Less formally, the equivalence relation ker on X, takes each function f: X → X to its kernel ker f. Likewise, ker ( ker ) is an equivalence relation on X ^ X.

Less formally, people also use loan words within day-to-day speech, although this has been on the decline in recent decades and among younger generations.

Less formally, a fly-front or button down shirt may be substituted.

Less formally, judges of a Superior Court are referred to as " Justice ' Surname '", and it is never appropriate to refer to such a judge as " Judge ' Surname.

Less formally, on occasions of political controversy in many countries and times the usage of marking the face of a political opponent on a poster with an " X " is a commonly understood way of expressing strong disapproval, sometimes even the wish to kill the person whose picture is so marked.

Less formally than the theoretical distinctions mentioned above, two main types of signals encountered in practice are analog and digital.

Less formally, a group ring is a generalization of a given group, by attaching to each element of the group a " weighting factor " from a given ring.

Less than three months after the two territories were formally merged in December 1956, the Gold Coast gained independence as Ghana in March 1957.

" Less than a week later, however, McAllister announced his plan to formally retire from the NFL at the conclusion of the playoffs.

Less formally, M ( n ) is the count of square-free integers up to n that have an even number of prime factors, minus the count of those that have an odd number.

Less formally, such a person may be referred to as a refugee, although that term has a specific narrower legal definition.

Less formally, it is the number of linear combinations included in the sum of squares defining Q < sub > i </ sub >, provided that these linear combinations are linearly independent.

Less formally, this means that from the system's outputs it is possible to determine the behaviour of the entire system.

Less formally, " second-in-command " is a term used, usually unofficially and sometimes jocularly, for any deputy.

Less than a month later, on May 1, the Army formally charged MacDonald with the murder of his family.

Less formally, verse endings are usually also indicated by a two horizontal dots following the word with a silluq.

Less formally, hot and high can also describe a botched landing approach, where a fixed-wing aircraft is too fast ( hot ) and too high above the glidepath: since the only way to increase the rate of descent is to increase speed, and the aircraft is already too fast, it is unlikely that the approach can be salvaged.

Less formally, one can think of it as a conduit between the two entities ; one entity can insert bytes into the conduit, and the other entity then receives them.

Less than a month and only 5 games after becoming manager at QPR, Paul Hart parted with the club on 14 January 2010.

During the shows, the band held a spoof of The Price is Right, quizzing the contestants on various Less Than Jake " trivia ", having them play a few games from the shows, using the games to determine which album they'd play selections from, and giving prizes to the winners.

Less remembered is that it began a turnaround for the Nationals, who won the game in extra innings and started to win frequently, a trend that continued for more than three decades, building up an astounding 30 wins against only 6 losses and 1 tie ( during 1959-1962, two games were held each year ).

Speak & Math had five distinct learning games: Solve It, Word Problems, Greater Than / Less Than, Write It, and Number Stumper, all playable at three levels of difficulty.

Less grandiose, they became a feature of the games, but could not be considered exceptional.

Less than a month later, on 15 January 2010, only five games into his QPR career, Hart left the club.

Less than two years later, the Sooners and the rest of Division I-A were playing seven to ten games each season on television.

Less ambitiously, specific CSC fields are often studied under their own names with no reference to the more general field of study, focusing instead on the technology with only minimal attention to the collaboration implied, e. g. video games, videoconferences.

Less than a month after the Citicasters acquisition announcement, and in the wake of Fox's acquisition of the rights to National Football League games ( announced some time earlier ), News Corporation ( Fox's parent company ) made a deal with New World which moved the Fox affiliations to most of New World's stations.

: This section contains Xbox business articles, gaming news, ' Hard Stuff ' ( a section that reviews contraptions related to an Xbox console ), ' 2, 000 Pennies or Less ' ( a section that shows the best cheap games that can be bought for either Xbox or Xbox 360 ), the codes of the month, ' Forza Showroom ' ( a brief column that shows some of the best Forza Motorsport 2 car designs that people have made ), a section for competing against the OXM crew in games like Lost Planet, Halo 3, Gears of War, and more, ' Media Ho!

Less ambitious freeway plans may be more successful -- especially when the roadways and interchanges are raised, allowing for cross access at many points and providing parking areas below the ramp.

Less dramatic improvements are possible.

Less common are tandems, lowriders, tall bikes, fixed gear, folding models, amphibious bicycles and recumbents ( one of which was used to set the IHPVA Hour record ).

Less obvious is the fact that Puzzle Bobble also features all the enemies from Bubble Bobble, which are trapped inside the bubbles and fly out when the bubbles pop.

Less common are cardiac problems including cardiomyopathy and cardiac arrhythmia disorders.

Less illustrious uses refer to folklore and urban legend and a variety of explanatory narratives which are constructed with methodological flaws or biases.

Less than 1 % of all runway models are known to make more than $ 1000 dollars USD for every fashion showcase.

Less politically, most faiths have any number of people that are believed to have been touched by divine forces: saints, prophets, heroes, oracles, martyrs, and enlightened beings, among others.

Less common species such as Exmoor Horn and Cheviot are also to be found on Dartmoor.

Less common are well-documented cases with enough evidence to support the accusation.

Less than one-half of Ethiopia ’ s towns and cities are connected to the national grid.

Less than 10 % are Christians, mostly Roman Catholics.

Less than 65 % of children of primary school age are actually enrolled.

Less common are bara — larger, often heavily muscled and sometimes hairy males, the yaoi counterpart of the " bear " in gay pornography — as well as oyaji ( meaning " daddy " or " uncle "), featuring middle-aged and elderly men ; these types are mainly found in material aimed at gay men, which may be called bara or ' men's love ' ( ML ), and is considered to be distinct from yaoi.

Less likely is the commonly proposed derivation from Welsh arth " bear " + ( g ) wr " man " ( earlier * Arto-uiros in Brittonic ); there are phonological difficulties with this theory — notably that a Brittonic compound name * Arto-uiros should produce Old Welsh * Artgur and Middle / Modern Welsh * Arthwr and not Arthur ( in Welsh poetry the name is always spelled Arthur and is exclusively rhymed with words ending in-ur-never words ending in-wr-which confirms that the second element cannot be wr " man ").

Less common are proportional pneumatic valves or even various electrical actuators.

Less radical protests are also discussed, such as the various movements aimed at putting an end to sweatshop labour.

Less often seen are noun-verb combinations of two words, such as the line " The silence whistles " from Nathan Alterman's Summer Night, or in a record album title like Sounds of Silence.

* Less code required when applications are object oriented.

Less commonly, postage stamps are made of materials other than paper, such as embossed foil ( sometimes of gold ).

Less labor-intensive tools are more common now: a microplane or fine grater can be used to grind small amounts ; a coffee grinder is useful for larger amounts.

Less common are cherrywood, olivewood, maple, mesquite, oak, and bog-wood.

Less common are stems made of reeds, bamboo, or hollowed out pieces of wood.

Less frequently used types of materials include stag antler, buffalo horn and bone, as the time and effort needed to create one is often too much when conventional slides are available.