Lec 55: Statement and proof of Open Mapping Theorem
★
★
★
★
☆
4/5
Tuit catalog
Synthesis notes of video analyses, assessed and condensed, in French and English.
49,374 tuit
·
936 channels
·
42 domains
·
Last update: Oct 14, 2026
Agriculture & Food
147
AI — Models & Research
4198
AI — News & Applications
1950
AI & Society
993
Archaeology
133
Arts & Architecture
1387
Astronomy & Cosmology
3582
Biology
2013
Chemistry
332
Climate & Ecology
970
Computing & Cybersecurity
3723
Control & Robotics
348
Earth Sciences & Geography
275
Economics & Finance
3378
Education
711
Energy
1342
Engineering & Technology
3143
Foresight & Science Fiction
344
Geopolitics & Defence
529
History
706
Hobbies & Practical
338
Language & Linguistics
308
Law & Justice
551
Literature & Writing
885
Mathematics
2139
Media & Information
283
Medicine & Health
2926
Neuroscience
416
Paleontology
91
Personal Development
848
Philosophy & Ethics
833
Physics
3304
Politics & Institutions
651
Psychology
567
Religion & Beliefs
240
Science — General & History
1691
Society & Culture
1036
Space Exploration
885
Sports
85
Transport & Mobility
148
Urban Planning & Mobility
84
Video Games
861
VSC
Advice on careers and achieving success
77
TRP
Aerospace and aviation technology
863
PBF
Algebra
251
PBMW
Algebraic geometry
154
PBPD
Algebraic topology
54
UMB
Algorithms and data structures
57
KNBT
Alternative and renewable energy industries
129
THV
Alternative and renewable energy sources and technology
160
MKJD
Alzheimer’s, dementia, Parkinson’s disease and other neurodegenerative diseases
66
QDHA
Ancient Greek and Roman philosophy
48
NHC
Ancient history
31
JBFU
Animals and society
22
TTB
Applied optics
36
NKDS
Archaeological sites
32
NK
Archaeology
43
NKD
Archaeology by period
29
AM
Architecture
32
UYQD
Artificial general intelligence (AGI)
46
UYQ
Artificial intelligence (AI)
1949
LNQH
Artificial intelligence law and regulations
20
VSPM
Assertiveness, motivation, self-esteem and positive mental attitude
331
TTDS
Astronautics
987
PGG
Astronomical observation: observatories, equipment and methods
109
PG
Astronomy, space and time
906
PHVB
Astrophysics
120
PHM
Atomic and molecular physics
73
MKJA
Autism Spectrum Disorder
20
TJFM
Automatic control engineering
70
TRPS
Aviation skills and piloting
22
KFFK
Banking
23
THYB
Battery technology
144
PBTB
Bayesian inference
31
PSB
Biochemistry
303
RNCB
Biodiversity
33
PSAD
Bioethics
35
DNBH
Biography: historical, political and military
81
DNBM
Biography: philosophy and social sciences
20
DNBR
Biography: royalty
25
DNBT
Biography: science, technology and medicine
61
DNBL
Biography: writers
39
PS
Biology, life sciences
23
MQW
Biomedical engineering
21
PHVN
Biophysics
26
TCB
Biotechnology
56
TNK
Building construction and materials
22
KJ
Business and Management
54
KJJ
Business and the environment; sustainable approaches to business
39
KJD
Business innovation
29
KJC
Business strategy
31
PBKA
Calculus
41
PBK
Calculus and mathematical analysis
60
MJD
Cardiovascular medicine
30
JNR
Careers guidance
33
PSAN1
Cellular and molecular neuroscience
21
PSF
Cellular biology (cytology)
121
JPQB
Central
51
PN
Chemistry
27
MJCL2
Chemotherapy
26
JMC
Child, developmental and lifespan psychology
24
AMVD
City and town planning: architectural aspects
29
NHWR3
Civil wars
20
PHD
Classical mechanics
192
RNPG
Climate change
213
RBPC
Climatology and climate modelling
31
MBGR1
Clinical trials
21
UTC
Cloud computing
24
GPJ
Coding theory and cryptology
39
JMR
Cognition and cognitive psychology
122
PSAN5
Cognitive and behavioural neuroscience
237
GTK
Cognitive studies
39
PBV
Combinatorics and graph theory
52
GTC
Communication studies
33
TJK
Communications engineering
35
DSM
Comparative literature
23
LNCH
Competition law
20
PBKD
Complex analysis, complex variables
60
PSAX
Computational biology
88
KNTV
Computer and video game industry
190
UYF
Computer architecture and logic design
111
URH
Computer fraud and hacking
253
UDX
Computer games
592
UGG
Computer games design
230
UYM
Computer modelling and simulation
23
UT
Computer networking and communications
24
UY
Computer science
59
UR
Computer security
690
URJ
Computer viruses, Trojans and worms
29
UYQV
Computer vision
117
PHFC
Condensed matter physics (liquid state and solid state physics)
129
RNKH
Conservation of wildlife and habitats
22
JBGX
Conspiracy theories
49
LNDX
Constitution
31
JPZ
Corruption in politics, government and society
30
PGK
Cosmology and the universe
1003
CBV
Creative writing and creative writing guides
20
JKVF
Criminal investigation and detection
39
GPH
Data science and analysis
36
GTS
Decolonisation of knowledge
48
KCM
Development economics and emerging economies
63
GTP
Development studies
37
PSC
Developmental biology
36
MBNH3
Dietetics and nutrition
25
PBMP
Differential and Riemannian geometry
39
PBKJ
Differential calculus and equations
92
UBJ
Digital and information technologies: social and ethical aspects
987
UB
Digital and Information technology: general topics
33
UXA
Digital Humanities
46
KCVM
Digital or internet economics
37
WNA
Dinosaurs and the prehistoric world: general interest
69
JPSD
Diplomacy
32
JBFM
Disability: social aspects
22
JBCT5
Disinformation and misinformation
71
ATFR
Documentary films
23
RNFD
Drought and water supply
22
PHDT
Dynamics and statics
78
QDHC
East Asian and Indian philosophy
27
PSAF
Ecological science, the Biosphere
35
KCX
Economic and financial crises and disasters
32
KCA
Economic theory and philosophy
35
KC
Economics
21
JN
Education
22
JNDH
Education: examinations and assessment
30
JNK
Educational administration and organization
20
JNV
Educational equipment and technology, computer-aided learning (CAL)
68
JNC
Educational psychology
26
JNF
Educational strategies and policy
21
JPHF
Elections and referenda
34
TRV
Electric vehicles
57
THR
Electrical engineering
58
KNBL
Electrical power generation and distribution industries
266
PHK
Electricity, electromagnetism and magnetism
265
TJFD
Electronic devices and materials
207
TJFC
Electronics: circuits and components
174
PHDB
Elementary mechanics
36
VSPQ
Emotions and emotional intelligence
22
MJG
Endocrinology
24
PHDY
Energy
24
LNCR
Energy and natural resources law
38
THYC
Energy efficiency
56
KNB
Energy industries and utilities
214
RNFY
Energy resources
53
THY
Energy, power generation, distribution and storage
353
TGMB
Engineering thermodynamics
23
TGMF
Engineering: Mechanics of fluids
22
TGMD
Engineering: Mechanics of solids
24
UFL
Enterprise software
53
KJH
Entrepreneurship
129
KCVG
Environmental economics
101
MBNH2
Environmental factors
50
RND
Environmental policy and protocols
192
RNA
Environmentalist thought and ideology
79
MBNS
Epidemiology and Medical statistics
115
SXE
eSports
24
QDTQ
Ethics and moral philosophy
51
PSVP
Ethology and animal behaviour
32
PBMH
Euclidean geometry
43
NHD
European history
24
PSAJ
Evolution
162
PSXE
Evolutionary anthropology
89
UYQE
Expert systems
26
ATFG
Film guides and reviews
101
ATFA
Film history, theory or criticism
41
ATFN
Film: styles and genres
342
KFF
Finance and the finance industry
36
KFFF
Financial technology (fintech)
33
RNFF
Food security and supply
34
PBKF
Functional analysis and transforms
29
PGM
Galaxies and stars
314
UMK
Games development and programming
41
JBSF
Gender studies, gender groups
25
JBSF1
Gender studies: women and girls
83
MKZV
Gene therapy
37
GTZ
General studies and General knowledge
27
UYQF
Generative artificial intelligence
2279
TCBG
Genetic engineering
49
PSAK
Genetics (non-medical)
636
RBG
Geology, geomorphology and the lithosphere
24
PHVG
Geophysics
36
JPSL
Geopolitics
291
THVG
Geothermal energy and power
34
PHDV
Gravity
33
KFFS
Green finance
56
PBG
Groups and group theory
104
MJF
Haematology
20
MBP
Health systems and services
36
JBFN
Health, illness or addiction: social aspects
23
VFMD
Health: Diets and nutrition
21
MJJ
Hepatology
40
JNM
Higher education, tertiary education
228
RBGF
Historical geology and palaeogeology
49
NHAH
Historiography
34
NH
History
38
AGA
History of art
40
UBB
History of Computing, digital and information technologies
49
TBX
History of engineering and technology
26
PBX
History of mathematics
31
NHQ
History of other geographical groupings and regions or specific cultures
25
PDX
History of science
148
KJZ
History of specific companies
24
NHK
History of the Americas
53
NHT
History: specific events and topics
25
JBFD
Housing and homelessness
21
PSX
Human biology
25
JPVH
Human rights, civil rights
39
THD
Hydrogen technologies
56
THVH
Hydropower
22
TTBM
Imaging systems and technology
23
MJCM
Immunology
96
PDR
Impact of science and technology on society
119
AMB
Individual architects and architectural firms
30
AGB
Individual artists, art monographs
33
ATFB
Individual film directors, film-makers
30
PDG
Industrial applications of scientific research and technological innovation
47
MJCJ
Infectious and contagious diseases
54
KNTX
Information technology industries
279
JWD
Information warfare
28
GTV
Institutions and learned societies: general
31
PBKL
Integral calculus and equations
26
JPSN
International institutions
24
JPS
International relations
24
KCLT
International trade and commerce
49
ATN
Internet and digital media: arts and performance
50
UBW
Internet: general works
40
JMHC
Interpersonal communication and skills
23
DNPB
Interviews
38
KFFM
Investment and securities
133
KJMV3
IT and information systems management
40
KCF
Labour
84
PHJL
Laser physics
48
TTBL
Laser technology and holography
22
PSA
Life sciences: general issues
22
DSRC
Literary companions, book reviews and guides
32
DSBB
Literary studies: ancient, classical and medieval
21
DSK
Literary studies: fiction, novelists and prose writers
70
DSC
Literary studies: poetry and poets
50
DSA
Literary theory
28
UYQM
Machine learning
1144
KCB
Macroeconomics
23
KJMB
Management: leadership and motivation
48
PSPM
Marine biology
21
NHTM
Maritime history
32
TGM
Materials science
45
MKCM
Materno-foetal medicine
41
PHU
Mathematical
157
PBCD
Mathematical logic
104
PBWH
Mathematical modelling
51
UYA
Mathematical theory of computation
211
PB
Mathematics
113
MFKH3
Maturation and ageing
60
JBCT
Media studies
26
JBCT1
Media studies: internet, digital media and society
62
JBCT4
Media studies: journalism
84
MBPM
Medical administration and management
20
MBF
Medical and health informatics
57
MFN
Medical genetics
165
MKS
Medical imaging
20
MBGL
Medical laboratory testing and techniques
20
PHVD
Medical physics
20
MBGR
Medical research
53
RBPM
Meteorology
29
PSG
Microbiology (non-medical)
53
JBFH
Migration, immigration and emigration
31
JWK
Military and defence strategy
38
UMS
Mobile and handheld device programming
22
PSD
Molecular biology
166
KCBM
Monetary economics
76
GLZ
Museology and heritage studies
48
TBN
Nanotechnology
25
UYX
Natural computing
827
RNR
Natural disasters
26
UYQL
Natural language and machine translation
143
WN
Nature and the natural world: general interest
47
UTN
Network security
55
UTP
Networking standards and protocols
25
UYQN
Neural networks and fuzzy systems
432
MKJ
Neurology and clinical neurophysiology
55
PSAN
Neurosciences
115
KNTP2
News media and journalism
21
PNRL
Nuclear chemistry, photochemistry and radiation
26
RNQ
Nuclear issues
29
MKR
Nuclear medicine
66
PHN
Nuclear physics
110
THK
Nuclear power and engineering
192
PBH
Number theory
187
PBKS
Numerical analysis
39
MQC
Nursing
20
MQCA
Nursing fundamentals and skills
34
RBKC
Oceanography (seas and oceans)
50
MJCL
Oncology
125
KJSG
Online marketing
27
PHJ
Optical physics
155
PBU
Optimization
29
TTMW
Ordnance, weapons technology
20
PNN
Organic chemistry
65
RBX
Palaeontology
91
MKB
Palliative medicine
33
UYFP
Parallel processing
27
PHP
Particle and high-energy physics
132
GTU
Peace studies and conflict resolution
39
MBNH
Personal and public health
22
VSB
Personal finance
49
KJMV2
Personnel and human resources management
31
KNBP
Petroleum, oil and gas industries
89
MKG
Pharmacology
61
QD
Philosophy
45
JNA
Philosophy and theory of education
29
PBB
Philosophy of mathematics
30
QDTM
Philosophy of mind
72
PDA
Philosophy of science
149
QDTK
Philosophy: epistemology and theory of knowledge
123
QDTL
Philosophy: logic
47
QDTJ
Philosophy: metaphysics and ontology
41
PNR
Physical chemistry
68
PH
Physics
184
PHDF
Physics: Fluid mechanics
51
JMM
Physiological psychology, neuropsychology, biopsychology
25
MFG
Physiology
51
PSTB
Plant biology
30
PHFP
Plasma physics
32
KCP
Political economy
112
JPHL
Political leaders and leadership
41
JPA
Political science and theory
26
JPHV
Political structures
43
JP
Politics and government
64
RNP
Pollution and threats to the environment
32
PDZM
Popular and recreational mathematics
79
WNX
Popular astronomy and space
796
QDXB
Popular philosophy: Meaning of life
26
VSP
Popular psychology
190
PDZ
Popular science
420
JPWG
Pressure groups, protest movements and non-violent action
27
URD
Privacy and data protection
34
PBT
Probability and statistics
241
TDCX
Process engineering technology and techniques
21
TGP
Production and industrial engineering
40
UMX
Programming and scripting languages: general
102
UMA
Programming techniques
34
JMA
Psychological theory, systems, schools and viewpoints
24
JM
Psychology
66
JMQ
Psychology: emotions
27
JMT
Psychology: states of consciousness
35
JMS
Psychology: the self, ego, identity, personality
21
MKGW
Psychopharmacology
37
JPP
Public administration
36
KFFD
Public finance and taxation
43
MBN
Public health and preventive medicine
65
PHQ
Quantum physics (quantum mechanics and quantum field theory)
893
JBFA1
Racism and racial discrimination
29
PBKB
Real analysis, real variables
40
MFGG
Regional physiology
25
PHR
Relativity physics
316
QRAM2
Religion and politics
22
QRAM3
Religion and science
26
DNP
Reportage, journalism or collected columns
69
GPS
Research methods
97
TJFM1
Robotics
278
KJS
Sales and marketing
42
KJMV7
Sales and marketing management
44
UFLS
SAP (Systems, applications and products in databases)
24
FLU
Science fiction: aliens
77
FLW
Science fiction: space exploration
200
FLS
Science fiction: space opera
35
PDK
Science funding and policy
66
PD
Science: general issues
53
PDM
Scientific research
51
NHWR7
Second World War
48
VS
Self-help, personal development and practical advice
25
CFG
Semantics, discourse analysis, stylistics
32
GTD
Semiotics
63
PSAN4
Sensory and motor systems
21
TJKH
Signal processing
34
NHTS
Slavery, enslaved persons and abolition of slavery
28
NHTB
Social and cultural history
69
JBF
Social and ethical issues
33
QDTS
Social and political philosophy
81
JBFX
Social attitudes
20
JBFZ
Social forecasting, future studies
29
RNT
Social impact of environmental issues
41
JMH
Social, group or collective psychology
65
CFB
Sociolinguistics
38
UMZ
Software Engineering
75
UMZT
Software testing and verification
27
THVS
Solar power
183
PGS
Solar system: the Sun and planets
321
TTDX
Space exploration
539
TTD
Space science
278
CBP
Speaking in public: advice and guides
22
DNS
Speeches
40
PHS
Statistical physics
53
PBWL
Stochastics
43
RNU
Sustainability
55
TVF
Sustainable agriculture
22
JNU
Teaching of a specific subject
30
ATJ
Television
41
ATJS
Television: styles and genres
20
ATD
Theatre studies
26
PGC
Theoretical and mathematical astronomy
75
AMA
Theory of architecture
22
ABA
Theory of art
49
PHH
Thermodynamics and heat
32
PGZ
Time (chronology), time systems and standards
46
PBP
Topology
24
RPT
Transport planning and policy
20
RPC
Urban and municipal planning and policy
56
MBNK
Vaccination
28
RBC
Volcanology and seismology
34
PHDS
Wave mechanics (vibration and acoustics)
39
UGB
Web graphics and design
24
UMW
Web programming
71
THVW
Wind power
28
CBW
Writing and editing guides
27
PSV
Zoology and animal sciences
22
Lec 55: OFDM Capacity
★
★
★
★
☆
4/5
Lec 54: Capacity of a Gaussian Channels
★
★
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★
☆
4/5
Lec 53: Capacity of a DMCs
★
★
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★
☆
4/5
Lec 52: Channel Capacity
★
★
★
★
☆
4/5
Lec 51: OFDM
★
★
★
★
☆
4/5
Lec 50: Channel Estimation
★
★
★
★
☆
4/5
Lec 49: MMSE equalization II
★
★
★
★
☆
4/5
Lec 45: Mini-LED Device Fabrication and Applications
★
★
★
★
☆
4/5
Lec 44: Light-Emitting Characteristics of LEDs
★
★
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★
☆
4/5
Lec 43: Fundamentals of LEDs
★
★
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★
☆
4/5
Lec 42: MiniLEDs-Backlight Technology
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★
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★
☆
4/5
Lec 41: Autostereoscopic & Advanced 3D Displays
★
★
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★
☆
4/5
Lec 35: Facial Animation & Deformation
★
★
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★
☆
4/5
Lec 34: Keyframing & Character Animation
★
★
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★
☆
4/5
Lec 33: Animation Principles
★
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★
☆
4/5
Le ZEvent explose, OpenAI inquiète, Méta et Google répliquent, et NVidia épate
ZEvent explodes, OpenAI worries, Meta and Google respond, and Nvidia impresses
★
★
★
☆
☆
3/5
Le piège Copilot : vous payez pour prendre du retard.
The Copilot Trap: You’re Paying to Fall Behind.
★
★
★
★
☆
4/5
Le moment où le métier de développeur a basculé
The moment when the developer profession shifted
★
★
★
★
☆
4/5
Le Grand Debunk de la Santé 1 - Olivier Hertel, idée reçue "Les vaccins provoquent l'autisme"
The Great Health Debunk 1 - Olivier Hertel, common misconception "Vaccines cause autism"
★
★
★
★
☆
4/5
Le Grand Debunk de la Santé 1 - Dr Bruno Raynard, idée reçue "Jeûner permet de soigner le cancer"
The Great Health Debunk 1 - Dr. Bruno Raynard, common myth: "Fasting can cure cancer"
★
★
★
★
☆
4/5
La Mafia del Alcohol - Te esconde la Verdad.
The Alcohol Mafia - Hides the Truth from You.
★
★
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★
☆
4/5
Guide Onimusha Action - 04 - Labo Souterrain - Grand Nue
Onimusha Action Guide - 04 - Underground Lab - Grand Nue
★
★
★
☆
☆
3/5
GPT 6 Astra is a freak
★
★
★
★
☆
4/5
Google vient de lancer son IA de cybersécurité la plus puissante à ce jour
Google has just launched its most powerful cybersecurity AI to date
★
★
★
☆
☆
3/5
Fable 5.1 : Anthropic reprend la première place !
Fable 5.1: Anthropic takes back the top spot!
★
★
★
☆
☆
3/5
ECUACIÓN DIFERENCIAL HOMOGÉNEA | Cambio y = xv paso a paso
HOMOGENEOUS DIFFERENTIAL EQUATION | Substitution y = xv step by step
★
★
★
★
☆
4/5