901 |
| callnumber-search | QA901 |
| callnumber-sort | QA 3901 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 4000 |
| classification_tum | MTA 309f |
| ctrlnum | (OCoLC)246113850 (DE-599)BVBBV013032703 |
| dewey-full | 532/.00285/53042 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.00285/53042 |
| dewey-search | 532/.00285/53042 |
| dewey-sort | 3532 3285 553042 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV013032703 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:16:38Z |
| institution | BVB |
| isbn | 3764339950 0817639950 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008878535 |
| oclc_num | 246113850 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-523 DE-634 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-523 DE-634 |
| physical | XIV, 575 S. graph. Darst. 25 cm |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Modeling and simulation in science, engineering and technology |
| spelling | Kiselev, Sergej P. 1956- Verfasser (DE-588)121731146 aut Foundations of fluid mechanics with applications problem solving using Mathematica Sergey P. Kiselev ; Evgenii V. Vorozhtsov ; Vasily M. Fomin Boston ; Basel ; Berlin Birkhäuser 1999 XIV, 575 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Mathematica (Computer file) Strömungsmechanik - Lehrbuch Strömungsmechanik - Mathematica 3.0 Datenverarbeitung Fluid mechanics Fluid mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Mathematica Programm (DE-588)4268208-3 s DE-604 Vorožcov, Evgenij V. 1946- Verfasser (DE-588)121730611 aut Fomin, Vasilij M. 1940- Verfasser (DE-588)121731189 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kiselev, Sergej P. 1956- Vorožcov, Evgenij V. 1946- Fomin, Vasilij M. 1940- Foundations of fluid mechanics with applications problem solving using Mathematica Mathematica (Computer file) Strömungsmechanik - Lehrbuch Strömungsmechanik - Mathematica 3.0 Datenverarbeitung Fluid mechanics Fluid mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4077970-1 |
| title | Foundations of fluid mechanics with applications problem solving using Mathematica |
| title_auth | Foundations of fluid mechanics with applications problem solving using Mathematica |
| title_exact_search | Foundations of fluid mechanics with applications problem solving using Mathematica |
| title_full | Foundations of fluid mechanics with applications problem solving using Mathematica Sergey P. Kiselev ; Evgenii V. Vorozhtsov ; Vasily M. Fomin |
| title_fullStr | Foundations of fluid mechanics with applications problem solving using Mathematica Sergey P. Kiselev ; Evgenii V. Vorozhtsov ; Vasily M. Fomin |
| title_full_unstemmed | Foundations of fluid mechanics with applications problem solving using Mathematica Sergey P. Kiselev ; Evgenii V. Vorozhtsov ; Vasily M. Fomin |
| title_short | Foundations of fluid mechanics with applications |
| title_sort | foundations of fluid mechanics with applications problem solving using mathematica |
| title_sub | problem solving using Mathematica |
| topic | Mathematica (Computer file) Strömungsmechanik - Lehrbuch Strömungsmechanik - Mathematica 3.0 Datenverarbeitung Fluid mechanics Fluid mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Mathematica (Computer file) Strömungsmechanik - Lehrbuch Strömungsmechanik - Mathematica 3.0 Datenverarbeitung Fluid mechanics Fluid mechanics Data processing Mathematica Programm Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878535&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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