Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

* Given a small, privileged set of inputs ( e. g., reserved words for a compiler ), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.

According to pioneering Angkor scholar Maurice Glaize, " Given the very particular charm of Banteay Srei — its remarkable state of preservation and the excellence of a near perfect ornamental technique — one should not hesitate, of all the monuments of the Angkor group, to give it the highest priority.

Given a perfect graph G, Lovász forms a graph G * by replacing each vertex v by a clique of t < sub > v </ sub > vertices, where t < sub > v </ sub > is the number of distinct maximum independent sets in G that contain v. It is possible to correspond each of the distinct maximum independent sets in G with one of the maximum independent sets in G *, in such a way that the chosen maximum independent sets in G * are all disjoint and each vertex of G * appears in a single chosen set ; that is, G * has a coloring in which each color class is a maximum independent set.

Given this success, it may come as a nasty shock that it seems to be very difficult, mathematically speaking, to construct rotating stellar models in which a perfect fluid interior is matched to an asymptotically flat vacuum exterior.

Given the perfect state of conservation, in special circumstances, this mansion often hosts certain cultural events.

Given capital mobility and perfect substitutability, investors would be expected to hold those assets offering greater returns, be they domestic or foreign assets.

Given two groups G and H and a group homomorphism f: G → H, let K be a normal subgroup in G and φ the natural surjective homomorphism G → G / K ( where G / K is a quotient group ).

" Given the elimination of these pernicious influences, Marx allowed that " normal conditions of spontaneous development " of the rural commune could exist.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).

Given their vertical-cavity geometry, VCSOAs are resonant cavity optical amplifiers that operate with the input / output signal entering / exiting normal to the wafer surface.

Given a normalized light vector l ( pointing from the light source toward the surface ) and a normalized plane normal vector n, one can work out the normalized reflected and refracted rays:

Given that any proposition containing conjunction, disjunction, and negation can be equivalently rephrased using conjunction and negation alone ( the conjunctive normal form ), we can now handle any compound proposition.

Given a ring R and a unit u in R, the map ƒ ( x ) = u < sup >− 1 </ sup > xu is a ring automorphism of R. The ring automorphisms of this form are called inner automorphisms of R. They form a normal subgroup of the automorphism group of R.

Given two intersecting planes described by and, the dihedral angle between them is defined to be the angle between their normal directions:

Given the great depth of Lake Tahoe, and the locations of the normal faults within the deepest portions of the lake, modeling suggests that earthquakes on these faults can trigger tsunamis.

Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

Given 100 balls, some of them red and some blue, a human with normal color vision can easily separate them into red ones and blue ones.

Given the observed percentage difference p − q ( 2 % or 0. 02 ) and the standard error of the difference calculated above (. 03 ), any statistical calculator may be used to calculate the probability that a sample from a normal distribution with mean 0. 02 and standard deviation 0. 03 is greater than 0.

Given that it would be complicated to perform this test on every patient with sleep-related breathing problems, some suggest that measuring bicarbonate levels in normal ( venous ) blood would be a reasonable screening test.

Given then a normal extension L of K, with automorphism group Aut ( L / K ) = G, and containing α, any element g ( α ) for g in G will be a conjugate of α, since the automorphism g sends roots of p to roots of p. Conversely any conjugate β of α is of this form: in other words, G acts transitively on the conjugates.

Given our current estimate of the parameters θ < sup >( t )</ sup >, the conditional distribution of the Z < sub > i </ sub > is determined by Bayes theorem to be the proportional height of the normal density weighted by τ:

Given an incident direction from the surface to the light source and the surface normal direction the specularly reflected direction ( all unit vectors ) is:

Given that the angle of incidence is larger than the critical angle ( with respect to the normal of the surface ) and the refractive index is lower on the other side of the boundary relative to the incident ray, TIR will occur and no light will be able to pass through.

Given that ( A ) the Georges are among the most rational, principled and educated persons on the planet, and ( B ) their differences from normal humans are purely physical, they conclude that in any situation where the Three laws would come into play, their own orders should take priority over that of a regular human.

Given the low accelerations placed on the spacecraft while in the outer solar system, MOND may be in effect, modifying the normal gravitational equations.

Given only the artwork and outline to work with during production, writer Yoshinori Kitase felt that one early scene of the character approaching a castle was too " boring to make completely normal ", and decided to ad-lib a scene with one of his accompanying soldiers dusting off his boots in the middle of a desert.

Given an arbitrary square matrix, the elementary divisors used in the construction of the Jordan normal form do not exist over F, so the invariant factors a < sub > i </ sub >( x ) as given above must be used instead.

Given the predictable timeline of childhood behavior, he proposed " libido development " as a model of normal childhood sexual development, wherein the child progresses through five psychosexual stages — ( i ) the oral, ( ii ) the anal, ( iii ) the phallic, ( iv ) the latent, and ( v ) the genital — in which the source pleasure is in a different erogenous zone.

Given that sound levels at such events usually exceed recommended safe levels of exposure, this is a problem which is probably showing up variations between people, which may be genetic, or the result of stress or ill-health, or it may be caused by abnormal response in the tensor tympani and stapedius muscles which function in the normal acoustic reflex response that protects the inner ear from loud sounds.

Given any group G, the group consisting of only the identity element is a trivial group and being a subgroup of G is called the trivial subgroup of G.

Given such a G-module M, it is natural to consider the subgroup of G-invariant elements:

Given any subgroup < math > G < GL ( V )</ math > of the general linear group,

Given an arbitrary category C, a representation of G in the category C is a functor from G to C. Such a functor selects an object of C and a subgroup of automorphisms of that object.

Given an integer n > 1, let H be any subgroup of the multiplicative group

Given a Fuchsian group, that is, a discrete subgroup Γ of PSL ( 2, R ), Γ acts on H via linear fractional transformation.

Given a cyclic subgroup

Given a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

Given the above-mentioned considerations, many critics of coca eradication believe the fundamental goal of the U. S. government is to constrict the flow of income to the Colombian Marxist rebel movement, FARC, which is heavily funded by the illegal drug trade, rather than combating drugs per se.

Given below are the fundamental differences between physical goods and services:

Given this fundamental logical difficulty, there has been very little experimental investigation by parapsychologists of retrocognition.

Given an oriented manifold M of dimension n with fundamental class, and a G-bundle with characteristic classes, one can pair a product of characteristic classes of total degree n with the fundamental class.

Given a fundamental domain for the group action ( for the full, orientation-reversing symmetry group, a ( 2, 3, 7 ) triangle ), the reflection domains ( images of this domain under the group ) give a tiling of the quartic such that the automorphism group of the tiling equals the automorphism group of the surface – reflections in the lines of the tiling correspond to the reflections in the group ( reflections in the lines of a given fundamental triangle give a set of 3 generating reflections ).

Given an action of a group G on a topological space X by homeomorphisms, a fundamental domain ( also called fundamental region ) for this action is a set D of representatives for the orbits.

Given the geometric approach, the consideration of homogeneous equations and homogeneous co-ordinates is fundamental, for the same reasons that projective geometry is the dominant approach in algebraic geometry.

Given this fundamental equality, it was just as reasonable for them to represent their gods in animal form ( Gilbert, Qtd.

Given the fundamental idea of a rational function on a general variety V, or in other words of a function f in the function field of V,

Given a 3-manifold ( not necessarily compact ) with finitely generated fundamental group, there is a compact three-dimensional submanifold, called the compact core or Scott core, such that its inclusion map induces an isomorphism on fundamental groups.

Given this labeling of the roots, the solution of the fundamental orbital equation is

Given its fundamental nature, exploratory research often concludes that a perceived problem does not actually exist.

Given a group presentation by generators and relations, one gets a 2-complex with that fundamental group.