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, 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 formally structured games are also played out in internet forums, where players manage governments and nations according to a set of agreed rules, such as the MOCpages-based 21st Century World group.

Less can be said about the Asterales themselves with certainty, although since several families in Asterales contain trees, the ancestral member is most likely to have been a tree or shrub.

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 than 0. 1 % of an oral dose is eliminated unchanged in the 24 hour urine of humans.

Less is known about secondary endosymbionts.

Not numbered among the Twelve Apostles, unless he is identified as James the Less, James was nonetheless a very important figure: Paul described him as " the brother of the Lord " in Galatians 1: 19 and as one of the three " pillars of the Church " in 2: 9.

Less commonly, a single nodule is responsible for the excess hormone secretion, called a " hot " nodule.

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.

James Todd Spader ( born February 7, 1960 ) is an American actor best known for his eccentric roles in films such as Pretty in Pink ; Less Than Zero ; Sex, Lies, and Videotape ; Crash ; Stargate ; and Secretary.

Less than a seventh the size of Mongolia, at 199, 951 square kilometers, Kyrgyzstan is one of the smaller Central Asian states.

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 ").

The principle most likely finds its origins in similar concepts, such as Occam's razor, Leonardo da Vinci's " Simplicity is the ultimate sophistication ", Mies Van Der Rohe's " Less is more ", or Antoine de Saint Exupéry's " It seems that perfection is reached not when there is nothing left to add, but when there is nothing left to take away ".

* Worse is better ( Less is more )

Less common is the Budo-Goromo, which has a darker ( burgundy ) hi overlay that gives it the appearance of bunches of grapes.

It is featured in several music videos, including Marilyn Manson's " Mobscene ", the 2002 music video to Elvis Presley vs. JXL remix of " A Little Less Conversation ", the 2007 music video to Christina Aguilera's song " Candyman ", the 2008 video release from Millencolin ; Detox and the music videos to Movits!

Less than one hour from the centre of the city, it is possible to see Little Penguins in all months, including visiting sensitive areas where they remain on land for extended periods for the purposes of moulting.

Less than two miles heading east along the A95 from Maggieknockater is the site for Moray's most demanding Mountain Biking trails, " The Moray Monster Trails ".

Less than three years ago, the nation ’ s tourism budget was U. S. $ 400, 000 ; today, it is over $ 2 million.

Less than a year after retiring as a player, the Blues retired number 24 in his honor on March 16, 1992.

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 modular procedures, often used in small or quickly written programs, tend to interact with a large number of variables in the execution environment, which other procedures might also modify.

Less common but more severe were the canings administered by Pop ( see Eton Society below ) in the form of a " Pop-Tanning ", in which a large number of hard strokes were inflicted by the President of Pop in the presence of all Pop members.

* Less risk of entering an incorrect patient ID for a study – modalities that support DICOM worklists can retrieve identifying patient information ( patient name, patient number, accession number ) for upcoming cases and present that to the technologist, preventing data entry errors during acquisition.

Gainesville is traditionally well known for its music scene and has spawned a number of bands and musicians including Tom Petty and the Heartbreakers, Stephen Stills, Don Felder and Bernie Leadon of The Eagles, The Motels, Against Me !, Less Than Jake, Hot Water Music, John Vanderslice, Sister Hazel, and For Squirrels.

Less than half the number of acres planted with tomatoes in the early 1990s were planted in 1997.

Less than half of students are Caucasian, with nearly a quarter of the student body identifying as Asian, and a significant number of Latina and African-American students.

Less than 1 % of the current contents of the universe is in neutrinos, but WMAP's measurements have found, for the first time in 2008, that the data prefers the existence of a cosmic neutrino background with an effective number of neutrino flavors of 4. 4 ± 1. 5, consistent with the expectation of 3. 06.

According to BBC News, during an interview with the More or Less team's Tim Harford, the Count said his favorite number is 34, 969.

* The Count was interviewed in character on the BBC Radio 4 economics programme More or Less on December 11, 2009, where he mentioned his favorite number, 34969.

Less commonly, nuclear warheads have been mounted on a small number of air-to-air missile types ( such as the AIM-26 Falcon ) although these are not known to have ever been used in combat.

* Bernhard Riemann publishes his paper on number theory, die Anzahl der Primzahlen unter einer gegebenen (" On the Number of Primes Less Than a Given Magnitude ") including the Riemann zeta function and Riemann hypothesis.

Less widely known, right at the end of Series 1 production and prior to the transitional " Series 1½ " referred to below, a very small number of Series 1 cars were produced with open headlights.

Greater Than / Less Than involves whether the number on the left is greater than or less than the number on the right.

Less than 200 copies separated So Why So Sad from Found That Soul placing it 1 place higher at number 8, because the overwhelming majority of the sales that week were by the fans buying both.

Less than 200 copies separated " Found That Soul " from " So Why So Sad " placing it 1 place lower at number 9, because the overwhelming majority of the sales that week were by the fans buying both.

The caller guesses the number of tea cups shown in the video lead in, with Vaughan responding " More tea, vicar " if the number is too low ; " Less tea, vicar " if too high.

In early 2001, Capdown toured with a number of established American bands, including Less Than Jake and didn't play the Deconstruction touring festival with Pennywise and Lagwagon.