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.

The substructure consisting of a nucleobase plus sugar is termed a nucleoside.

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.

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.

Features of interest ( known as leads ) are subjected to more detailed seismic surveys which work on the principle of the time it takes for reflected sound waves to travel through matter ( rock ) of varying densities and using the process of depth conversion to create a profile of the substructure.

The 100 m long Nysa Bridge, a tunnel-like substructure, was the second largest of its kind in antiquity.

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.

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

Basal bodies originate from and have a substructure similar to that of centrioles, with nine peripheral microtubule triplets ( see structure at bottom center of image )

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

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.

It is provable in ZF that ∞ satisfies a somewhat weaker reflection property, where the substructure ( V < sub > α </ sub >, ∈, U ∩ V < sub > α </ sub >) is only required to be ' elementary ' with respect to a finite set of formulas.

** Aircraft description: Glider with a wooden substructure

The contract for the construction was of the station substructure and connecting lines was given to Messrs. Waring, with the Barlow's assistant Campion as supervisor.

As the earlier images suggest, polyphenol compositions are normally limited to carbon, hydrogen and oxygen in undefined proportion, with the preeminent substructure being the phenol unit.

Hence, the substructure has been removed, and the bellows moved to the back of the instrument, where they are operated with one hand while the other plays the keyboard.

The intensive component of search is called atom-by-atom-searching ( ABAS ), in which a mapping of the search substructure atoms and bonds with the target molecule is sought.

As extended under Sulla, the sanctuary of Fortune came to occupy a series of five vast terraces, which, resting on gigantic masonry substructure and connected with each other by grand staircases, rose one above the other on the hill in the form of the side of a pyramid, crowned on the highest terrace by the round temple of Fortune.

A circular design developed by Major Rice in February 1901 had good all round visibility, and the lack of corners did away with the need for a substructure.

Basal bodies originate from and have a substructure similar to that of centrioles, with nine peripheral microtubule triplets ( see structure at bottom center of image ).

In this case N is called an elementary substructure of M if every first-order σ-formula φ ( a < sub > 1 </ sub >, …, a < sub > n </ sub >) with parameters a < sub > 1 </ sub >, …, a < sub > n </ sub > from N is true in N if and only if it is true in M.

A substructure N of M is elementary if and only if it passes the Tarski – Vaught test: Every first-order formula φ ( x, b < sub > 1 </ sub >, …, b < sub > n </ sub >) with parameters in N that has a solution in M also has a solution in N when evaluated in M. One can prove that two structures are elementary equivalent with the Ehrenfeucht – Fraïssé games.

N is an elementary substructure of M if N and M are structures of the same signature σ such that for all first-order σ-formulas φ ( x < sub > 1 </ sub >, …, x < sub > n </ sub >) with free variables x < sub > 1 </ sub >, …, x < sub > n </ sub >, and all elements a < sub > 1 </ sub >, …, a < sub > n </ sub > of N, φ ( a < sub > 1 </ sub >, …, a < sub > n </ sub >) holds in N if and only if it holds in M:

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.

But due to stringent building laws in Germany, the roof had to be reinforced with a substructure.