The frequencies are related to the eigenvalues of the Hessian matrix, which contains second derivatives.

; Incidence matrix: The graph is represented by a matrix of size | V | ( number of vertices ) by | E | ( number of edges ) where the entry edge contains the edge's endpoint data ( simplest case: 1-incident, 0-not incident ).

This echelon matrix contains a wealth of information about: the rank of is 5 since there are 5 non-zero rows in ; the vector space spanned by the columns of has a basis consisting of the first, third, fourth, seventh and ninth column of ( the columns of the ones in ), and the *' s tell you how the other columns of can be written as linear combinations of the basis columns.

Each hip comprises an outer fleshy layer, the hypanthium, which contains 5 – 160 " seeds " ( technically dry single-seeded fruits called achenes ) embedded in a matrix of fine, but stiff, hairs.

Cartilage is composed of specialized cells called chondrocytes that produce a large amount of extracellular matrix composed of Type II collagen ( except Fibrocartilage which also contains type I collagen ) fibers, abundant ground substance rich in proteoglycan, and elastin fibers.

Internally the mine contains a layer of C-4 explosive behind a matrix of about seven hundred steel balls ( about as big as # 3 buckshot ) set into an epoxy resin.

Let P < sup >− 1 </ sup > DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.

The coherency matrix contains all second order statistical information about the polarization.

Nevertheless, the density matrix contains all the information necessary to calculate any measurable property of the mixed state.

: Magma contains asymptotically-fast algorithms for all fundamental dense matrix operations, such as Strassen multiplication.

where is the same matrix as except that it contains only the largest singular values ( the other singular values are replaced by zero ).

This contains a ceramic mass of zinc oxide grains, in a matrix of other metal oxides ( such as small amounts of bismuth, cobalt, manganese ) sandwiched between two metal plates ( the electrodes ).

For larger matrices, the expressions for the coefficients c < sub > k </ sub > of the characteristic polynomial in terms of the matrix components become increasingly complicated ; but they can also be expressed in terms of traces of powers of the matrix A, using Newton's identities ( at least when the ring contains the rational numbers ), thus resulting in more compact expressions ( but which involve divisions by certain integers ).

The most common type of LCD display contains, besides the polarizing sheets and cells of liquid crystal, a matrix of TFTs to make a TFT-LCD.

Each matrix contains the letter form for a single character of a font of type ; i. e., a particular type design in a particular size.

The UMX standard contains two subsystems, BMX, a basic 4-2-4 encoded matrix ( different from Regular Matrix ), and QMX, a 4-4-4 system.

The T × k matrix X contains all exogenous regressors from all equations, but without repetitions ( that is, matrix X should be of full rank ).

* Decomposition:, where D is a nonnegative diagonal matrix, and U and V are unitary matrices, and denotes the conjugate transpose of V ( or simply the transpose, if V contains real numbers only ).

A special class of closed-cell foams is known as syntactic foam, which contains hollow particles embedded in a matrix material.

Let T be the matrix of preprocessed training examples, where each column contains one mean-subtracted image.

The aorta consists of a heterogeneous mixture of smooth muscle, nerves, intimal cells, endothelial cells, fibroblast-like cells, and a complex extracellular matrix.

Graywacke sandstones are a heterogeneous mixture of lithic fragments and angular grains of quartz and feldspar, and / or grains surrounded by a fine-grained clay matrix.

More commonly, these sediments lose their original structure through the mixture processes associated to the subglacial transport and they solely contribute to form the more or less uniform matrix of the till.

However if the kets in the mixture are orthonormal then the original probabilities p < sub > j </ sub > are recoverable as the eigenvalues of the density matrix.

The Inclenberg was an abrupt, steep-sided mound of glacial till typical of Manhattan Island's still-unmodified post-glacial terrain: this " hill of the rudest and most heterogeneous mixture of stone and gravel and boulders, cemented together into a matrix of almost impenetrable density existed, crowning the underlying schist ...

The decoherence irreversibly converts the " averaged " or " environmentally traced over " density matrix from a pure state to a reduced mixture ; it is this that gives the appearance of wavefunction collapse.

These are often a mixture of several ceramic materials, or metal matrix composites which combine ceramic compounds with metal.

A perfectly coherent state has a density matrix ( also called the " statistical operator ") that is a projection onto the pure coherent state, while a mixed state is described by a classical probability distribution for the pure states that make up the mixture.

Each chondrite group has a distinctive mixture of chondrules, refractory inclusions, matrix ( dust ), and other components and a characteristic grain size.

The various steps in the purification process may free the protein from a matrix that confines it, separate the protein and non-protein parts of the mixture, and finally separate the desired protein from all other proteins.

When analyzing gas samples, however, the carrier is sometimes selected based on the sample's matrix, for example, when analyzing a mixture in argon, an argon carrier is preferred, because the argon in the sample does not show up on the chromatogram.

The paper is impregnated with a solid-state mixture of a dye and a suitable matrix ; a combination of a fluoran leuco dye and an octadecylphosphonic acid is an example.

In February 1985, Tanaka found that by using a mixture of ultra fine metal powder in glycerol as a matrix, an analyte can be ionized without losing its structure.

MCFCs are high-temperature fuel cells that use an electrolyte composed of a molten carbonate salt mixture suspended in a porous, chemically inert ceramic matrix of beta-alumina solid electrolyte ( BASE ).

During the plate collisions, these rocks were considerably faulted and crushed into melange, which is a mixture of ground-up matrix and resistant pockets of rock floating within.

The matrix can be reused to create hundreds, or thousands, of identical sorts so that the same character appearing anywhere within the book will appear very uniform, giving rise, over time, to the development of distinct styles of typefaces or fonts.

For practical purposes it might be challenging to actually compute the inverse matrix, given that some input-output tables are in excess of hundreds of sectors.

The enzymes of the citric acid cycle are located in the mitochondrial matrix, with the exception of succinate dehydrogenase, which is bound to the inner mitochondrial membrane as part of Complex II.

Membrane assembly and maintenance requires three of these ( peroxins 3, 16, and 19 ) and may occur without the import of the matrix ( lumen ) enzymes.

* Secretory vesicles hold the enzymes that are used to make the cell walls of plants, protists, fungi, bacteria, and Archaea cells as well as the extracellular matrix of animal cells.

The peptidoglycan matrix is very rigid, so these enzymes break down the peptidoglycan matrix in small sections so that growth and division of cells can occur.

Biofilm matrix degrading enzymes may be useful as anti-biofilm agents.

However, it has been shown more recently that, throughout the lifetime of a person, tenocytes in the tendon actively synthesize ECM components as well as enzymes such as matrix metalloproteinases ( MMPs ) can degrade the matrix.

Not all proteins remain within the cell and many are exported, for example digestive enzymes, hormones and extracellular matrix proteins.

An understanding of ECM structure and composition also helps in comprehending the complex dynamics of tumor invasion and metastasis in cancer biology as metastasis often involves the destruction of extracellular matrix by enzymes such as serine and threonine proteases and matrix metalloproteinases.

Neutrophil granulocyte migrates from the blood vessel to the matrix, sensing proteolytic enzymes, in order to determine intercellular connections ( to the improvement of its mobility ) and envelop bacteria through phagocytosis.

In addition, several hydrolytic enzymes, such as members of the cathepsin and matrix metalloprotease ( MMP ) groups, are released to digest the organic components of the matrix.

In the mitochondrion, the matrix contains soluble enzymes that catalyze the oxidation of pyruvate and other small organic molecules.

It is caused by a deficiency in one of the enzymes needed to break down the glycosaminoglycan heparan sulfate ( which is found in the extra-cellular matrix and on cell surface glycoproteins ).

Mononuclear cells can be released from soft tissues by enzymatic digestion with enzymes such as collagenase, trypsin, or pronase, which break down the extracellular matrix.

In the mitochondrion, the matrix contains soluble enzymes that catalyze the oxidation of pyruvate and other small organic molecules.

The enzymes used in fatty acid oxidation in animal cells are located in the mitochondrial matrix ( as was demonstrated by Eugene P. Kennedy and Albert Lehninger in 1948 ).

Ameloblasts secrete organic matrix: enamel proteins and enzymes.

The " carnitine shuttle " is composed of three enzymes that utilize carnitine to facilitate the import of hydrophobic long-chain fatty acids from the cytosol into the mitochondrial matrix for the production of energy via β-oxidation.

The osteoclast removes the mineralized matrix and collagen by secreting enzymes.