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Mathematical function
In mathematics, the family of Debye functions is defined by D n ( x ) = n x n ∫ 0 x t n e t − 1 d t . {\displaystyle D_{n}(x)={\frac {n}{x^{n}}}\int _{0}^{x}{\frac
Debye_function
Dutch-American physical chemist (1884–1966)
Peter Joseph William Debye (/dɪˈbaɪ/ dib-EYE; born Petrus Josephus Wilhelmus Debije, Dutch: [ˈpeːtrʏz dəˈbɛiə]; March 24, 1884 – November 2, 1966) was
Peter_Debye
Method in physics
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific
Debye_model
Scientific method to study solutions, gels, and other polymeric systems
the structure can be carried out explicitly and result in a sort of Debye function: S D ( k → ) = 2 ( k R g ) 4 [ ( k R g ) 2 − 1 + e − ( k R g ) 2 ] {\displaystyle
Polymer_scattering
see Debye–Scherrer method Debye–Sears method Debye–Waller factor Debye force Debye frequency, see also Debye model Debye function, see also Debye model
List of things named after Peter Debye
List_of_things_named_after_Peter_Debye
Model describing the departures from ideality in solutions of electrolytes and plasmas
The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes
Debye–Hückel_theory
Function in thermodynamics and statistical physics
partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of the
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Family of solutions to related differential equations
developments and references. Following Debye (1909), the notation ψn, χn is sometimes used instead of Sn, Cn. The Bessel functions have the following asymptotic
Bessel_function
Measure of electrostatic effect and how far it persists
In plasmas and electrolytes, the Debye length λ D {\displaystyle \lambda _{\text{D}}} (Debye radius or Debye–Hückel screening length), is a measure of
Debye_length
Electrically insulating substance able to be polarised by an applied electric field
described in terms of permittivity as a function of frequency, which can, for ideal systems, be described by the Debye equation. On the other hand, the distortion
Dielectric
Special mathematical function
3,\ldots )~.\end{aligned}}} In terms of the incomplete zeta functions or "Debye functions" (Abramowitz & Stegun 1972, § 27.1): Z n ( z ) = 1 ( n − 1 )
Polylogarithm
Damping of electric fields
the Debye or Thomas–Fermi wave vector. Note that this potential has the same form as the Yukawa potential. This screening yields a dielectric function that
Electric-field_screening
Plasma layer with a positive charge
The Debye sheath (also electrostatic sheath) is a layer in a plasma which has a greater density of positive ions, and hence an overall excess positive
Debye_sheath
Concept in crystallography
The Debye–Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering
Debye–Waller_factor
Relaxation model
When α = 0 {\displaystyle \alpha =0} , the Cole-Cole model reduces to the Debye model. When α > 0 {\displaystyle \alpha >0} , the relaxation is stretched
Cole–Cole_equation
Statistical description for the behavior of fermions
Parastatistics Logistic function Sigmoid function The F–D distribution is a type of mathematical function called a logistic function or sigmoid function. Note that
Fermi–Dirac_statistics
Force of attraction or repulsion between molecules and neighboring particles
force Cation–π, σ–π and π–π bonding Van der Waals forces – Keesom force, Debye force, and London dispersion force Cation–cation bonding Salt bridge (protein
Intermolecular_force
Technique in physical chemistry
be neglected (P(θ)→1). Therefore, the Zimm equation is simplified to the Debye equation, as follows: K c Δ R ( θ , c ) = 1 M w + 2 A 2 c {\displaystyle
Static_light_scattering
Generalized version of classical Green's function
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations
Multiscale_Green's_function
Probability distribution
Thompson, D. E. Cox and J. B. Hastings (1987). "Rietveld refinement of Debye-Scherrer synchrotron X-ray data from Al2O3". Journal of Applied Crystallography
Voigt_profile
Mathematical function common in physics
Dishon et al. 1985. Hilfer, J. (2002). "H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems".
Stretched exponential function
Stretched_exponential_function
Norwegian-American physical chemist and theoretical physicist (1903-1976)
Peter Debye was teaching, and confronted Debye, telling him his theory was wrong. He impressed Debye so much that he was invited to become Debye's assistant
Lars_Onsager
Physics of many interacting particles
probability density function is proportional to some function of the ensemble parameters and random variables. Thermodynamic state functions are described by
Statistical_mechanics
Model in electromagnetism
relaxation is an empirical modification of the Debye relaxation model in electromagnetism. Unlike the Debye model, the Havriliak–Negami relaxation accounts
Havriliak–Negami_relaxation
Model of a crystalline solid
oscillators of the same frequency. The independence assumption is relaxed in the Debye model. While the model provides qualitative agreement with experimental
Einstein_solid
Basic statistical model
photon distribution function will involve a non-zero chemical potential. (Hermann 2005) Another massless Bose gas is given by the Debye model for heat capacity
Gas_in_a_box
State of matter
plasma parameter Λ, representing the number of charge carriers within the Debye sphere is much higher than unity. It can be readily shown that this criterion
Plasma_(physics)
been proposed for some disordered systems, most interestingly Debye's scattering function for a Gaussian polymer chain derived during World War II, where
Unified_scattering_function
Scattering of an electromagnetic plane wave by a sphere
Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic
Mie_scattering
Symmetry breaking through the vacuum state
"Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order". Phys. Rev. B. 82 (15) 155138.
Spontaneous_symmetry_breaking
Electrokinetic potential in colloidal dispersions
Smoluchowski's theory is valid only for a sufficiently thin double layer, when the Debye length, 1 / κ {\displaystyle 1/\kappa } , is much smaller than the particle
Zeta_potential
Rayleigh–Gans approximation, also known as Rayleigh–Gans–Debye approximation and Rayleigh–Gans–Born approximation, is an approximate solution to light
Rayleigh–Gans_approximation
Molecular interface between a surface and a fluid
so-called Debye-Huckel approximation holds. It yields the following expression for electric potential Ψ in the spherical DL as a function of the distance
Double layer (surface science)
Double_layer_(surface_science)
Statistical ensemble of particles in thermodynamic equilibrium
many important ensemble averages can be directly calculated from the function Ω(µ, V, T). In the case where more than one kind of particle is allowed
Grand_canonical_ensemble
first proved in 1912 by Brouwer. The Debye functions are named in honor of Peter Debye, who came across this function (with n = 3) in 1912 when he analytically
List_of_Dutch_discoveries
Measure of the ability of a solution containing electrolytes to conduct electricity
Onsager gave a theoretical explanation of Kohlrausch's law by extending Debye–Hückel theory. Conductivity of low- and non-polar solutions is very low
Conductivity_(electrolytic)
Behaviour of metals at low temperatures
scattering of conduction electrons by lattice vibrations (phonons) below Debye temperature. The theory was initially put forward by Felix Bloch in 1930
Bloch–Grüneisen_law
Empirical extension of Debye–Hückel theory
The Davies equation is an empirical extension of Debye–Hückel theory which can be used to calculate activity coefficients of electrolyte solutions at
Davies_equation
Measure of the electric polarizability of a dielectric material
called dielectric relaxation and for ideal dipoles is described by classic Debye relaxation. Second are the resonance effects, which arise from the rotations
Permittivity
Number of available physical states per energy unit
mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the
Density_of_states
Quantum theory of interacting electron gas
recovers the 3D wave number from Thomas–Fermi screening. For reference, Debye–Hückel screening describes the non-degenerate limit case. The result is
Lindhard_theory
Sum of the inverses of the positive cubes
physics, for instance, when evaluating the two-dimensional case of the Debye model and the Stefan–Boltzmann law. The reciprocal of ζ(3) (0.8319073725807
Apéry's_constant
Interactions between groups of atoms that do not arise from chemical bonds
the London dispersion forces between "instantaneously induced dipoles", Debye forces between permanent dipoles and induced dipoles, and the Keesom force
Van_der_Waals_force
Quantification of the electrical interactions between ions in solution
colloids and other heterogeneous systems. That is, the Debye length, which is the inverse of the Debye parameter (κ), is inversely proportional to the square
Ionic_strength
Device used to measure plasma
the I–V characteristic of the Debye sheath, that is, the current density flowing to a surface in a plasma as a function of the voltage drop across the
Langmuir_probe
Thermodynamic extension of Debye–Hückel theory
coefficients as a function of ionic strength. This theory was very successful for dilute solutions of 1:1 electrolytes and, as discussed below, the Debye–Hückel
Pitzer_equations
Description of a quantum-mechanical system
physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark,
Schrödinger_equation
Elliptic partial differential equation
plays a role in the development of the Debye–Hückel theory of dilute electrolyte solutions. Using a Green's function, the potential at distance r from a
Poisson's_equation
Empirical thermodynamic law
observed decrease of the heat capacity at low temperatures in diamond. Peter Debye followed in 1912 with a new model based on Max Planck's photon gas, where
Dulong–Petit_law
developed it in 1950. The Cole–Davidson equation is a generalization of the Debye relaxation keeping the initial increase of the low frequency wing of the
Cole–Davidson_equation
Theorem in quantum mechanics
mathematics of quantum mechanics. According to the theorem, the many-body wave function for elementary particles with integer spin (bosons) is symmetric under
Spin–statistics_theorem
Heat required to raise the temperature of a given unit of mass of a substance
characteristic Einstein temperatures or Debye temperatures can be made by the methods of Einstein and Debye discussed below. However, attention should
Specific_heat_capacity
Extension of Laplace's method for approximating integrals
method of steepest descent was first published by Debye (1909), who used it to estimate Bessel functions and pointed out that it occurred in the unpublished
Method_of_steepest_descent
Intensive quantity, heat capacity per amount of substance
in metals. These are not degrees of freedom treated in the Einstein or Debye theories. Since the bulk density of a solid chemical element is strongly
Molar_heat_capacity
Measure of positive and negative charges
The SI unit for electric dipole moment is the coulomb-metre (C⋅m). The debye (D) is a CGS unit of measurement used in atomic physics and chemistry. Theoretically
Electric_dipole_moment
Thermodynamic potential used in statistical mechanics
processes in open systems. The grand potential is the characteristic state function for the grand canonical ensemble. The grand potential is defined by Φ G
Grand_potential
Branch of physics
relations – Equation relating transport coefficients to correlation functions Green's function (many-body theory) – Correlators of field operators Materials
Condensed_matter_physics
Mathematical model of ferromagnetism in statistical mechanics
Z_{\beta }=\sum _{\sigma }e^{-\beta H(\sigma )}} is the partition function. For a function f {\displaystyle f} of the spins ("observable"), one denotes by
Ising_model
(Stokes–Einstein–Sutherland) equation (translational diffusion) Stokes–Einstein–Debye equation (rotational diffusion) Stokes approximation Navier–Stokes equations
List of things named after George Gabriel Stokes
List_of_things_named_after_George_Gabriel_Stokes
Polarization in dielectric spectroscopy
Press, p211 Debye relaxation Dielectric dispersion Dielectric function Dielectrophoresis Dipole Permittivity Ellipsometry Linear response function Kramers–Kronig
Maxwell–Wagner–Sillars polarization
Maxwell–Wagner–Sillars_polarization
Measure of a substance's ability to resist or conduct electric current
the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
Periodic boundary condition in solid-state physics
condition. Historically, the Born-von Karman boundary condition is, like the Debye model, an improvement upon the Einstein model of solids, the first quantum
Born–von Karman boundary condition
Born–von_Karman_boundary_condition
Technique for the characterisation of crystalline materials
have been developed to account for the specimen-detector displacement in Debye-Scherrer (transmission) and Bragg-Brentano (reflection) geometries. Correction
Rietveld_refinement
Effect where increased ionic strength results in increased solubility
"salting out". Initial salting in at low concentrations is explained by the Debye–Huckel theory. Proteins are surrounded by the salt counterions (ions of
Salting_in
Term in semiconductor electrochemistry
{N}_{D}\left(w\right)} . This method only provides a spatial resolution of the order of a Debye length λ D {\displaystyle {\lambda }_{D}} . In systems where more than one
Mott–Schottky_plot
Indian mathematician
Garrappa (July 2015). "On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics". Journal of Computational Physics. 293:
Tilak_Raj_Prabhakar
Interpretation of quantum mechanics
Einstein's explanation of the photoelectric effect, Einstein and Peter Debye's work on the specific heat of solids, Niels Bohr and Hendrika Johanna van
Copenhagen_interpretation
Type of boundary condition in mathematics
conductor's surface that has a linear 'softness' of the surface charge Debye layer i.e. a linear quantum capacitance that appears in series with the
Robin_boundary_condition
Law of Ostwald for dissociation of electrolytes
conductivity as a function of concentration is actually due to attraction between ions of opposite charge as expressed in the Debye-Hückel-Onsager equation
Law_of_dilution
^{2}\tau _{\sigma }^{2})}}} These are often called the Debye equations since were first derived by P. Debye for the case of dielectric relaxation phenomena.
Anelasticity
Separation of electric charge in a molecule
factor of 10−10 statcoulomb being 0.208 units of elementary charge, so 1.0 debye results from an electron and a proton separated by 0.208 Å. A useful conversion
Chemical_polarity
Description of multiple particle in physics
system. In the language of quantum mechanics this means that the wave function of the system is invariant up to a phase with respect to the interchange
Particle_statistics
Formula in X-ray diffraction and crystallography
that preserve the long-range order of the lattice only give rise to the Debye-Waller factor, which reduces peak heights but does not broaden them. However
Scherrer_equation
Type of electric dipole moment
moment is the Coulomb-meter (Cm); a more conveniently sized unit is the Debye (D). For a transition where a single charged particle changes state from
Transition_dipole_moment
Chinese-American physicist (1926–2024)
Grand canonical NPH Isoenthalpic–isobaric NPT Isothermal–isobaric Models Debye Einstein Ising Potts Potentials Internal energy Enthalpy Helmholtz free
Tsung-Dao_Lee
viscosity of a solution (it is usually positive) and can be calculated from Debye–Hückel theory, B is a coefficient that characterises the solute–solvent
Jones–Dole_equation
In electrochemistry, region surrounding an electrode in solution
diffuse layer arises from electrostatics and its thickness is governed by the Debye length, whereas the diffusion layer arises from driven (non-equilibrium)
Diffusion_layer
Concept in non-equilibrium physics
functions corresponding to excitations in the system. The main mathematical object in the Keldysh formalism is the non-equilibrium Green's function (NEGF)
Keldysh_formalism
Ensemble of states at a constant temperature
many important ensemble averages can be directly calculated from the function F(N, V, T). An alternative but equivalent formulation for the same concept
Canonical_ensemble
Book by Roger Penrose
although still far below 25 ms. Hameroff's group also suggested that the Debye layer of counterions could screen thermal fluctuations, and that the surrounding
Shadows_of_the_Mind
typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of nanometers. The
Double_layer_forces
Resistance to thermal flow between two materials
interface. Finally, the Debye temperature between the materials is significantly different. As a result, bismuth, which has a low Debye temperature, has many
Interfacial thermal resistance
Interfacial_thermal_resistance
Idealization of a large number of atomic-sized systems
thermodynamic quantities of interest, often in terms of the appropriate partition function. The concept of an equilibrium or stationary ensemble is crucial to many
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Ensemble of states at constant pressure
Z^{-1}e^{-\beta (E_{i}+pV_{i})}} , where Z {\displaystyle Z} is the partition function, E i {\displaystyle E_{i}} is the internal energy of the system in microstate
Isothermal–isobaric_ensemble
Dynamics of fluids confined in nanoscale structures
because the characteristic physical scaling lengths of the fluid, (e.g. Debye length, hydrodynamic radius) very closely coincide with the dimensions of
Nanofluidics
Concept in condensed matter physics
e^{2}n}{k_{\rm {B}}T}},} i.e. 1/k0 is given by the familiar formula for Debye length. In the opposite extreme, in the low-temperature limit T = 0, electrons
Thomas–Fermi_screening
Measure of the relative pressure change due to a temperature change
T}}\right)_{V}} . Usually, Mie-Grüneisen-Debye and other Quasi harmonic approximation (QHA) based state functions are being used to estimate volumes and
Thermal_pressure_coefficient
Equation used for physiological interfaces, polymer science, and semiconductors
overestimates the potential as a function of distance from the surface. This overestimation is visible at distances less than half the Debye length, where the decay
Poisson–Boltzmann_equation
Theorem on magnetism
atom in 1913. The Langevin function is often seen as the classical theory of paramagnetism, while the Brillouin function is the quantum theory of paramagnetism
Bohr–Van_Leeuwen_theorem
Electric charges present on the surface of a solid
{\displaystyle x} , and λ D {\displaystyle \lambda _{D}} is defined as the Debye length. Which leads to the simple expression: σ = ε ε 0 ψ 0 λ D {\displaystyle
Surface_charge
Description of the behaviour of bosons
a grand partition function and replacing E {\displaystyle E} with N ε {\displaystyle N\varepsilon } , the grand partition function takes the form Z =
Bose–Einstein_statistics
Statistical distribution used in many-particle mechanics
i N i {\displaystyle \textstyle N=\sum _{i}N_{i}} , Z is the partition function: Z = ∑ i g i e − ε i / k B T {\displaystyle \textstyle Z=\sum _{i}g_{i}e^{-\varepsilon
Maxwell–Boltzmann_statistics
Spectroscopic technique
multiplying the scattered single-photoelectron wave function ϕ j {\displaystyle \phi _{j}} by the Debye–Waller factor: W j = exp ( − Δ k j 2 U j 2 ¯ )
X-ray photoelectron spectroscopy
X-ray_photoelectron_spectroscopy
Equation in physics
screening models like Thomas–Fermi screening in solid-state physics and Debye screening in plasmas. Without loss of generality, we will take λ to be non-negative
Screened_Poisson_equation
Measure of the deviation of position over time
mixing phenomena in environmental engineering. It prominently appears in the Debye–Waller factor (describing vibrations within the solid state) and in the
Mean_squared_displacement
Computational quantum mechanical modelling method to investigate electronic structure
In dilute gases the direct correlation function is simply the pair-wise interaction between particles (Debye–Huckel equation). The Ornstein–Zernike equation
Density_functional_theory
Description of physical properties at the atomic and subatomic scale
work of Planck, Einstein and Bohr mentioned above, Einstein and Peter Debye's work on the specific heat of solids, Bohr and Hendrika Johanna van Leeuwen's
Quantum_mechanics
Statistical mechanics theorem relating non-equilibrium work to free energy differences
Now, if one defines a generic reaction coordinate of the system as a function of the Cartesian coordinates of the constituent particles ( e.g. , a distance
Crooks_fluctuation_theorem
Elementary particle or quantum of light
interpretation of the wave function was inspired by Einstein's later work searching for a more complete theory. In 1910, Peter Debye derived Planck's law of
Photon
Measure of the electric polarizability of a dielectric, compared with that of a vacuum
Archer, G. G.; Wang, P. (1990). "The Dielectric Constant of Water and Debye-Hückel Limiting Law Slopes". Journal of Physical and Chemical Reference
Relative_permittivity
DEBYE FUNCTION
DEBYE FUNCTION
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, an Egyptian functionary.
Biblical
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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.
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.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, Functionary of the Interior.
Male
English
Variant spelling of English Daye, DEYE means "day."
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.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, a great functionary.
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
, the son of the functionary Heknofre.
DEBYE FUNCTION
DEBYE FUNCTION
Girl/Female
British, Danish, English, Swedish
Blind; Sixth
Surname or Lastname
English
English : habitational name from either of two places in East Yorkshire and Cumbria named Brigham, from Old English brycg ‘bridge’ + hÄm ‘homestead’ or hamm ‘enclosure hemmed in by water’.Thomas Brigham (c. 1603–53) came from London to Cambridge, MA, in 1635.
Boy/Male
Australian, Gaelic, Greek, Irish, Scottish
Young Dog; Scottish Gaelic; The Child; Virile; Dove; Similar to Cailean
Boy/Male
Bengali, Hindu, Indian, Kannada, Telugu
Priest; One who have Very Good Knowledge
Girl/Female
Indian
Great; Success
Male
Polish
Variant spelling of Polish GabryÅ, GABRYSZ means "man of God"Â or "warrior of God."
Girl/Female
Arabic
The Woman
Girl/Female
American, British, Christian, English, German, Latin
Crowned with Laurels; Variant of Laura or Lora Referring to the Laurel Tree; Sweet Bay Tree Symbolic of Honor and Victory; Laurel Tree; Sweet Bay Tree
Girl/Female
Tamil
Rice, Immortal, Unscathed, Perfect, Untouched i.e. divinity
Boy/Male
American, Australian, British, Chinese, Christian, Danish, English, French, German, Hawaiian, Hebrew, Irish, Italian, Polish, Shakespearean
Gift of God; Given by God; God has Given
DEBYE FUNCTION
DEBYE FUNCTION
DEBYE FUNCTION
DEBYE FUNCTION
DEBYE FUNCTION
pl.
of Functionary
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.
v. t.
To assign to some function or office.
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.
a.
Destitute of function, or of an appropriate organ. Darwin.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
v. i.
To die.
a.
Pertaining to the function of an organ or part, or to the functions in general.
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
a.
Pertaining to, or connected with, a function or duty; official.
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.
adv.
In a functional manner; as regards normal or appropriate activity.
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.
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.
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.
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
v. i.
Alt. of Functionate