These cases, for all their rarity, are so dramatic that friends and relations repeat the story until the general population may get an entirely false notion of how often the hymen is a serious problem to newly-weds.

The theory that they were defensive military structures is not accepted by many modern archaeologists ( see the ' general references ' below ), while the alternative notion that they were farmhouses is dismissed by some others.

Its singular contribution to AI and psychology in general is the notion of a semantic network.

In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

In general topological spaces, however, the different notions of compactness are not equivalent, and the most useful notion of compactness — originally called bicompactness — involves families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact for the general notion, and reserve the term compact for topological spaces that are both Hausdorff and quasi-compact.

This ultimately led to the notion of a compact operator as an offshoot of the general notion of a compact space.

It was this notion of compactness that became the dominant one, because it was not only a stronger property, but it could be formulated in a more general setting with a minimum of additional technical machinery, as it relied only on the structure of the open sets in a space.

The dissenters were discontented with the general leftward trend in USCJ policies over the previous decades, such as " prayer book revision, egalitarianism, redefining halakhic boundaries of sexual relationships, and advocacy of Israel accepting conversions that are non-halakhic even by Conservative standards "., and the Union suggests that " The Conservative Movement thus appears to endorse the notion that changing societal norms can supersede the proper application of halakhic sources ".

In the late 1990s Wilfried Sieg analyzed Turing's and Gandy's notions of " effective calculability " with the intent of " sharpening the informal notion, formulating its general features axiomatically, and investigating the axiomatic framework ".

" Even today, though these errors have been recognized for more than a century, the general notion that Lao Tzu was Christ's forerunner has lost none of its romantic appeal.

There does exist in Filipino an equivalent, gender-neutral term for the professional that carries the more general notion of " healer ", traditional ( for example, an albuláryo ) or otherwise: manggagámot.

In contrast to Positivism, which held that statements are meaningless if they cannot be verified or falsified, Popper claimed that falsifiability is merely a special case of the more general notion of criticizability, even though he admitted that empirical refutation is one of the most effective methods by which theories can be criticized.

This explanation may imply that IQ tests do not necessarily measure a general intelligence factor, especially not Raven's as often argued, but instead may measure different types of intelligence that are developed by different experiences ( this argument is against the notion of an underlying general intelligence, or g factor ).

The notion of greatest common divisor can more generally be defined for elements of an arbitrary commutative ring, although in general there need not exist one for every pair of elements.

Some people use realization for the general notion and reserve the term representation for the special case of linear representations.

He proposes that most commonly accepted social institutions — including the notion of State, property as a right, natural rights in general, and the very notion of society — were mere spooks in the mind.

Beginning in the late 19th and early 20th century however, policies such as Woodrow Wilson's mission to " make the world safe for democracy " were often backed by military force, but more often effected from behind the scenes, consistent with the general notion of hegemony and imperium of historical empires ..

Much subsequent controversy about Rousseau's work has hinged on disagreements concerning his claims that citizens constrained to obey the general will are thereby rendered free: The notion of the general will is wholly central to Rousseau's theory of political legitimacy.

Using Rousseau's thought as an example, Arendt identified the notion of sovereignty with that of the general will.

Halliday's notion of language functions, or " metafunctions ", became part of his general linguistic theory.

Therefore, the congruence of its secants, that is the image of a general plane field of lines, is of order Af and class Af.

Finally, the image of a general bundle of lines is a congruence whose order is the order of the congruence of invariant lines, namely Af and whose class is the order of the image congruence of a general plane field of lines, namely Af.

The same type of construction works in the general case of congruence equations.

In general, congruence relations play the role of kernels of homomorphisms, and the quotient of a structure by a congruence relation can be formed.

::* Congruence ( general relativity ), in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of space time, or a bundle of world lines

If X and Y are algebraic structures of some fixed type ( such as groups, rings, or vector spaces ), and if the function f from X to Y is a homomorphism, then ker f will be a subalgebra of the direct product X × X. Subalgebras of X × X that are also equivalence relations ( called congruence relations ) are important in abstract algebra, because they define the most general notion of quotient algebra.

An important class of congruence subgroups is given by reduction of the ring of entries: in general given a group such as the special linear group SL ( n, Z ) we can reduce the entries to modular arithmetic in Z / NZ for any N > 1, which gives a homomorphism

However, there is no canonical way to do this in general: in particular for the conformal connection of a sphere congruence, it is not possible to separate the motion of the point of contact from the rest of the motion in a natural way.

This congruence is extensively used in, for example, the quadratic sieve, general number field sieve, continued fraction factorization, Dixon's factorization, and so on.

Jastorf culture extended south to the fringes of the northern Hallstatt provinces, while towards the north a general congruence with the late phases of the Northern Bronze Age can be noted.

The more general Ramanujan – Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent ( k − 1 )/ 2 where k is the weight of the form.

It turns out that the most general pp-wave spacetime has only one Killing vector field, the null geodesic congruence.

In general relativity, a congruence ( more properly, a congruence of curves ) is the set of integral curves of a ( nowhere vanishing ) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime.

In general relativity, a timelike congruence in a four-dimensional Lorentzian manifold can be interpreted as a family of world lines of certain ideal observers in our spacetime.

Describing the mutual motion of the test particles in a null geodesic congruence in a spacetime such as the Schwarzschild vacuum or FRW dust is a very important problem in general relativity.

* congruence ( general relativity ), for a derivation of the kinematical decomposition and of Raychaudhuri's equation.

The threat of effective anti-trust action, provoked by `` gouging the public '' through price increases not justified by cost increases, and fears of endangering relations with customers, Congress, the general public and the press, all operate to keep price increases in some relation to cost increases.

There is general agreement also that sex union between husbands and wives as an expression of mutual affection without relation to procreation is right ''.

There is a general view that citizenship in ancient times was a simpler relation than modern forms of citizenship, although this view has come under scrutiny.

Derrida will prefer to follow the more " fruitful paths ( formalization )" of a general semiotics without falling in what he considered " a hierarchizing teleology " privileging linguistics, and speak of ' mark ' rather than of language, not as something restricted to mankind, but as prelinguistic, as the pure possibility of language, working every where there is a relation to something else.

Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).

Euler discussed a generalization of Euclidean geometry called affine geometry, which retains the fifth postulate unmodified while weakening postulates three and four in a way that eliminates the notions of angle ( whence right triangles become meaningless ) and of equality of length of line segments in general ( whence circles become meaningless ) while retaining the notions of parallelism as an equivalence relation between lines, and equality of length of parallel line segments ( so line segments continue to have a midpoint ).

Boyle ’ s law, Charles ’ law and Avogadro ’ s law could be combined to give a general relation between the volume, pressure, temperature and the number of moles of a particular gas.

Today, the name Coriolis has become strongly associated with meteorology, but all major discoveries about the general circulation and the relation between the pressure and wind fields were made without knowledge about Gaspard Gustave Coriolis.

When a person's actions are completely virtuous in all matters in relation to others, Aristotle calls her " just " in the sense of " general justice ;" as such this idea of justice is more or less coextensive with virtue.

In general terms, a calculus is a formal system that consists of a set of syntactic expressions ( well-formed formulæ or wffs ), a distinguished subset of these expressions ( axioms ), plus a set of formal rules that define a specific binary relation, intended to be interpreted as logical equivalence, on the space of expressions.

* Define a b as " not b < a " ( i. e., take the inverse complement of the relation ), which corresponds to defining a ~ b as " neither a < b nor b < a "; these relations and ~ are in general not transitive ; however, if they are, ~ is an equivalence ; in that case "<" is a strict weak order.

" In general ," he wrote, " it may be affirmed that there is no such passion in human mind, as the love of mankind, merely as such, independent of personal qualities, or services, or of relation to ourselves.

Social geography is the branch of human geography that is most closely related to social theory in general and sociology in particular, dealing with the relation of social phenomena and its spatial components.

The general theory provides the law of gravitation, and its relation to other forces of nature.

Yale University Professor of Humanities Harold Bloom ( no relation to Allan ) has also argued strongly in favor of the canon, and in general the canon remains as a represented idea in many institutions, though its implications continue to be debated.

The so-called Heidegger controversy raises general questions about the relation between Heidegger's thought and his connection to National Socialism.

The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants by mapping them, for example, to groups which have a great deal of manageable structure in a way that respects the relation of homeomorphism ( or more general homotopy ) of spaces.

Key historical developments in physics include Isaac Newton's theory of universal gravitation and classical mechanics, an understanding of electricity and its relation to magnetism, Einstein's theories of special and general relativity, the development of thermodynamics, and the quantum mechanical model of atomic and subatomic physics.

The relation of Henry IV with his Silesian relatives in general was not good.

Interestingly, the ability to unconsciously and relatively accurately tally the frequency of events appears to have little or no relation to the individual's age, education, intelligence, or personality, thus it may represent one of the fundamental building blocks of human orientation in the environment and possibly the acquisition of procedural knowledge and experience, in general.

Derrida will prefer to follow the more " fruitful paths ( formalization )" of a general semiotics without falling in what he considered " a hierarchizing teleology " privileging linguistics, and speak of ' mark ' rather than of language, not as something restricted to mankind, but as prelinguistic, as the pure possibility of language, working every where there is a relation to something else.

The propagandistic rhetoric changed in relation to events and the atmosphere of Napoleon's reign, focusing first on his role as a general in the army and identification as a soldier, and moving to his role as emperor and a civil leader.

They define standardised general relation types, together with the kinds of things that may be related by such a relation type.