With this modification of notation, as right modules if and only if there exists a unique idempotent e such that and.

With infix notation, one easy mnemonic for remembering the order of operation is:

With the availability of good standard notation tutor books, teaching is possibly moving in this direction.

With the squares labeled as in algebraic notation, the white king starts on e1 and the black king on e8.

With his theory connecting musical notation with poetic meter, he developed a unique style of poetry written in logaoedic dactyls, which was strongly influenced by the works of his beloved Anglo-Saxon poets.

With 12-hour time notation, most authorities recommend avoiding confusion by using " noon ", " 12 noon ", or " 12: 00 noon ".

With this notation, the Hodge conjecture becomes:

With 12-hour time notation, authorities recommend avoiding confusion between noon and midnight by using " midnight ", " 12 midnight ", or " 12: 00 midnight.

With appropriate software, the computer can handle sound generation, mixing of tracks, music notation, musical instruction, and other music composition tasks.

With the scarcity of chess literature in his small town, he learned about chess notation from the chess puzzles in the daily newspaper, and compiled a handwritten collection of almost 1000 games.

With this notation, Dickson's lemma may be stated in several equivalent forms:

With the use of a radix point, the notation can be extended to include fractions and the numeric expansions of real numbers.

With this notation, the &# 8472 ; function satisfies the following differential equation:

With some abuse of notation, one may write this as

With this notation the velocity becomes:

The cover of the first printing included the notation, " With minor modifications, it is also suitable for use with ADVANCED DUNGEONS & DRAGONS "; this was removed from later printings.

With the introduction of subtractive notation, XIV ( 14 ) no longer represents the same number as XVI but rather is an alternate way of writing XIIII.

With the multi-index notation the rule states more generally:

With a small rearrangement this can be rewritten in vector notation as the eigenvector equation

The propagation velocity of electromagnetic waves in free space, an idealized standard reference state ( like absolute zero for temperature ), is conventionally denoted by c < sub > 0 </ sub >:< ref > With ISO 31-5, NIST and the BIPM have adopted the notation c < sub > 0 </ sub >.</ ref >

With Big O notation, we say that some term " is " ( given some function g, where x is one of f < nowiki >'</ nowiki > s parameters ).

With mathematical notation, Rosenblatt also described circuitry not in the basic perceptron, such as the exclusive-or circuit, a circuit whose mathematical computation could not be processed until after the backpropagation algorithm was created by Werbos ( 1975 ).

With Charles-Victor Mauguin, he invented an international standard notation for crystallographic groups known as the Hermann – Mauguin notation or International notation.

With the Renaissance, tyrannicide — or assassination for personal or political reasons — became more common again in Western Europe.

With ISO / IEC 80000-13, this common meaning was codified in a formal standard.

With the original 110 and 300 baud modems of the late 1970s, BBSes were particularly slow and file transfers were typically limited to text files ( lists of BBS systems were a common example ) and small software applications, typically terminal programs for accessing BBSes.

With the transition from English law, which had common law crimes, to the new legal system under the U. S. Constitution, which prohibited ex post facto laws at both the federal and state level, the question was raised whether there could be common law crimes in the United States.

With normal use, small reductions in white cell count and serum sodium are common ; however, in rare cases, the loss of platelets may become life-threatening.

With it Erasmus challenged common assumptions, painting the clergy as educators who should share the treasury of their knowledge with the laity.

With the present day all difference has disappeared ; philosophers are not monks, for we find them generally in connection with the world, participating with others in some common work or calling.

With knowledge of his sexuality becoming more common beginning in the 1970s, some film historians and gay studies scholars have detected homosexual themes in Whale's work, particularly in Bride of Frankenstein in which a number of the creative people associated with the cast, including Ernest Thesiger and Colin Clive, were alleged to be gay or bisexual.

With the widespread use of the original acronym as a common noun, actual optical amplifiers have come to be referred to as " laser amplifiers ", notwithstanding the apparent redundancy in that designation.

With this common touch and broad appeal, he subsequently led the party to victory in the election against the Progressive Conservative Party led by George Drew.

With the growth of industrialism and the introduction of machinery, longer hours became far more common, with 14 – 15 hours being the norm, and 16 not at all uncommon.

With variation between species, the most common dental formula is:

With the vitamin B < sub > 1 </ sub > deficiency beri-beri being common during the First World War, the spread became more popular.

With literally thousands in existence, micronations of the second type are by far the most common.

With the shift in the 1990s towards heavier, long-wheelbase models and light towing, V6 engines became more common and some automakers dropped their four-cylinder engines from their lineup.

With a relatively substantial road network, car travel is common in Niue.

With the advent of the early music movement, smaller orchestras where players worked on execution of works in styles derived from the study of older treatises on playing became common.

Efficiency and common problems: With only one cylinder in plunger pumps, the fluid flow varies between maximum flow when the plunger moves through the middle positions, and zero flow when the plunger is at the end positions.

With a play by mail game, the players can play whenever they choose, since responses need not be immediate ; this is sometimes referred to as turn-based gaming and is common among browser-based games.

With the constitutional reforms of 1972, these parties created a common front, the Tamil United Front ( later Tamil United Liberation Front ).

Another common element is fast-talking, witty repartee ( You Can't Take It With You, His Girl Friday ).

With a rejection on his record from such a legendary officer, Martok could no longer even serve as a common soldier.

With the introduction of the printing press to Britain by William Caxton in 1476, printed works became both more common and more economically important.

With the revival of the Roman law in the 14th century in Europe, this Latin term was used to refer to the legal standing of persons ( such as the various " estates of the realm "-noble, common, and clerical ), and in particular the special status of the king.