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structures) is said to have polynomial delay if the time between the output of any one structure and the next is bounded by a polynomial function of the input
Polynomial_delay
Delays experienced through a linear time-invariant system
a polynomial Laplace transform form, then the mathematical definition for group delay above may be solved analytically in closed form. A polynomial transfer
Group_delay_and_phase_delay
Logical formulation of graph properties
the n {\displaystyle n} -vertex graphs that model the property, with polynomial delay (as a function of n {\displaystyle n} ) per graph. A similar analysis
Logic_of_graphs
Task of computing complete subgraphs
there is no polynomial-delay algorithm unless P = NP. On the basis of this result, it is possible to list all maximal cliques in polynomial time, for families
Clique_problem
Algorithm that outputs all solutions to a problem
can be produced in polynomial time in the input size and in the number i. Polynomial delay, the class of problems where the delay between two consecutive
Enumeration_algorithm
Type of analog linear filter in electronics
scaling the H ( s ) {\displaystyle H(s)} polynomials to the inverse of that frequency. To scale the polynomials, simply append ω c {\displaystyle \omega
Bessel_filter
In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential
Exponential_polynomial
Edges that hit all cycles in a graph
All minimal feedback arc sets can be listed by an algorithm with polynomial delay per set. Unsolved problem in mathematics Does the feedback arc set
Feedback_arc_set
Economical computational problem
for congestion games with more general delay functions (not bounded-degree polynomial), attaining any polynomial approximation of PNE is PLS-complete.
Nash_equilibrium_computation
Type of differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time
Delay_differential_equation
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary
Computation of cyclic redundancy checks
Computation_of_cyclic_redundancy_checks
American computer scientist
needed] Her dissertation, on algorithms for listing structures with polynomial delay, won the Distinguished Dissertations in Computer Science prize. Goldberg
Leslie_Ann_Goldberg
Field of electrical engineering
analyzed using linear methods. Polynomial signal processing is a type of non-linear signal processing, where polynomial systems may be interpreted as conceptually
Signal_processing
Type of signal processing filter
operator. The denominator is a Butterworth polynomial in s {\displaystyle s} . The Butterworth polynomials may be written in complex form as above, but
Butterworth_filter
Formula whose values are the prime numbers
c} may be negative, in which case there is a delay before primes are produced. Similarly, other polynomials (of higher degree) produces finite sequences
Formula_for_primes
Mathematical formula expressing equality
equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials. The sides of a polynomial equation contain
Equation
Type of pseudorandom binary sequence
These sequences may be represented as coefficients of primitive. polynomials in a polynomial ring over Z/2Z. Practical applications for MLS include measuring
Maximum_length_sequence
Type of analog or digital filter
used to modify the group delay to a more desirable shape. The transmission zeros design utilizes characteristic polynomials, K(S), to place the transmission
Chebyshev_filter
A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
Device for suppressing part of a signal
difference between these filter families is that they all use a different polynomial function to approximate to the ideal filter response. This results in
Filter_(signal_processing)
Field-equations in general relativity
tensor, they can be arranged in a form that contains the metric tensor in polynomial form and without its inverse. First, the determinant of the metric in
Einstein_field_equations
Type of two-dimensional barcode
. The primitive polynomial is x 8 + x 4 + x 3 + x 2 + 1 {\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1} , corresponding to the polynomial number 285, with
QR_code
Study of periodic events in biological life cycles
Tallgrass Prairie National Preserve, Kansas (dots) fitted with a local polynomial regression model (loess in red) and a 2 standard error band (blue). Data
Phenology
Polynomial root-finding algorithm
algorithm which calculates the root of largest absolute value of a univariate polynomial. The method works under the condition that there is only one root (possibly
Bernoulli's_method
Method to solve optimization problems
polynomial-time algorithm? Does LP admit a strongly polynomial-time algorithm to find a strictly complementary solution? Does LP admit a polynomial-time
Linear_programming
Arrangement of mirrors
orthogonal set of functions (over two-dimensions) such as Hermite polynomials or the Ince polynomials. Unstable laser resonators on the other hand, have been shown
Optical_cavity
Numerical method for solving physical or engineering problems
defined with polynomial and even non-polynomial shapes (e.g., ellipse or circle). Examples of methods that use higher degree piecewise polynomial basis functions
Finite_element_method
Pattern defining an infinite sequence of numbers
This is an example of a linear recurrence with polynomial coefficients of order 1, with the simple polynomial (in n) n {\displaystyle n} as its only coefficient
Recurrence_relation
Lattice network
time delay, although the procedure does become tedious for the higher orders. A more convenient way of deriving the coefficients of the polynomials is to
Lattice_delay_network
Mapping arbitrary data to fixed-size values
division by a polynomial modulo 2 instead of an integer to map n bits to m bits. In this approach, M = 2m, and we postulate an mth-degree polynomial Z(x) = xm
Hash_function
Model of computation
problem that can be computed in polynomial time by a deterministic Turing machine can also be computed by a polynomial-size circuit family. It is further
Boolean_circuit
In control theory, when an LTI system and its inverse are causal and stable
in the case of transfer functions which can be expressed as ratios of polynomials. In the continuous-time case, such systems translate into networks of
Minimum_phase
Principle suggesting that time travel paradoxes are inherently impossible
in polynomial time, and Scott Aaronson later extended this result to show that the model could also be used to solve PSPACE problems in polynomial time
Novikov self-consistency principle
Novikov_self-consistency_principle
Function used in signal processing
discrete-time windows. A kth-order B-spline basis function is a piece-wise polynomial function of degree k − 1 that is obtained by k-fold self-convolution of
Window_function
Function specifying the behavior of a component in an electronic or control system
{\displaystyle u=e^{\lambda t}} . That substitution yields the characteristic polynomial p L ( λ ) = λ n + a 1 λ n − 1 + ⋯ + a n − 1 λ + a n {\displaystyle p_{L}(\lambda
Transfer_function
Stability criterion in control theory
1+G(s)H(s)=0} holds. In systems without pure delay, the product G ( s ) H ( s ) {\displaystyle G(s)H(s)} is a rational polynomial function and may be expressed as
Root_locus_analysis
Class of games in game theory
that, in any weighted network CG with linear delay functions, finds a PNE in pseudo-polynomial time (polynomial in the number of players n and the sum of
Congestion_game
Delayed temperature response
"An improved lumped analysis for transient heat conduction by using the polynomial approximation method". Heat and Mass Transfer. 43 (11): 1151–1156. doi:10
Thermal_inertia
in Aerospace, Seoul. S.E. Hamamci, "A robust polynomial-based control for stable processes with time delay", Electrical Engineering, vol: 87, pp.163–172
Coefficient_diagram_method
Type of error-correcting code using convolution
that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution'
Convolutional_code
Chinese-American mechanical engineer
systems and time-delay Two-dimensional quadratic dynamical systems Two-dimensional cubic dynamical Systems Two-dimensional polynomial dynamical Systems
Albert_C.J._Luo
Scientific area at the interface between computer science and mathematics
simplification of expressions, differentiation using the chain rule, polynomial factorization, indefinite integration, etc. Computer algebra is widely
Computer_algebra
Filter in electronics and signal processing
deviation of the Gaussian distribution. The Gaussian transfer function polynomials may be synthesized using a Taylor series expansion of the square of Gaussian
Gaussian_filter
Type of equation involving matrix-valued functions
{\displaystyle M(\lambda )=A_{0}+\lambda A_{1}+\lambda ^{2}A_{2}.} The polynomial eigenvalue problem: M ( λ ) = ∑ i = 0 m λ i A i . {\displaystyle M(\lambda
Nonlinear_eigenproblem
Software programming optimization technique
refraining redundant computations to accommodate any form of ambiguous CFG in polynomial time (Θ(n4) for left-recursive grammars and Θ(n3) for non left-recursive
Memoization
Differential equation that is linear with respect to the unknown function
any. The solutions of homogeneous linear differential equations with polynomial coefficients are called holonomic functions. This class of functions is
Linear_differential_equation
that the PoA when all delay functions are linear is exactly 2.618. They also showed that, when the delay functions are polynomials of degree d, the PoA
Price of anarchy in congestion games
Price_of_anarchy_in_congestion_games
Problem in control theory
; Mahony, R. (1998). "Output Dead Beat Control for a Class of Planar Polynomial Systems". SIAM Journal on Control and Optimization. 36 (1): 253–272. CiteSeerX 10
Dead-beat_control
by combining the unique encoding capability of Chebyshev polynomials with dispersive delay-based decoding. DCMA enhances spectrum utilization by allowing
Microwave analog signal processing
Microwave_analog_signal_processing
Signals broadcast by GPS satellites
generator polynomial is x → x10 + x3 + 1, and initial state is 11111111112. B is the output of the second LFSR whose generator polynomial is x → x10
GPS_signals
Class of numerical techniques
the Taylor polynomial can be used to analyze local truncation error. Using the Lagrange form of the remainder from the Taylor polynomial for f ( x 0
Finite_difference_method
Proof that a number is prime
integer factorization lie in NP, the class of problems verifiable in polynomial time given a solution. These problems already trivially lie in co-NP.
Primality_certificate
Sequence that reads the same forwards and backwards
Palindroma, a genus of spiders with palindromic species names Palindromic polynomial Yreka, California, which has the palindromic Yreka Bakery and Yrella Gallery
Palindrome
Mathematical curve outputted from a specific pair of parametric equations
{\displaystyle \delta ={\frac {N-1}{N}}{\frac {\pi }{2}}} are Chebyshev polynomials of the first kind of degree N. This property is exploited to produce
Lissajous_curve
Type of functional equation (mathematics)
polynomial equation in the unknown function and its derivatives, the degree of the differential equation is, depending on the context, the polynomial
Differential_equation
Restricted model of non-universal quantum computation
third level of the polynomial hierarchy When combined these two facts along with Toda's theorem result in the collapse of the polynomial hierarchy, which
Boson_sampling
Methods of calculating definite integrals
interpolating functions are polynomials. In practice, since polynomials of very high degree tend to oscillate wildly, only polynomials of low degree are used
Numerical_integration
Mathematical transform that expresses a function of time as a function of frequency
distributions. The tempered distributions include well-behaved functions of polynomial growth, distributions of compact support as well as all the integrable
Fourier_transform
Foundational principle in quantum physics
an integer), then, if ab > 1, f = 0, while if ab = 1, then there is a polynomial P of degree ≤ N such that f ( x ) = P ( x ) e − a π x 2 . {\displaystyle
Uncertainty_principle
Description of physical properties at the atomic and subatomic scale
, 2 , … . {\displaystyle n=0,1,2,\ldots .} where Hn are the Hermite polynomials H n ( x ) = ( − 1 ) n e x 2 d n d x n ( e − x 2 ) , {\displaystyle
Quantum_mechanics
Technique to solve differential equations
transformed into algebraic problems, usually the problem of solving a polynomial equation. The idea of representing the processes of calculus, differentiation
Operational_calculus
Branch of machine learning
by Alexey Ivakhnenko and Lapa in 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron to handle more
Deep_learning
Integral transform useful in probability theory, physics, and engineering
ordinary differential equations and integral equations with algebraic polynomial equations, and by replacing convolution with multiplication. For example
Laplace_transform
arithmetical hierarchy and polynomial hierarchy classify the degree to which problems are respectively computable and computable in polynomial time. For instance
Limits_of_computation
Scheme for controlling errors in data over noisy communication channels
satellites orbiting distant planets, retransmission due to errors would create a delay of several hours. FEC is also widely used in modems and in cellular networks
Error_correction_code
Variable used for specification
{k}}=n(n-1)(n-2)\cdots (n-k+1)} , defines a polynomial function of n (when k is considered a parameter), but is not a polynomial function of k (when n is considered
Parameter
Branch of engineering and mathematics
system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability;
Control_theory
Computational model used in machine learning
Valentin Lapa in the Soviet Union (1965). They regarded it as a form of polynomial regression, generalizing Rosenblatt's perceptron. A 1971 paper described
Neural network (machine learning)
Neural_network_(machine_learning)
Dimensionless quantity in fluid dynamics
guarantees that there exists no general form for the roots of these polynomials). It is first determined whether M is indeed greater than 1.0 by calculating
Mach_number
Programmable machine that processes data
advanced analog machines that could solve real and complex roots of polynomials, which were published in 1901 by the Paris Academy of Sciences. Charles
Computer
Property of operations
p.8. Balmaceda, Jose Maria. "Idempotents in Certain Matrix Rings Over Polynomial Rings". International Electronic Journal of Algebra. doi:10.24330/IEJA
Idempotence
Subset of artificial intelligence
polynomial time. There are two kinds of time complexity results: Positive results show that a certain class of functions can be learned in polynomial
Machine_learning
the discrete logarithm problem Polynomial long division: an algorithm for dividing a polynomial by another polynomial of the same or lower degree Risch
List_of_algorithms
Computer expansion bus standard
XORing a known binary polynomial as a "scrambler" to the data stream in a feedback topology. Because the scrambling polynomial is known, the data can
PCI_Express
Any of a set of standard configurations of Redundant Arrays of Independent Disks
hardware implementation (ASIC or FPGA). There is a special choice of polynomial from H. Peter Anvin used by Linux, which allows for efficient implementation
Standard_RAID_levels
Nowhere analytic, infinitely differentiable function
doi:10.1090/S0002-9947-1935-1501802-5, MR 1501802 Dimitrov, Youri (2006). Polynomially-divided solutions of bipartite self-differential functional equations
Fabius_function
Use of digital computers as system controllers
criterion determines the discrete system stability about its characteristic polynomial. The digital controller can also be designed in the s-domain (continuous)
Digital_control
Text used for user authentication to prove identity
secure do not store passwords at all, but a one-way derivation, such as a polynomial, modulus, or an advanced hash function. Roger Needham invented the now-common
Password
19th century proposed mechanical computer
trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts
Analytical_engine
Device for suppressing part of a discretely-sampled signal
discrete frequency-domain transfer function is written as the ratio of two polynomials. For example: H ( z ) = ( z + 1 ) 2 ( z − 1 2 ) ( z + 3 4 ) {\displaystyle
Digital_filter
'Best' approximation of a function by a rational function of given order
compute a Padé approximant is via the extended Euclidean algorithm for the polynomial greatest common divisor. The relation R ( x ) = P ( x ) / Q ( x ) = T
Padé_approximant
Software optimization technique
theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation)
Lazy_evaluation
Early packet switching network (1969–1990)
Protocol (packet voice) was decades away.[citation needed] The Purdy Polynomial hash algorithm was developed for the ARPANET to protect passwords in 1971
ARPANET
Serial communications protocol
widely known as CRC-16-MODBUS, whose polynomial is x16 + x15 + x2 + 1 (normal hexadecimal algebraic polynomial being 8005 and reversed A001). Example
Modbus
Model that describes the programmable interface of a computer processor
than 3 operands (registers or memory accesses), such as the VAX "POLY" polynomial evaluation instruction. Due to the large number of bits needed to encode
Instruction_set_architecture
Multivalued function in mathematics
replaced by a quadratic polynomial in x: where r1 and r2 are real distinct constants, the roots of the quadratic polynomial. Here, the solution is a
Lambert_W_function
Synchronization of a Novel Chaotic System Pickover Polynomial Type-A Polynomial Type-B Polynomial Type-C Quadrup Two Orbit Fractal Rikitake chaotic attractor
List_of_chaotic_maps
Computational problem of graph theory
categories. Unlike the shortest path problem, which can be solved in polynomial time in graphs without negative cycles, shortest path problems which include
Shortest_path_problem
Academic journal
ratio, Zeckendorf representations, Binet forms, Fibonacci polynomials, and Chebyshev polynomials. However, many other topics, especially as related to recurrences
Fibonacci_Quarterly
Electronic device
distributed components such as transmission lines), will be the ratio of two polynomials in s {\displaystyle s} , i.e. a rational function of s {\displaystyle
Electronic_filter
Integral expressing the amount of overlap of one function as it is shifted over another
sequences are the coefficients of two polynomials, then the coefficients of the ordinary product of the two polynomials are the convolution of the original
Convolution
gate 14 US7429A 74x30 1 single 8-input NAND gate 14 SN74LS30 74x31 6 hex delay elements (two 6ns, two 23-32ns, two 45-48ns) 16 SN74LS31 74x32 4 quad 2-input
List of 7400-series integrated circuits
List_of_7400-series_integrated_circuits
no known algorithm that finds the optimum solution and terminates in a polynomial time constraint. ITU-T G.707/Y.1322 (01/07), Network node interface for
Virtual_concatenation
Simple polynomial map exhibiting chaotic behavior
by the quadratic difference equation It is a recurrence relation and a polynomial mapping of degree 2. It is often referred to as an archetypal example
Logistic_map
German polymath and scholar (1777–1855)
theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Mathematicians
Carl_Friedrich_Gauss
Graphical method of determining the stability of a dynamical system
can be determined by examining the roots of the desensitivity factor polynomial 1 + G ( s ) H ( s ) {\displaystyle 1+G(s)H(s)} , e.g. using the Routh
Nyquist_stability_criterion
the original on 2014-07-19 Kleinrock, Leonard (December 1962). Message Delay in Communication Nets with Storage (PDF) (Thesis). Cambridge: Massachusetts
List of pioneers in computer science
List_of_pioneers_in_computer_science
Numerical eigenvalue calculation
p(A)v_{1}} for some polynomial p {\displaystyle p} of degree at most m − 1 {\displaystyle m-1} ; the coefficients of that polynomial are simply the coefficients
Lanczos_algorithm
Swedish mathematician and concert pianist
like polynomial factorization (or in Enflo's construction of an operator without an invariant subspace). Enflo's idea of "concentration of polynomials at
Per_Enflo
Practice and study of secure communication techniques
discrete logarithms, both of which are not yet proven to be solvable in polynomial time (P) using only a classical Turing-complete computer. Much public-key
Cryptography
POLYNOMIAL DELAY
POLYNOMIAL DELAY
Biblical
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Boy/Male
Indian
The delayer
Boy/Male
Muslim
The delayer
Male
Hebrew
 Variant spelling of Hebrew Delayah, DELAYA means "God has drawn."
Female
English
(תֶּרַח) English feminine form of Hebrew Terach, TARAH means "delay" and "station." In the bible, this is the name of a place in the wilderness where the Israelites stopped on their Exodus. Variant spelling of English Tara, meaning "hill."Â
Female
English
English unisex form of Hebrew Terach, TERAH means "delay" and "station." In the bible, this is the name of a place in the wilderness where the Israelites stopped on their Exodus. It is also the name of the father of Abraham.
Male
Hebrew
(דְּלָיָהוּ) Variant form of Hebrew Delayah, DELAYAHU means "God has drawn."
Male
English
Anglicized form of Hebrew Delayah, DELAIAH means "God has drawn." Hebrew name meaning "God has drawn." In the bible, this is the name of several characters, including a descendant of Zerubbabel.
Male
English
Anglicized unisex form of Hebrew Terach, TERAH means "delay" and "station." In the bible, this is the name of a place in the wilderness where the Israelites stopped on their Exodus. It is also the name of the father of Abraham.
Male
Hebrew
(דְּלָיָה) Hebrew name DELAYAH means "God has drawn." In the bible, this is the name of several characters, including a descendant of Zerubbabel.
Girl/Female
Australian, Irish
From the Alder Grove
Male
English
Anglicized form of Hebrew Terach, TAHATH means "delay" and "station." In the bible, this is the name of a place in the wilderness where the Israelites stopped on their Exodus.Â
Male
Hebrew
(תֶּרַח) Hebrew name TERACH means "delay" and "station." In the bible, this is the name of a place in the wilderness where the Israelites stopped on their Exodus. It is also the name of the father of Abraham.
POLYNOMIAL DELAY
POLYNOMIAL DELAY
Girl/Female
Indian
Hundred thousand Lakh = million
Boy/Male
Hindu, Indian, Marathi, Punjabi, Sikh
Whole; Entire
Boy/Male
Hindu, Indian
Behaviour
Boy/Male
Indian, Sanskrit
Brave
Girl/Female
Tamil
Vyadhinashini | வà¯à®¯à®¾à®¤à¯€à®¨à®¾à®·à¯€à®¨à¯€
Vanquisher of ailments
Girl/Female
Hindu, Indian
Goddess Parvati
Boy/Male
Biblical
Right hand; numbering; preparing.
Boy/Male
American, British, English
From the Birch Tree Island
Girl/Female
Arabic
Well Mannered
Surname or Lastname
English (Bedfordshire)
English (Bedfordshire) : patronymic from Shreeve.
POLYNOMIAL DELAY
POLYNOMIAL DELAY
POLYNOMIAL DELAY
POLYNOMIAL DELAY
POLYNOMIAL DELAY
n.
A polynomial name or term.
p. pr. & vb. n.
of Delay
v. t.
To delay; to procrastinate.
a.
Without stop or delay.
n.
To retard; to stop, detain, or hinder, for a time; to retard the motion, or time of arrival, of; as, the mail is delayed by a heavy fall of snow.
imp. & p. p.
of Delay
v. i.
The act of waiting; a delay; a halt.
v. i.
To pass time; to delay.
n.
An expression composed of two or more terms, connected by the signs plus or minus; as, a2 - 2ab + b2.
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
n.
One who delays; one who lingers.
a.
Possessing the same number of factors of a given kind; as, a homogeneous polynomial.
a.
Kept in port or at anchor by storms; delayed by bad weather; as, a weather-bound vessel.
adv.
By delays.
a.
Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.
adv.
Immediately; without loss of time; without delay.
adv.
Immediately; at once; without delay.
n. & a.
Same as Polynomial.
n.
A polynomial of four terms connected by the signs plus or minus.
pl.
of Delay