Furthermore, during certain events, such as the Fillmore Independence Day ( United States ) | 4th of July Festival, Fillmore May Festival extra law enforcement is required to patrol in order to maintain safety regulations.

Furthermore, let p ( x | y ) = p ( x, y ) / p ( y ).

* If F is algebraically closed and char ( F ) does not divide | G |, then the number of irreducible characters of G is equal to the number of conjugacy classes of G. Furthermore, in this case, the degrees of the irreducible characters are divisors of the order of G ( and they even divide the index of the center of G in G if ).

Furthermore, the factor is nonzero when | z | ≤ R, because

Furthermore, if R is a commutative superalgebra, then supermatrix multiplication is a bilinear operation, so that M < sub > p | q </ sub >( R ) forms a superalgebra over R.

Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings.

Furthermore, because f is differentiable at g ( a ) by assumption, Q is continuous at g ( a ).

Furthermore, for mathematicians, according to this formula the gluon color field can be represented by a SU ( 3 )- Lie algebra-valued " curvature "- 2-form where is a " vector potential "- 1-form corresponding to G and is the ( antisymmetric ) " wedge product " of this algebra, producing the " structure constants " f < sup > abc </ sup >.

Furthermore, if the morphism f is a monomorphism, then so is the morphism ker a → ker b, and if g is an epimorphism, then so is coker b → coker c.

Furthermore, for each f for which f ( 1 ) ≠ 0 there exists a g such that f * g =

Furthermore, Marx seems to believe that the former ( and hence, of both ) is ' imminent ' ( c. f.

Furthermore, f is Lebesgue integrable on

Furthermore, if, and if the Frobenius endomorphism of F is an automorphism, g may be written as, and in particular, ; a contradiction of the irreducibility of f. Therefore, if F possesses an inseparable irreducible ( non-zero ) polynomial, then the Frobenius endomorphism of F cannot be an automorphism ( where F is assumed to have prime characteristic p ).

Furthermore, the polynomial f ( Y )= Y < sup > p </ sup >− X is inseparable.

Furthermore, it is easy to check that f < sup > − 1 </ sup > ( like any inverse image map ) preserves finite intersections and arbitrary unions and therefore is a morphism of frames.

Furthermore, let S be a subset of P that has a least upper bound s. Then f preserves the supremum of S if the set f ( S ) =

If f is flat and locally of finite presentation, then f is universally open .< ref > EGA IV < sub > 2 </ sub >, Théorème 2. 4. 6 .</ ref > However, if f is faithfully flat and quasi-compact, it is not in general true that f is open, even if X and Y are noetherian .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( i ).</ ref > Furthermore, no converse to this statement holds: If f is the canonical map from the reduced scheme X < sub > red </ sub > to X, then f is a universal homeomorphism, but for X noetherian, f is never flat .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( ii ).</ ref >

Furthermore, of the song Beauty Fiend, she stated: “ Beauty Fiend is meant to be a real ‘ f ** ck you ’ of a song ... I ’ m not here to be your sex symbol, I ’ m not here to be your pretty girl on the cover.

Furthermore, it may happen that all polynomial invariants f take the same value on a given pair of points u and v in V, yet these points are in different orbits of the G-action.

Furthermore, if b < sub > 1 </ sub > and b < sub > 2 </ sub > are both coprime with a, then so is their product b < sub > 1 </ sub > b < sub > 2 </ sub > ( modulo a it is a product of invertible elements, and therefore invertible ); this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.

Furthermore, RS codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b + 1 consecutive bit errors can affect at most two symbols of size b.

Furthermore, the admissibility of expert testimony is governed by Rule 104 ( a ), not Rule 104 ( b ); thus, the Judge must find it more likely than not that the expert's methods are reliable and reliably applied to the facts at hand.

Furthermore, stage ( b ) corresponds to Chris Alexander's " tree " city, while ( c ) is similar to his " lattice " system ( following his dictum " the city is not a tree ").

Furthermore, proved that the predecessor relation gives rise to a complete lattice when restricted to the set of minimal ( a, b )- separators in G.

Furthermore, increases in assessment shall not exceed the lower of: a ) 3 % of assessed value from prior year ; or b ) percentage change in CPI.

Furthermore, the site has no system of checking and verifying the a ) truthfulness of the fact that the post is by a genuine student / pupil and b ) the truthfulness of the account of the teacher's ability.

Furthermore, the act stated in section 3 ( b ) that if misappropriation is, " willful and malicious " the court may award damages up to twice what would otherwise be entitled under section 3 ( a ).

Furthermore, while Neuromancer < nowiki >'</ nowiki > s narrator may have had an unusual " voice " for science fiction, much older examples can be found: Gibson's narrative voice, for example, resembles that of an updated Raymond Chandler, as in his novel The Big Sleep ( 1939 ).

Furthermore, all solutions x of this system are congruent modulo the product, N = n < sub > 1 </ sub > n < sub > 2 </ sub >… n < sub > k </ sub >.

Furthermore, Oman presents in its stratigraphic record a large negative carbon isotope excursion, within the Shuram Formation that is clearly away from any glacial evidence < ref name = LeGuerroue2006b >

Furthermore, these two probabilities are equally as likely as any other 21-flip combinations that can be obtained ( there are 2, 097, 152 total ); all 21-flip combinations will have probabilities equal to 0. 5 < sup > 21 </ sup >, or 1 in 2, 097, 152.

Furthermore, aside from helium and hydrogen, it is the least dense element in a solid or liquid state, being only 2 / 3 as dense as liquid nitrogen ( 0. 808 g / cm < sup > 3 </ sup >).

Furthermore, whenever p is a Sophie Germain prime — that is, 2p + 1 is also prime — and 2p + 1 is congruent to 1 or 7 mod 8, then 2p + 1 will be a factor of 2 < sup > p </ sup >− 1.

Furthermore, insulating materials such as silicon dioxide ( SiO < sub > 2 </ sub >), when exposed to photons with energy greater than the band gap, release free electrons and holes which subsequently cause adverse charging.

Furthermore, ι < sup >− 1 </ sup > is also continuous, so ι is a homeomorphism.

Furthermore, this splits into the two spin spaces Δ < sub >+</ sub >

Furthermore, the net potential difference of the galactic electric field in interstellar space is only 1. 6 × 10 < sup >− 19 </ sup > volt.

Furthermore, this fixed point can be found as follows: start with an arbitrary element x < sub > 0 </ sub > in X and define an iterative sequence by x < sub > n </ sub >

Furthermore, maximal ideals can be generalized by defining a maximal sub-bimodule M of a bimodule B to be a proper sub-bimodule of M which is contained by no other proper sub-bimodule of M. So, the maximal ideals of R are exactly the maximal sub-bimodules of the bimodule < sub > R </ sub > R < sub > R </ sub >.

Furthermore, the strict relations < and > are of little use in many non-total orders and hence no additional terminology is introduced for them.

Furthermore, MgB < sub > 2 </ sub > superconducts at temperatures higher than LTS ( its critical temperature is 39 K, compared with less than 10 K for NbTi and 18. 3 K for Nb < sub > 3 </ sub > Sn ), introducing the possibility of using it at 10-20 K in cryogen-free magnets or perhaps eventually in liquid hydrogen.

Furthermore, the conductivity can undergo a quantization in energy: i. e. the energy of the electrons going through a nanowire can assume only discrete values, which are multiples of the Von Klitzing constant G = 2e < sup > 2 </ sup >/ h ( where e is the charge of the electron and h is the Planck constant ).