* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

Bernard set out to convince these other regions to rally behind Innocent.

# An unavoidable set contains regions such that every map must have at least one region from this collection.

The Hong Kong Government has also set up the Hong Kong Tourism Board with offices in other countries and regions to promote tourism.

With a grant from the Rockefeller Foundation, Hoover set up health units to work in the flooded regions for a year.

While the number of regions is somewhat stable ( the only modification to the original set is the separation of Molise from Abruzzo ), there has been a tendency in later years to create new provinces, such as Crotone, Verbania, Lodi, Biella, Lecco and others.

His use of routier mercenaries in the central regions had rapidly eaten away his remaining support in this area too, which set the stage for a sudden collapse of Angevin power.

Convectional currents are easily set up within the airmass whenever there is little instability in the airmass as a result of a slight to a very high orographic uplift in mountainous regions like the obudu plateau or the heating of the land which can trigger the formation of cumulonimbus cloud leading to thunderstorms within the airmass.

The centerpiece of the deregulation was the establishment of two categories of basic services licenses: Local loop ( LL ), for fixed line telecommunication within the 14 PTCL regions, and Long-distance and International ( LDI ), for connectivity between regions .” Two sets of criteria set by the regulatory authorities must be met before an operator is allowed to start operation: one for the issuance of a license and another for the maintenance of service quality.

* Considering the enclosed regions as point sets, we can find the area of the enclosed point set.

There is not a set pattern for promoter regions as there are for consensus sequences.

The remoteness of the Volga Region, the Ural Region, Siberia, and the Far East was favourable for the anti-Bolshevik powers, and the Whites set up a number of organizations in the cities of these regions.

In 2012 that percentage is expected to lower to 5. 3 % due to a set of tough reforms in the autonomous regions and central government, they begin to meet the objectives.

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time ( a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a ' space-like surface ') and draw an " embedding diagram " depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an " Einstein – Rosen bridge ".

The Treaty of San Stefano was signed on 3 March 1878 and set up an autonomous Bulgarian principality on the territories of the Second Bulgarian Empire, including the regions of Moesia, Thrace and Macedonia, though the state was de jure only autonomous but de facto functioned independently.

British commanders had trained on the lessons of the Crimean War, and were adept at battalion and regimental set pieces with columns manoeuvring in jungles, deserts and mountainous regions.

A complete series box set featuring all 90 episodes in a collector's edition box has been released in regions 1 & 2.

By the 1530s, small groups of Portuguese traders and prospectors penetrated the interior regions seeking gold, where they set up garrisons and trading posts at Sena and Tete on the Zambezi River and tried to gain exclusive control over the gold trade.

In forensic biology, pollen can tell a lot about where a person or object has been, because regions of the world, or even more particular locations such a certain set of bushes, will have a distinctive collection of pollen species.

* Most of the regions depended on a lord or count in name only, the cities effectively being ruled by guilds and councils and, although in theory part of a kingdom, their interaction with their rulers was regulated by a strict set of liberties describing what the latter could and could not expect from them.

Heath did not divide Britain into regions, choosing instead to await the report of the Crowther Commission on the constitution ; the ten Government Office Regions were eventually set up by the Major government in 1994.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:

Other terms such as character set, character map, and code page are used almost interchangeably, but these terms have related but distinct meanings described below.

Additional milieu were provided by Chaosium with the release of Dreamlands, a boxed supplement containing additional rules needed for playing within the Lovecraft Dreamlands, a large map and a scenario booklet, and Cthulhu By Gaslight, another boxed set which moved the action from the 1920s to the 1890s.

* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.

Other attributes also set each map apart, for example, restrictions on the placement of initial settlements, whether tiles are distributed randomly, the number of victory points needed to win, and special victory point awards, usually for building on islands across the sea.

In projective geometry, an ellipse can be defined as the set of all points of intersection between corresponding lines of two pencils of lines which are related by a projective map.

A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.

Power sets: The power set functor P: Set → Set maps each set to its power set and each function to the map which sends to its image.

One can also consider the contravariant power set functor which sends to the map which

The original Gamma World boxed set ( containing a 56-page rulebook, a map of a devastated North America, and dice ) was released in 1978.

A unary operation f, that is, a map from some set S into itself, is called idempotent if, for all x in S,

The Second Thule Expedition ( 1916 – 1918 ) was larger with a team of seven men, which set out to map a little known area of Greenland's north coast.

This was the approach taken by the STAGE2 Mobile Programming System, which used a rudimentary macro compiler ( called SIMCMP ) to map the specific instruction set of a given computer to counterpart machine-independent macros.

Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.

Phonology relates to phonetics via the set of distinctive features, which map the abstract representations of speech units to articulatory gestures, acoustic signals, and / or perceptual representations.

Using statistics collected from tens of thousands of coincidence events, a set of simultaneous equations for the total activity of each parcel of tissue along many LORs can be solved by a number of techniques, and, thus, a map of radioactivities as a function of location for parcels or bits of tissue ( also called voxels ) may be constructed and plotted.

Weapons appear as level items, spawning at regular intervals in set locations on the map.

It included two ten-sided dice, a large set of cardboard counters, and a folding map with a futuristic city on one side and various wilderness areas on the other for use with the included adventure, SF-0: Crash on Volturnus.

A first countable, separable Hausdorff space ( in particular, a separable metric space ) has at most the continuum cardinality c. In such a space, closure is determined by limits of sequences and any sequence has at most one limit, so there is a surjective map from the set of convergent sequences with values in the countable dense subset to the points of X.

expansion set with new units and a new map.