The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G. Specifically, the image of G under a homomorphism is isomorphic to where ker ( φ ) denotes the kernel of φ.

Specifically, the process was first used by the English " Good Parliament " against Baron Latimer in the second half of the 14th century.

Specifically, the chiefs sought protection from the French, " the tribe of Marion ", and it is the first known plea for British intervention written by Māori.

Specifically, Balcones Heights drew local attention in late 2006 for being the first location in the San Antonio area to approve the installation of " red-light cameras "; angering many citizens.

Specifically, the QUT Business School is accredited with AMBA, EQUIS, and AACSB, making it one of very few business schools in the world, and the first in Australia, to obtain this Triple Crown of international accreditation.

Specifically, they were first documented in the 14th century.

Specifically, the altered structure of the duplex induced by the pseudouridine places the 2 ' OH of the bulged adenosine in a favorable position for the first step of splicing.

Specifically, at the time in which an individual first hears of an event, the degree of unexpectedness and surprise is the first step in the registration of the event.

Specifically, the hypothesis predicts that “ as the infusion of mass media information into a social system increases, higher socioeconomic status segments tend to acquire this information faster than lower socioeconomic-status population segments so that the gap in knowledge between the two tends to increase rather than decrease ” Phillip J. Tichenor, then Associate Professor of Journalism and Mass Communication, George A. Donohue, Professor of Sociology, and Clarice, N. Olien, Instructor in Sociology – three University of Minnesota researchers – first proposed the knowledge gap hypothesis in 1970.

Specifically, sign conditions are imposed on the sequence of principal minors ( determinants of upper-left-justified sub-matrices ) of the bordered Hessian, the smallest minor consisting of the truncated first 2m + 1 rows and columns, the next consisting of the truncated first 2m + 2 rows and columns, and so on, with the last being the entire bordered Hessian.

Specifically, he corrected Ptolmey ’ s estimate of the length of the Mediterranean sea from 62 degrees to the correct value of 42 degrees In his treatise on the solar year, which survives only in a Hebrew translation, he was the first to demonstrate the motion of the solar apogee relative to the fixed background of the stars.

Specifically, first grade.

Specifically, the worker caste is referenced for the first time, prior episodes had only mentioned the religious and warrior castes.

Specifically, the amplifier measures voltage in the first few milliseconds of the cycle, generates the error signal, and spends the rest of the cycle passing current to reduce that error.

Specifically, the Act expanded the Medicare program to provide protection against catastrophic medical expenses and for the first time, provided coverage under the Medicare program for prescription drugs.

Specifically, presuppositionalists describe Thomistic ( also " Traditional " or " Classical ") apologetics as concentrating on the first aspect of apologetics with its logical proofs for the existence of God, simply assuming common ground with the non-Christian and utilizing a piece-by-piece methodology.

Specifically, it was the first successful network variety series starring an African American.

Specifically, duration can be formulated as the first derivative of the price with respect to the interest rate, and convexity as the second derivative ( see: Bond duration closed-form formula ; Bond convexity closed-form formula ).

Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question, and the convexity as the second derivative.

Specifically, Jesus first touched the man's ears, and touched his tongue after spitting, and then said Ephphatha !, an Aramaic word meaning Be opened.

Specifically, the school's endowment was comparatively lower than similar schools, the physical plant was in need of revitalization, and enrollment was suffering due to the opening of the town's first public high school in 1939.

It dominated the Grammy Awards of 1999, winning Record of the Year marking the first time to be won by a Canadian, Song of the Year, Best Female Pop Vocal Performance and Best Song Written Specifically for a Motion Picture or Television.

Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows ( and their five labels ), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph.

Specifically, the γ subunit includes four particular Cystathionine beta synthase ( CBS ) domains giving AMPK its ability to sensitively detect shifts in the AMP: ATP ratio.

Specifically, Princes of the Blood used four front-facing dragons, Qin Wang had two front-facing and two side-facing dragons, and Jun Wang had four side-facing ones ; all had five claws on each foot.

Specifically, they are found in four locations-Cheenkannipuzha ( a major tributary of Velapattanam River ), the Achankovil river, the Chaliyar river and near Mundakayam town.

Specifically the four interactions to be unified are:

Specifically it would be called a dimer if it contains two subunits, a trimer if it contains three subunits, and a tetramer if it contains four subunits.

" Specifically, Bartels focuses on four questions:

Specifically identified here are the four features namely, Red Cinder Dome, Pakushin cone, the Sugarloaf and the Point Kadin vents.

Specifically, it could be considered as advocating a National Health Service, such as was created in Britain four decades later-since a doctor who is employed by the state and gets a fixed salary for treating whoever needs medical attention would not face the dilemma discussed in the foreword.

Specifically, Van der Waals strain is considered a form of strain where the interacting atoms are at least four bonds away from each other.

Specifically, the theory contains the following four tenets in its hypotheses:

Specifically chapter four of the ISO / IEC 11179 metadata registry standard covers data element definition quality standards.

Specifically, in verses 13: 14 – 17, He instructs them, 14 " If I then, your Lord and Teacher, have washed your feet, you also ought to wash one another ’ s feet.

Specifically, it is the density altitude at which flying in a clean configuration, at the best rate of climb airspeed for that altitude and with all engines operating and producing maximum continuous power, will produce a given rate of climb ( usually 100 feet per minute climb or 30 meters per minute, and 500 feet per minute climb for jet airplanes ).

Specifically to the Kern watershed, an oral history was taken from Roy De Voe, who claimed to have seen " very old beaver sign " on the east side of the Kern River at Funston Meadow ( elevation 6, 476 feet ) in 1946.

Specifically, Ded Moroz is often shown wearing a heel-length fur coat, a semi-round fur hat, and valenki or jackboots on his feet.

Specifically, in a Cuban television interview days after the shootdown took place, Roque, from within Cuba, stated, " I personally have violated air space, specifically the last was on January 9, 1996. where I got a call the day before to participate in a flight to Havana where thousands of leaflets were going to be released from a height of more than 9, 500 feet at a distance of less than 10 miles from the coast.

Specifically, it can be used to test the equivalence principle, to probe dark matter, and test neutrino physics.

Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

Specifically, the associativity and commutativity determine when repeated calculation can or cannot be avoided.

") appears to be much easier than the problem of actually finding the factors of N. Specifically, the former can be solved in polynomial time ( in the number n of digits of N ) with the AKS primality test.

Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder ( it can come quite close to the other cylinder ).

Specifically, it can be shown that for prime p > 2, M < sub > p </ sub >

Specifically, in an environment where it is considered important to know the probability of a fraudulent login in order to accept the risk, one can ensure that the total number of possible passwords multiplied by the time taken to try each one ( assuming the greatest conceivable computing resources ) is much greater than the password lifetime.

Specifically, he demonstrated an upper limit, known as Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.

Specifically, since electrons decay slowly from them, they can be piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal.

Specifically, a construct in a language is called syntactic sugar if it can be removed from the language without any effect on what the language can do: functionality and expressive power will remain the same.

Specifically, since logical language can only reflect the world, any discussion of the mystical, that which lies outside of the metaphysical subject's world, is meaningless.

This can be shown using the concept of left cosets of H in G. The left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x

Specifically, they share the idea that the reality of God is completely inaccessible to human beings and that man can only come to see God through a spiritual journey in which knowledge < nowiki >< nowiki ></ nowiki > is rejected in favour of meditation.

Specifically, collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy.

Specifically it takes time, demonstrating that the integer factorization problem can be efficiently solved on a quantum computer and is thus in the complexity class BQP.

Specifically, the closure of A can be constructed as the intersection of all of these closed supersets.

Specifically, critics argue that the costs and energy used in collection and transportation detract from ( and outweigh ) the costs and energy saved in the production process ; also that the jobs produced by the recycling industry can be a poor trade for the jobs lost in logging, mining, and other industries associated with virgin production ; and that materials such as paper pulp can only be recycled a few times before material degradation prevents further recycling.

Specifically, a function f is periodic with period P if the graph of f is invariant under translation in the x-direction by a distance of P. This definition of periodic can be extended to other geometric shapes and patterns, such as periodic tessellations of the plane.

Specifically, given two quantities, p and q, and a rational number m / n we can say that the ratio of p to q is less than, equal to, or greater than m / n when np is less than, equal to, or greater than mq respectively.

Specifically, the matrix M can be decomposed as:

Specifically, one can define the ( Earth-referenced ) electrochemical potential μ < sub > A </ sub > of a body " A " as the work needed to transfer an electron from the Fermi level of the Earth to the Fermi level of body " A ".