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Computer Science
Algorithms
Assembly Language (ASM)
Automatically Execution
Base-indexed Addressing Mode
Basic Structure of Golang Programs
Binary Search
Bit Accuracy
Boolean Function
Boolean Logic
Boolean Satisfiability Problem (SAT)
Bubble Sort
C Programing Language
Church–Turing Thesis
Circuits (Computer Science)
Combinational Circuits
Complexity Classes
Computability
Computational Abstraction
Computational Complexity
Computational Connectivity
Computational Effectiveness
Computational Modularity
Computational Thinking
Computational Universality
Computer Memory
Computer Network
Computer Network Topology
Computer Science
Data Representation
Decision Problem
Divide-and-conquer Algorithm
Flip-flop
Full Adder
Fundamental Theorem of Software Engineering
Gödel's Incompleteness Theorem
Golang
Golang Basic Types and Operators
Indirection
Instruction Pipeline
Instruction Set
Introduction to Computer Science
Knuth's Definition of Algorithm
Linux Permission
Linux References
Logic Gate
Master Theorem
Mathematical Logic
Memory Address
Multiplication Algorithm
Naming and Namespace
P Versus NP Problem
Pointer
Predicate Logic
Print Format
Protocol Stack
Quick Sort
Ripple-carry Adder
RSA Encryption
Seamless Transition
Sequential Circuits
Serial Adder
Software Stack on a von Neumann Computer
Space Complexity
Stable Marriage Problem
Ternary Search
Time Complexity
Turing Machine
Unicode
UTF-8
von Neumann Architecture
Machine Learning
Activation Functions
Bandit Slippery Walk (BSW) Environment
Bandit Walk (BW) Environment
Batch Normalization
Computer Vision
Convolutional Neural Networks (CNNs)
Cross Entropy Loss
Deep Learning
Denoising Diffusion Probabilistic Models (DDPM)
Dynamic Programming
Epsilon-Greedy Algorithm
ERM Learning
Frozen Lake (FL) Environment
Gird World (GW) Environment
Global Pooling
Gradient Ascent
Gradient Descent
Guidance in Diffusion Models
Hands-on Reinforcement Learning
He Initialization
Introduction to Reinforcement Learning
Layer Normalization
Logistic Regression
Long Short-Term Memory (LSTM)
Loss Functions
Machine Learning
Markov Decision Process, MDP
Markov Property
Multi-armed Bandit
Multilayer Perceptrons
Non-maximum Suppression
Object Detection
Occupancy Measure
OpenAI Gym toolkit
PAC learning model
Rectified Linear Unit (ReLU)
Recurrent Neural Networks (RNNs)
Reinforcement Learning
Review DDPM
Semantic Segmentation
Sigmoid Function
Softmax
Stable Activations and Gradients in Deep Learning
Stochastic Differential Equation (SDE)
Stochastic Gradient Descent (SGD)
Temporal Difference, TD
Thompson Sampling Algorithm
Understanding Machine Learning - From Theory to Algorithms
Upper Confidence Bound Algorithm, UCB
Variational Auto-Encoder (VAE)
Word Embedding
Xavier Initialization
Mathematics
23 Fall Analysis Notes
Abelian Group
Abstraction
Adjugate Matrix
Affine Transformation
Analytical Geometry in Space
Basis and Dimension
Bayes' Theorem
Bernoulli and Binomial Distributions
Bessel Inequality
Beta Distribution
Bilinear Form
Binomial Coefficients and Identities
Bipartite Graphs
Bounded Set
Cardinality of Sets
Cartesian Products
Catalan Numbers
Category
Category Theory
Cayley-Hamilton Theorem
Central Limit Theorem
Characteristic of a Ring
Characteristic Polynomial
Chi-Squared Distribution
Chinese Remainder Theorem (CRT)
Circulant Matrix
Compact Space
Complex Numbers
Conditional Expectation
Conditional Extremum
Conditional Probability
Consistency and Asymptotic Normality
Continuous Function
Continuous Random Variables
Continuous-Time Fourier Transform
Convolution
Convolution (Continuous)
Convolution (Discrete)
Convolution Algebra
Coordinate Transformation
Counting
Covariance and Correlation
Cover (Topology)
Curve Integral
Cyclic Subspace
Derive Fourier Transform from Fourier Series
Diagonal Matrix
Diagonalization
Differential of Mappings
Differential of Multivariable Functions
Dirac Comb
Dirac Delta Function
Discrete Mathematics
Discrete Mathematics Midterm
Discrete-Time Fourier Transform
Distributions of Random Variables
Division Ring
Dual Space
Eigenvectors and Characteristic Polynomial
Elementary Divisors
Equivalence Relation
Euclidean Space
Euler and Hamilton Paths
Euler Integral
Euler's Formula
Euler's Theorem
Euler's Totient Function
Evidence Lower Bound (ELBO)
Exgcd - Extended Euclidean Algorithm
Exponential Distribution
Extremum of Multivariable Functions
F-distribution
Fermat's Little Theorem
Field
Fourier Series
Fourier Series (Real)
Fourier Transform
Function Series
Fundamental Theorem of Symmetric Polynomials
Gamma Distribution
Gauss's Divergence Theorem
Gauss's Lemma and Eisenstein's Irreducibility Criterion
Gaussian Integral
General Definition of Probability
General Linear Group
General Linear Position
Generalized Eigenvectors and Eigenspaces
Generalized Permutations and Combinations
Generating Functions
Generating Permutations and Combinations
Geometric and Hypergeometric Distributions
Graph
Graph Coloring
Graph Connectivity
Graph Isomorphism
Graph Theory
Group
Group Theory
Hamilton Quaternion
Hermitian Conjugate
Hoeffding's Inequality
Householder Transformation and Matrix
Hypothesis Test
Implicit Function
Improper Integrals
Inclusion-Exclusion
Indexed Family
Indicator Function
Indicator Random Variables
Injective, Surjective and Bijective
Integral Domain
Integrals with Parameters
Interval Estimation
Invariant Subspace
Inversion
Jensen's Inequality
Joint Distributions
Jordan Canonical Form
Jordan Canonical Form Life Saver
Kronecker Delta
Kullback–Leibler Divergence
Law of Large Numbers
Law of the Unconscious Statistician (LOTUS)
Least Squares Method
Lie Algebra
Lie Group
Likelihood Function
Limit of Multivariable Functions
Linear Algebra
Linear Algebra 23 Fall Final
Linear Algebra 24 Spring Final
Linear Algebra 24 Spring Midterm
Linear Isomorphism
Linear Map
Linear Map on Linear Independent Vectors
Linear Operator
Linear Space
Logic and Proofs
Logic Equivalences
Mathematical Analysis
Mathematical Analysis 23 Fall Final
Mathematical Analysis 24 Spring Final
Mathematical Analysis 24 Spring Midterm
Mathematical Expectation
Mathematical Induction
Mathematics
Matrix Determinant
Matrix Exponential
Matrix Inverse
Matrix Minor
Matrix Rank
Matrix Representation of Linear Map
Matrix Trace
Maximum a Posteriori Probability (MAP)
Maximum Likelihood Estimation (MLE)
Methods of Proving Theorems
Metric Space
Minimal Polynomial
Modular Arithmetic
Modular Inverse
Monoid
Multinomial Distribution
Multiple Integral
Multisets
Multivariate Polynomial Ring
Nash Equilibrium
Nested Interval Theorem
Neyman-Pearson Lemma
Normal Distribution (Gaussian Distribution)
Normal Operator and Normal Matrix
Number Theory
Orthogonal Canonical Forms
Orthogonal Group
Parameters Estimation
Parseval's Theorem
Partially Ordered Set
Pearson's chi-squared Test
Permutation
Planar Graphs
Planar Point Set
Point Estimation
Poisson Distribution
Polynomial Series
Power Series
Power Sets
Predicates and Quantifiers
Prime Element
Primitive Roots and Discrete Logarithms
Probability Theory
Probability Theory Final
Probability Theory Midterm
Projection
Propositional Logic
Quadratic Forms
Quotient Space
Random Variables
Real Quadratic Forms
Relations (Mathematics)
Ring
Rules of Inference
Set
Shortest-Path Problems
Skew-symmetric Bilinear Form and Sympletic Plane
Smooth Function
Smooth Manifold
Solving Linear Recurrence Relations
Special Linear Group
Special Orthogonal Group
Special Unitary Group
Spectral Decomposition
Standard Error
Stationary Point
Statistics
Stirling's Formula
Stokes' Curl Theorem
Student's t-distribution
Subsequence
Sufficient and Complete Statistics
Surface Integral
Survival Function
Sylvester Inequality
Symmetric Group
Symplectic Group
Table Method for Integration by Parts
Taylor Series of Multivariable Functions
The Basics of Counting
The Pigeonhole Principle
Topological Space
Transformations of Random Variables
Tricks on Vectors
Tweedie's Formula
Unbiasedness and Efficiency
Uniform Distributions
Uniformly Minimum Variance Unbiased Estimate, UMVUE
Unimodality
Unique Factorization Domain, UFD
Unitary Group
Variance
Variational Inference
Zero-One Matrix (0-1 Matrix)
Physics
AC Power
Amplitude-splitting Interferometer
Angular Magnification
Blackbody Radiation
Boltzmann Distribution
Boundary Condition
Conductors and Dielectrics in Electric Fields
Crystal Polarization Optics
Depth of Field, DOF
Diffraction of Light
Electrodynamics
Electromagnetic Induction
Electromagnetic Waves and Energy Flux Density
Electrostatic Field
Entropy
Equation of State
Equipartition Theorem
Foundations of Applied Optics
Fourier Optics
Fourier Transform in Optics
Fraunhofer Diffraction
Free Energy
Fresnel Diffraction
Fresnel Equations
Grating
Hydromechanics
Imagery
Interference of Waves
Introduction to Geometrical Optics
Introduction to Molecular Dynamics Theory
Introduction to Optics
Introduction to Photometry
Introduction to Thermodynamics
Laser
Laws of Thermodynamics
Light Absorption
Light Dispersion
Liquid
Magnetic Circuit
Magnetic Fields in Matter
Maxwell Distribution of Speed
Maxwell Relationship
Mean Free Path
Mechanics
Multi-beam Interference
Numerical Aperture
Optical Information
Optical Systems
Optics
Optics Final Review
Optics Midterm Review
Optics Midterm Test
Phase Transition
Physics
Polarization
Processes of Ideal Gases
Radiometry
Representation of Electromagnetic Waves
Resonant Circuit and Quality Factor Q
Response Function
Rigid Body
Scattering of Light
Special Relativity
Standard State
Static Magnetic Field
Steady Current
Temperature and Equilibrium State
The First Law of Thermodynamics
The Second Law of Thermodynamics
The Third Law of Thermodynamics
Thermodynamic Temperature Scale
Thermodynamics
Thermodynamics Final
Thermodynamics Midterm Review
Three-phase Circuit
Transport Process of Gases
Vacuum Level
Van der Waals Equation of State
Vibrations and Waves
Wavefront-splitting Interferometer
Project Notes
How to Draw UCAS via Fourier Series
Researches
Papers
A ConvNet for the 2020s
An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale
Asymmetric Non-local Neural Networks for Semantic Segmentation
Attention Is All You Need
BEiT: BERT Pre-Training of Image Transformers
BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding
BiSeNet V2: Bilateral Network with Guided Aggregation for Real-time Semantic Segmentation
BiSeNet: Bilateral Segmentation Network for Real-time Semantic Segmentation
CCNet: Criss-Cross Attention for Semantic Segmentation
Classifier-Free Diffusion Guidance
Context Encoding for Semantic Segmentation
Deep High-Resolution Representation Learning for Visual Recognition
DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs
Denoising Diffusion Implicit Models
Diffusion Models Beat GANs on Image Synthesis
Dual Attention Network for Scene Segmentation
Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation
End-to-End Object Detection with Transformers
Fast R-CNN
Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks
Feature Pyramid Networks for Object Detection
Focal Loss for Dense Object Detection
Fully Convolutional Networks for Semantic Segmentation
GCNet: Non-local Networks Meet Squeeze-Excitation Networks and Beyond
Generative Adversarial Networks
GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models
Hierarchical Text-Conditional Image Generation with CLIP Latents
High-Resolution Image Synthesis with Latent Diffusion Models
ICNet for Real-Time Semantic Segmentation on High-Resolution Images
Learning Transferable Visual Models From Natural Language Supervision
Mask R-CNN
Masked Autoencoders Are Scalable Vision Learners
Masked-attention Mask Transformer for Universal Image Segmentation
Neural Discrete Representation Learning
Non-local Neural Networks
OneFormer: One Transformer to Rule Universal Image Segmentation
Per-Pixel Classification is Not All You Need for Semantic Segmentation
Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding
PointRend: Image Segmentation as Rendering
Progressive Distillation for Fast Sampling of Diffusion Models
PSANet: Point-wise Spatial Attention Network for Scene Parsing
Pyramid Scene Parsing Network
R-FCN: Object Detection via Region-based Fully Convolutional Networks
RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation
Rethinking Atrous Convolution for Semantic Image Segmentation
Rich feature hierarchies for accurate object detection and semantic segmentation
SAM 2: Segment Anything in Images and Videos
Scalable Diffusion Models with Transformers
SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers
Segment Anything
Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation
Segmenter: Transformer for Semantic Segmentation
Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition
SSD: Single Shot MultiBox Detector
Swin Transformer: Hierarchical Vision Transformer using Shifted Windows
Training Region-based Object Detectors with Online Hard Example Mining
U-Net: Convolutional Networks for Biomedical Image Segmentation
Vision Transformers for Dense Prediction
YOLO9000: Better, Faster, Stronger
YOLOv3: An Incremental Improvement
You Only Look Once: Unified, Real-Time Object Detection
Research Index
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Nested Interval Theorem
Nested Interval Theorem
区间套
一串
区间套
是实数中的一串区间
I
n
使得对于每一个
n
都有
I
n
+
1
是
I
n
的子集.
区间套定理
关于区间套的主要问题在于探讨所有区间
I
n
的交集（记作
J
）的性状.
Graph View
Table of Contents
区间套
区间套定理
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Mathematical Analysis
Polynomial Series