This latter reaction is in accord with the reported decomposition of Af.

The small reaction occurring at 337-degrees-C is probably caused by decomposition of occluded nitrates, and perhaps by a small amount of some hydrous material other than Af.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

If the direct-sum decomposition ( A ) is valid, how can we get hold of the projections Af associated with the decomposition??

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

# As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and its sums of squares indicate the variance of each component of the decomposition ( or, equivalently, each set of terms of a linear model ).

For example, the Banach – Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.

In the formation of an ordinary agate, it is probable that waters containing silica in solution — derived, perhaps, from the decomposition of some of the silicates in the lava itself — percolated through the rock and deposited a siliceous coating on the interior of the vapour-vesicles.

The first deposit on the wall of a cavity, forming the " skin " of the agate, is generally a dark greenish mineral substance, like celadonite, delessite or " green earth ", which are rich in iron probably derived from the decomposition of the augite in the enclosing volcanic rock.

The volatile hydride generated by the reaction that occurs is swept into the atomization chamber by an inert gas, where it undergoes decomposition.

If sugars are heated so that all water of crystallisation is driven off, then caramelization starts, with the sugar undergoing thermal decomposition with the formation of carbon, and other breakdown products producing caramel.

In fact, the decomposition of hydrogen peroxide is so slow that hydrogen peroxide solutions are commercially available.

The decomposition process is aided by shredding the plant matter, adding water and ensuring proper aeration by regularly turning the mixture.

A decomposition reaction is the opposite of a synthesis reaction, where a more complex substance breaks down into its more simple parts.

Pyrolysis gas chromatography mass spectrometry is a method of chemical analysis in which the sample is heated to decomposition to produce smaller molecules that are separated by gas chromatography and detected using mass spectrometry.

In deflagration, the decomposition of the explosive material is propagated by a flame front which moves slowly through the explosive material, in contrast to detonation.

This term is used to describe an explosive phenomenon whereby the decomposition is propagated by an explosive shock wave traversing the explosive material.

Douglass prepared his sample of Af by thermal decomposition of aqueous chromic acid at 300 - 325-degrees-C.

This reduction has been accomplished by the general methods of linear algebra, i.e., by the primary decomposition theorem.

It further prevents the pollution of ground water by controlling the fecal matter decomposition before entering the system.

This technique is also very useful for compounds which boil beyond their decomposition temperature at atmospheric pressure and which would therefore be decomposed by any attempt to boil them under atmospheric pressure.

While the resource inputs are generally controlled by external processes like climate and parent material, the availability of these resources within the ecosystem is controlled by internal factors like decomposition, root competition or shading.

While the resource inputs are generally controlled by external processes like climate and parent material, the availability of these resources within the ecosystem is controlled by internal factors like decomposition, root competition or shading.

The carbon and nutrients in dead organic matter are broken down by a group of processes known as decomposition.

The rate of decomposition is governed by three sets of factors — the physical environment ( temperature, moisture and soil properties ), the quantity and quality of the dead material available to decomposers, and the nature of the microbial community itself.

Soil disturbance like tilling increase decomposition by increasing the amount of oxygen in the soil and by exposing new organic matter to soil microbes.

Other reasons include: a ) changes in plant canopy caused by shifts in plant biomass production associated with moisture regime ; b ) changes in litter cover on the ground caused by changes in both plant residue decomposition rates driven by temperature and moisture dependent soil microbial activity as well as plant biomass production rates ; c ) changes in soil moisture due to shifting precipitation regimes and evapo-transpiration rates, which changes infiltration and runoff ratios ; d ) soil erodibility changes due to decrease in soil organic matter concentrations in soils that lead to a soil structure that is more susceptible to erosion and increased runoff due to increased soil surface sealing and crusting ; e ) a shift of winter precipitation from non-erosive snow to erosive rainfall due to increasing winter temperatures ; f ) melting of permafrost, which induces an erodible soil state from a previously non-erodible one ; and g ) shifts in land use made necessary to accommodate new climatic regimes.

When reheated for lamp-working and similar uses, the working conditions should control the temperature and oxidation as required for the original batch melt: keep the temperature below the melting point of copper ( 1084. 62 ° C ) and use an oxygen-poor reducing flame, or risk decomposition into the failure modes described above.

Of more interest are the two rapid forms of decomposition, deflagration and detonation.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

In concluding this section, we should like to give an example which illustrates some of the ideas of the primary decomposition theorem.

It is a special case of the more general Helmholtz decomposition which works in dimensions greater than three as well.

Huygens ' principle when applied to an aperture simply says that the far-field diffraction pattern is the spatial Fourier transform of the aperture shape, and this is a direct by-product of using the parallel-rays approximation, which is identical to doing a plane wave decomposition of the aperture plane fields ( see Fourier optics ).

Fragmentation processes, which break through these protective layers, accelerate the rate of microbial decomposition.

Freeze-thaw cycles also affect decomposition — freezing temperatures kill soil microorganisms, which allows leaching to play a more important role in moving nutrients around.

Soils which are rich in clay minerals tend to have lower decomposition rates, and thus, higher levels of organic matter.

He called the decomposition of a group into its left and right cosets a proper decomposition if the left and right cosets coincide, which is what today is known as a normal subgroup.

* An object-oriented program structure in which a class serves as the basic unit of decomposition.

However, in the context of explosives, stability commonly refers to ease of detonation, which is concerned with kinetics ( i. e., rate of decomposition ).

All standard military explosives may be considered to have a high degree of stability at temperatures from – 10 to + 35 ° C, but each has a high temperature at which its rate of decomposition rapidly accelerates and stability is reduced.

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 ).

Another point of view, which turns out to be very useful to analyze the algorithm, is that Gaussian elimination computes a matrix decomposition.