Contents of vault
- 1D representation of the C₃ᵥ point group
- A group has exactly one identity element
- A metric space is a topological space
- Abelian group
- About the diagonal time component in Lorentz transformation matrices
- Abrasion of particles in granular materials summary
- Absolute convergence implies convergence in a Banach space
- Absolute convergence
- Acceleration of a particle
- Accumulation point
- Accuracy of the kernel approximation of functions
- Addition of angular momenta
- Addition of spin-½ operators
- Affine space
- Algebra of endomorphisms of a vector space
- Algebra over a field
- Algebraically closed field
- Algorithm for finding the regular representation of a group
- An isomorphism maps a zero vector to a zero vector
- Angular momentum of a particle
- Angular momentum operator
- Angular velocity of a particle
- Approximating the shear zone in split bottom granular material simulations using accurate function fitting
- Approximating the shear zone in split bottom granular material simulations using grid approximation
- Approximating the shear zone in split bottom granular material simulations using particle approximation
- Approximating the shear zone in split bottom granular material simulations using simple function fitting
- Arc length
- Attenuation coefficient
- Attenuation of scattering caused by thermal motion
- Avoiding allocations in Rust using the
take method
- Axioms of quantum mechanics
- Banach space
- Basis for a topology
- Basis of a subspace can be extended to a basis of the vector space
- Basis of a vector space
- Basis of crystal
- Basis of direct sum vector space
- Basis of operator
- Bijection
- Binary relation
- Binomial coefficients
- Binomial theorem
- Bloch electron
- Bloch's theorem
- Born rule
- Bosons and fermions
- Boundary of a subset in a metric space
- Boundary of a subset in a topological space
- Boundary point in a metric space
- Bounded linear map
- Bounded set
- Bragg condition
- Bravais lattice
- Brillouin zone
- Building LIGGGHTS
- Building VTK
- Calculating line or path integrals
- Calculating the areas of triangles on a mesh
- Canonical coordinates
- Canonical momentum
- Cartesian coordinate system
- Cartesian product
- Cauchy sequence
- Cauchy–Schwarz inequality
- Cayley's theorem
- Central element of a group
- Central space
- Changing natural variables
- Character of a representation
- Characteristic of a field
- Charge distribution
- Classical bit
- Closed ball on a metric space
- Closed physical system
- Closed set of a topology
- Closed set
- Closure of a subset in a metric space
- Closure of a subset in a topological space
- Commissar definition
- Commutator of operators
- Commutator of position and momentum operators
- Commuting matrices
- Commuting operators have a common set of eigenvectors
- Compact set in Euclidean space
- Compact support
- Comparing the time direction of timelike four-vectors
- Comparison of cosets and conjugacy classes
- Comparison of group action and ring action
- Complement of a set
- Complete metric space
- Complete orthonormal set
- Complete set of operators
- Completeness of irreducible representation matrix elements
- Complex refractive index
- Conjugacy class
- Conjugate equivalent
- Consequences of the grand orthogonality theorem
- Conservation of energy in conservative fields
- Conservation theorem for the angular momentum of a single particle
- Conservation theorem for the kinetic momentum of a single particle
- Conservative force field
- Conservative vector field
- Conserved quantity in quantum mechanics
- Continuity equation for the probability density function in quantum mechanics
- Continuous function
- Continuous mapping
- Continuous mappings in terms of open sets
- Convergence and divergence
- Convergence in a topological space
- Convergence of an infinite series in a normed space
- Convergence of sequences in metric spaces
- Convex function
- Convex hull
- Convex set
- Coordinate rotations
- Coordinate vector
- Coordinates of a vector
- Coset
- Cosets as equivalence classes
- Coulomb's law
- Countable set
- Cross product
- Crystal
- Curl
- De Broglie wavelength
- De Morgan laws
- Debye model
- Decomposable representation
- Default trait in Rust
- Degenerate eigenstates of irreducible representations
- Degenerate eigenvalue
- Degenerate state
- Degree of polynomial
- Degrees of freedom
- Dense set in a topological space
- Dense set
- Derivative of trigonometric functions
- Derivative
- Determinant
- Determining angle distribution in shear zones in granular material simulations
- Determining the shear zone of split bottom sheared granular materials from simulation data
- Dictionary form of verbs in German
- Differences between phentermine resin and salt
- Differentiability classes
- Differential equation
- Dimension of vector space
- Dirac delta function
- Dirac picture
- Direct product of group representations
- Direct product of groups
- Direct sum of group representations
- Direct sum of matrices
- Direct sum of vector spaces
- Direction of forces in conservative force fields
- Discount factor
- Discrete topology
- Discussion of the multiplicative identity in rings
- Disjoint sets
- Displaying triangle meshes using plotly
- Divergence of r̂ over r²
- Divergence of sequences in metric spaces
- Divergence theorem
- Divergence
- Dot product
- Double-slit experiment
- Dual basis is a basis of the dual space
- Drawing triangle meshes in TikZ
- Dual space
- Dual basis
- Edge of a polygon
- Ehrenfest theorem
- Eigenspace
- Eigenvalue
- Eigenvalues of Hermitian operators are real
- Eigenvalues of angular momentum operators
- Eigenvector
- Eigenvectors of Hermitian operators are orthogonal
- Elastic scattering on crystals
- Electric field
- Ellipsoid
- Empty set
- Endomorphism of a vector space
- Enums in Rust
- Equation of motion from the potential energy
- Equilibrium point
- Equipotential surfaces
- Equivalence class
- Equivalence relation
- Equivalent representations
- Equivalent sets
- Euclidean space
- Euler angles to rotation matrix in the (3,1,3) convention
- Euler angles
- Even function
- Event in a sample space
- Every convergent sequence in a metric space is a Cauchy sequence
- Every element of a group has exactly one inverse
- Every reducible unitary representation is fully reducible
- Examples of group action
- Examples of metric spaces
- Examples of superquadrics
- Execution order in functional languages
- Execution order in imperative languages
- Expectation value in quantum mechanics
- Expectation value of velocity of Bloch electrons
- Exponentiation
- Extension field
- Factorial
- Feminine nouns in German
- Fermat's principle
- Faithful representation
- Fibonacci sequence
- Field
- Finite set
- Finite-dimensional vector space
- Flowchart for identifying point groups
- First countable topology
- Flux quantization in type-I superconductors
- For a given subgroup, each coset is represented by one of its elements
- Force
- Formula when at least two events are true out of three
- Fourier transform
- Frame of reference
- Fully reducible representation
- Function space
- Functional programming
- Fundamental theorem of algebra
- GCGS system of units
- Galileo's principle of relativity
- Gamma function
- Gaussian beam
- Gaussian function
- Gaussian integral
- General form of the Schrödinger equation for one particle in 1D
- General form of the Schrödinger equation for one particle in any dimension
- General linear group
- Generating uniform sphere meshes
- Generator of a vector space
- Geometrical optics
- Geometric multiplicity of an eigenvalue
- Gradient in spherical coordinates
- Gradient theorem
- Gradient
- Grammatical gender in German
- Grand orthogonality theorem
- Granular material simulations of January 2022
- Granular material
- Gravitational constant
- Gravitational force between two point masses
- Gravitational force by a mass distribution
- Gravitational vector field
- Group action
- Group automorphism
- Group conjugation
- Group endomorphism
- Group homomorphism
- Group isomorphism
- Hamiltonian mechanics
- Group
- Hamiltonian of ideal gas
- Hamiltonian operator
- Harmonic approximation of lattice vibrations
- Hamiltonian
- Hartree-Fock approximation
- Hausdorff expansion
- Hausdorff topological space
- Heaviside-Lorentz system of units
- Heisenberg picture
- Helium atom in quantum mechanics
- Helmholtz equation
- Helmholtz's theorem
- Hermitian matrix
- Hermitian adjoint
- Homogeneous function
- Hilbert space
- Homonym nouns in German
- Huygens-Fresnel principle
- Hyperbolic cosine
- Hyperbolic sine
- Hyperbolic tangent
- I-indexed family
- Ideal gas is normal system
- Ideal gas
- Identical particles
- Identity matrix
- Image of a function
- Imperative programming
- Improper rotation matrix
- Inertial frame of reference
- Infinite set
- Infinite-dimensional vector space
- Injective function
- Inner product space
- Inner product
- Install Alacritty terminfo to ssh host
- Integer power of a group element
- Integral arctan √x+1
- Integral ln x+2
- Integral x arctan x
- Integration by parts
- Interior of a set in a metric space
- Interior of a subset in a topological space
- Interior point of a set in a metric space
- International System of Units
- Intersection of eigenspaces
- Intersection of sets
- Intersection of subspaces is a subspace
- Invariant subspace
- Inverse of the product of two elements of a monoid
- Inverse of vector space isomorphism is also linear
- Irreducible representation
- Isolated point on a topology
- Isomorphism is an equivalence relation between vector spaces
- Kernel approximation of a function
- Kernel approximation of derivatives
- Kernel of a group homomorphism
- Kernel of a linear map
- Kinetic energy of a particle
- Kinetic momentum
- Kronecker delta
- Kronecker product
- LIGGGHTS
- Lagrange's theorem
- Laplace's demon
- Laplacian
- Lattice constant
- Lattice plane
- Lattice vibrations
- Left and right identities of associative operations are the same
- Levi-Civita symbol
- Lie group
- Lightcone in Minkowski space
- Lightlike vector
- Lightray
- Limit
- Line segment
- Linear combination
- Linear combinations stay in subspace
- Linear functional
- Linear map
- Linear span
- Linear subspace
- Linearly dependent
- Linearly independent
- Liouville's theorem
- Lorentz transformation
- Lorentz transformations form a group
- Lorentz transformations leave the metric invariant
- Maclaurin series
- Macroscopic system
- Macrostate
- Mapping a sphere mesh into a superquadric
- MarbleRun documentation
- Maschke's theorem
- Masculine nouns in German
- Matrix inverse
- Matrix multiplication
- Matrix
- Maturity in finance
- Maxwell's equations
- Metric space
- Metric
- Microscopic system
- Miller index
- Microstate
- Minkowski spacetime
- Minkowski metric
- Momentum operator
- Minor of matrix
- Monoid
- Motivation for change of bases in Minkowski space time
- Mulliken symbols
- Multiple of eigenvector is also an eigenvector
- Multiplication table of finite groups
- Nabla operator
- Natural homomorphism of group theory
- Names and values in imperative and functional programming languages
- Neighborhood
- Neumann's principle
- Neuter nouns in German
- Newton's first law of motion
- Newton's laws of motion
- Newton's principle of determinacy
- Newton's second law of motion
- Newton's third law of motion
- Newtonian mechanics
- Non-orthochronous Lorentz transformation
- Norm of inner product spaces
- Norm
- Normal subgroup
- Normal system
- Normal topological space
- Normalization of the wave function
- Normed space
- Noun plurals in German
- Nowhere dense set in a topological space
- Nullity
- Number of states of 3D ideal gas
- Number of states of a classical system
- OSM Node
- OSM Relation
- OSM Tag
- OSM Way
- Object-oriented programming
- Observable
- Odd and even functions
- Odd function
- Open Database License
- Open ball on a metric space
- Open neighborhood of a point
- Open neighborhood of a subset
- Open rectangles
- Open set of a topology
- Open set
- OpenStreetMap
- Opening LIGGGTHS output VTK files in Python
- Opening VTK output in ParaView from LIGGGHTS
- Operations on group subsets
- Operator boundedness and domain in quantum mechanics
- Operator norm
- Operators in quantum mechanics
- Operators with a common set of eigenvectors commute
- Optical path difference
- Optical path length
- Orbit-stabilizer theorem
- Orbit
- Order of a group element
- Order of a group
- Orthochronous Lorentz transformation
- Orthogonal complement
- Orthogonal group
- Orthogonal matrix
- Orthogonal space
- Orthogonal vectors
- Orthonormal vectors
- Outer product
- Outputting VTK files in LIGGGHTS
- Palindrome number
- ParaView
- Paraxial approximation
- Particle approximation in SPH
- Pauli matrices
- Penetration depth
- Permittivity
- Personal pronouns in German
- Phase space in Hamiltonian mechanics
- Phentermine
- Phonon density of states
- Photon energy
- Photon momentum
- Photon transport simulation using the Monte Carlo method in Rust
- Planck constant
- Plane in geometry
- Point charge
- Point group
- Poisson bracket
- Poisson brackets of the canonical coordinates
- Polar coordinate system
- Polycrystal
- Polygon
- Polynomial
- Position of a particle
- Position operator
- Possible rotational symmetries of a lattice
- Postulates of the double-slit experiment
- Potential energy
- Power set
- Poynting vector
- Preimage
- Present tense in German
- Present value of a series of fixed payments
- Present value
- Primitive cell
- Primitive translation vectors
- Probability current density
- Probability density for the position in quantum mechanics
- Processing the angles and angular momentum in sheared granular material simulations
- Product rule with cross products
- Product rule
- Product topology
- Project Euler
- Projection into irreducible subspaces
- Proper rotation matrix
- Proper subset
- Pythagorean triple
- Quantum mechanical time derivative
- Quantum mechanics
- Quantum state
- Quotient group
- Rank of a linear map
- Rank of matrix
- Reciprocal lattice
- Reducible representation
- Refraction
- Refractive index
- Regular expression
- Regular representation of the C₃ᵥ point group
- Regular representation of the cyclic point group of order 3
- Regular representation of the inversion point group
- Regular representation
- Relative permittivity
- Relative topology
- Remove link references generated by Foam
- Repetition in functional languages
- Repetition in imperative languages
- Replacing LaTeX custom norms to avoid new command
- Representation
- Right-hand rule
- Ring
- Robust ellipse detection written in Rust
- Root of a function
- Rotation matrix to Euler angles in the (3,1,3) convention
- Saddle point equilibrium
- Rotation matrix
- Sample space
- Scalar triple product
- Scattering on polycrystals
- Scattering on random alloys
- Schrödinger equation in 1D
- Schrödinger equation
- Schrödinger picture
- Schur's lemmas
- Second countable topology
- Separable space
- Separate arrays convention for storing triangle meshes
- Sequence in a metric space
- Sequence
- Series
- Set difference
- Setting the default plot size in matplotlib
- Shadowing in Rust
- Shear zone
- Simple cubic lattice
- Simple rate for 1 year
- Simple rate
- Smarter projection into irreducible subspaces
- Smoothed particle hydrodynamics
- Smoothing kernel
- Smoothness
- Solenoidal vector field
- Spacelike vector
- Special linear group
- Special orthogonal group
- Speed of light
- Sphere mesh from Fibonacci lattice
- Sphere mesh from icosahedron subdivision
- Sphere mesh from octahedron subdivision
- Sphere mesh from spherical coordinates
- Sphere on a metric space
- Spherical coordinate system
- Spin
- Spin-½
- Spot in finance
- Square matrix
- Square-integrable functions
- Stabilizer subgroup
- Stable equilibrium
- Standard basis
- State density
- Status quo
- Stern-Gerlach experiment
- Stirling's approximation
- Stokes' theorem
- Subfield
- Subgroup
- Subset
- Subspace dimension is smaller
- Superquadrics
- Subspace of a metric space
- Surjective function
- Symmetric group
- Symmetric matrix
- Systems of units in electrodynamics
- Symmetry of a crystal
- Taylor series
- Tenor of contract
- Tensor product of linear maps
- Tensor product of vector spaces
- Tetragonal lattice
- The additive identity of a field is a multiplicative annihilator
- The debugging process
- The experimental discovery of the internal angular momentum
- The homomorphism theorem of group theory
- The normal Zeeman effect
- The order of an element in a finite group divides the order of the group
- The product of two nonzero field elements is nonzero
- The rank theorem
- The regular representation contains every irreducible representation
- The sequence space 𝓁ᵖ
- The spring model of lattice vibrations
- Thermodynamic equilibrium
- TikZ figure describing the uniplanar Jeffery motion
- Thermodynamic limit
- TikZ figure showing collision points on a single ellipsoid
- TikZ figure showing two colliding ellipsoids
- TikZ
- Time average of an observable
- Time dependence of expectation value in quantum mechanics
- Time derivatives with Poisson brackets
- Time evolution pictures in quantum mechanics
- Time to maturity
- Time-independent Schrödinger equation
- Timelike vector
- Topological space
- Topology
- Torque is the rate of change of angular momentum
- Torque
- Trace equals sum of eigenvalues
- Trace of matrix
- Transformation of eigenvectors
- Transpose
- Triangle subdivision for triangle meshes
- Triangle
- Trivial group
- Trivial representation
- Trivial topology
- Type-I superconductor
- Uncertainty
- Unbounded operator
- Union of sets
- Uniplanar Jeffery motion
- Unit cell
- Unit of an algebra
- Unitary matrix
- Unitary representation
- Unstable equilibrium
- Units of an associative algebra form a group
- Using stdc++.h with clang on macOS
- VTK
- Vacuum permittivity
- Variational method
- Vector potential
- Vector space automorphism
- Vector space isomorphism
- Vector space
- Vector spaces of same dimension are isomorphic
- Velocity of a particle
- Velocity operator in quantum mechanics
- Vertex
- Visualizing point distributions on a triangle mesh surface
- Volume and surface of an n-dimensional sphere
- Wave function collapse
- Wave function
- Wave optics
- Wavelength
- Wavenumber
- Wigner-Seitz cell
- Work done on a particle
- Work theorem
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- 2024-06-14