In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components ( which may reflect individual physical processes of interest, for example ), or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity ( i. e., independence or non-interaction ).

Firstly, decomposition of a function into non-interacting components generally permits more economical representations of the function.

It is equivalent to saying that the prime decomposition of the manifold has no acyclic components, and turns out to be equivalent to the condition that all geometric pieces of the manifold have geometries based on the two Thurston geometries S < sup > 2 </ sup >× R and S < sup > 3 </ sup >.

However, the decomposition of a vector into components is not unique, because it depends on the choice of the axes on which the vector is projected.

A work breakdown structure ( WBS ), in project management and systems engineering, is a deliverable oriented decomposition of a project into smaller components.

An alternative decomposition is into completely polarized ( zero determinant ) and unpolarized ( scaled identity matrix ) components.

The Fourier series describes the decomposition of periodic waveforms, such that any periodic waveform can be formed by the sum of a ( possibly infinite ) set of fundamental and harmonic components.

The resulting aeration of the soil leads to the oxidation of its organic components, such as peat, and this decomposition process may cause significant land subsidence.

If we are given the components of the strain tensor in an arbitrary orthonormal coordinate system, we can find the principal strains using an eigenvalue decomposition determined by solving the system of equations

These two stages contribute to the chemical process of decomposition, which breaks down the main components of the body

* Chemical decomposition, also called chemical breakdown, the breakdown of a substance into simpler components

The B-format signals are based on a spherical harmonic decomposition of the soundfield and correspond to the sound pressure ( W ), and the three components of the pressure gradient ( X, Y, and Z ) ( not to be confused with the related particle velocity ) at a point in space.

* Modular decomposition, for a proper generalization of connected components on undirected graphs

Furthermore, the velocity, temperature, and geopotential variables may be decomposed into mean and perturbation components using Reynolds decomposition.

The basic character components in Cangjie are usually called " radicals "; nevertheless, Cangjie decomposition is not based on traditional Kangxi radicals, nor is it based on standard stroke order ; it is in fact a simple geometric decomposition.

* Separation into components representing trend, seasonality, slow and fast variation, cyclical irregular: see decomposition of time series

In detail, let X and Y be smooth projective varieties, let be the decomposition of X into connected components, and let d < sub > i </ sub > := dim X < sub > i </ sub >.

The procedure is based on decomposition of all forces into components for which the lines of application ( pale dotted lines ) intersect at one point ( the so called pole, arbitrarily set at the right side of the illustration ).

In more mathematical terms, the CG coefficients are used in representation theory, particularly of compact Lie groups, to perform the explicit direct sum decomposition of the tensor product of two irreducible representations into irreducible representations, in cases where the numbers and types of irreducible components are already known abstractly.

Rapid aerobic composting will be thermophilic decomposition in which bacteria that thrive at high temperatures ( 40-60 ° C or 104-140 ° F ) oxidize ( break down ) the waste into its components, some of which are consumed in the process, reducing volume, and eliminating potential pathogens.

Just as Z is interpreted as the generating functional ( aka characteristic function ( al )/ moment-generating function ( al ) of the probability distribution function ( al ) e < sup >− S </ sup >/ Z ) of the time ordered VEVs / Schwinger function ( aka moments ) ( see path integral formulation ), E ( a. k. a. the second characteristic function ( al )/ cumulant-generating function ( al )) is the generator of " connected " time ordered VEVs / connected Schwinger functions ( i. e. the cumulants ) where connected here is interpreted in the sense of the cluster decomposition theorem which means that these functions approach zero at large spacelike separations, or in approximations using Feynman diagrams, connected components of the graph.

TGA is commonly employed in research and testing to determine characteristics of materials such as polymers, to determine degradation temperatures, absorbed moisture content of materials, the level of inorganic and organic components in materials, decomposition points of explosives, and solvent residues.

The most commonly used physical therapy interventions for cerebellar ataxia are vestibular habituation, proprioceptive neurofaciliation, Frenkel exercises, and balance training ; however, therapy is often highly individualized and gait and coordination training are large components of therapy.

The components that Tart identified have not, however, been validated by empirical studies.

By March 1963 however, after the visit of Colonel Michael Greene of the United States Army, and the resulting ' Greene Plan ,' the pattern of bilaterally agreed military assistance to various Congolese military components, instead of a single unified effort, was already taking shape.

Some ecological principles, however, do exhibit collective properties where the sum of the components explain the properties of the whole, such as birth rates of a population being equal to the sum of individual births over a designated time frame.

It is however often difficult to identify the specific components in diet that serve to increase or decrease cancer risk since many food, such as beef steak and broccoli, contain low concentrations of both carcinogens and anticarcinogens.

Despite this almost exclusive focus, however, Greek fire is best understood as a complete weapon system of many components, all of which were needed to operate together to render it effective.

The traditional hi-fi enthusiast, however, will build a system from separates ( or components ), often with each item from a different manufacturer specialising in a particular component.

Maximum performance, however, requires the highest quality components, which are usually the most expensive.

" Behe specifically explained that the " current definition puts the focus on removing a part from an already functioning system ", but the " difficult task facing Darwinian evolution, however, would not be to remove parts from sophisticated pre-existing systems ; it would be to bring together components to make a new system in the first place ".

Police could not identify any fingerprints on the devices other than those of the officers who had disarmed them ; however, Soliah's fingerprint, handwriting and signature were identified on a letter sent to order a fuse that could only be used for bomb-making purposes, and components matching those used in the police car bombs were found in a locked closet at the Precida Avenue hideout that Soliah lived in with the other members of SLA.

The earliest versions, however, especially those models with the Bosch K-Jetronic ( CIS ) injection system, have few electronic components and therefore can be repaired more easily provided spare parts can be found.

The Nordic Model, however, is not a single model with specific components or rules ; each of the Nordic countries has its own economic and social models, sometimes with large differences from its neighbours.

The SPLA components however are a lesser concern than the SAF components.

Many geologist however do not agree on how to separate the triangle parts into the single components so that the framework grains can be plotted.

Columbia was originally scheduled to lift off in late 1979, however the launch date was delayed by problems with both the SSME components, as well as the thermal protection system ( TPS ).

This treatment can be used effectively only a limited number of times for a given individual, however, as a bite victim will ultimately develop antibodies to neutralize the foreign animal antigens injected into them as components of the antivenin.

This analysis, however, only applies to the fast E1 and E2 components of nuclear EMP.

This method is sometimes called rules-based synthesis ; however, many concatenative systems also have rules-based components.

Eastman was the first major company, however, to mass-produce these components, when in 1889 Eastman realized that the dry-gelatino-bromide emulsion could be coated onto this clear base, eliminating the paper.

There are, however, components of electrical circuits which do not obey Ohm's law ; that is, their relationship between current and voltage ( their I – V curve ) is nonlinear ( or non-ohmic ).

An example is the dichroic prism, used in some camcorders, which uses several coatings to split light into red, green and blue components for recording on separate CCD arrays, however it is now more common to have a Bayer filter to filter individual pixels on a single CCD array.

BST theories resemble the many worlds interpretation ; however, " the main difference is that the BST interpretation takes the branching of history to be feature of the topology of the set of events with their causal relationships ... rather than a consequence of the separate evolution of different components of a state vector.

As can be seen, there are quite a number of steps involved in a PCI DMA transfer ; however, that poses little problem, since the PCI device or PCI bus itself are an order of magnitude slower than rest of components ( see list of device bandwidths ).

The 8600, however, belonged to the " old school " in terms of its physical construction, and it used individual components soldered to circuit boards.