Subsequent mods have been somewhat easier to make ( since most of the hard work was done for the 1965 mod ).

The Who, inspired by the melodicism of The Beatles and the driving rhythms of American R & B, released several songs —" I Can't Explain ", " The Kids Are Alright ", " Substitute ", " I'm a Boy " and " Happy Jack "— in their early mod phase ( 1965 – 1966 ) that can be considered the first true power pop songs.

The next mod released was one based on the 1969 Formula One season.

For Christmas 2011, a new single seater mod came available. The F2 1967 Mod provide new accurate cars shapes, drivers, car sounds and physics. The Formula 2 physics were intended to get close racing online, with most of the cars sharing the same Ford Cosworth FVA 1600cc engine. Despite this, as others GPL mods, the F2 mod benefit of the extended 11 different cars slots with their individual handling. In 1967, drivers took part in no less than 23 Formula 2 races.

One may consider the ring of integers mod n, where n is squarefree.

One category of mod, " bots ", were introduced to provide surrogate players in multiplayer mode.

* One of the wonders buildable in the " Rise and fall of the Roman Empire " mod for Sid Meier's Civilization III is called the " Portus Ostiae "

One of the easiest ways to unlock an older AMD Athlon XP CPU was the pin mod method, because it was possible to unlock the CPU without a permanent modification of any bridges.

If N is a prime number, then the set of non-zero indices n = 1 ,..., N – 1 forms a group under multiplication modulo N. One consequence of the number theory of such groups is that there exists a generator of the group ( sometimes called a primitive root ), an integer g such that n = g < sup > q </ sup > ( mod N ) for any non-zero index n and for a unique q in 0 ,..., N – 2 ( forming a bijection from q to non-zero n ).

One downside of this type of mod is that leaked content can be revealed.

One graphical enhancement mod, entitled Rebirth, replaces many low-polygonal models with higher quality ones.

One notorious example is the " Hot Coffee " mod for Grand Theft Auto: San Andreas which allowed users to access an incomplete simulation of sexual intercourse that was removed from the game before release, but for which code remained in the game.

One such mod which gained notability was Inferno, which sets its story decades after the conclusion of FreeSpace 2.

One of the main entrances is via the NOIDA mod which is also called NEW Kondli mod.

One application of the mod 2 Steenrod algebra that is fairly elementary is the following theorem.

One of the earliest mods was F3 vehicle mod, which became very popular for some time and was later officially included in the game, although with fictitious branding.

One noteworthy result is that the sequence 2 < sup > k </ sup > a mod 1 is uniformly distributed for almost all, but not all, irrational a.

Naturally, the mod simulates the 1966 F1 season, with the cars themselves being based on the late season grid to allow as many cars as possible to be nearer the three litre engine formula that the 1966 rules allowed, as opposed to the two litre engines that some teams ran early in the season.

Another new feature with this mod is that car choice has been expanded from 7 to 16 ( out of a possible 19 ) and more tracks than 64 per season can be installed.

This has led to the development of several new mods such as a mod to rebuild the game for the 1996-97 season, an AHL modification, KHL ( including many other European hockey leagues ), and a classics mod, as well as seasonal updates to rosters, gameplay, faces and game clocks ( like ESPN, NBC, Versus and etc.

Normally, one fumocy is 14 luncations, so the new accumulator would be 0 + 14 * 26 mod 49, but, as mentioned, above, the last of the 18 fumocies is only 13 lunations, so the accumulator for the first New Moon is 0 + 13 * 26 mod 49 =

But each term of the last summation can either be 0 ( if n / p < sup > j </ sup > mod 1 < 1 / 2 ) or 1 ( if n / p < sup > j </ sup > mod 1 ≥ 1 / 2 ) and all terms with j > log < sub > p </ sub >( 2n ) are 0.

The last condition is sometimes called the Cartan condition: it means that η defines an absolute parallelism on P. The second condition implies that η is already injective on vertical vectors and that the 1-form η mod, with values in, is horizontal.

Movie Battles II or MBII is a team-based, last man standing multiplayer mod of the shooter game Star Wars Jedi Knight: Jedi Academy inspired by the popular first person shooter Counter-Strike.

Last known operator was RNoN with the T1 mod 1 ( G7a with wire-guidance: Although 4 modifications to the torpedo where carried out over the years-the last with computerized control in 1992-the same designation " mod 1 " was applied throughout its service ).

Two different routes to Apulia diverged at this point, one ( Via Aurelia Aeclanensis ) leading through the modern Ariano to Herdoniae, the other ( the Via Appia of the Empire ) passing the Lacus Ampsanctus and going on to Aquilonia and Venusia ; while the road from Aeclanum to Abellinum ( mod.

Teamplay is also frequently played with one or another mod.

The two primes, p and q, should both be congruent to 3 ( mod 4 ) ( this guarantees that each quadratic residue has one square root which is also a quadratic residue ) and gcd ( φ ( p-1 ), φ ( q-1 )) should be small ( this makes the cycle length large ).

Even in places such as grocery stores or clothing stores, genres are utilized to form an ordered flow to determine the differences between smaller classes within one particular subject, pointing out the differences between fruit and dairy, and punk to mod.

If a is any number coprime to n then a is in one of these residue classes, and its powers a, a < sup > 2 </ sup >, ..., a < sup > k </ sup > ≡ 1 ( mod n ) are a subgroup.

This is because for a to be a residue ( mod n ) it has to be a residue modulo every prime that divides n, but the Jacobi symbol will equal one if for example a is a non-residue for exactly two of the primes which divide n.

The band is remembered as one of the most acclaimed and influential mod groups of the 1960s.

* A splitting field of over is ; the polynomial has no roots in, i. e., − 1 is not a square there, because 7 is not equivalent to 1 ( mod 4 ).< ref > Instead of applying this characterization of odd prime moduli for which − 1 is a square, one could just check that the set of squares in is the set of classes of 0, 1, 4, and 2, which does not include the class of − 1 ≡ 6 .</ ref >

The ability to mod the game is one of the project's goals.

In detail, the space of homomorphisms from G to the ( cyclic ) group of order p, is a vector space over the finite field A non-trivial such map has as kernel a normal subgroup of index p, and multiplying the map by an element of ( a non-zero number mod p ) does not change the kernel ; thus one obtains a map from

For example, each moderator is given a limited number of " mod points ," each of which can be used to moderate an individual comment up or down by one point.

A common example of one kind of modding is video game console mod chips, which can allow users to play homemade games, games legitimately purchased in other regions, or legal backup copies, but can also allow illegal unauthorized copies by allowing the player to play personally recorded CD or DVD copies of video games.

Another variant, described in ( US Patent 3, 796, 830 ; Nov 1971 ), uses a 64-bit key operating on a 32-bit block, using one addition mod 4 and a singular 4-bit S-box.

There is a simple one line non-recursive method of implementing the above k mod 4 method of finding the turn direction in code.

Mechwarrior: Living Legends was the recipient of the ModDB 2009 Mod of the Year and-due to rules preventing one mod from winning the same award twice-an Honorable Mention in 2010.

This argument is much more complicated than the direct argument by reduction mod p. It does however allow one to see, in terms of algebraic number theory, how frequently Eisenstein's criterion might apply, after some change of variable ; and so limit severely the possible choices of p with respect to which the polynomial could have an Eisenstein translate ( that is, become Eisenstein after an additive change of variables as in the case of the p-th cyclotomic polynomial ).

An example is Team Reaction, one of the most prolific mod teams to date, most notably known for QPong and Jailbreak.

Then things suddenly are back to normal ( less the loyalty mod ) and two main characters debrief each other on a park bench, trying to understand how the " smeared " humanity was able to control events BEFORE people were all infected with the eigen-mod and WHY the " smeared " humanity chose to return the world to normal ( one theory put forward is that they reached the edge of the bubble, had a nice chat with the aliens and decided to go home and enjoy life as it was ).

Poincaré duality holds for any coefficient ring, so long as one has taken an orientation with respect to that coefficient ring ; in particular, since every manifold has a unique orientation mod 2, Poincaré duality holds mod 2 without any assumption of orientation.

The pushout of these maps is the direct sum of A and B. Generalizing to the case where f and g are arbitrary homomorphisms from a common domain Z, one obtains for the pushout a quotient group of the direct sum ; namely, we mod out by the subgroup consisting of pairs ( f ( z ),- g ( z )).