Still, we must remember that we cannot construct and justify generalizations of this sort unless we are ready to consider many special instances of influence moving between such areas as theology, philosophy, political thought, and literature.

On C, from the point P at Af to the point Q at Af, we construct the chord, and upon the chord as a side erect a square in such a way that as S approaches zero the square is inside C.

In the C-plane we construct a set of rectangular Cartesian coordinates u, V with the origin at Q and such that both C and Af have finite slope at Q.

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.

Knowing Marlborough's destination, Tallard and Villeroi met at Landau in Alsace on 13 June to rapidly construct an action plan to save Bavaria, but the rigidity of the French command system was such that any variations from the original plan had to be sanctioned by Versailles.

Behavior as used in computer science is an anthropomorphic construct that assigns " life " to the activities carried out by a computer, computer application, or computer code in response to stimuli, such as user input.

Bioartificial organs, which use both synthetic and biological components, are also a focus area in research, such as with hepatic assist devices that use liver cells within an artificial bioreactor construct.

The term is parallel to-ology in English, being used to construct the names of academic fields: the Chinese names of fields such as physics, chemistry, biology, political science, economics, and sociology all end in xué.

The advantage of such a system lies in its ability to expand its own capacity rapidly and without additional human effort ; in essence, the initial investment required to construct the first clanking replicator would have an arbitrarily large payoff with no additional labor cost, with future returns discounted by their present value.

Settlers can also alter terrain, build improvements such as mines and irrigation, build roads to connect cities, and later in the game they can construct railroads which offer unlimited movement.

* It is not difficult to construct spacetimes which have naked singularities, but which are not " physically reasonable ;" the canonical example of such a spacetime is perhaps the " superextremal " < math > M <| Q |</ math > Reissner-Nordstrom solution, which contains a singularity at that is not surrounded by a horizon.

In this sense, Euclidean geometry is more concrete than many modern axiomatic systems such as set theory, which often assert the existence of objects without saying how to construct them, or even assert the existence of objects that cannot be constructed within the theory.

While it may be mathematically possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.

But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are presently the only way to construct appropriate models.

This connection is of such power that every individuality is under its dominion, and yet at the same time can construct for itself an inward world.

Note that while such perfect price discrimination is still a theoretical construct, it is becoming increasingly real with advances of information technology and micromarketing.

Anabolism uses energy to construct components of cells such as proteins and nucleic acids.

It is possible to construct a mechanical system such that the point trajectories in all components lie in concentric spherical shells around a fixed point.

In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ ( n ), together with a function g that takes a positive integer n and outputs a positive integer g ( n ) such that

However, when confronted with totally unexpected phenomena, such as the first evidence for invisible radiation, experimental scientists often use the same approach as historical scientists: construct a set of hypotheses about the causes and then look for a " smoking gun ".

Cordon Sanitaires, however, have been increasingly abandoned over the past two decades in multi-party democracies as the pressure to construct broad coalitions in order to win elections-along with the increased willingness of outsider parties themselves to participate in government-has led to many such parties entering electoral and government coalitions.

These characteristics can be used to construct many other ( sometimes surprising ) cryptographic protocols and applications, such as digital cash, password-authenticated key agreement, multi-party key agreement, time-stamping services, non-repudiation protocols, etc.

For each pushdown automaton one may construct a pushdown automaton such that, and vice versa, for each pushdown automaton one may construct a pushdown automaton such that

As part of his efforts to improve the accuracy of the calendar, Bianchini was commissioned by Pope Clement XI to construct an important meridian line in the Basilica of Santa Maria degli Angeli e dei Martiri ( the Basilica of Saint Mary of the Angels and the Martyrs ) in Rome, a device for calculating the position of the sun and stars.

He also followed up on the work done by Meton of Athens to measure the length of the year and construct an accurate lunisolar calendar.

Aquinas uses this principle to construct an objection to God's existence, an objection which he in turn answers and refutes generally ( cf.

In matrix mechanics, the correspondence principle was built in and was used to construct the theory.

In linear problems, for example, a family of linearly independent solutions can be used to construct general solutions through the superposition principle.

It superficially seems clear that the resulting extended number system cannot agree with the reals on all properties that can be expressed by quantification over sets, because the goal is to construct a nonarchimedean system, and the Archimedean principle can be expressed by quantification over sets, but this is just plain wrong.

This principle is used to construct vertical antennas substantially shorter than the 1 / 4 wavelength at which the antenna is resonant.

Note that it is possible in principle to carefully construct in-place algorithms that don't modify data ( unless the data is no longer being used ), but this is rarely done in practice.

* Interactive applet to construct trajectories using principle of least action

In 1965, the Nordic Council agreed in principle to build a new international airport on Saltholm, to replace the airport at Kastrup, and to construct a bridge-and-tunnel link across the island to connect Copenhagen and Malmö.

These techniques exploit the fact that the evanescent field contains information beyond the diffraction limit which can be used to construct very high resolution images, in principle beating the diffraction limit by a factor proportional to how far into the near field an imaging system extends.

Colonel Albert Deport, at the time the Director of the Atelier de Construction de Puteaux ( APX ), and asked him whether he could construct a gun on the general principle of the Haussner long-cylinder recoil without infringing the existing patents.

Assuming we have a sorting network of size n, we can construct a network of size by " inserting " an additional number into the already sorted subnet ( using the principle behind insertion sort ).

Venturi tubes are more expensive to construct than a simple orifice plate which uses the same principle as a tubular scheme, but the orifice plate causes significantly more permanent energy loss.

The Crown is regarded as a corporation, with the monarch, vested as she is with all powers of state, at the centre of a construct in which the power of the whole is shared by multiple institutions of government acting under the sovereign's authority ; the Crown has thus been described as the underlying principle of Canada's institutional unity, with the executive formally called the Queen-in-Council, the legislature the Queen-in-Parliament, and the courts as the Queen on the Bench.

In cryptanalysis, the piling-up lemma is a principle used in linear cryptanalysis to construct linear approximation to the action of block ciphers.

This principle is used to construct an equivalent electric circuit representation of the two configurations of the spin-valve.

Similarly, it can be used to construct surgery presentations of triangulated 3-manifolds, although the procedure is not explicitly written as an algorithm in principle it should have polynomial run-time in the number of tetrahedra of the given 3-manifold triangulation.

In 1963, the same principle was used outdoors to construct the Bird Thicket, ten aviaries surrounded by dense bushes and designed in various habitat settings, which visitors can enter through wire netted doors and curtains of cords.

In 1892 Sir James Dewar invented a container that could keep liquids hot or cold ( the thermos ) which led three men – Tsiolkovsky, Robert Goddard, and Hermann Oberth – to construct a large thermal flask for either liquid hydrogen and oxygen or for solid fuel combustion for use in rocket propulsion, applying the thermal flask principle to keep rocket fuel cold and successfully using it for the V-2 rocket and the Saturn V rocket that put man on the moon.

For each kind of data definition, the book explains how to organize the program in principle, thus enabling a programmer who encounters a new form of data to still construct a program systematically.