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In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and
Constrained_geometry_complex
Coordination complex of a metal and cyclopentadienyl groups
Cyclopentadienyl complexes Decamethylcobaltocene, a powerful reducing agent derived from "Cp*". A constrained geometry organotitanium complex An ansa-metallocene
Cyclopentadienyl_complex
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real
Complex_polytope
Property of a mathematical space
coordinates that are needed for defining the position of a point that is constrained to be on the object. For example, the dimension of a point is zero; the
Dimension
Form of an object
other object properties, such as color, texture, or material type. In geometry, shape excludes information about the object's position, size, orientation
Shape
that facilitate the incorporation of these comonomers, e.g., constrained geometry complexes. Comonomers are often employed to improve the plastification
Comonomer
Parameter in coordination chemistry
hydrogenation reactions also implement phosphine-mediated catalysts. Constrained geometry complex Josiphos ligands van Leeuwen, P. W. N. M.; Kamer, P. C. J.; Reek
Bite_angle
Chemical reaction where catalyst and reactants are in the same phase of matter
almost exclusively conducted with soluble rhodium- and cobalt-containing complexes. A related carbonylation is the conversion of alcohols to carboxylic acids
Homogeneous_catalysis
Topics referred to by the same term
granule cell Clebsch-Gordan coefficient in representation theory Constrained geometry complex, a kind of catalyst Color-glass condensate, a type of matter
CGC
Branch of computer science
Computational geometry is a branch of computer science devoted to the study of algorithms that can be stated in terms of geometry. Some purely geometrical
Computational_geometry
Mathematical set with some added structure
"congruent") constrained by a number of axioms. Analytic geometry made great progress and succeeded in replacing theorems of classical geometry with computations
Space_(mathematics)
Infinitely detailed mathematical structure
models appear more complex H tree – Right-angled fractal canopy Infinite regress – Philosophical problem Lacunarity – Term in geometry and fractal analysis
Fractal
Point where a mathematical object behaves irregularly
singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory. In
Singularity_(mathematics)
Mathematical idealization of the trace left by a moving point
aspects which were not directly accessible to the geometry of the time, to do with singular points and complex solutions. Since the nineteenth century, curve
Curve
Ethylene polymerization catalyst
innovations include ansa-metallocenes, Cs-symmetric fluorenyl-Cp ligands, constrained geometry catalysts, Some Kaminsky-inspired catalysts use of chiral metallocenes
Kaminsky_catalyst
One-dimensional complex manifold
analytic or algebraic geometry. The corresponding statement for higher-dimensional objects is false, i.e. there are compact complex 2-manifolds which are
Riemann_surface
American organometallic chemist
cocatalysts, and new polymers. His discovery of constrained geometry catalysts (see Constrained geometry complex), single-site catalysts for olefin polymerization
James_C._Stevens
Video game templates
Brush-based modeling is extensively used in constructive solid geometry, a technique that builds complex surfaces by combining simpler ones using Boolean operations
Brush_(video_games)
Subdivision of a planar object into triangles
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object
Triangulation_(geometry)
Triangulation method
In computational geometry, a Delaunay triangulation or Delone triangulation of a set of points in the plane subdivides their convex hull into triangles
Delaunay_triangulation
Study of organic compounds containing metal(s)
heterogeneously via Ziegler–Natta catalysis and homogeneously, e.g., via constrained geometry catalysts. Most processes involving hydrogen rely on metal-based
Organometallic_chemistry
Field of geometry closely arranging circles on a plane
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and
Circle_packing
Chemical compound
high thermal stability to the resulting complexes. This stability is in part ascribed to the constrained geometry of the pincer, which inhibits cyclometallation
Transition metal pincer complex
Transition_metal_pincer_complex
Regular tiling of the Euclidean plane
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane consisting of four squares around every vertex
Square_tiling
3D computer graphics program
animation between multiple curves, and animate the weight. Objects can be constrained to animate with other objects in many ways — including look at, orientation
Autodesk_3ds_Max
Generalization of a quadrant to any dimension
In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions. In
Orthant
Concept in geometry and topology
while the real projective plane is not. The complex line at infinity was much used in nineteenth century geometry. In fact one of the most applied tricks
Line_at_infinity
Numerical optimization process
using the duality of the SOS polynomial program and a relaxation for constrained polynomial optimization using positive-semidefinite matrices, see the
Sum-of-squares_optimization
Chemical compound
families of highly active catalysts. Work in this area led to constrained geometry complexes, which are not bent metallocenes, but exhibit related structural
Bent_metallocene
Regular tiling of the plane
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where
Triangular_tiling
Upcoming video game
RTX Mega Geometry is included to accelerate the building of bounding volume hierarchies (BVHs) for ray tracing against complex Nanite geometry. Lower-resolution
Gears_of_War:_E-Day
Matrix equal to its conjugate-transpose
mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose. That is, if
Hermitian_matrix
Number of atoms in a ligand that bond to the central atom of a coordination complex
tetradentate trien can bind via three geometries. Tripodal tetradentate ligands, e.g. tris(2-aminoethyl)amine, are more constrained, and on octahedra leave two
Denticity
Motion of a certain space that preserves at least one point
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe
Rotation_(mathematics)
Problem of finding the optimal shape under given conditions
parametrization of the geometry is defined. Such parametrization is very important in CAE field where goal functions are usually complex functions evaluated
Shape_optimization
Geometric concept of a 2D space with "points at infinity" adjoined
model of elliptic geometry. The complex projective plane CP2 arises when K is taken to be the complex numbers, C. It is a closed complex 2-manifold, and
Projective_plane
Basic question in geometry and topology
. Many classical theorems in Riemannian geometry show that manifolds with positive curvature are constrained, most dramatically the 1/4-pinched sphere
Classification_of_manifolds
U.S. lecture series in science and math
"The Interior-Point Revolution in Constrained Optimization" 1999 Chuu-Lian Terng, Northeastern University, "Geometry and Visualization of Surfaces" 2000
AWM/MAA_Falconer_Lecture
American physicist
field theories. Unlike standard chiral multiplets, which are constrained by Kähler geometry, twisted multiplets allow for the formulation of sigma models
Sylvester_James_Gates
Flat-sided three-dimensional shape
polygons. Orthogonal polyhedra are used in computational geometry, where their constrained structure has enabled advances in problems unsolved for arbitrary
Polyhedron
Number, approximately 3.14
of geometry as a power series, or as the solution of a differential equation. In a similar spirit, π can be defined using properties of the complex exponential
Pi
German polymath and scholar (1777–1855)
contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability. Gauss was director of the Göttingen Observatory
Carl_Friedrich_Gauss
Number of values in the final calculation of a statistic that are free to vary
regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Trapezohedron with eight faces
In geometry, a tetragonal trapezohedron, or deltohedron, is the second in an infinite series of trapezohedra, which are dual to the antiprisms. It has
Tetragonal_trapezohedron
Four-dimensional analogues of the regular polyhedra in three dimensions
existence of a regular 4-polytope { p , q , r } {\displaystyle \{p,q,r\}} is constrained by the existence of the regular polyhedra { p , q } , { q , r } {\displaystyle
Regular_4-polytope
3D computer graphics software
creating and modifying curves objects was added to Geometry Nodes; in the same release, the Geometry Nodes workflow was completely redesigned with fields
Blender_(software)
Open-source computer-aided design software
solids can then be constrained to ensure that the designed model's dimensions meet necessary requirements. Plane and solid geometry Replace hand-solved
SolveSpace
Method in geometry for representing a polygon by a topological skeleton
In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton. It is similar in some ways to the medial axis but differs
Straight_skeleton
Structural feature in geology
and thus develops a sinusoidal geometry. In a stratigraphic sequence, beds are geometrically and physically constrained by their neighbours. Similarity
Chevron_(geology)
Metric on a smooth statistical manifold
In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a
Fisher_information_metric
Regular tiling of a two-dimensional space
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex
Hexagonal_tiling
Straight path on a curved surface or a Riemannian manifold
topic of sub-Riemannian geometry deals with the paths that objects may take when they are not free, and their movement is constrained in various ways. This
Geodesic
Theory of subatomic structure
arbitrary Lagrangian. In string theory, the possibilities are much more constrained: by the 1990s, physicists had argued that there were only five consistent
String_theory
Field of chemistry
reaction and/or enhanced selectivity . Because enzymes are structurally complex and difficult to modify, supramolecular catalysts offer a potentially simpler
Supramolecular_catalysis
Computer-based generation of digital images
algorithm. Complex models can be built by combining simpler objects, in the paradigms of object-oriented programming. In Euclidean geometry, a translation
2D_computer_graphics
Statistical shape analysis technique
Procrustes Superimposition (PS) of an object with respect to another. a constrained orthogonal Procrustes problem, subject to det(R) = 1 (where R is an orthogonal
Procrustes_analysis
English mathematician, mathematical physicist (born 1931)
4-dimensional complex space with the metric signature (2,2). In 1971, he discovered spin networks, which later came to form the geometry of spacetime in
Roger_Penrose
5-dimensional hypercube
In five-dimensional geometry, a 5-cube (or penteract) is a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and
5-cube
Branch of mathematics
calculus. Calculus provides a generalization of concepts from elementary geometry and algebra. For example, instead of describing the slope of a straight
Calculus
a complex coordinated elastic buckling of the strut members. The resulting geometry is similar to a Jahn–Teller distortion of an octahedral complex with
Reversibly assembled cellular composite materials
Reversibly_assembled_cellular_composite_materials
efficient manner. Those parts of the geometry that are regular can have structured grids and those that are complex can have unstructured grids. These grids
Types_of_mesh
groups approach to noncommutative geometry one starts with the algebra and a choice of first order calculus but constrained by covariance under a quantum
Quantum_differential_calculus
Computing joint values of a kinematic chain from a known end position
a constrained system of rigid bodies, or kinematic chain. The kinematic equations of a robot can be used to define the loop equations of a complex articulated
Inverse_kinematics
Choi, Youngsoo (2011). "PDE-constrained Optimization and Beyond" (PDF). Heinkenschloss, Matthias (2008). "PDE Constrained Optimization" (PDF). SIAM Conference
List of named differential equations
List_of_named_differential_equations
Visible regularity of form found in the natural world
that develops on vertebrate brains is caused by a physical process of constrained expansion dependent on two geometric parameters: relative tangential
Patterns_in_nature
Martian volcano, highest point on Mars
Sulci). Spreading also occurred to the southeast; however, it was more constrained in that direction by the Tharsis rise, which presented a higher-friction
Olympus_Mons
Framework of superstring theory
relationship between geometry and the commutative algebra of coordinates is the starting point for much of modern geometry. Noncommutative geometry is a branch
M-theory
Geological feature
of 40 km (25 mi). In some sections, the MHT features a flat-ramp-flat geometry due to the presence of a midcrustal ramp beneath the High Himalayas before
Main_Himalayan_Thrust
Method for satisfying the Newtonian motion of a rigid body which consists of mass points
reach a certain level of convergence does rise as molecular geometry becomes more complex. To reach 64 bit computer accuracy (a relative tolerance of
Constraint (computational chemistry)
Constraint_(computational_chemistry)
membranes that are constrained to be planar, and cylindrically shaped proteins will be less stable in membranes that are constrained to have high curvature
Membrane_curvature
Technique to solve partial differential equations
(PINNs) to solve nonlinear partial differential equations on arbitrary complex-geometry domains. The XPINNs further push the boundaries of both PINNs and conservative
Physics-informed neural networks
Physics-informed_neural_networks
Several equations of degree 1 to be solved simultaneously
relatively complex system. Very often, and in this article, the coefficients and solutions of the equations are constrained to be real or complex numbers
System_of_linear_equations
Ion or molecule bound to a metal atom
functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or
Ligand
Various molecular structures formed only by rotation about single bonds
in polytetrafluoroethylene changes the stereochemistry from the zigzag geometry to that of a helix due to electrostatic repulsion of the fluorine atoms
Rotamer
Adjusting the complexity of a 3D model representation to save storage and computation
when distant or moving fast. Although most of the time LOD is applied to geometry detail only, the basic concept can be generalized. Recently, LOD techniques
Level of detail (computer graphics)
Level_of_detail_(computer_graphics)
Arrangement of points on a sphere
minimum electrostatic potential energy configuration of N electrons constrained to the surface of a unit sphere that repel each other with a force given
Thomson_problem
Arrangement of spheres within a space
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical
Sphere_packing
Math/physics concept
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving
Connection_form
Designing products to facilitate 3D printing
alloy compositions, process parameters and structural geometries. However, always a constrained subset of the design space (design subspace) is under
Design for additive manufacturing
Design_for_additive_manufacturing
Process of achieving a goal by overcoming obstacles
Cunningham, A. E. (1991). "Reading as constrained reasoning". In Sternberg, R. J.; Frensch, P. A. (eds.). Complex problem solving: Principles and mechanisms
Problem_solving
Sums of sets of vectors are nearly convex
The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. The lemma may be intuitively
Shapley–Folkman_lemma
Area of mathematics
generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference
Dynamical_systems_theory
Method of using light to measure a 3D object
resulting distortions of the projected pattern reveals the object's solid geometry through triangulation, enabling the creation of a 3D model of the object
Structured_light
Computational problem
object from the source to destination. The term is used in computational geometry, computer animation, robotics and computer games. For example, consider
Motion_planning
Angle in physical organic chemistry
Bürgi–Dunitz angle (BD angle) is one of two angles that fully define the geometry of "attack" (approach via collision) of a nucleophile on a trigonal unsaturated
Bürgi–Dunitz_angle
Concept in geometry
τ , υ , α {\displaystyle \rho ,\sigma ,\tau ,\upsilon ,\alpha } are constrained by ρ + σ + τ + υ + 2 α = n , {\displaystyle \rho +\sigma +\tau +\upsilon
Angles_between_flats
Hypothetical approach to quantum gravity with emergent spacetime
between the lattice of spacetime events and geometry. Consequently, the Lagrangian of CDT is constrained by the initial assumptions to the extent that
Causal dynamical triangulation
Causal_dynamical_triangulation
Application of Clifford algebra
of classical mechanics to be constructed. The plane-based approach to geometry may be contrasted with the approach that uses the cross product, in which
Plane-based_geometric_algebra
In complex geometry, an Inoue surface is any of several complex surfaces of Kodaira class VII. They are named after Masahisa Inoue, who gave the first
Inoue_surface
Mathematics of convex functions and sets
applications to optimization, functional analysis, variational analysis, convex geometry, economics, and related fields. A set is convex if it contains every line
Convex_analysis
Theory in supersymmetric gauge theory
special Kähler geometry on the moduli space of vacua in Seiberg–Witten theory can be identified with the geometry of the base of complex completely integrable
Seiberg–Witten_theory
Mechanical engineering tolerancing (ISO)
develop a common language to specify macro geometry (size, form, orientation, location) and micro-geometry (surface texture) of products or parts of products
Geometrical Product Specification and Verification
Geometrical_Product_Specification_and_Verification
Style of English Gothic architecture
elaborate whole, with traceried windows, ornate surface decoration, complex geometry and intricate vaulting. The style saw the introduction of new architectural
Decorated_Gothic
Mathematical function having a characteristic S-shaped curve or sigmoid curve
distribution function of a Cauchy distribution. A sigmoid function is constrained by a pair of horizontal asymptotes as x → ± ∞ {\displaystyle x\rightarrow
Sigmoid_function
Systematic representation of the surface of a sphere or ellipsoid onto a plane
several fields of pure mathematics, including differential geometry, projective geometry, and manifolds. However, the term map projection refers specifically
Map_projection
Structures that connect circuit elements in an integrated circuit
divided by width). The width, spacing, AR, and ultimately, pitch, are constrained in their minimum and maximum values by design rules that ensure the interconnect
Interconnect (integrated circuits)
Interconnect_(integrated_circuits)
Local supercluster home to the Milky Way
PMID 25186900. S2CID 205240232. Klypin, Anatoly; et al. (October 2003). "Constrained Simulations of the Real Universe: The Local Supercluster". The Astrophysical
Virgo_Supercluster
Least-weight tree connecting graph vertices
telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would
Minimum_spanning_tree
Navigation and surveillance technique
utilize uninvertible measurement equations — Enables, e.g., use of complex problem geometries such as an ellipsoidal earth's surface. Can utilize measurements
Pseudo-range_multilateration
Assembly of systems connected to manage forces and movement
forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are
Linkage_(mechanical)
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CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
CONSTRAINED GEOMETRY-COMPLEX
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