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, 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 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 menacing versions such as the one recorded by Reverend Elkanah Walker exist.

Less commonly, innovative cooks use cranberries to add tartness to savory dishes such as soups and stews.

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

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.

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 ".

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.

By 1996, genre acts such as Reel Big Fish and Less Than Jake were being signed to major labels.

Less strict rules were applied in Ireland, allowing Irish brewers such as Guinness to continue to brew beers closer to pre-war strengths.

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

Less commonly, " mechanic's stethoscopes " are used to listen to internal sounds made by machines, such as diagnosing a malfunctioning automobile engine by listening to the sounds of its internal parts.

Less invasive imaging methods such as x-rays or ultrasounds do not work because the vocal cords are surrounded by cartilage which distort image quality.

Less common events include natural disasters such as tornadoes, hurricanes, typhoons and ice storms.

Less known performers such as Ana María Iriarte, Inés Ribadeneira, Toñy Rosado, Carlos Munguía, Renato Cesari, and others frequently lent their voices to the recordings.

* Less affluent nations such as India, Malaysia, and Vietnam also saw tremendous improvements in economic prosperity and quality of life during the 1990s.

Less adversarial approaches to divorce settlements have recently emerged, such as mediation and collaborative divorce settlement, which negotiate mutually acceptable resolution to conflicts.

Less than a few hundred of such kidney donations have been performed.

Less expensive anamorphic systems such as Panavision and the more expensive 70 mm format became standard during the later 1950s and 1960s.

Less common, but not unusual, sashimi ingredients are vegetarian items such as yuba ( bean curd skin ) and raw red meats, such as beef, known as gyuunotataki, and horse, known as basashi.

Less frequently, individual strategic attacks are made against ' point ' targets, such as Britain's RAF Bomber Command attacks against the Ruhr dams by means of the bouncing bomb designed by Barnes Wallis in May 1943.

Less commonly, the use of the plural may be extended to other grammatical person, such as the " royal we " ( majestic plural ).

Less frequently used or manipulated elements, and elements that benefit from isolation ( such as wild species ) are farther away.

Commonly, longer novellas are referred to as novels ; Strange Case of Dr Jekyll and Mr Hyde and Heart of Darkness are sometimes called novels, as are many science fiction works such as The War of the Worlds and Armageddon 2419 A. D. Less often, longer works are referred to as novellas.