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, 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, the inner product of x with itself is always nonnegative.

Furthermore, some testing procedures employ a hydrolysis step prior to quantitation that converts the metabolic products to morphine, yielding a result that may be many times larger than with a method that examines each product individually.

Furthermore, the value of a commercial product comes in part from the necessary work of its inventors.

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, stage efficiency is the product of blade efficiency and nozzle efficiency, or

Furthermore, Jack Warner, who had little regard for his company's short film product, reputedly was so ignorant of his animation division that he was mistakenly convinced that the unit produced cartoons of Mickey Mouse, rival company Walt Disney Pictures ' flagship character.

Furthermore, he sold off the unit's pre-1948 library for a mere $ 3000 each, which proved a short sighted transaction in light of the considerable long term value that the company's animation product proved to have.

Furthermore many CAD applications now offer advanced rendering and animation capabilities so engineers can better visualize their product designs.

Furthermore aisle ends are extremely popular with product manufacturers, who pay top dollar to have their products located there ( Browne, 2010 ).

Furthermore, in some emerging economies, western fast food represents an expensive niche product price well above the price of traditional staples — i. e. the Big Mac is not a mainstream ' cheap ' meal as it is in the West, but a luxury import for the middle classes and foreigners.

Furthermore, some fragrances with the same product name but having a different concentration name may not only differ in their dilutions, but actually use different perfume oil mixtures altogether.

Furthermore, the product of two symplectic matrices is, again, a symplectic matrix.

Furthermore, a brand audit seeks to determine whether or not a business is perceived as an industry leader in technology, offering product or service innovations, along with exceptional customer service, among other relevant issues that customers use to decide on a brand of preference.

Furthermore, if two functions are given with value zero at x, then their product has derivative 0 at x, by the product rule.

Furthermore, his product plan was still very much in the formative stage and never reached the sophistication of the Delphi offering.

Furthermore, many venture capital firms will only seriously evaluate an investment in a start-up company otherwise unknown to them if the company can prove at least some of its claims about the technology and / or market potential for its product or services.

Furthermore, the NRC makes a widespread impact on product developments through its involvement in supporting the small to medium-sized business sector.

Furthermore, flexion and extension in the lumbal spine is the product of a combination of rotation and translation in the sagittal plane between each vertebra.

Furthermore, one does not even require an explicit representation for: it suffices to know that V is an inner product space.

Furthermore since a restricted ( 2 users ) version of the product was freely available without registration, contacting all WinGate users to notify of security issues was impossible, and therefore even long after the security problems were resolved there were still many insecure installations in use.

Furthermore I can identify each design.

Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

Furthermore, Linda & Morris Tannehill argue that no coercive monopoly of force can arise on a truly free market and that a government's citizenry can ’ t desert them in favor of a competent protection and defense agency.

Furthermore, considering that some of these roads seem to go nowhere, experts suggest that they can be linked — especially the Great North Road — to astronomical observations, solstice marking, and agricultural cycles.

Furthermore, mixing matter and antimatter can lead to the annihilation of both, in the same way that mixing antiparticles and particles does, thus giving rise to high-energy photons ( gamma rays ) or other particle – antiparticle pairs.

Furthermore, only bishops and presbyters ( priests ) ordained by bishops in the apostolic succession can validly celebrate or " confect " several of the other sacraments, including the Eucharist, reconciliation of penitents, confirmation and anointing of the sick.

Furthermore, many viruses express p53 inhibitors that can bind p53 and inhibit its transcriptional transactivation activity.

Furthermore, in the case of the obese woman, a breast lift ( mastopexy ) procedure, with or without a breast volume reduction, can be part of an upper-body lift and contouring for the woman who has undergone massive body weight loss.

Furthermore, the wood is often so porous, that if the varnish is stripped off the inexpensive bokken, one can see the use of wood fillers to fill the holes.

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 the Council affirmed against Protestant doctrine that the grace of God can be forfeited through mortal sin.

Furthermore, if the same device with no explicit performance specs beyond the Compact Disc logo initially handles nonstandard discs reliably, there is no assurance that it will not later stop doing so, and in that case, there is no assurance that it can be made to do so again by service or adjustment.

Furthermore the thick prods are a bit less efficient at releasing energy, but more energy can be stored by a crossbow.

Furthermore, in chemistry, four types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.

Furthermore, a train of backpropagating action potentials artificially generated at the soma can induce a calcium action potential ( a dendritic spike ) at the dendritic initiation zone in certain types of neurons.

Furthermore, the PIN structure can be found in many power semiconductor devices, such as IGBTs, power MOSFETs, and thyristors.

Furthermore, there are tangos among round dances, participation dances can involve tango mixers, and tango-style dances may be used in ice dancing or in burlesque theatre.

Furthermore, convolutions can be used to efficiently compute DFTs via Rader's FFT algorithm and Bluestein's FFT algorithm.

Furthermore, it can enable indigenous communities to “ reclaim and revalue their languages and cultures, and in so doing, improve the educational success of indigenous students .”

Furthermore, it can be integrated into current gun systems.

Furthermore, under certain idealized conditions one can theoretically recover S ( ƒ ) and s ( t ) exactly.

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, for a sequence of positive weights with sum we can define weighted power means as follows: