If N is a substructure of M, then both N and M can be interpreted as structures in the signature σ < sub > N </ sub > consisting of σ together with a new constant symbol for every element of N. N is an elementary substructure of M if and only if N is a substructure of M and N and M are elementarily equivalent as σ < sub > N </ sub >- structures.

In the language consisting of the binary functions + and ×, binary relation <, and constants 0 and 1, the structure ( Q, +, ×, <, 0, 1 ) is a substructure of ( R, +, ×, <, 0, 1 ).

In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure, thus it is not known to be made up of smaller particles.

If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.

Representation of an organic compound | organic hydroxyl group, where R represents a hydrocarbon or other organic moiety, the red and grey spheres represent oxygen and hydrogen atoms, respectively, and the rod-like connections between these, covalent chemical bond s. A hydroxyl is a chemical functional group containing an oxygen atom connected by a covalent bond to a hydrogen atom, a pairing that can be simply understood as a substructure of the water molecule.

As a result, warhead components are contained within an aluminium honeycomb substructure, sheathed in pyrolytic graphite-epoxy resin composite, with a heat-shield layer on top which is constructed out of 3-Dimensional Quartz Phenolic.

The substructure of a GMC is a complex pattern of filaments, sheets, bubbles, and irregular clumps.

By the first isomorphism theorem, the image of A under ƒ is a substructure of B isomorphic to the quotient of A by this congruence.

Furthermore, the pyramid substructure is reminiscent of the plan of Khasekhemwy ’ s mud-brick funerary enclosure at Abydos.

The substructure of the South Tomb is entered through a tunnel-like corridor with a staircase that descends about 30m before opening up into the pink granite burial chamber.

It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure ( described below ).

Finding the shortest path in a graph using optimal substructure ; a straight line indicates a single edge ; a wavy line indicates a shortest path between the two vertices it connects ( other nodes on these paths are not shown ); the bold line is the overall shortest path from start to goal.

Likewise, in computer science, a problem that can be broken down recursively is said to have optimal substructure.

Consequently, the first step towards devising a dynamic programming solution is to check whether the problem exhibits such optimal substructure.

For example, given a graph G =( V, E ), the shortest path p from a vertex u to a vertex v exhibits optimal substructure: take any intermediate vertex w on this shortest path p. If p is truly the shortest path, then the path p < sub > 1 </ sub > from u to w and p < sub > 2 </ sub > from w to v are indeed the shortest paths between the corresponding vertices ( by the simple cut-and-paste argument described in CLRS ).

Occasionally, the reason behind such Ramsey-type results is that the largest partition class always contains the desired substructure.

The Ara Pacis is seen to embody without conscious effort the deep-rooted ideological connections among cosmic sovereignty, military force and fertility that were first outlined by Georges Dumézil, connections which are attested in early Roman culture and more broadly in the substructure of Indo-European culture at large.

In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed efficiently from optimal solutions of its subproblems.

Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proved by induction that this is optimal at each step ( Cormen et al.

This is an example of optimal substructure.

Such an example is likely to exhibit optimal substructure.

As an example of a problem that is unlikely to exhibit optimal substructure, consider the problem of finding the cheapest airline ticket from Buenos Aires to Moscow.

If minimizing the local functions is a problem of " lower order ", and ( specifically ) if, after a finite number of these reductions, the problem becomes trivial, then the problem has an optimal substructure.

Firstly, a cardinal κ is inaccessible if and only if κ has the following reflection property: for all subsets U ⊂ V < sub > κ </ sub >, there exists α < κ such that is an elementary substructure of.

Each family line can be considered a substructure.

His tomb still exists on the plateau between Lake Gygaea and the river Hermus to the north of Sardis — a large mound of earth with a substructure of huge stones.

Beam bridges are horizontal beams supported at each end by substructure units and can be either simply supported when the beams only connect across a single span, or continuous when the beams are connected across two or more spans.

The density, temperature, and substructure of the intracluster X-Ray gas therefore represents the entire thermal history of cluster formation.

Marx differentiated between base and superstructure, with the base ( or substructure ) referring to the economic system, and superstructure, to the cultural and political system.

Cultures who built substructure mounds include the Troyville culture, Coles Creek culture, Plaquemine culture and Mississippian cultures.

By recording full sets of reflections at three different wavelengths ( far below, far above and in the middle of the absorption edge ) one can solve for the substructure of the anomalously diffracting atoms and thence the structure of the whole molecule.

The arena substructure was partly excavated in 1810 – 1814 and 1874 and was fully exposed under Benito Mussolini in the 1930s.

Unlike the other " White City " buildings, it was constructed with a brick substructure under its plaster facade.

It has a substructure of walls twenty feet thick at eleven foot intervals, so that from a distance one has the impression of woods overhanging their native mountains.

Due to high longitudinal and transverse loads acting over the bridge and to accommodate movements between the superstructure and substructure, Oresund Bridge was equipped with bearings weighing as high as 20, 000kg per bearing, which are capable of bearing vertical loads up to 96, 000KN in longitudinal direction, and up to 40, 000KN in transverse direction.

But in Chaldea there are some enormous masses of ruins, evidently remains of the vast mounds which formed the substructure of their temples.

The MSA ( Multi-Dimensional Scalogram Analysis ) of René Lysloff and Jim Matson ( A New Approach to the Classification of Sound-Producing Instruments, Ethnomusicology, Spring / Summer, 1985, also at mywebspace. wisc. edu ), using 37 variables, including characteristics of the sounding body, resonator, substructure, sympathetic vibrator, performance context, social context, and instrument tuning and construction, corroborated the taxonomy of Schaeffner, producing 2 categories, aerophones and the chordophone-membranophone-idiophone combination.

The substructure lay in a 4m deep rectangular pit, and had mudbrick walls rising to 6 m. Three sides were extended and built out to create eight shallow steps rising at an angle of 49 °.

A nucleotide is an organic molecule consisting of a nitrogenous heterocyclic nucleobase ( a purine or a pyrimidine ), a pentose sugar ( deoxyribose in DNA or ribose in RNA ), and a phosphate or polyphosphate group.

This acquisition is a matched, perfect set -- consisting of two sofas six feet long, plus six sidechairs and two armchairs.

The Austro-Asiatic languages are well known for having a " sesquisyllabic " pattern, with basic nouns and verbs consisting of a reduced minor syllable plus a full syllable.

The completed films included the seven-episode Why We Fight series — consisting of Prelude to War ( 1942 ), The Nazis Strike ( 1942 ), Divide and Conquer ( 1943 ), The Battle of Britain ( 1943 ), The Battle of Russia ( 1943 ), The Battle of China ( 1944 ), War Comes to America ( 1945 ) – plus Know Your Enemy: Japan ( 1945 ), Tunisian Victory ( 1945 ), and Two Down and One to Go ( 1945 ) that do not bear the Why We Fight banner ; as well as the African-American related, The Negro Soldier ( 1944 ).

Fandom ( consisting of fan plus the suffix-dom, as in kingdom, freedom, etc.

As of November 2011, there are 191 ICAO members, consisting of 190 of the 193 UN members ( all but Dominica, Liechtenstein, and Tuvalu ), plus the Cook Islands.

There, the input is performed by two sets of three keys plus a space bar ( as in the Perkins Brailler ), while output is via a refreshable braille display consisting of a row of electromechanical character cells, each of which can raise or lower a combination of six ( or in some cases, eight ) round-tipped pins.

A semi-trailer truck, also known as a semi, tractor-trailer, truck and trailer, transfer truck, 18-wheeler, mack truck, big rig ( US ), transport ( Canada ), artic ( UK and Ireland ), or lorry ( UK ), is an articulated vehicle consisting of a towing engine ( tractor in the United States, prime mover in Australia or truck in Ireland, the United Kingdom, Canada and New Zealand ), and a semi-trailer ( plus possible additional trailers ) that carries the freight.

Compatible sideband transmission is usually single-sideband ( SSB ) amplitude-modulation-equivalent ( AME ) transmission consisting of the emission of the carrier plus the upper sideband.

A coronal mass ejection ( CME ) is an ejected plasma consisting primarily of electrons and protons ( in addition to small quantities of heavier elements such as helium, oxygen, and iron ), plus the entraining coronal closed magnetic field regions.

This is called the low-noise blockconverter ( LNB ), and the unit consisting of the horn plus the converter is called the LNB with feedhorn ( LNBF ).

In 1979, before the Uganda-Tanzania War, the Ugandan armed forces were reported, by the IISS, as consisting of 20, 000 land forces personnel, with two four-battalion brigades and five other battalions of various types, plus a training regiment.

The Constitution of Bhutan provides for a government consisting of three main branches – executive, legislative, and judicial – plus the officially apolitical Dratshang Lhentshog ( Monastic Affairs Commission ) of the Drukpa Kagyu state religion.

With the board of directors consisting of Kevin and Brian Blume plus Gygax, Gygax was primarily a figurehead president and CEO of the corporation, with Brian Blume as president of creative affairs and Kevin Blume as president of operations, as of 1981.

Guaraní only allows syllables consisting of a vowel or a consonant plus a vowel ; syllables ending in a consonant or two or more consonants together are not possible.

The county was initially divided into three townships: Berrien Township, consisting of present-day townships of Berrien, Oronoko, and Lake plus a two-mile strip north of that territory ; St. Joseph Township, consisting of everything north of Berrien Township ; and Niles Township, consisting of everything south of Berrien Township.

The new line-up ( consisting of Lydon, earlier members Bruce Smith and Lu Edmonds, plus multi-instrumentalist Scott Firth ) played to generally positive reviews in late 2009.

Jämtland County ( Jämtlands län ) is a county or län in the middle of Sweden consisting of the provinces of Jämtland and Härjedalen, along with minor parts of Hälsingland and Ångermanland, plus two tiny uninhabited strips of Lapland and Dalarna.

It comprised two battalions ( commanded by Colonel Gabriel Thorman and Colonel Marcus Saussure ) of 809 men each, consisting of four companies of Swiss troops plus four non-Swiss companies, for a total of 1618 men.

A famous victory for the Plains Nations was the Battle of the Little Big Horn in 1876, when Col. George Armstrong Custer and two hundred plus members of the 7th Cavalry were killed by a force consisting of Native Americans from the Lakota, Northern Cheyenne, and Arapaho nations.

The first part consisted of the first two movements of the symphony as it is now known plus Blumine, and the second consisting of the funeral-march and finale.

* Wireless LAN-networks consisting of zero or more access points plus devices

Modern Swedish is written with a 29-letter alphabet consisting of the modern 26-letter Latin alphabet plus 3 other letters: ' å ', ' ä ' and ' ö ', added after the letter " z ".