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Type of functions, in mathematical analysis
In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear
Holonomic_function
Differential equation that is linear with respect to the unknown function
called holonomic functions. This class of functions is stable under sums, products, differentiation, integration, and contains many usual functions and special
Linear_differential_equation
Topics referred to by the same term
and time t {\displaystyle t\,\!} Holonomic module in the theory of D-modules Holonomic function, a smooth function that is a solution of a linear homogeneous
Holonomic
Formal power series
have a holonomic generating function are equivalent. Holonomic functions are closed under the Hadamard product operation ⊙ on generating functions. The
Generating_function
Computation of an antiderivatives
special functions such as Airy function, error function, Bessel functions, and all hypergeometric functions. A fundamental property of holonomic functions is
Symbolic_integration
Pattern defining an infinite sequence of numbers
elementary functions and special functions have a Taylor series whose coefficients satisfy such a recurrence relation (see holonomic function). Solving
Recurrence_relation
In mathematics and mathematical physics, a coordinate basis or holonomic basis for a differentiable manifold M is a set of basis vector fields {e1, .
Holonomic_basis
Type of constraints for mechanical systems
is a continuous function. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but
Holonomic_constraints
Thermodynamic quantity
process function X may be either holonomic or non-holonomic. For a holonomic process function, an auxiliary state function (or integrating factor) λ may
Process_function
Type of functional equation (mathematics)
These lead to special functions, which may be defined as solutions of linear differential equations (see Holonomic function). A non-linear differential
Differential_equation
Module over a sheaf of differential operators
operators. The strongest results are obtained for over-determined systems (holonomic systems), and on the characteristic variety cut out by the symbols, which
D-module
Differential equation containing derivatives with respect to only one variable
special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function). When
Ordinary differential equation
Ordinary_differential_equation
Quantum interpretation of neuroscience
Holonomic brain theory is a branch of neuroscience investigating the idea that consciousness is formed by quantum effects in or between brain cells. Holonomic
Holonomic_brain_theory
System configuration relative to another
their derivatives. Constraints of this type are known as non-holonomic. First-order non-holonomic constraints have the form g ( q , q ˙ , t ) = 0 , {\displaystyle
Generalized_coordinates
Method to solve constrained optimization problems
kinematic chains. They are also useful for imposing non-holonomic constraints. Given a set of holonomic constraint equations f j ( q , t ) = 0 {\displaystyle
Lagrange_multiplier
Dutch mathematician and computer scientist
de Bruijn prize van der Hoeven, Joris (1999). "Fast evaluation of holonomic functions". Theoretical Computer Science. 210: 199–215. doi:10.1016/S0304-3975(98)00102-9
Joris_van_der_Hoeven
Finite or infinite ordered list of elements
For most holonomic sequences, there is no explicit formula for expressing a n {\displaystyle a_{n}} as a function of n. Nevertheless, holonomic sequences
Sequence
Partial differential equation technique
differential relation, as this is a function in one variable. A holonomic solution to this relation is a function whose derivative is nowhere vanishing
Homotopy_principle
Q-analog of the ordinary derivative
Rajković, P. M.; Marinković, S. D. (July 2007). "Properties of q-holonomic functions". Journal of Difference Equations and Applications. 13 (7): 621–638
Q-derivative
{\displaystyle \mathbb {R} ^{1+n}} . A Pfaffian constraint is integrable iff it is holonomic. Otherwise, it is non-integrable or nonholonomic. A Pfaffian constraint
Pfaffian_constraint
Fringe hypothesis
explain the function of the brain within the framework of quantum field theory with implications on consciousness. Karl Pribram's holonomic brain theory
Quantum_mind
Polynomial related to differential operators
{\displaystyle b(s)} . Its existence can be shown using the notion of holonomic D-modules. Kashiwara (1976) proved that all roots of the Bernstein–Sato
Bernstein–Sato_polynomial
American-Brazilian-British scientist (1917–1992)
Pribram, Bohm was involved in the early development of the holonomic model of the functioning of the brain, a model for human cognition that is drastically
David_Bohm
Austrian neuroscientist (1919–2015)
the fields of cognitive psychology, cognitive science, neuropsychology, holonomic brain theory, and holographic consciousness. He was a professor at Georgetown
Karl_H._Pribram
German mathematician and computer scientist
on computer algebra, particularly on holonomic functions, with applications to combinatorics, special functions, knot theory, and physics. Together with
Christoph_Koutschan
Japanese mathematician (1928–2023)
known for founding the fields of algebraic analysis, hyperfunctions, and holonomic quantum fields. He was a professor at the Research Institute for Mathematical
Mikio_Sato
Differential calculus on function spaces
principle (or the action principle) states that the motion of a conservative holonomic (integrable constraints) mechanical system is such that the action integral
Calculus_of_variations
Formulation of classical mechanics
energy. One or more of the particles may each be subject to one or more holonomic constraints; such a constraint is described by an equation of the form
Lagrangian_mechanics
Concept in mathematics
(for regular holonomic D-modules): there is a functor DR called the de Rham functor, that is an equivalence from the category of holonomic D-modules on
Riemann–Hilbert correspondence
Riemann–Hilbert_correspondence
Japanese mathematician (born 1951)
integrable systems and their correlation functions, and his work with Mikio Sato and Tetsuji Miwa on holonomic quantum fields and isomonodromic deformation
Michio_Jimbo
Concept in differential geometry
About the second part: "It is remarkably hard to find the etymology of holonomic (or holonomy) on the web. I found the following (thanks to John Conway
Holonomy
Topics referred to by the same term
Primary constraint, secondary constraint, etc. in Hamiltonian mechanics Holonomic constraints, also called integrable constraints, (depending on time and
Constraint
Manifold upon which it is possible to perform calculus
{\displaystyle \partial _{k}={\frac {\partial }{\partial x_{k}}}} define a holonomic basis of the tangent space. The collection of tangent spaces at all points
Differentiable_manifold
Math/physics concept
_{i}{}^{k}(\mathbf {e} ).} For simplicity, suppose that the frame e is holonomic, so that dθi = 0. Then, employing now the summation convention on repeated
Connection_form
Study of the brain related to specific psychological processes and behaviors
primate brains. This work would influence the establishment of Pribram's Holonomic brain theory. Lashley also proposed that a portion of a functional area
Neuropsychology
Blueprint for intelligent agents
Tang, Y.; Rasmussen, D. (29 November 2012). "A Large-Scale Model of the Functioning Brain". Science. 338 (6111): 1202–1205. Bibcode:2012Sci...338.1202E.
Cognitive_architecture
Mathematical model of the time dependence of a point in space
for a phase space A Euclidean Space such as configuration space due to holonomic constraints A discrete structure like a graph. A set of diffeomorphisms
Dynamical_system
Disorder of consciousness
longitudinally characterize neuroplasticity in both brain structure and function following severe injuries. Utilizing DTI and other neuroimaging techniques
Minimally_conscious_state
Awareness of internal and external existence
consciousness. Notable theories falling into this category include the holonomic brain theory of Karl Pribram and David Bohm, and the Orch-OR theory formulated
Consciousness
Theory of a quantum origin of consciousness
Copenhagen interpretation Electromagnetic theories of consciousness Holonomic brain theory Many-minds interpretation Penrose interpretation Quantum
Orchestrated objective reduction
Orchestrated_objective_reduction
Computational problem
algorithms have been developed to handle variants of this basic problem. Holonomic Manipulator arms (with dynamics) Nonholonomic Drones Cars Unicycles Planes
Motion_planning
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
integrability of a system's constraint equations determines whether the system is holonomic or nonholonomic. In microeconomic theory, Frobenius' theorem can be used
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Infinite sequence of numbers satisfying a linear equation
D-finite or holonomic sequence is a natural generalization where the coefficients of the recurrence are allowed to be polynomial functions of n {\displaystyle
Constant-recursive_sequence
Quantum algebra version of the Knizhnik–Zamolodchikov equations
Frenkel, I. B.; Reshetikhin, N. Yu. (1992), "Quantum affine algebras and holonomic difference equations", Comm. Math. Phys., 146 (1): 1–60, Bibcode:1992CMaPh
Quantum_KZ_equations
Physical law for entropy and heat
quantity of energy quasi-statically transferred as heat is a holonomic process function, in other words, δ Q = T d S {\displaystyle \delta Q=TdS} . Though
Second_law_of_thermodynamics
Array of numbers describing a metric connection
with the Levi-Civita connection, by working in coordinate frames (called holonomic coordinates) where the torsion vanishes. For example, in Euclidean spaces
Christoffel_symbols
Mechanical system whose constraints are independent of time
{\sqrt {(x-x_{0}\cos \omega t)^{2}+y^{2}}}-L=0.} Lagrangian mechanics Holonomic system Nonholonomic system Rheonomous Mass matrix Goldstein, Herbert (1980)
Scleronomous
Symmetries in a gravitational theory
viewpoint, general covariant transformations are treated as particular (holonomic) reference frame transformations in general relativity. In mathematics
General covariant transformations
General_covariant_transformations
Branch of physics describing the motion of objects without considering forces
sliders and cam joints that define the construction of the system, called holonomic constraints, and (ii) constraints imposed on the velocity of the system
Kinematics
constructing the algebra of virtual and actual displacements when the holonomic constraints are given by a differential form and he introduced the important
Nikolay_Gur'yevich_Chetaev
Tensor index notation for tensor-based calculations
Differential form Differential geometry Exterior algebra Hodge star operator Holonomic basis Matrix calculus Metric tensor Multilinear algebra Multilinear subspace
Ricci_calculus
Search algorithm
incremental distance Δq from qnear in the direction of qrand. (According to in holonomic problems, this should be omitted and qrand used instead of qnew.) It has
Rapidly_exploring_random_tree
Integrable rigid bodies in classical mechanics
which are in fact the only integrable cases when the system is subject to holonomic constraints. In addition to the energy, each of these tops involves two
Lagrange, Euler, and Kovalevskaya tops
Lagrange,_Euler,_and_Kovalevskaya_tops
Approach to general relativity
0} . Thus, it is sometimes said that tetrad coordinates provide a non-holonomic basis. For example, the Riemann curvature tensor is defined for general
Tetrad_formalism
Formulation of physics
like scalar equations of the form Constraints of the form (5) are called holonomic and scleronomic. In terms of the radius-vector r {\displaystyle \displaystyle
Newtonian_dynamics
Actions in the present are dependent on previous decisions or experiences
dynamics, and diminishing returns. In physics and mathematics, a non-holonomic system is a physical system in which the states depend on the physical
Path_dependence
Numerical integration algorithm
through a sheet of cloth without forming a sound wave. Another way to solve holonomic constraints is to use constraint algorithms. One way of reacting to collisions
Verlet_integration
mechanical engineer. Gheorghe Vrânceanu: discovered the notion of non-holonomic spaces. Traian Vuia: built the first fixed wing aircraft that could take
List of Romanian inventors and discoverers
List_of_Romanian_inventors_and_discoverers
Japanese mathematician (born 1949)
his collaborators published a long series of works (Holonomic quantum fields, Studies on holonomic quantum fields) in the Proc. Japan Academy and Pub.
Tetsuji_Miwa
Type of system in classical mechanics
formulations to be mathematically equivalent. If a physical system is both a holonomic system and a monogenic system, then it is possible to derive Lagrange's
Monogenic_system
Attempt to extend Yang–Mills theory to gravity
\vartheta _{a}=\vartheta _{a}^{\lambda }\partial _{\lambda }} is a non-holonomic frame. For instance, if K {\displaystyle K} is the Cartan connection,
Gauge_gravitation_theory
Construction in differential topology
The Cartan distribution is spanned by all tangent planes to graphs of holonomic sections; that is, sections of the form jrφ for φ a section of π. The
Jet_bundle
principle of least constraint. The Udwadia–Kalaba method applies to both holonomic constraints and nonholonomic constraints, as long as they are linear with
Udwadia–Kalaba_formulation
Russian-American mathematician
Jean-Luc; Kashiwara, Masaki (October 1981). "Kazhdan-Lusztig conjecture and holonomic systems". Inventiones Mathematicae. 64 (3). Springer-Verlag: 387–410.
Alexander_Beilinson
Aspect of computational chemistry
interactions. In these models, bonding interactions are implicitly treated by holonomic constraints. The electrostatic interaction is modeled using Coulomb's
Water_model
Episode of Neon Genesis Evangelion
linked the Dummy System, based on Rei's personality, to Karl H. Pribram's holonomic brain theory, according to which memory is not an activity limited to
Those women longed for the touch of others' lips, and thus invited their kisses
Those_women_longed_for_the_touch_of_others'_lips,_and_thus_invited_their_kisses
Overview of mechanics based on the least action principle
{q} (t),t)} and this relation holds for all times t, then q are called holonomic constraints. Vector r is explicitly dependent on t in cases when the constraints
Analytical_mechanics
Method for satisfying the Newtonian motion of a rigid body which consists of mass points
enforced using the method of Lagrange multipliers. Given a set of n linear (holonomic) constraints at the time t, σ k ( t ) := ‖ x k α ( t ) − x k β ( t ) ‖
Constraint (computational chemistry)
Constraint_(computational_chemistry)
Theory of gravity
natural basis, associated with local coordinates (U, xμ), i.e., in the holonomic frame ∂μ, the (local) connection coefficients of the Weitzenböck connection
Teleparallelism
On linear differential equations with certain properties
algebraic connections with regular singularities and more generally regular holonomic D-modules or flat algebraic connections with regular singularities on
Hilbert's twenty-first problem
Hilbert's_twenty-first_problem
University American Works on robotics, mechanical system control and non-holonomic constraints. 1945 Hendrik W. Bode Lecture Prize (2011) B. Ross Barmish
List of people in systems and control
List_of_people_in_systems_and_control
Ontological concepts for quantum theory
74–83. Joye, S.R. (2017). The Little Book of Consciousness: Pribram's Holonomic Brain Theory and Bohm's Implicate Order, The Viola Institute, ISBN 978-0-9988785-4-6
Implicate_and_explicate_order
One of six awards by the Wolf Foundation
algebraic analysis, including hyperfunction theory and microfunction theory, holonomic quantum field theory, and a unified theory of soliton equations. John
Wolf_Prize_in_Mathematics
Concept in algebraic geometry
(2007, Lecture 16, Polyhedral Geometry) Iyengar et al. (2007, Lecture 24, Holonomic Rank and Hypergeometric Systems) Brodmann & Sharp (1998, 1.2.2) Brodmann
Local_cohomology
Linear recurrence equation
combinatorics. The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite. From the late 1980s, the first algorithms were
P-recursive_equation
Object in differential geometry
the connection coefficients defining the connection. If the basis is holonomic then the Lie brackets vanish, γ k i j = 0 {\displaystyle \gamma ^{k}{}_{ij}=0}
Torsion_tensor
Quantization method for constrained Hamiltonian systems with second-class constraints
never taken into account. In Lagrangian mechanics, if the system has holonomic constraints, then one generally adds Lagrange multipliers to the Lagrangian
Dirac_bracket
{m^{2}}{2}}A^{2}-{\frac {m^{2}}{2}}\phi ^{2}\right]} . Dirac bracket Holonomic constraint Analysis of flows Ingemar Bengtsson. "Constrained Hamiltonian
First-class_constraint
chip, called "Tangle Lake". Japanese researchers demonstrate universal holonomic quantum gates. An integrated photonic platform for quantum information
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Software
mapping (using an EKF or graph-based method), and a Simulink model of a non-holonomic vehicle. Flying quadrotor robots, and includes a detailed Simulink model
Robotics_Toolbox_for_MATLAB
Holographic principle Holographic sensor Holography Holon (physics) Holonomic basis Holonomic constraints Holstein–Herring method Holstein–Primakoff transformation
Index_of_physics_articles_(H)
Subbundle of the tangent bundle
{\displaystyle \Delta \subseteq TM} is called bracket-generating (or non-holonomic, or it is said to satisfy the Hörmander condition) if taking a finite
Distribution (differential geometry)
Distribution_(differential_geometry)
History of robots History of technology HK-47 HOAP Hod Lipson Hollywood Holonomic Homayoun Seraji Home automation Honda E series Honda P series How I Met
Index_of_robotics_articles
(2013b), "Permutations avoiding 4321 and 3241 have an algebraic generating function", Discrete Mathematics & Theoretical Computer Science 5286, arXiv:1306
Enumerations of specific permutation classes
Enumerations_of_specific_permutation_classes
Landmark textbook in classical mechanics by E. T. Whittaker
nonholonomic systems, up to which point all the systems discussed were holonomic and conservative. Chapter nine discusses action principles, such as the
Analytical Dynamics of Particles and Rigid Bodies
Analytical_Dynamics_of_Particles_and_Rigid_Bodies
monodromy data of a generic Fuchsian system are governed by the integrable holonomic system of partial differential equations which now bear his name: ∂ A
Isomonodromic_deformation
Month in 1919
Born: Karl H. Pribram, Austrian-American medical scientist, developed the holonomic brain theory; in Vienna, Republic of German-Austria (present-day Austria)
February_1919
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, a great functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, an Egyptian functionary.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, the son of the functionary Heknofre.
Biblical
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Male
Egyptian
, a high Egyptian functionary.
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
Boy/Male
Hindu, Indian, Kannada, Tamil, Telugu
Lord Venkateshwara
Biblical
according to variable songs or tunes,
Girl/Female
Christian & English(British/American/Australian)
Variant of Louisa
Girl/Female
Gujarati, Hindu, Indian
Blooming
Boy/Male
Tamil
Male
English
Variant spelling of English Colton, COLTEN means "Cola's settlement."
Boy/Male
Sikh
Gurus service
Boy/Male
Indian
Without Worries
Girl/Female
Hindu
Boy/Male
English Irish Teutonic
Derivative of the Scandinavian god of battle 'Tyr.' Tuesday was named for Tyr.
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
HOLONOMIC FUNCTION
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
pl.
of Functionary
a.
Pertaining to the function of an organ or part, or to the functions in general.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
a.
Of or pertaining to the vessels of animal and vegetable bodies; as, the vascular functions.
a.
Of, pertaining to, or designating, certain secret tribunals which flourished in Germany from the end of the 12th century to the middle of the 16th, usurping many of the functions of the government which were too weak to maintain law and order, and inspiring dread in all who came within their jurisdiction.
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.
v. i.
Alt. of Functionate
a.
Having relation to growth or nutrition; partaking of simple growth and enlargement of the systems of nutrition, apart from the sensorial or distinctively animal functions; vegetal.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
adv.
In a functional manner; as regards normal or appropriate activity.
a.
Destitute of function, or of an appropriate organ. Darwin.
a.
Pertaining to, or connected with, a function or duty; official.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
n.
The doctrine that all the functions of a living organism are due to an unknown vital principle distinct from all chemical and physical forces.
v. t.
To assign to some function or office.
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.