Therefore as analog signal processing systems become more complex, they may ultimately degrade signal resolution to such an extent that their performance is surpassed by digital systems.

Regulation is the complex orchestration of events starting with an extracellular signal such as a hormone and leading to an increase or decrease in the activity of one or more proteins.

Higher clock rates in increasingly complex CPUs make it more difficult to keep the clock signal in phase ( synchronized ) throughout the entire unit.

While removing the global clock signal makes the design process considerably more complex in many ways, asynchronous ( or clockless ) designs carry marked advantages in power consumption and heat dissipation in comparison with similar synchronous designs.

Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.

Upon receptor activation, the intracellular receptor domain activates the GTPase, which in turn activates other molecules of the signal transduction chain, either via the α unit or the βγ complex.

The number of hormone molecules available for complex formation is usually the key factor in determining the level at which signal transduction pathways are activated, the number of hormone molecules available being determined by the concentration of circulating hormone, which is in turn influenced by the level and rate at which they are secreted by biosynthetic cells.

that is, the generated beam amplitude is the complex conjugate of the signal beam amplitude.

Although the simplest reflexes may be mediated by circuits lying entirely within the spinal cord, more complex responses rely on signal processing in the brain.

This is because it tends to require more complex receiving hardware and there can be ambiguity problems in determining whether, for example, the signal has changed phase by + 180 ° or-180 °.

PM changes the phase angle of the complex envelope in direct proportion to the message signal.

The heart of BETA's processing capability consisted of 63 dedicated fast Fourier transform ( FFT ) engines, each capable of performing a 2 < sup > 22 </ sup >- point complex FFTs in two seconds, and 21 general-purpose personal computers equipped with custom digital signal processing boards.

The SECAM sub carrier, being a simple FM signal, does not need such complex processing.

The total strength of signal amplification by a GPCR is determined by the lifetimes of the ligand-receptor complex and receptor-effector protein complex and the deactivation time of the activated receptor and effectors through intrinsic enzymatic activity.

Then, the single-sideband complex signal centered at zero is upconverted to a real signal, by another pair of quadrature mixers, to the desired center frequency.

As the more complex sound signal is broken into the smaller sub-sounds, different levels are created, where at the top level we have complex sounds, which are made of simpler sounds on lower level, and going to lower levels even more, we create more basic and shorter and simpler sounds.

In particular, if a complex harmonic signal with a sinusoidal component with amplitude, angular frequency and phase

* An optional signal sensing domain ( SSD ) ( e. g., a ligand binding domain ), which senses external signals and, in response, transmit these signals to the rest of the transcription complex, resulting in up-or down-regulation of gene expression.

A trigger condition can range from simple ( such as triggering on a rising or falling edge of a single signal ) to the very complex ( such as configuring the analyzer to decode the higher levels of the TCP / IP stack and triggering on a certain HTTP packet ).

An equivalent baseband signal or equivalent lowpass signal is – in analog and digital modulation methods with constant carrier frequency ( for example ASK, PSK and QAM, but not FSK ) – a complex valued representation of the modulated physical signal ( the so called passband signal or RF signal ).

Alternate hydrogen bonding patterns, such as the wobble base pair and Hoogsteen base pair, also occur — in particular, in RNA — giving rise to complex and functional tertiary structures.

A classic application for a pair of class-A devices is the long-tailed pair, which is exceptionally linear, and forms the basis of many more complex circuits, including many audio amplifiers and almost all op-amps.

As with any other ionic compound, this complex ion could in principle pair with a counterion to form a salt.

* 2012 – The Damascus bombings were carried out using a pair of car bombs detonated by suicide bombers outside of a military intelligence complex in Damascus, Syria, killing 55 people and injuring 400 others

Higher quality for complex tasks costs higher effort, reduced duration for simpler tasks comes with noticeably lower quality – the meta-analysis " suggests that pair programming is not uniformly beneficial or effective ".

High fashion shoes may be made of very expensive materials in complex construction and sell for thousands of dollars a pair.

In Weaver's method, the band of interest is first translated to be centered at zero, conceptually by modulating a complex exponential with frequency in the middle of the voiceband, but implemented by a quadrature pair of sine and cosine modulators at that frequency ( e. g. 2 kHz ).

The final implementation replaced the integrator with a Predictor implemented with a two pole complex pair low pass filter designed to approximate the long term average speech spectrum.

All types of DSL employ highly complex digital signal processing algorithms to overcome the inherent limitations of the existing twisted pair wires.

The electronic structure of a coordination complex can be described in terms of the set of ligands each donating a pair of electrons to a metal centre.

In this vein, the discriminant is a symmetric function in the roots which reflects properties of the roots – it is zero if and only if the polynomial has a multiple root, and for quadratic and cubic polynomials it is positive if and only if all roots are real and distinct, and negative if and only if there is a pair of distinct complex conjugate roots.

Wrens have loud and often complex songs, sometimes given in duet by a pair.

In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs.

The earliest Liubo boards to have been discovered are a pair of ornately decorated stone boards from a 4th century BCE tomb in the royal tomb complex of the State of Zhongshan at Pingshan in Hebei.

His role as " Ouyang " earned him the Best Actor Award at the Hong Kong Film Critics Society Awards, and Happy Together ( 1997 ), which depicted a complex relationship between a a pair of gay lovers ), in which he played " Ho Po-wing ", who goes to Argentina with his lover ( played by Tony Leung Chiu-wai ).

All real numbers ( except zero ) have exactly one real cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots.

A real number has one real cube root and two further cube roots which form a complex conjugate pair.

The visual system accomplishes a number of complex tasks, including the reception of light and the formation of monocular representations ; the construction of a binocular perception from a pair of two dimensional projections ; the identification and categorization of visual objects ; assessing distances to and between objects ; and guiding body movements in relation to visual objects.

It seems to me that N.C., in his editorial `` Confrontation '' ( SR, Mar. 25 ), has hit upon the real problem that bothers all of us in a complex world: how do we retain our personal relationship with those who suffer??

Basic theories, such as arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that the axioms being used are the axioms of Zermelo – Fraenkel set theory with choice, abbreviated ZFC, or some very similar system of axiomatic set theory like Von Neumann – Bernays – Gödel set theory, a conservative extension of ZFC.

It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.

Numbers such as π that are not algebraic are said to be transcendental ; almost all real and complex numbers are transcendental.

These quantum numbers only occur in certain combinations of values, and their physical interpretation changes depending on whether real or complex versions of the atomic orbitals are employed.

* The complex numbers form a 2-dimensional unitary associative algebra over the real numbers.

* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

* The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers.

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

Here K denotes the field of real numbers or complex numbers, I is a closed and bounded interval b and p, q are real numbers with 1 < p, q < ∞ so that

If A is a self-adjoint operator, then is always a real number ( not complex ).

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

This property is found in the real and complex numbers ; for instance, |- 6 × 5 | ≤ |- 6 |×| 5 |.

The theory of real Banach algebras can be very different from the theory of complex Banach algebras.

For example, the spectrum of an element of a complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.

* The set of real ( or complex ) numbers is a Banach algebra with norm given by the absolute value.

* The set of all real or complex n-by-n matrices becomes a unital Banach algebra if we equip it with a sub-multiplicative matrix norm.

* Every commutative real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers.

for an arbitrary real or complex number α ( the order of the Bessel function ); the most common and important cases are for α an integer or half-integer.

Both J < sub > α </ sub >( x ) and Y < sub > α </ sub >( x ) are holomorphic functions of x on the complex plane cut along the negative real axis.

In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.